diff --git a/app_data/sheets/contents.json b/app_data/sheets/contents.json index dcd25cb..142cd9a 100644 --- a/app_data/sheets/contents.json +++ b/app_data/sheets/contents.json @@ -698,6 +698,9 @@ "data_list_name": "esm_topics", "_xlsxPath": "EFM_topics_high_level_sheets.xlsx", "_metadata": { + "searching_for_this": { + "type": "boolean" + }, "block2_illust_flex": { "type": "number" }, @@ -716,6 +719,16 @@ "type": "number" } } + }, + "test_list": { + "flow_type": "data_list", + "flow_name": "test_list", + "_xlsxPath": "EFM_high_level_sheets.xlsx", + "_metadata": { + "torf": { + "type": "boolean" + } + } } }, "data_pipe": {}, diff --git a/app_data/sheets/data_list/efm_pow_list.json b/app_data/sheets/data_list/efm_pow_list.json index f150c88..e60e0ad 100644 --- a/app_data/sheets/data_list/efm_pow_list.json +++ b/app_data/sheets/data_list/efm_pow_list.json @@ -53,7 +53,7 @@ "topic_theme_1": "NPV_QC10_QC", "notes_block_start": 4, "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWACoinFlipFirstMoves2.svg", + "block1_illust": "ESMIll/ESMPOWACoinFlipFirstMoves1.svg", "block1_illust_max_size": "360px", "block2_type": "illust_below", "block2_illust": "ESMIll/ESMPOWACoinFlipStart1.svg", @@ -315,183 +315,6 @@ "block3_text": "**Exploration:** Make drawings like these for other people to count the triangles and trapezoids.", "block4_text": "**The Challenge:** The square in the upper left has four smaller triangles plus four more triangles made out of pairs of smaller triangles. So it has eight triangles in all. It has no trapezoids in it.\n\nThe square in the upper right corner eight triangles in the inside square and eight more in the big square, so 16 triangles in all. It has four trapezoids.\n\nThe triangle in the bottom has a total of 12 triangles and six trapezoids." }, - { - "id": "esm_pow_a_find_pieces_2", - "level": "B", - "topic_theme_1": "Geom_Shape_SN2D3D", - "topic_theme_2": "Geom_Shape_CompDecomp", - "topic_theme_3": "NPV_QC10_QC", - "notes_block_start": 4, - "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWBFindingthePieces2Intro.svg", - "block1_illust_max_size": "360px", - "block2_type": "illust_below", - "block2_illust": "ESMIll/ESMPOWBFindingthePieces2Challenge.svg", - "block2_illust_max_size": "360px", - "block3_type": "all_text", - "block4_type": "all_text", - "name": "Finding the Pieces - 2", - "_translations": { - "name": {}, - "block1_text": {}, - "block2_text": {}, - "block3_text": {}, - "block4_text": {} - }, - "_translatedFields": { - "name": { - "eng": "Finding the Pieces - 2" - }, - "block1_text": { - "eng": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). A **parallelogram** is a four-sided figure that has two pairs of parallel sides. In the large triangle on the left, there are five triangles marked – the four colored triangles and the entire triangle. The same large triangle in the middle has one of its three trapezoids colored in green. The same large triangle on the right has one of its three parallelograms colored in red." - }, - "block2_text": { - "eng": "**The Challenge:** In each of these figures, count the number of triangles, trapezoids, and parallelograms." - }, - "block3_text": { - "eng": "**Exploration:** Make drawings like these for other people to count the triangles, parallelograms, and trapezoids." - }, - "block4_text": { - "eng": "**The Challenge:** Work on organized counting using these two figures. The second one requires a lot of careful counting.\n\n**The large triangle on the left:**\n\nIt has 9 small triangles (base 1), 3 intermediate triangles (base 2), and 1 large triangle (base 3), for a total of 13 triangles.\n\nIt has 9 small trapezoids (base 2 top 1), 3 intermediate trapezoids (base 3 top 2), and 3 large trapezoids (base 3 top 1), for a total of 15 trapezoids.\n\nIt has 9 small parallelograms (sides 1 and 1) and 6 intermediate parallelograms (sides 2 and 1), for a total of 15 parallelograms.\n\n**The large triangle on the right:**\n\nThe large triangle on the right has 16 small triangles (base 1), 7 small intermediate triangles (base 2), 3 large intermediate triangles (base 3), and 1 large triangle (base 4), for a total of 27 triangles. \nIt has 18 small trapezoids (base 2 top 1), 9 longer small trapezoids (base 3 top 2), 3 very long small trapezoids (base 4 top 3), 9 intermediate trapezoids (base 3 top 1), 3 intermediate longer trapezoids (base 4 top 2), and 3 large trapezoids (base 4 top 1), for a total of 18 + 9 + 3 + 9 + 3 + 3 = 45 trapezoids.\n\nIt has 18 small parallelograms (sides 1 and 1), 18 long small parallelograms (sides 2 and 1), 6 longer small parallelograms (sides 3 and 1), and 3 intermediate parallelograms (sides 2 and 2), for a total of 18 + 18 + 6 + 3 = 45 parallelograms." - } - }, - "block1_text": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). A **parallelogram** is a four-sided figure that has two pairs of parallel sides. In the large triangle on the left, there are five triangles marked – the four colored triangles and the entire triangle. The same large triangle in the middle has one of its three trapezoids colored in green. The same large triangle on the right has one of its three parallelograms colored in red.", - "block2_text": "**The Challenge:** In each of these figures, count the number of triangles, trapezoids, and parallelograms.", - "block3_text": "**Exploration:** Make drawings like these for other people to count the triangles, parallelograms, and trapezoids.", - "block4_text": "**The Challenge:** Work on organized counting using these two figures. The second one requires a lot of careful counting.\n\n**The large triangle on the left:**\n\nIt has 9 small triangles (base 1), 3 intermediate triangles (base 2), and 1 large triangle (base 3), for a total of 13 triangles.\n\nIt has 9 small trapezoids (base 2 top 1), 3 intermediate trapezoids (base 3 top 2), and 3 large trapezoids (base 3 top 1), for a total of 15 trapezoids.\n\nIt has 9 small parallelograms (sides 1 and 1) and 6 intermediate parallelograms (sides 2 and 1), for a total of 15 parallelograms.\n\n**The large triangle on the right:**\n\nThe large triangle on the right has 16 small triangles (base 1), 7 small intermediate triangles (base 2), 3 large intermediate triangles (base 3), and 1 large triangle (base 4), for a total of 27 triangles. \nIt has 18 small trapezoids (base 2 top 1), 9 longer small trapezoids (base 3 top 2), 3 very long small trapezoids (base 4 top 3), 9 intermediate trapezoids (base 3 top 1), 3 intermediate longer trapezoids (base 4 top 2), and 3 large trapezoids (base 4 top 1), for a total of 18 + 9 + 3 + 9 + 3 + 3 = 45 trapezoids.\n\nIt has 18 small parallelograms (sides 1 and 1), 18 long small parallelograms (sides 2 and 1), 6 longer small parallelograms (sides 3 and 1), and 3 intermediate parallelograms (sides 2 and 2), for a total of 18 + 18 + 6 + 3 = 45 parallelograms." - }, - { - "id": "esm_pow_a_find_pieces_3", - "level": "B", - "topic_theme_1": "Geom_Shape_SN2D3D", - "topic_theme_2": "Geom_Shape_CompDecomp", - "notes_block_start": 4, - "block1_type": "all_text", - "block2_type": "illust_below", - "block2_illust": "ESMIll/ESMPOWBFindingthePieces3Challenge.svg", - "block2_illust_max_size": "360px", - "block3_type": "all_text", - "block4_type": "illust_below", - "block4_illust": "ESMIll/ESMPOWBFindingthePieces3Answers.svg", - "block4_illust_max_size": "360px", - "name": "Finding the Pieces - 3", - "_translations": { - "name": {}, - "block1_text": {}, - "block2_text": {}, - "block3_text": {}, - "block4_text": {} - }, - "_translatedFields": { - "name": { - "eng": "Finding the Pieces - 3" - }, - "block1_text": { - "eng": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). A **parallelogram** is a four-sided figure that has two pairs of parallel sides. A **rectangle** is a four-sided figure with four right angles. A **square** is a rectangle with four equal sides. A **right triangle** is a triangle with a right angle." - }, - "block2_text": { - "eng": "**The Challenge:** Break this figure up using trapezoids, parallelograms, rectangles, squares and right triangles. Use as few pieces as you can." - }, - "block3_text": { - "eng": "**Exploration:** How many ways can you find to do this using this fewest number of pieces?" - }, - "block4_text": { - "eng": "**The Challenge:** Here are two ways to break this drawing into four figures. The answer on the left uses a square, a parallelogram, a right triangle, and a rectangle. The answer on the right uses a square, two trapezoids, and a rectangle. There are other answers, such as changing the first answer by turning the square and parallelogram into a trapezoid and a right triangle. How many answers can your students find?" - } - }, - "block1_text": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). A **parallelogram** is a four-sided figure that has two pairs of parallel sides. A **rectangle** is a four-sided figure with four right angles. A **square** is a rectangle with four equal sides. A **right triangle** is a triangle with a right angle.", - "block2_text": "**The Challenge:** Break this figure up using trapezoids, parallelograms, rectangles, squares and right triangles. Use as few pieces as you can.", - "block3_text": "**Exploration:** How many ways can you find to do this using this fewest number of pieces?", - "block4_text": "**The Challenge:** Here are two ways to break this drawing into four figures. The answer on the left uses a square, a parallelogram, a right triangle, and a rectangle. The answer on the right uses a square, two trapezoids, and a rectangle. There are other answers, such as changing the first answer by turning the square and parallelogram into a trapezoid and a right triangle. How many answers can your students find?" - }, - { - "id": "esm_pow_a_find_pieces_4", - "level": "B", - "topic_theme_1": "Geom_Shape_SN2D3D", - "topic_theme_2": "Geom_Shape_CompDecomp", - "topic_theme_3": "NPV_QC10_QC", - "notes_block_start": 3, - "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWBFindingthePieces4Intro.svg", - "block1_illust_max_size": "360px", - "block2_type": "illust_below", - "block2_illust": "ESMIll/ESMPOWBFindingthePieces4Challenge.svg", - "block2_illust_max_size": "360px", - "block3_type": "illust_below", - "block3_illust": "ESMIll/ESMPOWBFindingthePieces4Answers.svg", - "block3_illust_max_size": "360px", - "name": "Finding the Pieces - 4", - "_translations": { - "name": {}, - "block1_text": {}, - "block2_text": {}, - "block3_text": {} - }, - "_translatedFields": { - "name": { - "eng": "Finding the Pieces - 4" - }, - "block1_text": { - "eng": "**Introduction:** The figure on the left has a shaded part in red and an unshaded part. The figure on the right shows how to fill the unshaded part with seven exact copies of the shaded part." - }, - "block2_text": { - "eng": "**The Challenge:** In these two figures, there is a shaded part and an unshaded part. Find out how many times the shaded part will exactly fit into the unshaded part." - }, - "block3_text": { - "eng": "**The Challenge:** In the left figure, there are 7 triangles like the red one. In the right figure, there are four L-shaped pieces like the red one." - } - }, - "block1_text": "**Introduction:** The figure on the left has a shaded part in red and an unshaded part. The figure on the right shows how to fill the unshaded part with seven exact copies of the shaded part.", - "block2_text": "**The Challenge:** In these two figures, there is a shaded part and an unshaded part. Find out how many times the shaded part will exactly fit into the unshaded part.", - "block3_text": "**The Challenge:** In the left figure, there are 7 triangles like the red one. In the right figure, there are four L-shaped pieces like the red one." - }, - { - "id": "esm_pow_a_find_pieces_5", - "level": "B", - "topic_theme_1": "Geom_Shape_SN2D3D", - "topic_theme_2": "Geom_Shape_CompDecomp", - "topic_theme_3": "NPV_QC10_QC", - "notes_block_start": 4, - "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWBFindingthePieces5Intro.svg", - "block1_illust_max_size": "360px", - "block2_type": "illust_below", - "block2_illust": "ESMIll/ESMPOWBFindingthePieces5Challenge.svg", - "block2_illust_max_size": "360px", - "block3_type": "all_text", - "block4_type": "illust_below", - "block4_illust": "ESMIll/ESMPOWBFindingthePieces5Answers.svg", - "block4_illust_max_size": "360px", - "name": "Finding the Pieces - 5", - "_translations": { - "name": {}, - "block1_text": {}, - "block2_text": {}, - "block3_text": {}, - "block4_text": {} - }, - "_translatedFields": { - "name": { - "eng": "Finding the Pieces - 5" - }, - "block1_text": { - "eng": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). The figure on the left can be broken into three pieces which are triangles. It can also be broken into two trapezoids." - }, - "block2_text": { - "eng": "**The Challenge:** For each of these two figures, find a way to break the figure into as few triangles as possible. Also find a way to break each figure into as few trapezoids as possible." - }, - "block3_text": { - "eng": "**Exploration:** Are there other ways to break these two figures into triangles or trapezoids in as few pieces?" - }, - "block4_text": { - "eng": "**The Challenge & Exploration:** One example of breaking up the two figures into triangles and trapezoids is given below. There are other possible choices for how to do it, so be sure to talk about all the different possibilities that everyone finds." - } - }, - "block1_text": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). The figure on the left can be broken into three pieces which are triangles. It can also be broken into two trapezoids.", - "block2_text": "**The Challenge:** For each of these two figures, find a way to break the figure into as few triangles as possible. Also find a way to break each figure into as few trapezoids as possible.", - "block3_text": "**Exploration:** Are there other ways to break these two figures into triangles or trapezoids in as few pieces?", - "block4_text": "**The Challenge & Exploration:** One example of breaking up the two figures into triangles and trapezoids is given below. There are other possible choices for how to do it, so be sure to talk about all the different possibilities that everyone finds." - }, { "id": "esm_pow_a_sum_groups_6", "level": "A", @@ -763,19 +586,21 @@ "block5_text": "**More Examples:** As in the original puzzles, the place to start is with the largest numbers – 10's, 9's, and 8's, and with the corners and edges." }, { - "id": "esm_pow_b_equal_sums_1", + "id": "esm_pow_b_diff_pyramids_6", "level": "B", "topic_theme_1": "NO_ASSD_AS10", - "notes_block_start": 3, + "notes_block_start": 4, "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWBEqualSums1Challenge.svg", + "block1_illust": "ESMIll/ESMPOWBDiffPyramid6Intro.svg", "block1_illust_max_size": "240px", - "block2_type": "all_text", - "block3_type": "illust_below", - "block3_illust": "ESMIll/ESMPOWBEqualSums1Answer.svg", - "block3_illust_max_size": "400px", - "block4_type": "all_text", - "name": "Equal Sums - 1", + "block2_type": "illust_below", + "block2_illust": "ESMIll/ESMPOWBDiffPyramid6Challenge.svg", + "block2_illust_max_size": "180px", + "block3_type": "all_text", + "block4_type": "illust_below", + "block4_illust": "ESMIll/ESMPOWBDiffPyramid6Solutions.svg", + "block4_illust_max_size": "400px", + "name": "Difference Pyramids - 6", "_translations": { "name": {}, "block1_text": {}, @@ -785,40 +610,40 @@ }, "_translatedFields": { "name": { - "eng": "Equal Sums - 1" + "eng": "Difference Pyramids - 6" }, "block1_text": { - "eng": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create five regions. Put a number in each of the five regions, using each of the numbers 1 to 5 exactly once, so that the sum of the numbers in each circle is the same." + "eng": "**Introduction:** These pyramids are called **Difference Pyramids.** The number on top is the difference of the two numbers below." }, "block2_text": { - "eng": "**Exploration:** How many different answers can you find? How do you know if you have found them all?" + "eng": "**The Challenge:** Place the numbers from 1 to 6 to make a Difference Pyramid." }, "block3_text": { - "eng": "**The Challenge & Exploration:** There are two solutions. The sum in each circle is 6 on the left and 7 on the right." + "eng": "**Exploration:** Find different ways this can be done. Are some of these essentially the same?" }, "block4_text": { - "eng": "Analyze the possibilities by letting A and B be the two numbers in the intersections of the circles. Let Sum be the common sum inside each circle. Then 3 x Sum = 1 + 2 + 3 + 4 + 5 + A + B = 15 + A + B.\n\nThe left side of 3 x Sum = 15 + A + B is a multiple of 3, so the right side is as well. This forces A + B to be a multiple of three. That leaves only three possibilities.\n\n* A + B = 3. In this case 3 x Sum = 15 + 3 = 18 tells us Sum = 6, and A and B are 1 and 2.\n* A + B = 6. In this case 3 x Sum = 15 + 6 = 21 tells us Sum = 7. A + B = 6 forces A and B to be either 1 and 5 or 2 and 4. Having A and B be 1 and 5 does not work (1 is repeated), so that leaves us with just 2 and 4.\n* A + B = 9. In this case 3 x Sum = 15 + 9 = 24 tells us Sum = 8, and A and B are 4 and 5. However, because A and B are both in the middle circle, it is not possible for A + B = 9 and yet the Sum is only 8. So this case cannot happen." + "eng": "**The Challenge & Exploration:** A good start is to realize that because 6 cannot be the difference of two cards, it must go on the bottom row. \n\nNext, the only way 5 can be the difference is if it is above the 6 and the 1. So, either 5 goes directly above the 6 (with the 1 next to the 6), or 5 is in the bottom row.\n\nAt this point it is useful to consider what makes solutions different. Because the mirror image of any solution is also a solution, it makes sense to ignore those. Ignoring mirror images will reduce the number of solutions to consider by half. \n\nFor example, we can assume that not only is the 6 in the bottom row, but it is either in the middle or the right side of the bottom row - if it were on the left side, we could take the mirror image of the whole puzzle and put it on the right side.\n\nUsing this thinking, the bottom row can have five possible layouts (up to using mirror images): 5 X 6, X 5 6, X 6 5, X 1 6, X 6 1.\n\nAt this point, it is a matter of working through the various possibilities. The only 5 X 6 that works is 5 2 6. It turns out X 5 6 never works. The only X 6 5 is 2 6 5. The only X 1 6 is 4 1 6, and the only X 6 1 is 4 6 1.\n\nSo, ignoring mirror images, there are four solutions:" } }, - "block1_text": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create five regions. Put a number in each of the five regions, using each of the numbers 1 to 5 exactly once, so that the sum of the numbers in each circle is the same.", - "block2_text": "**Exploration:** How many different answers can you find? How do you know if you have found them all?", - "block3_text": "**The Challenge & Exploration:** There are two solutions. The sum in each circle is 6 on the left and 7 on the right.", - "block4_text": "Analyze the possibilities by letting A and B be the two numbers in the intersections of the circles. Let Sum be the common sum inside each circle. Then 3 x Sum = 1 + 2 + 3 + 4 + 5 + A + B = 15 + A + B.\n\nThe left side of 3 x Sum = 15 + A + B is a multiple of 3, so the right side is as well. This forces A + B to be a multiple of three. That leaves only three possibilities.\n\n* A + B = 3. In this case 3 x Sum = 15 + 3 = 18 tells us Sum = 6, and A and B are 1 and 2.\n* A + B = 6. In this case 3 x Sum = 15 + 6 = 21 tells us Sum = 7. A + B = 6 forces A and B to be either 1 and 5 or 2 and 4. Having A and B be 1 and 5 does not work (1 is repeated), so that leaves us with just 2 and 4.\n* A + B = 9. In this case 3 x Sum = 15 + 9 = 24 tells us Sum = 8, and A and B are 4 and 5. However, because A and B are both in the middle circle, it is not possible for A + B = 9 and yet the Sum is only 8. So this case cannot happen." + "block1_text": "**Introduction:** These pyramids are called **Difference Pyramids.** The number on top is the difference of the two numbers below.", + "block2_text": "**The Challenge:** Place the numbers from 1 to 6 to make a Difference Pyramid.", + "block3_text": "**Exploration:** Find different ways this can be done. Are some of these essentially the same?", + "block4_text": "**The Challenge & Exploration:** A good start is to realize that because 6 cannot be the difference of two cards, it must go on the bottom row. \n\nNext, the only way 5 can be the difference is if it is above the 6 and the 1. So, either 5 goes directly above the 6 (with the 1 next to the 6), or 5 is in the bottom row.\n\nAt this point it is useful to consider what makes solutions different. Because the mirror image of any solution is also a solution, it makes sense to ignore those. Ignoring mirror images will reduce the number of solutions to consider by half. \n\nFor example, we can assume that not only is the 6 in the bottom row, but it is either in the middle or the right side of the bottom row - if it were on the left side, we could take the mirror image of the whole puzzle and put it on the right side.\n\nUsing this thinking, the bottom row can have five possible layouts (up to using mirror images): 5 X 6, X 5 6, X 6 5, X 1 6, X 6 1.\n\nAt this point, it is a matter of working through the various possibilities. The only 5 X 6 that works is 5 2 6. It turns out X 5 6 never works. The only X 6 5 is 2 6 5. The only X 1 6 is 4 1 6, and the only X 6 1 is 4 6 1.\n\nSo, ignoring mirror images, there are four solutions:" }, { - "id": "esm_pow_b_equal_sums_2", + "id": "esm_pow_b_diff_pyramids_10", "level": "B", "topic_theme_1": "NO_ASSD_AS10", - "notes_block_start": 3, + "notes_block_start": 4, "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWBEqualNumberSumsVennDiagram2.svg", + "block1_illust": "ESMIll/ESMPOWBDiffPyramid6Intro.svg", "block1_illust_max_size": "240px", - "block2_type": "all_text", - "block3_type": "illust_below", - "block3_illust": "ESMIll/ESMPOWBEqualNumberSumsVennDiagram2Answer.svg", - "block3_illust_max_size": "400px", + "block2_type": "illust_below", + "block2_illust": "ESMIll/ESMPOWBDiffPyramid10Challenge.svg", + "block2_illust_max_size": "180px", + "block3_type": "all_text", "block4_type": "all_text", - "name": "Equal Sums - 2", + "name": "Difference Pyramids - 10", "_translations": { "name": {}, "block1_text": {}, @@ -828,77 +653,83 @@ }, "_translatedFields": { "name": { - "eng": "Equal Sums - 2" + "eng": "Difference Pyramids - 10" }, "block1_text": { - "eng": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create six regions. Put a number in each of the six regions, using each of the numbers 1 to 6 exactly once, so that the sum of the numbers in each circle is the same." + "eng": "**Introduction:** These pyramids are called **Difference Pyramids.** The number on top is the difference of the two numbers below." }, "block2_text": { - "eng": "**Exploration:** How many different answers can you find? How do you know if you have found them all?" + "eng": "**The Challenge:** Place the numbers from 1 to 10 to make a Difference Pyramid." }, "block3_text": { - "eng": "**The Challenge & Exploration:** Here are the four solutions. To see why these are the only ones, let A, B, and C be the three regions where two circles intersect, and let Sum be the common sum for the three circles. Calculate the total sum in two ways. As the sum of the three circles, the sum is 3 x Sum. As the sum of all six numbers plus A, B, and C the sum is 1 + 2 + 3 + 4 + 5 + 6 + A + B + C. The two things are equal, so that gives us 3 x Sum = 21 + A + B + C. Dividing by 3, we have Sum = 7 + (A + B + C)/3.\n\nFor Sum to be an integer in this last equation, A + B + C must be evenly divisible by 3. This allows for only four possibilities for A + B + C - it is either 6, 9, 12, or 15, and the corresponding values for Sum are 9, 10, 11, or 12.\n\nThe four solutions given here have Sum values of 9, 10, 11, and 12. As we shall see, these are all of the solutions!" + "eng": "**Exploration:** Play with even larger pyramids." }, "block4_text": { - "eng": "To save some work, note that if we take one solution and subtract all the entries from 7, we get another solution. Also, note that the new solution will have a Sum value which is 21 - (old Sum). Hence, the solutions for Sum values 9 and 10 give us the solutions for Sum values 11 and 12.\n\nIf A + B + C = 6, then A, B, and C are 1, 2, and 3, and Sum = 9. That is the upper left solution.\n\nIf A + B + C = 9, then Sum = 10 and (A, B, C) is (1, 2, 6), (1, 3, 5), or (2, 3, 4). If you check it, (1, 2, 6) and (2, 3, 4) are impossible. This leaves the upper right solution as the only Sum = 10 solution.\n\nIf you compare “Equal Sums – 2” with “Magic Triangles – 1,” you will see that they are the same puzzle!" + "eng": "**The Challenge & Exploration:** Because 10 cannot be the difference of two cards, it must go on the bottom row. Similarly, either 9 is in the bottom row or it is in the next-to-the-bottom row above the 1 and the 10. The 8 and 7 cards are also good cards to focus on to get rid of possibilities.\n\nThis means the bottom row looks like one of the following (ignoring mirror images):\n\nX Y 9 10, X 9 Y 10, 9 X Y 10, X Y 10 9, X 9 10 Y, 9 X 10 Y, X Y 1 10, X 1 10 Y, X Y 10 1\n\nThat is a lot of possibilities to consider!\n\nFortunately, if you consider where 8 and 7 can go, the possibilities are reduced to the following list (assuming we haven’t missed any). It is easy to finish each of these once you have the bottom row.\n\n8 3 10 9, 9 3 10 8, 6 1 10 8, 8 1 10 6\n\nInvestigating pyramids of size 15, 21, or higher are for the truly dedicated.\n\nFrom the literature, there is only one solution (up to reflections) for 15, and its bottom row is {6, 14, 15, 3, 13}. Even more surprisingly, there are no solutions for 21, 28, and 36, and it has been conjectured that there are no solutions above that!" } }, - "block1_text": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create six regions. Put a number in each of the six regions, using each of the numbers 1 to 6 exactly once, so that the sum of the numbers in each circle is the same.", - "block2_text": "**Exploration:** How many different answers can you find? How do you know if you have found them all?", - "block3_text": "**The Challenge & Exploration:** Here are the four solutions. To see why these are the only ones, let A, B, and C be the three regions where two circles intersect, and let Sum be the common sum for the three circles. Calculate the total sum in two ways. As the sum of the three circles, the sum is 3 x Sum. As the sum of all six numbers plus A, B, and C the sum is 1 + 2 + 3 + 4 + 5 + 6 + A + B + C. The two things are equal, so that gives us 3 x Sum = 21 + A + B + C. Dividing by 3, we have Sum = 7 + (A + B + C)/3.\n\nFor Sum to be an integer in this last equation, A + B + C must be evenly divisible by 3. This allows for only four possibilities for A + B + C - it is either 6, 9, 12, or 15, and the corresponding values for Sum are 9, 10, 11, or 12.\n\nThe four solutions given here have Sum values of 9, 10, 11, and 12. As we shall see, these are all of the solutions!", - "block4_text": "To save some work, note that if we take one solution and subtract all the entries from 7, we get another solution. Also, note that the new solution will have a Sum value which is 21 - (old Sum). Hence, the solutions for Sum values 9 and 10 give us the solutions for Sum values 11 and 12.\n\nIf A + B + C = 6, then A, B, and C are 1, 2, and 3, and Sum = 9. That is the upper left solution.\n\nIf A + B + C = 9, then Sum = 10 and (A, B, C) is (1, 2, 6), (1, 3, 5), or (2, 3, 4). If you check it, (1, 2, 6) and (2, 3, 4) are impossible. This leaves the upper right solution as the only Sum = 10 solution.\n\nIf you compare “Equal Sums – 2” with “Magic Triangles – 1,” you will see that they are the same puzzle!" + "block1_text": "**Introduction:** These pyramids are called **Difference Pyramids.** The number on top is the difference of the two numbers below.", + "block2_text": "**The Challenge:** Place the numbers from 1 to 10 to make a Difference Pyramid.", + "block3_text": "**Exploration:** Play with even larger pyramids.", + "block4_text": "**The Challenge & Exploration:** Because 10 cannot be the difference of two cards, it must go on the bottom row. Similarly, either 9 is in the bottom row or it is in the next-to-the-bottom row above the 1 and the 10. The 8 and 7 cards are also good cards to focus on to get rid of possibilities.\n\nThis means the bottom row looks like one of the following (ignoring mirror images):\n\nX Y 9 10, X 9 Y 10, 9 X Y 10, X Y 10 9, X 9 10 Y, 9 X 10 Y, X Y 1 10, X 1 10 Y, X Y 10 1\n\nThat is a lot of possibilities to consider!\n\nFortunately, if you consider where 8 and 7 can go, the possibilities are reduced to the following list (assuming we haven’t missed any). It is easy to finish each of these once you have the bottom row.\n\n8 3 10 9, 9 3 10 8, 6 1 10 8, 8 1 10 6\n\nInvestigating pyramids of size 15, 21, or higher are for the truly dedicated.\n\nFrom the literature, there is only one solution (up to reflections) for 15, and its bottom row is {6, 14, 15, 3, 13}. Even more surprisingly, there are no solutions for 21, 28, and 36, and it has been conjectured that there are no solutions above that!" }, { - "id": "esm_pow_b_equal_sums_3", + "id": "esm_pow_b_equal_sums_1", "level": "B", "topic_theme_1": "NO_ASSD_AS10", "notes_block_start": 3, "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWBEqualNumberSums3.svg", + "block1_illust": "ESMIll/ESMPOWBEqualSums1Challenge.svg", "block1_illust_max_size": "240px", "block2_type": "all_text", "block3_type": "illust_below", - "block3_illust": "ESMIll/ESMPOWBEqualNumberSums3Answers.svg", + "block3_illust": "ESMIll/ESMPOWBEqualSums1Answer.svg", "block3_illust_max_size": "400px", - "name": "Equal Sums - 3", + "block4_type": "all_text", + "name": "Equal Sums - 1", "_translations": { "name": {}, "block1_text": {}, "block2_text": {}, - "block3_text": {} + "block3_text": {}, + "block4_text": {} }, "_translatedFields": { "name": { - "eng": "Equal Sums - 3" + "eng": "Equal Sums - 1" }, "block1_text": { - "eng": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create seven regions. Put a number in each of the seven regions, using each of the numbers 1 to 7 exactly once, so that the sum of the numbers in each circle is the same." + "eng": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create five regions. Put a number in each of the five regions, using each of the numbers 1 to 5 exactly once, so that the sum of the numbers in each circle is the same." }, "block2_text": { "eng": "**Exploration:** How many different answers can you find? How do you know if you have found them all?" }, "block3_text": { - "eng": "**The Challenge & Exploration:** The first question with these problems is what the possible sums in the circles are. Narrow this down by looking at the sum of the entries in two ways. Let A, B, and C be the three values where two circles intersect, let M be the value where all three circles intersect, and let Sum be the common sum in each circle. The sum of the three circles is 3 x Sum. That sum is also the sum of the numbers from 1 to 7 plus A + B + C plus 2 x M. Therefore, 3 x Sum = 28 + A + B + C + 2 x M.\n\nBefore going further with this, note that if we start with any solution, we can get a new solution by subtracting all the entries from 8. This will have the effect of replacing Sum by 32 - Sum. Because of this, we only need to look for values of Sum up to 16 - the remaining larger values can be obtained by subtracting those solution entries from 8.\n\nThe smallest A + B + C + 2 x M can be is 2 + 3 + 4 + 2 x 1 = 11. So the smallest Sum can be is (28 + 11) / 3 = 13. Consequently, we want to see which of the Sum values from 13 to 16 are possible. It turns out that they are all possible. \n\nHere is one solution for each Sum value starting at 13 and ending at 16. There are many more." + "eng": "**The Challenge & Exploration:** There are two solutions. The sum in each circle is 6 on the left and 7 on the right." + }, + "block4_text": { + "eng": "Analyze the possibilities by letting A and B be the two numbers in the intersections of the circles. Let Sum be the common sum inside each circle. Then 3 x Sum = 1 + 2 + 3 + 4 + 5 + A + B = 15 + A + B.\n\nThe left side of 3 x Sum = 15 + A + B is a multiple of 3, so the right side is as well. This forces A + B to be a multiple of three. That leaves only three possibilities.\n\n* A + B = 3. In this case 3 x Sum = 15 + 3 = 18 tells us Sum = 6, and A and B are 1 and 2.\n* A + B = 6. In this case 3 x Sum = 15 + 6 = 21 tells us Sum = 7. A + B = 6 forces A and B to be either 1 and 5 or 2 and 4. Having A and B be 1 and 5 does not work (1 is repeated), so that leaves us with just 2 and 4.\n* A + B = 9. In this case 3 x Sum = 15 + 9 = 24 tells us Sum = 8, and A and B are 4 and 5. However, because A and B are both in the middle circle, it is not possible for A + B = 9 and yet the Sum is only 8. So this case cannot happen." } }, - "block1_text": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create seven regions. Put a number in each of the seven regions, using each of the numbers 1 to 7 exactly once, so that the sum of the numbers in each circle is the same.", + "block1_text": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create five regions. Put a number in each of the five regions, using each of the numbers 1 to 5 exactly once, so that the sum of the numbers in each circle is the same.", "block2_text": "**Exploration:** How many different answers can you find? How do you know if you have found them all?", - "block3_text": "**The Challenge & Exploration:** The first question with these problems is what the possible sums in the circles are. Narrow this down by looking at the sum of the entries in two ways. Let A, B, and C be the three values where two circles intersect, let M be the value where all three circles intersect, and let Sum be the common sum in each circle. The sum of the three circles is 3 x Sum. That sum is also the sum of the numbers from 1 to 7 plus A + B + C plus 2 x M. Therefore, 3 x Sum = 28 + A + B + C + 2 x M.\n\nBefore going further with this, note that if we start with any solution, we can get a new solution by subtracting all the entries from 8. This will have the effect of replacing Sum by 32 - Sum. Because of this, we only need to look for values of Sum up to 16 - the remaining larger values can be obtained by subtracting those solution entries from 8.\n\nThe smallest A + B + C + 2 x M can be is 2 + 3 + 4 + 2 x 1 = 11. So the smallest Sum can be is (28 + 11) / 3 = 13. Consequently, we want to see which of the Sum values from 13 to 16 are possible. It turns out that they are all possible. \n\nHere is one solution for each Sum value starting at 13 and ending at 16. There are many more." + "block3_text": "**The Challenge & Exploration:** There are two solutions. The sum in each circle is 6 on the left and 7 on the right.", + "block4_text": "Analyze the possibilities by letting A and B be the two numbers in the intersections of the circles. Let Sum be the common sum inside each circle. Then 3 x Sum = 1 + 2 + 3 + 4 + 5 + A + B = 15 + A + B.\n\nThe left side of 3 x Sum = 15 + A + B is a multiple of 3, so the right side is as well. This forces A + B to be a multiple of three. That leaves only three possibilities.\n\n* A + B = 3. In this case 3 x Sum = 15 + 3 = 18 tells us Sum = 6, and A and B are 1 and 2.\n* A + B = 6. In this case 3 x Sum = 15 + 6 = 21 tells us Sum = 7. A + B = 6 forces A and B to be either 1 and 5 or 2 and 4. Having A and B be 1 and 5 does not work (1 is repeated), so that leaves us with just 2 and 4.\n* A + B = 9. In this case 3 x Sum = 15 + 9 = 24 tells us Sum = 8, and A and B are 4 and 5. However, because A and B are both in the middle circle, it is not possible for A + B = 9 and yet the Sum is only 8. So this case cannot happen." }, { - "id": "esm_pow_b_equal_sums_4", + "id": "esm_pow_b_equal_sums_2", "level": "B", "topic_theme_1": "NO_ASSD_AS10", "notes_block_start": 3, "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWBEqualNumberSums4.svg", + "block1_illust": "ESMIll/ESMPOWBEqualNumberSumsVennDiagram2.svg", "block1_illust_max_size": "240px", "block2_type": "all_text", "block3_type": "illust_below", - "block3_illust": "ESMIll/ESMPOWBEqualNumberSums4Answers.svg", + "block3_illust": "ESMIll/ESMPOWBEqualNumberSumsVennDiagram2Answer.svg", "block3_illust_max_size": "400px", "block4_type": "all_text", - "name": "Equal Sums - 4", + "name": "Equal Sums - 2", "_translations": { "name": {}, "block1_text": {}, @@ -908,85 +739,77 @@ }, "_translatedFields": { "name": { - "eng": "Equal Sums - 4" + "eng": "Equal Sums - 2" }, "block1_text": { - "eng": "**The Challenge:** Here is a diagram created by overlapping four circles. The overlapping circles create eight regions. Put a number in each of the eight regions, using each of the numbers 1 to 8 exactly once, so that the sum of the numbers in each circle is the same." + "eng": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create six regions. Put a number in each of the six regions, using each of the numbers 1 to 6 exactly once, so that the sum of the numbers in each circle is the same." }, "block2_text": { - "eng": "**Exploration:** How many different answers can you find? Do you think there are any more? What happens if you use other number ranges? Are there other interesting problems like this with intersecting circles?" + "eng": "**Exploration:** How many different answers can you find? How do you know if you have found them all?" }, "block3_text": { - "eng": "**The Challenge & Exploration:** Start by deciding which sums are possible for the common sum for all circles. Let Sum be that value. Let A, B, C, and D be the values of the four regions where two circles intersect. The sum of the four circles is 4 x Sum, and it is also 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + A + B + C + D. Then we have the equation 4 x Sum = 36 + A + B + C + D, so Sum = 9 + (A + B + C + D) / 4. The smallest that A + B + C + D can have is 1 + 2 + 3 + 4 = 10. This needs to be divisible, so it’s smallest possible value is 12, which means the smallest possible value is Sum = 9 + 12/4 = 12.\n\nNote that any solution can be turned into another solution by subtracting all entries from 9. Doing this will turn the old Sum into 27 - Sum. Consequently, the only possible values for Sum are 12, 13, 14, and 15. Because 12 and 15 are tied together, and 13 and 14 are tied together, we only need to check for solutions for 12 and 13.\n\nHere are solutions for Sum with values 12 and 13. It turns out these are the only ones for these two sums." + "eng": "**The Challenge & Exploration:** Here are the four solutions. To see why these are the only ones, let A, B, and C be the three regions where two circles intersect, and let Sum be the common sum for the three circles. Calculate the total sum in two ways. As the sum of the three circles, the sum is 3 x Sum. As the sum of all six numbers plus A, B, and C the sum is 1 + 2 + 3 + 4 + 5 + 6 + A + B + C. The two things are equal, so that gives us 3 x Sum = 21 + A + B + C. Dividing by 3, we have Sum = 7 + (A + B + C)/3.\n\nFor Sum to be an integer in this last equation, A + B + C must be evenly divisible by 3. This allows for only four possibilities for A + B + C - it is either 6, 9, 12, or 15, and the corresponding values for Sum are 9, 10, 11, or 12.\n\nThe four solutions given here have Sum values of 9, 10, 11, and 12. As we shall see, these are all of the solutions!" }, "block4_text": { - "eng": "Notice that the numbers in the center of circles not touching each other add up to the same thing. For example, in the leftmost diagram, 8 + 4 = 5 + 7. Prove that this always happens with a bit of algebra. Let K and L be the values in the centers of two of the opposite circles, and let M and N be the other two values. If we add up the regions for the two circles for K and L we get 2 x Sum = K + L + (A + B + C + D). Similarly, adding up the regions for the two circles for M and N gives 2 x Sum = M + N + (A + B + C + D). This forces K + L = M + N.\n\nAlso, note that since 4 x Sum = 36 + A + B + C + D, we get 2 x Sum = M + N + (4 x Sum - 36). Rewriting this we have M + N = 36 - 2 x Sum. For our four values of Sum, 12 through 15, the values of M + N are 12, 10, 8, and 6.\n\nBecause 12 = 4 + 8 = 5 + 7 are the only ways to get 12, the solution above for Sum = 12 is the only solution. While 10 = 2 + 8 = 3 + 7 = 4 + 6 suggests there are more possibilities for Sum = 13, a quick check of the three possible pairings of (2, 8), (3, 7), and (4, 6) shows that the solution above is the only one for Sum = 13." + "eng": "To save some work, note that if we take one solution and subtract all the entries from 7, we get another solution. Also, note that the new solution will have a Sum value which is 21 - (old Sum). Hence, the solutions for Sum values 9 and 10 give us the solutions for Sum values 11 and 12.\n\nIf A + B + C = 6, then A, B, and C are 1, 2, and 3, and Sum = 9. That is the upper left solution.\n\nIf A + B + C = 9, then Sum = 10 and (A, B, C) is (1, 2, 6), (1, 3, 5), or (2, 3, 4). If you check it, (1, 2, 6) and (2, 3, 4) are impossible. This leaves the upper right solution as the only Sum = 10 solution.\n\nIf you compare “Equal Sums – 2” with “Magic Triangles – 1,” you will see that they are the same puzzle!" } }, - "block1_text": "**The Challenge:** Here is a diagram created by overlapping four circles. The overlapping circles create eight regions. Put a number in each of the eight regions, using each of the numbers 1 to 8 exactly once, so that the sum of the numbers in each circle is the same.", - "block2_text": "**Exploration:** How many different answers can you find? Do you think there are any more? What happens if you use other number ranges? Are there other interesting problems like this with intersecting circles?", - "block3_text": "**The Challenge & Exploration:** Start by deciding which sums are possible for the common sum for all circles. Let Sum be that value. Let A, B, C, and D be the values of the four regions where two circles intersect. The sum of the four circles is 4 x Sum, and it is also 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + A + B + C + D. Then we have the equation 4 x Sum = 36 + A + B + C + D, so Sum = 9 + (A + B + C + D) / 4. The smallest that A + B + C + D can have is 1 + 2 + 3 + 4 = 10. This needs to be divisible, so it’s smallest possible value is 12, which means the smallest possible value is Sum = 9 + 12/4 = 12.\n\nNote that any solution can be turned into another solution by subtracting all entries from 9. Doing this will turn the old Sum into 27 - Sum. Consequently, the only possible values for Sum are 12, 13, 14, and 15. Because 12 and 15 are tied together, and 13 and 14 are tied together, we only need to check for solutions for 12 and 13.\n\nHere are solutions for Sum with values 12 and 13. It turns out these are the only ones for these two sums.", - "block4_text": "Notice that the numbers in the center of circles not touching each other add up to the same thing. For example, in the leftmost diagram, 8 + 4 = 5 + 7. Prove that this always happens with a bit of algebra. Let K and L be the values in the centers of two of the opposite circles, and let M and N be the other two values. If we add up the regions for the two circles for K and L we get 2 x Sum = K + L + (A + B + C + D). Similarly, adding up the regions for the two circles for M and N gives 2 x Sum = M + N + (A + B + C + D). This forces K + L = M + N.\n\nAlso, note that since 4 x Sum = 36 + A + B + C + D, we get 2 x Sum = M + N + (4 x Sum - 36). Rewriting this we have M + N = 36 - 2 x Sum. For our four values of Sum, 12 through 15, the values of M + N are 12, 10, 8, and 6.\n\nBecause 12 = 4 + 8 = 5 + 7 are the only ways to get 12, the solution above for Sum = 12 is the only solution. While 10 = 2 + 8 = 3 + 7 = 4 + 6 suggests there are more possibilities for Sum = 13, a quick check of the three possible pairings of (2, 8), (3, 7), and (4, 6) shows that the solution above is the only one for Sum = 13." + "block1_text": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create six regions. Put a number in each of the six regions, using each of the numbers 1 to 6 exactly once, so that the sum of the numbers in each circle is the same.", + "block2_text": "**Exploration:** How many different answers can you find? How do you know if you have found them all?", + "block3_text": "**The Challenge & Exploration:** Here are the four solutions. To see why these are the only ones, let A, B, and C be the three regions where two circles intersect, and let Sum be the common sum for the three circles. Calculate the total sum in two ways. As the sum of the three circles, the sum is 3 x Sum. As the sum of all six numbers plus A, B, and C the sum is 1 + 2 + 3 + 4 + 5 + 6 + A + B + C. The two things are equal, so that gives us 3 x Sum = 21 + A + B + C. Dividing by 3, we have Sum = 7 + (A + B + C)/3.\n\nFor Sum to be an integer in this last equation, A + B + C must be evenly divisible by 3. This allows for only four possibilities for A + B + C - it is either 6, 9, 12, or 15, and the corresponding values for Sum are 9, 10, 11, or 12.\n\nThe four solutions given here have Sum values of 9, 10, 11, and 12. As we shall see, these are all of the solutions!", + "block4_text": "To save some work, note that if we take one solution and subtract all the entries from 7, we get another solution. Also, note that the new solution will have a Sum value which is 21 - (old Sum). Hence, the solutions for Sum values 9 and 10 give us the solutions for Sum values 11 and 12.\n\nIf A + B + C = 6, then A, B, and C are 1, 2, and 3, and Sum = 9. That is the upper left solution.\n\nIf A + B + C = 9, then Sum = 10 and (A, B, C) is (1, 2, 6), (1, 3, 5), or (2, 3, 4). If you check it, (1, 2, 6) and (2, 3, 4) are impossible. This leaves the upper right solution as the only Sum = 10 solution.\n\nIf you compare “Equal Sums – 2” with “Magic Triangles – 1,” you will see that they are the same puzzle!" }, { - "id": "esm_pow_b_diff_pyramids_6", + "id": "esm_pow_b_equal_sums_3", "level": "B", "topic_theme_1": "NO_ASSD_AS10", - "notes_block_start": 4, + "notes_block_start": 3, "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWBDiffPyramid6Intro.svg", + "block1_illust": "ESMIll/ESMPOWBEqualNumberSums3.svg", "block1_illust_max_size": "240px", - "block2_type": "illust_below", - "block2_illust": "ESMIll/ESMPOWBDiffPyramid6Challenge.svg", - "block2_illust_max_size": "180px", - "block3_type": "all_text", - "block4_type": "illust_below", - "block4_illust": "ESMIll/ESMPOWBDiffPyramid6Solutions.svg", - "block4_illust_max_size": "400px", - "name": "Difference Pyramids - 6", + "block2_type": "all_text", + "block3_type": "illust_below", + "block3_illust": "ESMIll/ESMPOWBEqualNumberSums3Answers.svg", + "block3_illust_max_size": "400px", + "name": "Equal Sums - 3", "_translations": { "name": {}, "block1_text": {}, "block2_text": {}, - "block3_text": {}, - "block4_text": {} + "block3_text": {} }, "_translatedFields": { "name": { - "eng": "Difference Pyramids - 6" + "eng": "Equal Sums - 3" }, "block1_text": { - "eng": "**Introduction:** These pyramids are called **Difference Pyramids.** The number on top is the difference of the two numbers below." + "eng": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create seven regions. Put a number in each of the seven regions, using each of the numbers 1 to 7 exactly once, so that the sum of the numbers in each circle is the same." }, "block2_text": { - "eng": "**The Challenge:** Place the numbers from 1 to 6 to make a Difference Pyramid." + "eng": "**Exploration:** How many different answers can you find? How do you know if you have found them all?" }, "block3_text": { - "eng": "**Exploration:** Find different ways this can be done. Are some of these essentially the same?" - }, - "block4_text": { - "eng": "**The Challenge & Exploration:** A good start is to realize that because 6 cannot be the difference of two cards, it must go on the bottom row. \n\nNext, the only way 5 can be the difference is if it is above the 6 and the 1. So, either 5 goes directly above the 6 (with the 1 next to the 6), or 5 is in the bottom row.\n\nAt this point it is useful to consider what makes solutions different. Because the mirror image of any solution is also a solution, it makes sense to ignore those. Ignoring mirror images will reduce the number of solutions to consider by half. \n\nFor example, we can assume that not only is the 6 in the bottom row, but it is either in the middle or the right side of the bottom row - if it were on the left side, we could take the mirror image of the whole puzzle and put it on the right side.\n\nUsing this thinking, the bottom row can have five possible layouts (up to using mirror images): 5 X 6, X 5 6, X 6 5, X 1 6, X 6 1.\n\nAt this point, it is a matter of working through the various possibilities. The only 5 X 6 that works is 5 2 6. It turns out X 5 6 never works. The only X 6 5 is 2 6 5. The only X 1 6 is 4 1 6, and the only X 6 1 is 4 6 1.\n\nSo, ignoring mirror images, there are four solutions:" + "eng": "**The Challenge & Exploration:** The first question with these problems is what the possible sums in the circles are. Narrow this down by looking at the sum of the entries in two ways. Let A, B, and C be the three values where two circles intersect, let M be the value where all three circles intersect, and let Sum be the common sum in each circle. The sum of the three circles is 3 x Sum. That sum is also the sum of the numbers from 1 to 7 plus A + B + C plus 2 x M. Therefore, 3 x Sum = 28 + A + B + C + 2 x M.\n\nBefore going further with this, note that if we start with any solution, we can get a new solution by subtracting all the entries from 8. This will have the effect of replacing Sum by 32 - Sum. Because of this, we only need to look for values of Sum up to 16 - the remaining larger values can be obtained by subtracting those solution entries from 8.\n\nThe smallest A + B + C + 2 x M can be is 2 + 3 + 4 + 2 x 1 = 11. So the smallest Sum can be is (28 + 11) / 3 = 13. Consequently, we want to see which of the Sum values from 13 to 16 are possible. It turns out that they are all possible. \n\nHere is one solution for each Sum value starting at 13 and ending at 16. There are many more." } }, - "block1_text": "**Introduction:** These pyramids are called **Difference Pyramids.** The number on top is the difference of the two numbers below.", - "block2_text": "**The Challenge:** Place the numbers from 1 to 6 to make a Difference Pyramid.", - "block3_text": "**Exploration:** Find different ways this can be done. Are some of these essentially the same?", - "block4_text": "**The Challenge & Exploration:** A good start is to realize that because 6 cannot be the difference of two cards, it must go on the bottom row. \n\nNext, the only way 5 can be the difference is if it is above the 6 and the 1. So, either 5 goes directly above the 6 (with the 1 next to the 6), or 5 is in the bottom row.\n\nAt this point it is useful to consider what makes solutions different. Because the mirror image of any solution is also a solution, it makes sense to ignore those. Ignoring mirror images will reduce the number of solutions to consider by half. \n\nFor example, we can assume that not only is the 6 in the bottom row, but it is either in the middle or the right side of the bottom row - if it were on the left side, we could take the mirror image of the whole puzzle and put it on the right side.\n\nUsing this thinking, the bottom row can have five possible layouts (up to using mirror images): 5 X 6, X 5 6, X 6 5, X 1 6, X 6 1.\n\nAt this point, it is a matter of working through the various possibilities. The only 5 X 6 that works is 5 2 6. It turns out X 5 6 never works. The only X 6 5 is 2 6 5. The only X 1 6 is 4 1 6, and the only X 6 1 is 4 6 1.\n\nSo, ignoring mirror images, there are four solutions:" + "block1_text": "**The Challenge:** Here is a diagram created by overlapping three circles. The overlapping circles create seven regions. Put a number in each of the seven regions, using each of the numbers 1 to 7 exactly once, so that the sum of the numbers in each circle is the same.", + "block2_text": "**Exploration:** How many different answers can you find? How do you know if you have found them all?", + "block3_text": "**The Challenge & Exploration:** The first question with these problems is what the possible sums in the circles are. Narrow this down by looking at the sum of the entries in two ways. Let A, B, and C be the three values where two circles intersect, let M be the value where all three circles intersect, and let Sum be the common sum in each circle. The sum of the three circles is 3 x Sum. That sum is also the sum of the numbers from 1 to 7 plus A + B + C plus 2 x M. Therefore, 3 x Sum = 28 + A + B + C + 2 x M.\n\nBefore going further with this, note that if we start with any solution, we can get a new solution by subtracting all the entries from 8. This will have the effect of replacing Sum by 32 - Sum. Because of this, we only need to look for values of Sum up to 16 - the remaining larger values can be obtained by subtracting those solution entries from 8.\n\nThe smallest A + B + C + 2 x M can be is 2 + 3 + 4 + 2 x 1 = 11. So the smallest Sum can be is (28 + 11) / 3 = 13. Consequently, we want to see which of the Sum values from 13 to 16 are possible. It turns out that they are all possible. \n\nHere is one solution for each Sum value starting at 13 and ending at 16. There are many more." }, { - "id": "esm_pow_b_diff_pyramids_10", + "id": "esm_pow_b_equal_sums_4", "level": "B", "topic_theme_1": "NO_ASSD_AS10", - "notes_block_start": 4, + "notes_block_start": 3, "block1_type": "illust_below", - "block1_illust": "ESMIll/ESMPOWBDiffPyramid6Intro.svg", + "block1_illust": "ESMIll/ESMPOWBEqualNumberSums4.svg", "block1_illust_max_size": "240px", - "block2_type": "illust_below", - "block2_illust": "ESMIll/ESMPOWBDiffPyramid10Challenge.svg", - "block2_illust_max_size": "180px", - "block3_type": "all_text", + "block2_type": "all_text", + "block3_type": "illust_below", + "block3_illust": "ESMIll/ESMPOWBEqualNumberSums4Answers.svg", + "block3_illust_max_size": "400px", "block4_type": "all_text", - "name": "Difference Pyramids - 10", + "name": "Equal Sums - 4", "_translations": { "name": {}, "block1_text": {}, @@ -996,25 +819,25 @@ }, "_translatedFields": { "name": { - "eng": "Difference Pyramids - 10" + "eng": "Equal Sums - 4" }, "block1_text": { - "eng": "**Introduction:** These pyramids are called **Difference Pyramids.** The number on top is the difference of the two numbers below." + "eng": "**The Challenge:** Here is a diagram created by overlapping four circles. The overlapping circles create eight regions. Put a number in each of the eight regions, using each of the numbers 1 to 8 exactly once, so that the sum of the numbers in each circle is the same." }, "block2_text": { - "eng": "**The Challenge:** Place the numbers from 1 to 10 to make a Difference Pyramid." + "eng": "**Exploration:** How many different answers can you find? Do you think there are any more? What happens if you use other number ranges? Are there other interesting problems like this with intersecting circles?" }, "block3_text": { - "eng": "**Exploration:** Play with even larger pyramids." + "eng": "**The Challenge & Exploration:** Start by deciding which sums are possible for the common sum for all circles. Let Sum be that value. Let A, B, C, and D be the values of the four regions where two circles intersect. The sum of the four circles is 4 x Sum, and it is also 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + A + B + C + D. Then we have the equation 4 x Sum = 36 + A + B + C + D, so Sum = 9 + (A + B + C + D) / 4. The smallest that A + B + C + D can have is 1 + 2 + 3 + 4 = 10. This needs to be divisible, so it’s smallest possible value is 12, which means the smallest possible value is Sum = 9 + 12/4 = 12.\n\nNote that any solution can be turned into another solution by subtracting all entries from 9. Doing this will turn the old Sum into 27 - Sum. Consequently, the only possible values for Sum are 12, 13, 14, and 15. Because 12 and 15 are tied together, and 13 and 14 are tied together, we only need to check for solutions for 12 and 13.\n\nHere are solutions for Sum with values 12 and 13. It turns out these are the only ones for these two sums." }, "block4_text": { - "eng": "**The Challenge & Exploration:** Because 10 cannot be the difference of two cards, it must go on the bottom row. Similarly, either 9 is in the bottom row or it is in the next-to-the-bottom row above the 1 and the 10. The 8 and 7 cards are also good cards to focus on to get rid of possibilities.\n\nThis means the bottom row looks like one of the following (ignoring mirror images):\n\nX Y 9 10, X 9 Y 10, 9 X Y 10, X Y 10 9, X 9 10 Y, 9 X 10 Y, X Y 1 10, X 1 10 Y, X Y 10 1\n\nThat is a lot of possibilities to consider!\n\nFortunately, if you consider where 8 and 7 can go, the possibilities are reduced to the following list (assuming we haven’t missed any). It is easy to finish each of these once you have the bottom row.\n\n8 3 10 9, 9 3 10 8, 6 1 10 8, 8 1 10 6\n\nInvestigating pyramids of size 15, 21, or higher are for the truly dedicated.\n\nFrom the literature, there is only one solution (up to reflections) for 15, and its bottom row is {6, 14, 15, 3, 13}. Even more surprisingly, there are no solutions for 21, 28, and 36, and it has been conjectured that there are no solutions above that!" + "eng": "Notice that the numbers in the center of circles not touching each other add up to the same thing. For example, in the leftmost diagram, 8 + 4 = 5 + 7. Prove that this always happens with a bit of algebra. Let K and L be the values in the centers of two of the opposite circles, and let M and N be the other two values. If we add up the regions for the two circles for K and L we get 2 x Sum = K + L + (A + B + C + D). Similarly, adding up the regions for the two circles for M and N gives 2 x Sum = M + N + (A + B + C + D). This forces K + L = M + N.\n\nAlso, note that since 4 x Sum = 36 + A + B + C + D, we get 2 x Sum = M + N + (4 x Sum - 36). Rewriting this we have M + N = 36 - 2 x Sum. For our four values of Sum, 12 through 15, the values of M + N are 12, 10, 8, and 6.\n\nBecause 12 = 4 + 8 = 5 + 7 are the only ways to get 12, the solution above for Sum = 12 is the only solution. While 10 = 2 + 8 = 3 + 7 = 4 + 6 suggests there are more possibilities for Sum = 13, a quick check of the three possible pairings of (2, 8), (3, 7), and (4, 6) shows that the solution above is the only one for Sum = 13." } }, - "block1_text": "**Introduction:** These pyramids are called **Difference Pyramids.** The number on top is the difference of the two numbers below.", - "block2_text": "**The Challenge:** Place the numbers from 1 to 10 to make a Difference Pyramid.", - "block3_text": "**Exploration:** Play with even larger pyramids.", - "block4_text": "**The Challenge & Exploration:** Because 10 cannot be the difference of two cards, it must go on the bottom row. Similarly, either 9 is in the bottom row or it is in the next-to-the-bottom row above the 1 and the 10. The 8 and 7 cards are also good cards to focus on to get rid of possibilities.\n\nThis means the bottom row looks like one of the following (ignoring mirror images):\n\nX Y 9 10, X 9 Y 10, 9 X Y 10, X Y 10 9, X 9 10 Y, 9 X 10 Y, X Y 1 10, X 1 10 Y, X Y 10 1\n\nThat is a lot of possibilities to consider!\n\nFortunately, if you consider where 8 and 7 can go, the possibilities are reduced to the following list (assuming we haven’t missed any). It is easy to finish each of these once you have the bottom row.\n\n8 3 10 9, 9 3 10 8, 6 1 10 8, 8 1 10 6\n\nInvestigating pyramids of size 15, 21, or higher are for the truly dedicated.\n\nFrom the literature, there is only one solution (up to reflections) for 15, and its bottom row is {6, 14, 15, 3, 13}. Even more surprisingly, there are no solutions for 21, 28, and 36, and it has been conjectured that there are no solutions above that!" + "block1_text": "**The Challenge:** Here is a diagram created by overlapping four circles. The overlapping circles create eight regions. Put a number in each of the eight regions, using each of the numbers 1 to 8 exactly once, so that the sum of the numbers in each circle is the same.", + "block2_text": "**Exploration:** How many different answers can you find? Do you think there are any more? What happens if you use other number ranges? Are there other interesting problems like this with intersecting circles?", + "block3_text": "**The Challenge & Exploration:** Start by deciding which sums are possible for the common sum for all circles. Let Sum be that value. Let A, B, C, and D be the values of the four regions where two circles intersect. The sum of the four circles is 4 x Sum, and it is also 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + A + B + C + D. Then we have the equation 4 x Sum = 36 + A + B + C + D, so Sum = 9 + (A + B + C + D) / 4. The smallest that A + B + C + D can have is 1 + 2 + 3 + 4 = 10. This needs to be divisible, so it’s smallest possible value is 12, which means the smallest possible value is Sum = 9 + 12/4 = 12.\n\nNote that any solution can be turned into another solution by subtracting all entries from 9. Doing this will turn the old Sum into 27 - Sum. Consequently, the only possible values for Sum are 12, 13, 14, and 15. Because 12 and 15 are tied together, and 13 and 14 are tied together, we only need to check for solutions for 12 and 13.\n\nHere are solutions for Sum with values 12 and 13. It turns out these are the only ones for these two sums.", + "block4_text": "Notice that the numbers in the center of circles not touching each other add up to the same thing. For example, in the leftmost diagram, 8 + 4 = 5 + 7. Prove that this always happens with a bit of algebra. Let K and L be the values in the centers of two of the opposite circles, and let M and N be the other two values. If we add up the regions for the two circles for K and L we get 2 x Sum = K + L + (A + B + C + D). Similarly, adding up the regions for the two circles for M and N gives 2 x Sum = M + N + (A + B + C + D). This forces K + L = M + N.\n\nAlso, note that since 4 x Sum = 36 + A + B + C + D, we get 2 x Sum = M + N + (4 x Sum - 36). Rewriting this we have M + N = 36 - 2 x Sum. For our four values of Sum, 12 through 15, the values of M + N are 12, 10, 8, and 6.\n\nBecause 12 = 4 + 8 = 5 + 7 are the only ways to get 12, the solution above for Sum = 12 is the only solution. While 10 = 2 + 8 = 3 + 7 = 4 + 6 suggests there are more possibilities for Sum = 13, a quick check of the three possible pairings of (2, 8), (3, 7), and (4, 6) shows that the solution above is the only one for Sum = 13." }, { "id": "esm_pow_b_fill_blanks_1", @@ -1271,6 +1094,183 @@ "block4_text": "**Exploration:** Can you solve similar puzzles that break up a number range into common sums? How about four pairs using the numbers 0 to 7 or 1 to 8? How about 3 triplets from 0 to 8 or 1 to 9? How about 2 groups of 5 for the numbers from 0 to 9? Do you see any patterns for when it works and when it doesn’t?", "block5_text": "**The Challenge:** As with the other Fill in the Blanks puzzles, a child can just play with this and eventually arrive at the answers. That exploration involves a lot of good experiences, and there is no reason to avoid it.\n\nIf you want to be more systematic, the first question is: What is the common sum for these pairs of numbers? The five pairs have the same sum, and when we add them all up we get the same thing as adding the numbers up from 0 to 9. The sum from 0 to 9 is 45, so when we divide that by 5 we get 9 - the sum for each pair must be 9. Once that is established, the rest is simple:\n\n0 + 9 = 1 + 8 = 2 + 7 = 3 + 6 = 4 + 5.\n\n**Exploration:** The first step is to see whether the sum of the range of numbers can be broken into that many equal pieces. Also, note that it makes no difference whether we start at 0 or 1, so we’ll just look at starting at 0.\n\n**0 to 7 using 4 pairs:** The sum of the numbers from 0 to 7 is 28. Dividing 28 into 4 pairs gives a sum of 7 for each pair.\n\nThis is simple enough: 7 = 0 + 7 = 1 + 6 = 2 + 5 = 3 + 4.\n\n**0 to 2n - 1 using n pairs:** After looking at 0 to 7 and 0 to 9, the pattern is clear: write n as the n possible sums.\n\n**0 to 8 using 3 triplets:** The sum from 0 to 8 is 36. Dividing 36 into 3 triplets gives a sum of 12 for each triplet. The triplets will be largely driven by the three largest numbers (6, 7, 8), no two of which can be in a triplet together. This produces triplets (8, 0, 4), (7, 2, 3), and (6, 1, 5). This could also be done as (8, 1, 3), (7, 0, 5), and (6, 2, 4).\n\n**0 to 9 using 2 groups of 5:** The sum from 0 to 9 is 45. 45 cannot be divided evenly into two equal groups!\n\nThe very interested child may want to go exploring further to see more examples of when this works and when it doesn’t. What fun!" }, + { + "id": "esm_pow_a_find_pieces_2", + "level": "B", + "topic_theme_1": "Geom_Shape_SN2D3D", + "topic_theme_2": "Geom_Shape_CompDecomp", + "topic_theme_3": "NPV_QC10_QC", + "notes_block_start": 4, + "block1_type": "illust_below", + "block1_illust": "ESMIll/ESMPOWBFindingthePieces2Intro.svg", + "block1_illust_max_size": "360px", + "block2_type": "illust_below", + "block2_illust": "ESMIll/ESMPOWBFindingthePieces2Challenge.svg", + "block2_illust_max_size": "360px", + "block3_type": "all_text", + "block4_type": "all_text", + "name": "Finding the Pieces - 2", + "_translations": { + "name": {}, + "block1_text": {}, + "block2_text": {}, + "block3_text": {}, + "block4_text": {} + }, + "_translatedFields": { + "name": { + "eng": "Finding the Pieces - 2" + }, + "block1_text": { + "eng": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). A **parallelogram** is a four-sided figure that has two pairs of parallel sides. In the large triangle on the left, there are five triangles marked – the four colored triangles and the entire triangle. The same large triangle in the middle has one of its three trapezoids colored in green. The same large triangle on the right has one of its three parallelograms colored in red." + }, + "block2_text": { + "eng": "**The Challenge:** In each of these figures, count the number of triangles, trapezoids, and parallelograms." + }, + "block3_text": { + "eng": "**Exploration:** Make drawings like these for other people to count the triangles, parallelograms, and trapezoids." + }, + "block4_text": { + "eng": "**The Challenge:** Work on organized counting using these two figures. The second one requires a lot of careful counting.\n\n**The large triangle on the left:**\n\nIt has 9 small triangles (base 1), 3 intermediate triangles (base 2), and 1 large triangle (base 3), for a total of 13 triangles.\n\nIt has 9 small trapezoids (base 2 top 1), 3 intermediate trapezoids (base 3 top 2), and 3 large trapezoids (base 3 top 1), for a total of 15 trapezoids.\n\nIt has 9 small parallelograms (sides 1 and 1) and 6 intermediate parallelograms (sides 2 and 1), for a total of 15 parallelograms.\n\n**The large triangle on the right:**\n\nThe large triangle on the right has 16 small triangles (base 1), 7 small intermediate triangles (base 2), 3 large intermediate triangles (base 3), and 1 large triangle (base 4), for a total of 27 triangles. \nIt has 18 small trapezoids (base 2 top 1), 9 longer small trapezoids (base 3 top 2), 3 very long small trapezoids (base 4 top 3), 9 intermediate trapezoids (base 3 top 1), 3 intermediate longer trapezoids (base 4 top 2), and 3 large trapezoids (base 4 top 1), for a total of 18 + 9 + 3 + 9 + 3 + 3 = 45 trapezoids.\n\nIt has 18 small parallelograms (sides 1 and 1), 18 long small parallelograms (sides 2 and 1), 6 longer small parallelograms (sides 3 and 1), and 3 intermediate parallelograms (sides 2 and 2), for a total of 18 + 18 + 6 + 3 = 45 parallelograms." + } + }, + "block1_text": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). A **parallelogram** is a four-sided figure that has two pairs of parallel sides. In the large triangle on the left, there are five triangles marked – the four colored triangles and the entire triangle. The same large triangle in the middle has one of its three trapezoids colored in green. The same large triangle on the right has one of its three parallelograms colored in red.", + "block2_text": "**The Challenge:** In each of these figures, count the number of triangles, trapezoids, and parallelograms.", + "block3_text": "**Exploration:** Make drawings like these for other people to count the triangles, parallelograms, and trapezoids.", + "block4_text": "**The Challenge:** Work on organized counting using these two figures. The second one requires a lot of careful counting.\n\n**The large triangle on the left:**\n\nIt has 9 small triangles (base 1), 3 intermediate triangles (base 2), and 1 large triangle (base 3), for a total of 13 triangles.\n\nIt has 9 small trapezoids (base 2 top 1), 3 intermediate trapezoids (base 3 top 2), and 3 large trapezoids (base 3 top 1), for a total of 15 trapezoids.\n\nIt has 9 small parallelograms (sides 1 and 1) and 6 intermediate parallelograms (sides 2 and 1), for a total of 15 parallelograms.\n\n**The large triangle on the right:**\n\nThe large triangle on the right has 16 small triangles (base 1), 7 small intermediate triangles (base 2), 3 large intermediate triangles (base 3), and 1 large triangle (base 4), for a total of 27 triangles. \nIt has 18 small trapezoids (base 2 top 1), 9 longer small trapezoids (base 3 top 2), 3 very long small trapezoids (base 4 top 3), 9 intermediate trapezoids (base 3 top 1), 3 intermediate longer trapezoids (base 4 top 2), and 3 large trapezoids (base 4 top 1), for a total of 18 + 9 + 3 + 9 + 3 + 3 = 45 trapezoids.\n\nIt has 18 small parallelograms (sides 1 and 1), 18 long small parallelograms (sides 2 and 1), 6 longer small parallelograms (sides 3 and 1), and 3 intermediate parallelograms (sides 2 and 2), for a total of 18 + 18 + 6 + 3 = 45 parallelograms." + }, + { + "id": "esm_pow_a_find_pieces_3", + "level": "B", + "topic_theme_1": "Geom_Shape_SN2D3D", + "topic_theme_2": "Geom_Shape_CompDecomp", + "notes_block_start": 4, + "block1_type": "all_text", + "block2_type": "illust_below", + "block2_illust": "ESMIll/ESMPOWBFindingthePieces3Challenge.svg", + "block2_illust_max_size": "360px", + "block3_type": "all_text", + "block4_type": "illust_below", + "block4_illust": "ESMIll/ESMPOWBFindingthePieces3Answers.svg", + "block4_illust_max_size": "360px", + "name": "Finding the Pieces - 3", + "_translations": { + "name": {}, + "block1_text": {}, + "block2_text": {}, + "block3_text": {}, + "block4_text": {} + }, + "_translatedFields": { + "name": { + "eng": "Finding the Pieces - 3" + }, + "block1_text": { + "eng": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). A **parallelogram** is a four-sided figure that has two pairs of parallel sides. A **rectangle** is a four-sided figure with four right angles. A **square** is a rectangle with four equal sides. A **right triangle** is a triangle with a right angle." + }, + "block2_text": { + "eng": "**The Challenge:** Break this figure up using trapezoids, parallelograms, rectangles, squares and right triangles. Use as few pieces as you can." + }, + "block3_text": { + "eng": "**Exploration:** How many ways can you find to do this using this fewest number of pieces?" + }, + "block4_text": { + "eng": "**The Challenge:** Here are two ways to break this drawing into four figures. The answer on the left uses a square, a parallelogram, a right triangle, and a rectangle. The answer on the right uses a square, two trapezoids, and a rectangle. There are other answers, such as changing the first answer by turning the square and parallelogram into a trapezoid and a right triangle. How many answers can your students find?" + } + }, + "block1_text": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). A **parallelogram** is a four-sided figure that has two pairs of parallel sides. A **rectangle** is a four-sided figure with four right angles. A **square** is a rectangle with four equal sides. A **right triangle** is a triangle with a right angle.", + "block2_text": "**The Challenge:** Break this figure up using trapezoids, parallelograms, rectangles, squares and right triangles. Use as few pieces as you can.", + "block3_text": "**Exploration:** How many ways can you find to do this using this fewest number of pieces?", + "block4_text": "**The Challenge:** Here are two ways to break this drawing into four figures. The answer on the left uses a square, a parallelogram, a right triangle, and a rectangle. The answer on the right uses a square, two trapezoids, and a rectangle. There are other answers, such as changing the first answer by turning the square and parallelogram into a trapezoid and a right triangle. How many answers can your students find?" + }, + { + "id": "esm_pow_a_find_pieces_4", + "level": "B", + "topic_theme_1": "Geom_Shape_SN2D3D", + "topic_theme_2": "Geom_Shape_CompDecomp", + "topic_theme_3": "NPV_QC10_QC", + "notes_block_start": 3, + "block1_type": "illust_below", + "block1_illust": "ESMIll/ESMPOWBFindingthePieces4Intro.svg", + "block1_illust_max_size": "360px", + "block2_type": "illust_below", + "block2_illust": "ESMIll/ESMPOWBFindingthePieces4Challenge.svg", + "block2_illust_max_size": "360px", + "block3_type": "illust_below", + "block3_illust": "ESMIll/ESMPOWBFindingthePieces4Answers.svg", + "block3_illust_max_size": "360px", + "name": "Finding the Pieces - 4", + "_translations": { + "name": {}, + "block1_text": {}, + "block2_text": {}, + "block3_text": {} + }, + "_translatedFields": { + "name": { + "eng": "Finding the Pieces - 4" + }, + "block1_text": { + "eng": "**Introduction:** The figure on the left has a shaded part in red and an unshaded part. The figure on the right shows how to fill the unshaded part with seven exact copies of the shaded part." + }, + "block2_text": { + "eng": "**The Challenge:** In these two figures, there is a shaded part and an unshaded part. Find out how many times the shaded part will exactly fit into the unshaded part." + }, + "block3_text": { + "eng": "**The Challenge:** In the left figure, there are 7 triangles like the red one. In the right figure, there are four L-shaped pieces like the red one." + } + }, + "block1_text": "**Introduction:** The figure on the left has a shaded part in red and an unshaded part. The figure on the right shows how to fill the unshaded part with seven exact copies of the shaded part.", + "block2_text": "**The Challenge:** In these two figures, there is a shaded part and an unshaded part. Find out how many times the shaded part will exactly fit into the unshaded part.", + "block3_text": "**The Challenge:** In the left figure, there are 7 triangles like the red one. In the right figure, there are four L-shaped pieces like the red one." + }, + { + "id": "esm_pow_a_find_pieces_5", + "level": "B", + "topic_theme_1": "Geom_Shape_SN2D3D", + "topic_theme_2": "Geom_Shape_CompDecomp", + "topic_theme_3": "NPV_QC10_QC", + "notes_block_start": 4, + "block1_type": "illust_below", + "block1_illust": "ESMIll/ESMPOWBFindingthePieces5Intro.svg", + "block1_illust_max_size": "360px", + "block2_type": "illust_below", + "block2_illust": "ESMIll/ESMPOWBFindingthePieces5Challenge.svg", + "block2_illust_max_size": "360px", + "block3_type": "all_text", + "block4_type": "illust_below", + "block4_illust": "ESMIll/ESMPOWBFindingthePieces5Answers.svg", + "block4_illust_max_size": "360px", + "name": "Finding the Pieces - 5", + "_translations": { + "name": {}, + "block1_text": {}, + "block2_text": {}, + "block3_text": {}, + "block4_text": {} + }, + "_translatedFields": { + "name": { + "eng": "Finding the Pieces - 5" + }, + "block1_text": { + "eng": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). The figure on the left can be broken into three pieces which are triangles. It can also be broken into two trapezoids." + }, + "block2_text": { + "eng": "**The Challenge:** For each of these two figures, find a way to break the figure into as few triangles as possible. Also find a way to break each figure into as few trapezoids as possible." + }, + "block3_text": { + "eng": "**Exploration:** Are there other ways to break these two figures into triangles or trapezoids in as few pieces?" + }, + "block4_text": { + "eng": "**The Challenge & Exploration:** One example of breaking up the two figures into triangles and trapezoids is given below. There are other possible choices for how to do it, so be sure to talk about all the different possibilities that everyone finds." + } + }, + "block1_text": "**Introduction:** A **trapezoid** is a four-sided figure that has exactly one pair of parallel sides (parallel lines in a surface are lines that never meet). The figure on the left can be broken into three pieces which are triangles. It can also be broken into two trapezoids.", + "block2_text": "**The Challenge:** For each of these two figures, find a way to break the figure into as few triangles as possible. Also find a way to break each figure into as few trapezoids as possible.", + "block3_text": "**Exploration:** Are there other ways to break these two figures into triangles or trapezoids in as few pieces?", + "block4_text": "**The Challenge & Exploration:** One example of breaking up the two figures into triangles and trapezoids is given below. There are other possible choices for how to do it, so be sure to talk about all the different possibilities that everyone finds." + }, { "id": "esm_pow_b_sum_pyramids_1", "level": "B", diff --git a/app_data/sheets/data_list/esm_topic_list.json b/app_data/sheets/data_list/esm_topic_list.json index 83b46b4..e38e3fe 100644 --- a/app_data/sheets/data_list/esm_topic_list.json +++ b/app_data/sheets/data_list/esm_topic_list.json @@ -6,6 +6,7 @@ "rows": [ { "id": "MT_EAA_EandO", + "searching_for_this": false, "theme_id": "MT_EAA_", "strand_id": "MT", "block1_type": "all_text", @@ -41,6 +42,7 @@ }, { "id": "MT_EAA_MTinH", + "searching_for_this": false, "theme_id": "MT_EAA_", "strand_id": "MT", "block1_type": "illust_below", @@ -69,6 +71,7 @@ }, { "id": "MT_EAA_MTOA", + "searching_for_this": false, "theme_id": "MT_EAA_", "strand_id": "MT", "block1_type": "illust_below", @@ -112,6 +115,7 @@ }, { "id": "MT_EAA_MTDC", + "searching_for_this": false, "theme_id": "MT_EAA_", "strand_id": "MT", "block1_type": "all_text", @@ -156,6 +160,7 @@ }, { "id": "MT_EAA_MTC", + "searching_for_this": false, "theme_id": "MT_EAA_", "strand_id": "MT", "next_topic_1": "NPV_QC10_QC", @@ -177,6 +182,7 @@ }, { "id": "MT_EAA_MTPDA", + "searching_for_this": false, "theme_id": "MT_EAA_", "strand_id": "MT", "next_topic_1": "Geom_OP_PG", @@ -198,6 +204,7 @@ }, { "id": "MT_RWC_DRP", + "searching_for_this": false, "theme_id": "MT_RWC_", "strand_id": "MT", "next_topic_1": "MT_RWC_DRV", @@ -219,6 +226,7 @@ }, { "id": "MT_RWC_DRV", + "searching_for_this": false, "theme_id": "MT_RWC_", "strand_id": "MT", "prev_topic_1": "MT_RWC_DRP", @@ -241,6 +249,7 @@ }, { "id": "Geom_OP_PG", + "searching_for_this": false, "theme_id": "Geom_OP_", "strand_id": "Geom", "prev_topic_1": "MT_EAA_MTPDA", @@ -268,10 +277,10 @@ "eng": "Properties & Grouping" }, "block1_text": { - "eng": "**Properties are where everything starts:** Understanding that objects have properties is the beginning of mathematics, and more generally an understanding of the world. It is why very early training in math is so central to a child's success in all areas of learning.\n\n**Many types of properties:** There are a wide variety of types of properties. The listing below is just the start.\n\n* Color and shape – color names, round, flat, square\n* Size – large, small, medium, \n* Texture – rough, smooth, wet, dry, pointed, grooved\n* Sound – loud, soft, \n* Order – first, second\n\n**Properties for multiple objects:** Not only do individual objects have properties, but they can have properties that describe relationships between more than one object. There are basic comparison words for many of these properties: larger, largest, louder, and loudest. There are spatial relationship words such as under, over, next to, above, and inside." + "eng": "**Properties are where everything starts:** Understanding that objects have properties is the beginning of mathematics, and more generally an understanding of the world. It is why very early training in math is so central to a child's success in all areas of learning.\n\n**Many types of properties:** There are a wide variety of types of properties. The listing below is just the start.\n\n* Color and shape – color names, round, flat, square\n* Size – large, small, medium, larger, largest\n* Texture – rough, smooth, wet, dry, pointed, grooved\n* Sound – loud, soft, louder, \n* Order – first, second, third, last, next\n\n**Properties for multiple objects:** Not only do individual objects have properties, but they can have properties that describe relationships between more than one object. There are basic comparison words for many of these properties: larger, largest, louder, and loudest. There are spatial relationship words such as under, over, next to, above, and inside." }, "block2_accord": { - "eng": "Practice: Ask by Properties" + "eng": "Practice: Ask for things by Property" }, "block2_text": { "eng": "Practice using properties by asking the child to bring you something with that property. You could ask \"Please bring me something that is red.\" for example. As a child gets better at this, make the requests more complicated by combining more than one property – \"Find a round wooden thing.\"" @@ -289,8 +298,8 @@ "eng": "**A circle for each property:** Make this visible by drawing a big circle and having all the things that have a particular property put in that circle. For example, you could have all the things with a hole in them put in the circle.\n\nAs this becomes easy for your child, use two circles that overlap – one circle could be for triangles, the other for things with holes, and the common area to the two circles would be for triangles with holes." } }, - "block1_text": "**Properties are where everything starts:** Understanding that objects have properties is the beginning of mathematics, and more generally an understanding of the world. It is why very early training in math is so central to a child's success in all areas of learning.\n\n**Many types of properties:** There are a wide variety of types of properties. The listing below is just the start.\n\n* Color and shape – color names, round, flat, square\n* Size – large, small, medium, \n* Texture – rough, smooth, wet, dry, pointed, grooved\n* Sound – loud, soft, \n* Order – first, second\n\n**Properties for multiple objects:** Not only do individual objects have properties, but they can have properties that describe relationships between more than one object. There are basic comparison words for many of these properties: larger, largest, louder, and loudest. There are spatial relationship words such as under, over, next to, above, and inside.", - "block2_accord": "Practice: Ask by Properties", + "block1_text": "**Properties are where everything starts:** Understanding that objects have properties is the beginning of mathematics, and more generally an understanding of the world. It is why very early training in math is so central to a child's success in all areas of learning.\n\n**Many types of properties:** There are a wide variety of types of properties. The listing below is just the start.\n\n* Color and shape – color names, round, flat, square\n* Size – large, small, medium, larger, largest\n* Texture – rough, smooth, wet, dry, pointed, grooved\n* Sound – loud, soft, louder, \n* Order – first, second, third, last, next\n\n**Properties for multiple objects:** Not only do individual objects have properties, but they can have properties that describe relationships between more than one object. There are basic comparison words for many of these properties: larger, largest, louder, and loudest. There are spatial relationship words such as under, over, next to, above, and inside.", + "block2_accord": "Practice: Ask for things by Property", "block2_text": "Practice using properties by asking the child to bring you something with that property. You could ask \"Please bring me something that is red.\" for example. As a child gets better at this, make the requests more complicated by combining more than one property – \"Find a round wooden thing.\"", "block3_accord": "Practiice: Group by Property", "block3_text": "Practice grouping things with the same property. If the child has a collection of objects, ask to have all the round things put to one side.", @@ -299,6 +308,7 @@ }, { "id": "Geom_OP_SD", + "searching_for_this": false, "theme_id": "Geom_OP_", "strand_id": "Geom", "prev_topic_1": "Geom_OP_PG", @@ -348,7 +358,7 @@ "eng": "A fun activity for practicing with properties is to show your child a small set of objects and ask which of them doesn't belong. Challenge your child to identify the object that is not like the others and to explain why. Accept any reason that makes sense; your child may have an unusual reason.\n\nThis has also been called \"Find the Spy.\" The spy is the person who is an outsider pretending to be just like the other three. Discuss which of the four things is the most unusual.\n\nFor example, you could have pictures of some animals. Perhaps only one of them can fly. Maybe only one of them has two legs. This activity can provide fun challenges that let your child do some creative thinking with new concepts.\n\nAs another example, each of the following four shapes is different in some way from the other three. Shape 1 is a triangle, while the rest are squares. Shape 2 is the only one with a hole. Shape 3 is much smaller than the others. Shape 4 is blue while the others are red." }, "block5_accord": { - "eng": "Tip: Discuss all ideas" + "eng": "Tip: Be Open to All Ideas" }, "block5_text": { "eng": "Some of your children's ideas for comparisons may seem odd to you. Ask the student to talk about their thinking. It may be a new good idea, or it may be flawed, but either way it will lead to fresh understandings for the student and the listener." @@ -361,11 +371,12 @@ "block3_text": "If you hand a child a spoon and fork, there are many things the child might say. They are the same because you eat with both of them. They are also the same because you hold both of them, they are about the same size, or they are made of the same material. They are different because one is smooth and somewhat round, while the other is pointed.", "block4_accord": "Which On Doesn't Belong", "block4_text": "A fun activity for practicing with properties is to show your child a small set of objects and ask which of them doesn't belong. Challenge your child to identify the object that is not like the others and to explain why. Accept any reason that makes sense; your child may have an unusual reason.\n\nThis has also been called \"Find the Spy.\" The spy is the person who is an outsider pretending to be just like the other three. Discuss which of the four things is the most unusual.\n\nFor example, you could have pictures of some animals. Perhaps only one of them can fly. Maybe only one of them has two legs. This activity can provide fun challenges that let your child do some creative thinking with new concepts.\n\nAs another example, each of the following four shapes is different in some way from the other three. Shape 1 is a triangle, while the rest are squares. Shape 2 is the only one with a hole. Shape 3 is much smaller than the others. Shape 4 is blue while the others are red.", - "block5_accord": "Tip: Discuss all ideas", + "block5_accord": "Tip: Be Open to All Ideas", "block5_text": "Some of your children's ideas for comparisons may seem odd to you. Ask the student to talk about their thinking. It may be a new good idea, or it may be flawed, but either way it will lead to fresh understandings for the student and the listener." }, { "id": "Geom_Pat_Intro", + "searching_for_this": false, "theme_id": "Geom_Pat_", "strand_id": "Geom", "prev_topic_1": "Geom_OP_PG", @@ -417,6 +428,7 @@ }, { "id": "Geom_Pat_MSP", + "searching_for_this": false, "theme_id": "Geom_Pat_", "strand_id": "Geom", "block1_type": "all_text", @@ -470,6 +482,7 @@ }, { "id": "Geom_Shape_DS", + "searching_for_this": false, "theme_id": "Geom_Shape_", "strand_id": "Geom", "block1_type": "all_text", @@ -488,14 +501,15 @@ "eng": "**Properties:** Like all objects, shapes have many properties. Some of these properties are essential to defining and identifying the shape, and others are incidental. For example, a shape may have three flat sides, be red, and be made out of wood. The three flat sides are essential for understanding that it is a triangle.\n\n**Key Properties:** There are some key ingredients that make up describing, recognizing, and understanding the standard shapes. \n\n< graphic showing these bits of geometry about to be described >" }, "block2_text": { - "eng": "* 2D or 3D. There are 2-dimensional shapes that are flat like a piece of paper, and there are 3-dimensional shapes that have depth and are sometimes described as solid.\n* Faces. These are flat 2-dimensional shapes.\n* Edges / Sides. The edges or sides are the straight line segments at the edge of a face.\n* Corners / Points / Vertices. For shapes, the individual points of interest will be the ones where two (or more) edges meet. The technical word vertex (vertices) is a bit more advanced.\n* Angles. Two lines, or line segments, that meet in a point form an angle there.\n* Right Angles: Angles that look like the corner of a piece of paper are called right angles. They are also said to have 90 degrees, but that description should wait until they can count and understand the numbers up to 100 or 200.\n* Straight or Curved. Lines and faces can be straight or curved.\n* Same size. Describing edges as having the same size is important for differentiating different shapes within the same family.\n\n**Relative Positions:** Shapes may have positions relative to other shapes. Understanding those describing words is important for being able to describe scenes, and also describing how some shapes are made up of smaller shapes. These are words like: above, over, under, inside, beside, next to, behind, between, and near." + "eng": "* 2D or 3D. There are 2-dimensional shapes that are flat like a piece of paper, and there are 3-dimensional shapes that have depth and are sometimes described as solid.\n* Faces. These are flat, 2-dimensional shapes.\n* Edges / Sides. The edges or sides are the straight line segments at the edge of a face.\n* Corners / Points / Vertices. For shapes, the individual points of interest will be the ones where two (or more) edges meet. The technical word vertex (vertices) is a bit advanced for this age, but it can be used.\n* Angles. Two lines, or line segments, that meet in a point form an angle there.\n* Right Angles: Angles that look like the corner of a piece of paper are called right angles. They are also said to have 90 degrees, but that description should wait until they can count and understand the numbers up to 100 or 200.\n* Straight or Curved. Lines and faces can be straight or curved.\n* Same size. Describing two edges as having the same size is important for differentiating different shapes within the same family.\n\n**Relative Positions:** Shapes may have positions relative to other shapes. Understanding those describing words is important for being able to describe scenes, and also describing how some shapes are made up of smaller shapes. These are words like: above, over, under, inside, beside, next to, behind, between, and near." } }, "block1_text": "**Properties:** Like all objects, shapes have many properties. Some of these properties are essential to defining and identifying the shape, and others are incidental. For example, a shape may have three flat sides, be red, and be made out of wood. The three flat sides are essential for understanding that it is a triangle.\n\n**Key Properties:** There are some key ingredients that make up describing, recognizing, and understanding the standard shapes. \n\n< graphic showing these bits of geometry about to be described >", - "block2_text": "* 2D or 3D. There are 2-dimensional shapes that are flat like a piece of paper, and there are 3-dimensional shapes that have depth and are sometimes described as solid.\n* Faces. These are flat 2-dimensional shapes.\n* Edges / Sides. The edges or sides are the straight line segments at the edge of a face.\n* Corners / Points / Vertices. For shapes, the individual points of interest will be the ones where two (or more) edges meet. The technical word vertex (vertices) is a bit more advanced.\n* Angles. Two lines, or line segments, that meet in a point form an angle there.\n* Right Angles: Angles that look like the corner of a piece of paper are called right angles. They are also said to have 90 degrees, but that description should wait until they can count and understand the numbers up to 100 or 200.\n* Straight or Curved. Lines and faces can be straight or curved.\n* Same size. Describing edges as having the same size is important for differentiating different shapes within the same family.\n\n**Relative Positions:** Shapes may have positions relative to other shapes. Understanding those describing words is important for being able to describe scenes, and also describing how some shapes are made up of smaller shapes. These are words like: above, over, under, inside, beside, next to, behind, between, and near." + "block2_text": "* 2D or 3D. There are 2-dimensional shapes that are flat like a piece of paper, and there are 3-dimensional shapes that have depth and are sometimes described as solid.\n* Faces. These are flat, 2-dimensional shapes.\n* Edges / Sides. The edges or sides are the straight line segments at the edge of a face.\n* Corners / Points / Vertices. For shapes, the individual points of interest will be the ones where two (or more) edges meet. The technical word vertex (vertices) is a bit advanced for this age, but it can be used.\n* Angles. Two lines, or line segments, that meet in a point form an angle there.\n* Right Angles: Angles that look like the corner of a piece of paper are called right angles. They are also said to have 90 degrees, but that description should wait until they can count and understand the numbers up to 100 or 200.\n* Straight or Curved. Lines and faces can be straight or curved.\n* Same size. Describing two edges as having the same size is important for differentiating different shapes within the same family.\n\n**Relative Positions:** Shapes may have positions relative to other shapes. Understanding those describing words is important for being able to describe scenes, and also describing how some shapes are made up of smaller shapes. These are words like: above, over, under, inside, beside, next to, behind, between, and near." }, { "id": "Geom_Shape_SN2D3D", + "searching_for_this": false, "theme_id": "Geom_Shape_", "strand_id": "Geom", "prev_topic_1": "Geom_Shape_DS", @@ -518,7 +532,7 @@ "eng": "Shape Names – 2D & 3D" }, "block1_text": { - "eng": "**Learn shape names through exposure:** There are a lot of words to learn. However, if you make a habit of exposing children to these words, they will pick them up slowly but surely. Challenge your students to find examples of these shapes in the world around them. Make treasure hunt challenges of finding particularly hard to find shapes.\n\n**Important differentiators:** There are some important properties that children need to understand to be able to classify and name shapes.\n\n* Counting edges\n* Counting angles\n* Edges with same length.\n* Identifying right angles.\n\n< Graphic of 2D shapes >" + "eng": "**Learn shape names through exposure:** There are a lot of words to learn. However, if you make a habit of exposing children to these words, they will pick them up slowly but surely. Challenge your students to find examples of these shapes in the world around them. Make treasure hunt challenges of finding particularly hard to find shapes.\n\n**Important differentiators:** There are properties that children need to understand to be able to classify and name shapes.\n\n* Counting edges\n* Counting angles\n* Edges with same length.\n* Identifying right angles.\n\n< Graphic of 2D shapes >" }, "block2_text": { "eng": "**Names of 2D Shapes**\n\n* Circle\n* Triangle – 3 sides and 3 angles\n* Rectangle – 4 sides and 4 right angles (all equal of course)\n* Rhombus – 4 equal sides and 4 angles\n* Square – 4 equal sides and 4 right angles – it is both a rectangle and a rhombus.\n* Pentagon – 5 sides and 5 angles\n* Hexagon – 6 sides and 6 angles\n* Octagon – 8 sides and 8 angles\n\n**Polygons:** Except for the circle, these shapes are all examples of polygons. A polygon with equal sides and equal angles is called a **regular polygon.**\n\nIt is important to vary the size and orientation of these shapes when you draw them. If a child always sees a square with its sides going horizontally and vertically, they won't recognize squares when they are rotated and look like diamonds. The same is true for triangles.\n\n< Graphic of 3D shapes >" @@ -533,7 +547,7 @@ "eng": "Use straws or sticks and stick them together with clay, gum, or some other sticky substance." } }, - "block1_text": "**Learn shape names through exposure:** There are a lot of words to learn. However, if you make a habit of exposing children to these words, they will pick them up slowly but surely. Challenge your students to find examples of these shapes in the world around them. Make treasure hunt challenges of finding particularly hard to find shapes.\n\n**Important differentiators:** There are some important properties that children need to understand to be able to classify and name shapes.\n\n* Counting edges\n* Counting angles\n* Edges with same length.\n* Identifying right angles.\n\n< Graphic of 2D shapes >", + "block1_text": "**Learn shape names through exposure:** There are a lot of words to learn. However, if you make a habit of exposing children to these words, they will pick them up slowly but surely. Challenge your students to find examples of these shapes in the world around them. Make treasure hunt challenges of finding particularly hard to find shapes.\n\n**Important differentiators:** There are properties that children need to understand to be able to classify and name shapes.\n\n* Counting edges\n* Counting angles\n* Edges with same length.\n* Identifying right angles.\n\n< Graphic of 2D shapes >", "block2_text": "**Names of 2D Shapes**\n\n* Circle\n* Triangle – 3 sides and 3 angles\n* Rectangle – 4 sides and 4 right angles (all equal of course)\n* Rhombus – 4 equal sides and 4 angles\n* Square – 4 equal sides and 4 right angles – it is both a rectangle and a rhombus.\n* Pentagon – 5 sides and 5 angles\n* Hexagon – 6 sides and 6 angles\n* Octagon – 8 sides and 8 angles\n\n**Polygons:** Except for the circle, these shapes are all examples of polygons. A polygon with equal sides and equal angles is called a **regular polygon.**\n\nIt is important to vary the size and orientation of these shapes when you draw them. If a child always sees a square with its sides going horizontally and vertically, they won't recognize squares when they are rotated and look like diamonds. The same is true for triangles.\n\n< Graphic of 3D shapes >", "block3_text": "**Names of 3D Shapes**\n\n* Ball (Sphere)\n* Cylinder (round tube with end caps)\n* Box (Cube)\n* Pyramid – triangle or square base\n* Cone\n\nIn addition to basic questions about these shapes, a good way to practice them is to compare and contrast them – this will be covered in the next topic.", "block4_accord": "Make 3D models", @@ -541,6 +555,7 @@ }, { "id": "Geom_Shape_CompSort", + "searching_for_this": false, "theme_id": "Geom_Shape_", "strand_id": "Geom", "prev_topic_1": "Geom_Shape_SN2D3D", @@ -555,13 +570,14 @@ "eng": "Compare & Sort Shapes" }, "block1_text": { - "eng": "**Deeper Understanding:** Although mastery of the basic definitions of shapes is an essential starting point, one of the best ways to understand shapes more deeply is to compare, contrast, and sort them.\n\n**Same and Different:** Have a collection of objects, cut out shapes, or shapes on cards, and randomly select two of them – how are they different and how are they the same? For example, a rectangle and a square have four sides and all right angles, but the sides of a rectangle are not all the same size (though opposite sides are).\n\nFor four-sided shapes, which ones are also another kind of shape, and which are not? For example, are all rectangles squares, or are all squares rectangles? Are all squares rhombuses or are all rhombuses squares? Are all rectangles rhombuses or are all rhombuses rectangles?\n\nAsk for all sorts of comparisons. For example, what is similar and different when comparing a circle and a ball?\n\n**Sorting:** Give your students a collection shapes or objects and ask them to sort them into things that share at least one property. Let them decide which property to sort on, and then discuss their decision. Have one group do the sorting and then another group discover what property they used to sort on.\n\nEncourage non-obvious sorting categories. For example, shapes that have right angles or shapes that have no two sides the same length." + "eng": "**Deeper Shape Understanding:** Although mastery of the basic definitions of shapes is an essential starting point, one of the best ways to understand shapes more deeply is to compare, contrast, and sort them.\n\n**Same and Different:** Have a collection of objects, cut out shapes, or shapes on cards, and randomly select two of them – how are they different and how are they the same? For example, a rectangle and a square have four sides and all right angles, but the sides of a rectangle are not all the same size (though opposite sides are).\n\nFor four-sided shapes, which ones are also another kind of shape, and which are not? For example, are all rectangles squares, or are all squares rectangles? Are all squares rhombuses or are all rhombuses squares? Are all rectangles rhombuses or are all rhombuses rectangles?\n\nAsk for all sorts of comparisons. For example, what is similar and different when comparing a circle and a ball?\n\n**Sorting:** Give your students a collection of shapes or objects and ask them to sort them into things that share at least one property. Let them decide which property to sort on, and then discuss their decision. Have one group do the sorting and another group discover what property they used to sort on.\n\nEncourage non-obvious sorting categories. For example, shapes that have right angles or shapes that have no two sides the same length." } }, - "block1_text": "**Deeper Understanding:** Although mastery of the basic definitions of shapes is an essential starting point, one of the best ways to understand shapes more deeply is to compare, contrast, and sort them.\n\n**Same and Different:** Have a collection of objects, cut out shapes, or shapes on cards, and randomly select two of them – how are they different and how are they the same? For example, a rectangle and a square have four sides and all right angles, but the sides of a rectangle are not all the same size (though opposite sides are).\n\nFor four-sided shapes, which ones are also another kind of shape, and which are not? For example, are all rectangles squares, or are all squares rectangles? Are all squares rhombuses or are all rhombuses squares? Are all rectangles rhombuses or are all rhombuses rectangles?\n\nAsk for all sorts of comparisons. For example, what is similar and different when comparing a circle and a ball?\n\n**Sorting:** Give your students a collection shapes or objects and ask them to sort them into things that share at least one property. Let them decide which property to sort on, and then discuss their decision. Have one group do the sorting and then another group discover what property they used to sort on.\n\nEncourage non-obvious sorting categories. For example, shapes that have right angles or shapes that have no two sides the same length." + "block1_text": "**Deeper Shape Understanding:** Although mastery of the basic definitions of shapes is an essential starting point, one of the best ways to understand shapes more deeply is to compare, contrast, and sort them.\n\n**Same and Different:** Have a collection of objects, cut out shapes, or shapes on cards, and randomly select two of them – how are they different and how are they the same? For example, a rectangle and a square have four sides and all right angles, but the sides of a rectangle are not all the same size (though opposite sides are).\n\nFor four-sided shapes, which ones are also another kind of shape, and which are not? For example, are all rectangles squares, or are all squares rectangles? Are all squares rhombuses or are all rhombuses squares? Are all rectangles rhombuses or are all rhombuses rectangles?\n\nAsk for all sorts of comparisons. For example, what is similar and different when comparing a circle and a ball?\n\n**Sorting:** Give your students a collection of shapes or objects and ask them to sort them into things that share at least one property. Let them decide which property to sort on, and then discuss their decision. Have one group do the sorting and another group discover what property they used to sort on.\n\nEncourage non-obvious sorting categories. For example, shapes that have right angles or shapes that have no two sides the same length." }, { "id": "Geom_Shape_2Dof3DS", + "searching_for_this": false, "theme_id": "Geom_Shape_", "strand_id": "Geom", "prev_topic_1": "Geom_Shape_SN2D3D", @@ -583,6 +599,7 @@ }, { "id": "Geom_Shape_CompDecomp", + "searching_for_this": false, "theme_id": "Geom_Shape_", "strand_id": "Geom", "block1_type": "all_text", @@ -620,6 +637,7 @@ }, { "id": "NPV_QC10_QC", + "searching_for_this": false, "theme_id": "NPV_QC10_", "strand_id": "NPV", "prev_topic_1": "MT_EAA_MTC", @@ -643,15 +661,16 @@ "eng": "Mistakes" }, "block2_text": { - "eng": "Some standard mistakes are:\n\n* Leaving out or repeating a number during the sequence\n* Counting an object twice or missing an object\n* Not realizing to stop counting when all objects have been counted\n* Thinking there are more objects when the objects are larger.\n\nWhen a mistake occurs, demonstrate the right way to do the counting and move on. Don’t treat the errors as remarkable." + "eng": "Some standard mistakes children make are:\n\n* Leaving out or repeating a number during the sequence\n* Counting an object twice or missing an object\n* Not realizing to stop counting when all objects have been counted\n* Thinking there are more objects when the objects are larger.\n\nWhen a mistake occurs, demonstrate the right way to do the counting and move on. Don’t treat the errors as remarkable." } }, "block1_text": "**Surprisingly complicated:** Learning how to count and relating counting to quantities has many parts to it. Each part may take a while to be learned and there will be minor missteps along the way. Much of this is developmental and cannot be explicitly taught – instead, there needs to be exposure and practice until it clicks.\n\n* Unchanging order – The counting sequence is always the same.\n* One-to-one correspondence – Count a collection of objects by putting them in one-to-one correspondence with the numbers being said. The child can touch the objects as they count.\n* The last number is the quantity – When counting a group of objects, the last spoken number is the quantity of objects.\n* Order and rearrangement doesn’t change the count – The child can count the objects in any order, and the objects can be rearranged, and the count will always be the same.\n* Subgroups of bigger groups have smaller counts\n\n**Number Lines:** Use number lines to solidify number order and give a useful visual reference. Number lines should start from 0 and increase from left to right. Place these on walls, on paper, or on floors. On the ground, you can make a **number path,** which is a sequence of numbers big enough for a child to walk along. Use the number path for counting and for practicing addition and subtraction.", "block2_accord": "Mistakes", - "block2_text": "Some standard mistakes are:\n\n* Leaving out or repeating a number during the sequence\n* Counting an object twice or missing an object\n* Not realizing to stop counting when all objects have been counted\n* Thinking there are more objects when the objects are larger.\n\nWhen a mistake occurs, demonstrate the right way to do the counting and move on. Don’t treat the errors as remarkable." + "block2_text": "Some standard mistakes children make are:\n\n* Leaving out or repeating a number during the sequence\n* Counting an object twice or missing an object\n* Not realizing to stop counting when all objects have been counted\n* Thinking there are more objects when the objects are larger.\n\nWhen a mistake occurs, demonstrate the right way to do the counting and move on. Don’t treat the errors as remarkable." }, { "id": "NPV_QC10_CMQ10", + "searching_for_this": false, "theme_id": "NPV_QC10_", "strand_id": "NPV", "block1_type": "all_text", @@ -672,52 +691,72 @@ }, { "id": "NPV_QC10_Sub10", + "searching_for_this": false, "theme_id": "NPV_QC10_", "strand_id": "NPV", "block1_type": "all_text", "block2_type": "all_text", - "block3_type": "accord_all_text", + "block3_type": "all_text", + "block4_type": "all_text", + "block5_type": "accord_all_text", "name": "Subitizing to 10", "_translations": { "name": {}, "block1_text": {}, "block2_text": {}, - "block3_accord": {}, - "block3_text": {} + "block3_text": {}, + "block4_text": {}, + "block5_accord": {}, + "block5_text": {} }, "_translatedFields": { "name": { "eng": "Subitizing to 10" }, "block1_text": { - "eng": "**Subitizing is surprisingly important:** The word **subitizing** refers to recognizing a quantity at a glance. This skill is foundational for counting, particularly Counting On, understanding parts and wholes, adding, and subtracting.\n\nIt is an important conceptual step for a child in that they are learning to treat a group of individual things as a single new thing. This is a developmental step that may take a while and cannot be hurried. Practice will of course help develop a sense of how this works.\n\n**Small numbers to 4 or 5.** People are born with the ability to instantly recognize quantities of size 1, 2, and 3. With a bit of practice quantities of size 4 or 5 can be added to this list as a child develops a sense for quantities and numbers.\n\n< graphic showing some standard patterns for 3, 4, 5, 6, and 8. >" + "eng": "**Subitizing is surprisingly important:** The word **subitizing** refers to recognizing a quantity at a glance. This skill is foundational for counting, particularly Counting On, understanding parts and wholes, adding, and subtracting.\n\nIt is an important conceptual step for a child. They are learning to treat a group of individual things as a single new thing. This is a developmental step that may take a while and cannot be hurried. Practice will of course help develop a sense of how this works.\n\n**Small numbers to 4 or 5.** People are born with the ability to instantly recognize quantities of size 1, 2, and 3. With a bit of practice quantities of size 4 or 5 can be added to this list as a child develops a sense for quantities and numbers.\n\n< graphic showing some standard patterns for 3, 4, 5, 6, and 8. >" }, "block2_text": { - "eng": "**Use familiar arrangments:** As a child becomes familiar with certain patterns of dots, particularly the patterns on dice, those will begin to be instantly recognizable to them.\n\n< graphic of a ten frame with 7 dots - 5 in top row and 2 to the left on the second row >\n\n**Ten Frames:** Ten frames have many educational uses. One is to make it easier to learn how to subitize the quantities up to 10 when presented in a standard way in a ten frame.\n\n< graphic showing 5 dots in X pattern with 2 more dots scattered to the right >\n\n**Supports Counting On.** Once certain configurations become familiar, they can be built upon to make it easier to count larger quantities as well as gain confidence with Counting On. In the example above, instead of counting all 7 dots individually, a child may see that there are 5 dots with 2 more, and be able to Count On with \"5, 6, 7.\"" - }, - "block3_accord": { - "eng": "Tip: Five frames are not so useful" + "eng": "**Use familiar arrangments:** As a child becomes familiar with certain patterns of dots, particularly the patterns on dice, those will begin to be instantly recognizable to them.\n\n< graphic of a ten frame with 7 dots - 5 in top row and 2 to the left on the second row >" }, "block3_text": { + "eng": "**Ten Frames:** Ten frames have many educational uses. One is to make it easier to learn how to subitize the quantities up to 10 when presented in a standard way in a ten frame.\n\n< graphic showing 5 dots in X pattern with 2 more dots scattered to the right >" + }, + "block4_text": { + "eng": "**Supports Counting On.** Once certain configurations become familiar, they can be built upon to make it easier to count larger quantities as well as gain confidence with Counting On. In the example above, instead of counting all 7 dots individually, a child may see that there are 5 dots with 2 more, and be able to Count On with \"5, 6, 7.\"" + }, + "block5_accord": { + "eng": "Tip: Five frames are not as useful" + }, + "block5_text": { "eng": "Surprisingly, despite being like the fingers on one hand and being the upper half of a ten frame, five frames are not as effective at helping children learn to subitize and recognize quantities. Children have a much harder time making the leap to subitizing when given dots in a five frame rather than a ten frame." } }, - "block1_text": "**Subitizing is surprisingly important:** The word **subitizing** refers to recognizing a quantity at a glance. This skill is foundational for counting, particularly Counting On, understanding parts and wholes, adding, and subtracting.\n\nIt is an important conceptual step for a child in that they are learning to treat a group of individual things as a single new thing. This is a developmental step that may take a while and cannot be hurried. Practice will of course help develop a sense of how this works.\n\n**Small numbers to 4 or 5.** People are born with the ability to instantly recognize quantities of size 1, 2, and 3. With a bit of practice quantities of size 4 or 5 can be added to this list as a child develops a sense for quantities and numbers.\n\n< graphic showing some standard patterns for 3, 4, 5, 6, and 8. >", - "block2_text": "**Use familiar arrangments:** As a child becomes familiar with certain patterns of dots, particularly the patterns on dice, those will begin to be instantly recognizable to them.\n\n< graphic of a ten frame with 7 dots - 5 in top row and 2 to the left on the second row >\n\n**Ten Frames:** Ten frames have many educational uses. One is to make it easier to learn how to subitize the quantities up to 10 when presented in a standard way in a ten frame.\n\n< graphic showing 5 dots in X pattern with 2 more dots scattered to the right >\n\n**Supports Counting On.** Once certain configurations become familiar, they can be built upon to make it easier to count larger quantities as well as gain confidence with Counting On. In the example above, instead of counting all 7 dots individually, a child may see that there are 5 dots with 2 more, and be able to Count On with \"5, 6, 7.\"", - "block3_accord": "Tip: Five frames are not so useful", - "block3_text": "Surprisingly, despite being like the fingers on one hand and being the upper half of a ten frame, five frames are not as effective at helping children learn to subitize and recognize quantities. Children have a much harder time making the leap to subitizing when given dots in a five frame rather than a ten frame." + "block1_text": "**Subitizing is surprisingly important:** The word **subitizing** refers to recognizing a quantity at a glance. This skill is foundational for counting, particularly Counting On, understanding parts and wholes, adding, and subtracting.\n\nIt is an important conceptual step for a child. They are learning to treat a group of individual things as a single new thing. This is a developmental step that may take a while and cannot be hurried. Practice will of course help develop a sense of how this works.\n\n**Small numbers to 4 or 5.** People are born with the ability to instantly recognize quantities of size 1, 2, and 3. With a bit of practice quantities of size 4 or 5 can be added to this list as a child develops a sense for quantities and numbers.\n\n< graphic showing some standard patterns for 3, 4, 5, 6, and 8. >", + "block2_text": "**Use familiar arrangments:** As a child becomes familiar with certain patterns of dots, particularly the patterns on dice, those will begin to be instantly recognizable to them.\n\n< graphic of a ten frame with 7 dots - 5 in top row and 2 to the left on the second row >", + "block3_text": "**Ten Frames:** Ten frames have many educational uses. One is to make it easier to learn how to subitize the quantities up to 10 when presented in a standard way in a ten frame.\n\n< graphic showing 5 dots in X pattern with 2 more dots scattered to the right >", + "block4_text": "**Supports Counting On.** Once certain configurations become familiar, they can be built upon to make it easier to count larger quantities as well as gain confidence with Counting On. In the example above, instead of counting all 7 dots individually, a child may see that there are 5 dots with 2 more, and be able to Count On with \"5, 6, 7.\"", + "block5_accord": "Tip: Five frames are not as useful", + "block5_text": "Surprisingly, despite being like the fingers on one hand and being the upper half of a ten frame, five frames are not as effective at helping children learn to subitize and recognize quantities. Children have a much harder time making the leap to subitizing when given dots in a five frame rather than a ten frame." }, { "id": "NPV_QC10_Comp10", + "searching_for_this": false, "theme_id": "NPV_QC10_", "strand_id": "NPV", "block1_type": "all_text", "block2_type": "all_text", + "block3_type": "accord_all_text", + "block4_type": "accord_all_text", "name": "Comparing up to 10", "_translations": { "name": {}, "block1_text": {}, - "block2_text": {} + "block2_text": {}, + "block3_accord": {}, + "block3_text": {}, + "block4_accord": {}, + "block4_text": {} }, "_translatedFields": { "name": { @@ -727,14 +766,31 @@ "eng": "**Compare quantities in lines next to each other:** An easy and compelling way to compare quantities is to put them in two lines, one directly below the other. The shorter line is the smaller quantity and the longer line the larger quantity. As noted below, this works best if the items all have the same size and shape.\n\n< graphic showing 3 dots on one line above 5 dots on the next; perhaps with a \"3 < 5\" to the left or above it >" }, "block2_text": { - "eng": "**Using the sequence of numbers:** A more abstract way to compare two numbers is to see which one comes before the other in the counting sequence. This is too abstract as an initial way to teach comparison, but if it is frequently associated with the line-em-up method, it will become familiar and understood.\n\n**Use equal quantities sometimes:** Give appropriate amount of time to quantities that are the same so that children do not lose sight of this possibility.\n\n**Size may confuse quantity:** A child can quite reasonably see one large stick as being \"more sticks\" than two small sticks. Avoid this problem by using objects that are all the same size and shape until the concept of quantity is thoroughly understood.\n\n< graphic showing problems with size >\n\n**Start using symbols:** Teach the three symbols \"<\" \"=\" \">\" along with the numerals when doing comparing. Tell the child that the larger quantity goes on the wider side. Some people like to say that the inequality symbol is a hungry alligator, and the open mouth is open towards the larger quantity." + "eng": "**Using the sequence of numbers:** A more abstract way to compare two numbers is to see which one comes before the other in the counting sequence. This is too abstract as an initial way to teach comparison, but if it is frequently associated with the line-em-up method, it will become familiar and understood.\n\n**Use equal quantities sometimes:** Give appropriate amount of time to quantities that are the same so that children do not lose sight of this possibility." + }, + "block3_accord": { + "eng": "Mistake: Object Size versus Quantity" + }, + "block3_text": { + "eng": "**Size may confuse quantity:** A child can quite reasonably see one large stick as being \"more sticks\" than two small sticks. Avoid this problem by using objects that are all the same size and shape until the concept of quantity is thoroughly understood.\n\n< graphic showing problems with size >" + }, + "block4_accord": { + "eng": "Tip: Start Using Symbols" + }, + "block4_text": { + "eng": "Teach the three symbols \"<\" \"=\" \">\" along with the numerals when doing comparing. Tell the child that the larger quantity goes on the wider side. Some people like to say that the inequality symbol is a hungry alligator, and the open mouth is open towards the larger quantity." } }, "block1_text": "**Compare quantities in lines next to each other:** An easy and compelling way to compare quantities is to put them in two lines, one directly below the other. The shorter line is the smaller quantity and the longer line the larger quantity. As noted below, this works best if the items all have the same size and shape.\n\n< graphic showing 3 dots on one line above 5 dots on the next; perhaps with a \"3 < 5\" to the left or above it >", - "block2_text": "**Using the sequence of numbers:** A more abstract way to compare two numbers is to see which one comes before the other in the counting sequence. This is too abstract as an initial way to teach comparison, but if it is frequently associated with the line-em-up method, it will become familiar and understood.\n\n**Use equal quantities sometimes:** Give appropriate amount of time to quantities that are the same so that children do not lose sight of this possibility.\n\n**Size may confuse quantity:** A child can quite reasonably see one large stick as being \"more sticks\" than two small sticks. Avoid this problem by using objects that are all the same size and shape until the concept of quantity is thoroughly understood.\n\n< graphic showing problems with size >\n\n**Start using symbols:** Teach the three symbols \"<\" \"=\" \">\" along with the numerals when doing comparing. Tell the child that the larger quantity goes on the wider side. Some people like to say that the inequality symbol is a hungry alligator, and the open mouth is open towards the larger quantity." + "block2_text": "**Using the sequence of numbers:** A more abstract way to compare two numbers is to see which one comes before the other in the counting sequence. This is too abstract as an initial way to teach comparison, but if it is frequently associated with the line-em-up method, it will become familiar and understood.\n\n**Use equal quantities sometimes:** Give appropriate amount of time to quantities that are the same so that children do not lose sight of this possibility.", + "block3_accord": "Mistake: Object Size versus Quantity", + "block3_text": "**Size may confuse quantity:** A child can quite reasonably see one large stick as being \"more sticks\" than two small sticks. Avoid this problem by using objects that are all the same size and shape until the concept of quantity is thoroughly understood.\n\n< graphic showing problems with size >", + "block4_accord": "Tip: Start Using Symbols", + "block4_text": "Teach the three symbols \"<\" \"=\" \">\" along with the numerals when doing comparing. Tell the child that the larger quantity goes on the wider side. Some people like to say that the inequality symbol is a hungry alligator, and the open mouth is open towards the larger quantity." }, { "id": "NPV_QC10_Ordinals", + "searching_for_this": false, "theme_id": "NPV_QC10_", "strand_id": "NPV", "block1_type": "all_text", @@ -755,6 +811,7 @@ }, { "id": "NPV_QC10_WN10", + "searching_for_this": false, "theme_id": "NPV_QC10_", "strand_id": "NPV", "block1_type": "all_text", @@ -771,21 +828,22 @@ "eng": "Writing Numbers 0 to 10" }, "block1_text": { - "eng": "**Ways to Practice:** Just as with writing the alphabet letters, it will take lots of practice to make reasonably good numerals. It will take time and there is no hurry.\n\nHere are some ideas for ways to practice writing the numerals from 0 to 9: \n\n* If you cut out numerals made of sandpaper or some other tactile surface, those are excellent for having the child trace with a fingertip to get the flow of each numeral.\n* Choose initial ways to practice that make it easy to experiment and practice, and don't make it unpleasant to make mistakes. For example, have the child practice writing in dirt or sand, where a mistake is easily erased. \n* When the child starts writing on a white board or paper, make dashed or dotted versions of the numerals that they can practice with when writing their first numerals." + "eng": "**Ways to Practice:** Just as with writing the alphabet letters, it will take lots of practice to make reasonably good numerals. It will take time and there is no hurry.\n\nHere are some ideas for ways for practicing writing the numerals from 0 to 9: \n\n* Cut out numerals made of sandpaper or some other tactile surface. These are excellent for having a child trace with a fingertip to get the flow of each numeral.\n* Choose initial ways to practice that make it easy to experiment and practice, and don't make it forgiving to make mistakes. For example, have the child practice writing in dirt or sand, where a mistake is easily erased. \n* When the child starts writing on a white board or paper, make dashed or dotted versions of the numerals that they can practice with when writing their first numerals." }, "block2_accord": { "eng": "Mistakes" }, "block2_text": { - "eng": "Mistakes will be common and frequent at this early age. Even after initial mastery, numerals will sometimes be written reversed or upside down. Handle this calmly by simply writing the numeral correctly nearby and pointing out the difference to the child. These mistakes may persist for quite a while, and it is generally just a sign that the child is waiting to make a developmental step." + "eng": "Mistakes will be frequent at this early age. Even after initial mastery, numerals will sometimes be written reversed or upside down. Handle this calmly by simply writing the numeral correctly nearby and pointing out the difference to the child. These mistakes may persist for quite a while, and it is generally just a sign that the child is waiting to make a developmental step. \n\n< graphic of reversed and upside down numerals >" } }, - "block1_text": "**Ways to Practice:** Just as with writing the alphabet letters, it will take lots of practice to make reasonably good numerals. It will take time and there is no hurry.\n\nHere are some ideas for ways to practice writing the numerals from 0 to 9: \n\n* If you cut out numerals made of sandpaper or some other tactile surface, those are excellent for having the child trace with a fingertip to get the flow of each numeral.\n* Choose initial ways to practice that make it easy to experiment and practice, and don't make it unpleasant to make mistakes. For example, have the child practice writing in dirt or sand, where a mistake is easily erased. \n* When the child starts writing on a white board or paper, make dashed or dotted versions of the numerals that they can practice with when writing their first numerals.", + "block1_text": "**Ways to Practice:** Just as with writing the alphabet letters, it will take lots of practice to make reasonably good numerals. It will take time and there is no hurry.\n\nHere are some ideas for ways for practicing writing the numerals from 0 to 9: \n\n* Cut out numerals made of sandpaper or some other tactile surface. These are excellent for having a child trace with a fingertip to get the flow of each numeral.\n* Choose initial ways to practice that make it easy to experiment and practice, and don't make it forgiving to make mistakes. For example, have the child practice writing in dirt or sand, where a mistake is easily erased. \n* When the child starts writing on a white board or paper, make dashed or dotted versions of the numerals that they can practice with when writing their first numerals.", "block2_accord": "Mistakes", - "block2_text": "Mistakes will be common and frequent at this early age. Even after initial mastery, numerals will sometimes be written reversed or upside down. Handle this calmly by simply writing the numeral correctly nearby and pointing out the difference to the child. These mistakes may persist for quite a while, and it is generally just a sign that the child is waiting to make a developmental step." + "block2_text": "Mistakes will be frequent at this early age. Even after initial mastery, numerals will sometimes be written reversed or upside down. Handle this calmly by simply writing the numeral correctly nearby and pointing out the difference to the child. These mistakes may persist for quite a while, and it is generally just a sign that the child is waiting to make a developmental step. \n\n< graphic of reversed and upside down numerals >" }, { "id": "NPV_C20_Count20", + "searching_for_this": false, "theme_id": "NPV_C20_", "strand_id": "NPV", "next_topic_1": "NPV_C20_PV20", @@ -800,13 +858,14 @@ "eng": "Quantities and Counting to 20" }, "block1_text": { - "eng": "**Use two ten frames:** As the quantities become larger, it is essential to present them in organizaed forms. Using ten frames works well, and your children should be used to them by now. For numbers 11 to 20, use two ten frames with a completely filled ten frame to the left of the partially filled one.\n\n**Use bundles of ten:** Tie together bundles of ten objects that you want to work with. \n\n**Counting in English:** The numbers from 11 to 20 in English are not as easy as they should be. The two numbers 11 and 12 are particularly unusual. It would be so much easier if the numbers were named \"ten and one\" and \"ten and two,\" as they are in some languages. Similarly, 20 would be much easier as \"two tens.\" This lack of logical naming means that many of the numbers from 11 to 20 will need to be learned by exposure and practice, just as the numbers 0 to 10 were." + "eng": "**Use two ten frames:** As the quantities become larger, it is essential to present them in organizaed forms that makes them easier to understand. Using ten frames works well, and your children should be used to them by now. For numbers 11 to 20, use two ten frames with a completely filled ten frame to the left of the partially filled one.\n\n**Use bundles of ten:** An alternative to ten frames is to tie together bundles of ten objects that you want to work with. \n\n**Counting in English:** The numbers from 11 to 20 in English are not as easy to learn as they should be. The two numbers 11 and 12 are particularly unusual. It would be so much easier if the numbers were named \"ten and one\" and \"ten and two,\" as they are in some languages. Similarly, 20 would be much easier as \"two tens.\" This lack of logical naming means that many of the numbers from 11 to 20 will need to be learned by exposure and practice, just as the numbers 0 to 10 were." } }, - "block1_text": "**Use two ten frames:** As the quantities become larger, it is essential to present them in organizaed forms. Using ten frames works well, and your children should be used to them by now. For numbers 11 to 20, use two ten frames with a completely filled ten frame to the left of the partially filled one.\n\n**Use bundles of ten:** Tie together bundles of ten objects that you want to work with. \n\n**Counting in English:** The numbers from 11 to 20 in English are not as easy as they should be. The two numbers 11 and 12 are particularly unusual. It would be so much easier if the numbers were named \"ten and one\" and \"ten and two,\" as they are in some languages. Similarly, 20 would be much easier as \"two tens.\" This lack of logical naming means that many of the numbers from 11 to 20 will need to be learned by exposure and practice, just as the numbers 0 to 10 were." + "block1_text": "**Use two ten frames:** As the quantities become larger, it is essential to present them in organizaed forms that makes them easier to understand. Using ten frames works well, and your children should be used to them by now. For numbers 11 to 20, use two ten frames with a completely filled ten frame to the left of the partially filled one.\n\n**Use bundles of ten:** An alternative to ten frames is to tie together bundles of ten objects that you want to work with. \n\n**Counting in English:** The numbers from 11 to 20 in English are not as easy to learn as they should be. The two numbers 11 and 12 are particularly unusual. It would be so much easier if the numbers were named \"ten and one\" and \"ten and two,\" as they are in some languages. Similarly, 20 would be much easier as \"two tens.\" This lack of logical naming means that many of the numbers from 11 to 20 will need to be learned by exposure and practice, just as the numbers 0 to 10 were." }, { "id": "NPV_C20_PV20", + "searching_for_this": false, "theme_id": "NPV_C20_", "strand_id": "NPV", "prev_topic_1": "NPV_C20_Count20", @@ -821,33 +880,49 @@ "eng": "Place Value to 20" }, "block1_text": { - "eng": "**Expanded notation:** In the topic \"Quantities and Counting to 20,\" we used two ten frames, or making use of bundles of ten, to organize the counting and to make the quantities easier to understand. **Expanded Notation** does the same thing for written numbers. It is handy to introduce it now for understanding numbers between 10 and 20, and it will become an essential tool for breaking apart and understanding numbers above 100.\n\n**Example:** Expanded notation takes the contribution of each digit of a number and isolates it. In the number 17, the one represents 10, so 17 can be expanded to 10 + 7. Similarly, the expanded form of 276 is 200 + 70 + 6." + "eng": "**Expanded notation:** In the topic \"Quantities and Counting to 20,\" we used two ten frames, or made use of bundles of ten, to organize the counting and to make the quantities easier to understand. **Expanded Notation** does the same thing for written numbers. It is handy to introduce it now for understanding numbers between 10 and 20, and it will become an essential tool for breaking apart and understanding numbers above 100.\n\nExpanded notation takes the contribution of each digit of a number and isolates it. In the number 17, the one represents 10, so expand 17 as 10 + 7. Similarly, the expanded form of 276 is 200 + 70 + 6.\n\nExpanded notation is extremely useful for learning arithmetic operations with multi-digit numbers. This will be an important tool and it should be developed fully and practiced thoroughly." } }, - "block1_text": "**Expanded notation:** In the topic \"Quantities and Counting to 20,\" we used two ten frames, or making use of bundles of ten, to organize the counting and to make the quantities easier to understand. **Expanded Notation** does the same thing for written numbers. It is handy to introduce it now for understanding numbers between 10 and 20, and it will become an essential tool for breaking apart and understanding numbers above 100.\n\n**Example:** Expanded notation takes the contribution of each digit of a number and isolates it. In the number 17, the one represents 10, so 17 can be expanded to 10 + 7. Similarly, the expanded form of 276 is 200 + 70 + 6." + "block1_text": "**Expanded notation:** In the topic \"Quantities and Counting to 20,\" we used two ten frames, or made use of bundles of ten, to organize the counting and to make the quantities easier to understand. **Expanded Notation** does the same thing for written numbers. It is handy to introduce it now for understanding numbers between 10 and 20, and it will become an essential tool for breaking apart and understanding numbers above 100.\n\nExpanded notation takes the contribution of each digit of a number and isolates it. In the number 17, the one represents 10, so expand 17 as 10 + 7. Similarly, the expanded form of 276 is 200 + 70 + 6.\n\nExpanded notation is extremely useful for learning arithmetic operations with multi-digit numbers. This will be an important tool and it should be developed fully and practiced thoroughly." }, { "id": "NPV_C20_Comp20", + "searching_for_this": false, "theme_id": "NPV_C20_", "strand_id": "NPV", + "prev_topic_1": "NPV_C20_PV20", + "prev_topic_2": "NPV_C20_Count20", + "prev_topic_3": "NPV_QC10_Comp10", "block1_type": "all_text", + "block2_type": "accord_all_text", "name": "Comparing to 20", "_translations": { "name": {}, - "block1_text": {} + "block1_text": {}, + "block2_accord": {}, + "block2_text": {} }, "_translatedFields": { "name": { "eng": "Comparing to 20" }, "block1_text": { - "eng": "**Bigger or Smaller than 10:** For numbers from 0 to 20, the first step is to compare the two numbers to 10. Use ten frames or bundles to show that any number from 0 to 9 will be less than any number from 10 to 20. If both numbers are between 10 and 20, show that the amount each number is greater than 10 will decide which number is larger.\n\n< graphic showing 12 < 17 next to two pairs of ten frames for the two numbers >\n\n**Compare two-digit numbers tens first:** Emphasize that comparing numbers from 0 to 20 is done by looking first at whether they are between 0 and 10 or between 10 and 20 – this mindset will serve them well when they start comparing all two-digit numbers. For comparing two-digit numbers in general, they should compare the tens digit first and then the ones digit. \n\nFor example, 35 < 42 because any number in the 30s will be less than any number in the 40s. Along those same lines, 35 < 37 because both numbers are in the 30s, so you only need to compare 5 and 7." + "eng": "**Bigger or Smaller than 10:** For numbers from 0 to 20, the first step is to compare the two numbers to 10. Use ten frames or bundles to show that any number from 0 to 9 will be less than any number from 10 to 20. If both numbers are between 10 and 20, show that the amount each number is greater than 10 will decide which number is larger.\n\n< graphic showing 12 < 17 next to two pairs of ten frames for the two numbers >\n\n**Compare tens first in two-digit numbers:** Emphasize that comparing numbers from 0 to 20 is done by looking first at whether they are between 0 and 10 or between 10 and 20 – this mindset will serve them well when they start comparing all two-digit numbers.\n\nFor comparing two-digit numbers in general, compare the tens digit first and then the ones digit." + }, + "block2_accord": { + "eng": "Examples" + }, + "block2_text": { + "eng": "**Different tens:** 35 < 62 because any number in the 30s will be less than any number in the 60s.\n\n**Same tens:** 35 < 37 because both numbers are in the 30s, so you only need to compare 5 and 7." } }, - "block1_text": "**Bigger or Smaller than 10:** For numbers from 0 to 20, the first step is to compare the two numbers to 10. Use ten frames or bundles to show that any number from 0 to 9 will be less than any number from 10 to 20. If both numbers are between 10 and 20, show that the amount each number is greater than 10 will decide which number is larger.\n\n< graphic showing 12 < 17 next to two pairs of ten frames for the two numbers >\n\n**Compare two-digit numbers tens first:** Emphasize that comparing numbers from 0 to 20 is done by looking first at whether they are between 0 and 10 or between 10 and 20 – this mindset will serve them well when they start comparing all two-digit numbers. For comparing two-digit numbers in general, they should compare the tens digit first and then the ones digit. \n\nFor example, 35 < 42 because any number in the 30s will be less than any number in the 40s. Along those same lines, 35 < 37 because both numbers are in the 30s, so you only need to compare 5 and 7." + "block1_text": "**Bigger or Smaller than 10:** For numbers from 0 to 20, the first step is to compare the two numbers to 10. Use ten frames or bundles to show that any number from 0 to 9 will be less than any number from 10 to 20. If both numbers are between 10 and 20, show that the amount each number is greater than 10 will decide which number is larger.\n\n< graphic showing 12 < 17 next to two pairs of ten frames for the two numbers >\n\n**Compare tens first in two-digit numbers:** Emphasize that comparing numbers from 0 to 20 is done by looking first at whether they are between 0 and 10 or between 10 and 20 – this mindset will serve them well when they start comparing all two-digit numbers.\n\nFor comparing two-digit numbers in general, compare the tens digit first and then the ones digit.", + "block2_accord": "Examples", + "block2_text": "**Different tens:** 35 < 62 because any number in the 30s will be less than any number in the 60s.\n\n**Same tens:** 35 < 37 because both numbers are in the 30s, so you only need to compare 5 and 7." }, { "id": "NPV_CPV100_P", + "searching_for_this": false, "theme_id": "NPV_CPV100_", "strand_id": "NPV", "block1_type": "all_text", @@ -868,6 +943,7 @@ }, { "id": "NPV_C100_P", + "searching_for_this": false, "theme_id": "NPV_C100_", "strand_id": "NPV", "block1_type": "all_text", @@ -888,23 +964,28 @@ }, { "id": "NO_AS10_QAS", + "searching_for_this": false, "theme_id": "NO_AS10_", "strand_id": "NO", + "prev_topic_1": "NPV_QC10_QC", + "prev_topic_2": "NPV_C20_Count20", "block1_type": "all_text", "block2_type": "all_text", "block3_type": "all_text", - "block4_type": "accord_all_text", + "block4_type": "all_text", "block5_type": "accord_all_text", + "block6_type": "accord_all_text", "name": "Quantities for Add & Subtract", "_translations": { "name": {}, "block1_text": {}, "block2_text": {}, "block3_text": {}, - "block4_accord": {}, "block4_text": {}, "block5_accord": {}, - "block5_text": {} + "block5_text": {}, + "block6_accord": {}, + "block6_text": {} }, "_translatedFields": { "name": { @@ -917,34 +998,40 @@ "eng": "**Transition to Counting On:** As a student gets comfortable with seeing a set number of objects, such as 2, 3, 4, or 5 of them, use that familiarity to start practicing adding with Counting On. When you have 3 objects and 2 objects, instead of counting “1, 2, 3, 4, 5” you can point at the 3 objects and say “3,” and then continue the counting to include the 2 objects with “4, 5.”\n\n< show 3 things, a space, then 2 things – speech bubbles – “3” for first group, and “4, 5” on second. >" }, "block3_text": { - "eng": "Subtraction should be modeled as both “take away” and as “difference.”.\n\n**Take away:** Start with 5 objects, count them, and then take 2 away as you count “1, 2.” Count that there are 3 objects remaining. You can do this by counting down from 5 and keeping track of how many have been removed on your fingers: “5” (no fingers), “4” (1 finger, “3” (2 fingers).\n\n< 5 objects with 2 covered over (greyed out?) or moved slightly to the side with number bubble 1, 2 >\n\n**Difference:** Put 2 objects above 5 objects and count how many more objects the group of 5 has. You are finding how far apart they are, which is their difference. You can do this by Counting On from 2 and keeping track of the difference on your fingers: “2” (no fingers), “3” (1 finger), … “5” (3 fingers).\n\n< show what is described – 2 objects above 5 objects >" + "eng": "Subtraction should be modeled as both “take away” and as “difference.”.\n\n**Take away:** Start with 5 objects, count them, and then take 2 away as you count “1, 2.” Count that there are 3 objects remaining. You can do this by counting down from 5 and keeping track of how many have been removed on your fingers: “5” (no fingers), “4” (1 finger, “3” (2 fingers).\n\n< 5 objects with 2 covered over (greyed out?) or moved slightly to the side with number bubble 1, 2 >" }, - "block4_accord": { + "block4_text": { + "eng": "**Difference:** Put 2 objects above 5 objects and count how many more objects the group of 5 has. You are finding how far apart they are, which is their difference. You can do this by Counting On from 2 and keeping track of the difference on your fingers: “2” (no fingers), “3” (1 finger), … “5” (3 fingers).\n\n< show what is described – 2 objects above 5 objects >" + }, + "block5_accord": { "eng": "Tip: Number lines and paths" }, - "block4_text": { + "block5_text": { "eng": "A number line on a wall, or a number path, are useful environments for practicing adding and subtracting.\n\n**Addition:** On a number path, have the student start at 0 and then walk forward for the count of the first number. After that, have them walk forward counting out the second number. They are standing on the sum of the two numbers.\n\nThere are two ways to do subtraction on a number path. Let's use 7 - 3 as an example.\n\n**Take away:** Have a student stand at 7 and then walk back three steps to end on the 4.\n\n**Difference:** Have one student stand on 7 and another on 3, and then ask how many steps are between them." }, - "block5_accord": { + "block6_accord": { "eng": "Tip: Fingers are a good manipulative" }, - "block5_text": { + "block6_text": { "eng": "Fingers are a convenient set of objects to count for these small problems. One lovely thing about fingers is they are always available.\n\n**Addition:** Take 3 fingers on one hand and 2 fingers on another, then move the two hands together and count the 5 fingers.\n\n**Take away:** For 7 - 3, first put up 7 fingers and then count to 3 as you lower one finger at a time.\n\n**Difference:** For 7 - 3, first put up 3 fingers and then count \"1, 2, 3, 4\" as you raise one finger at a time until 7 fingers are raised." } }, "block1_text": "Counting a group of objects develops a connection between counting and quantities. Similarly, use counting two groups of objects to make addition and subtraction tangible. \n\n**Example:** Have a group of 3 objects and nearby have a group of 2 objects. First, count the 3 objects and the 2 objects separately. Then talk about what happens when you put the two groups together, that 3 objects plus 2 objects is 5 objects altogether.\n\n< 2 illustrations (or combined somehow) of 3 objects, 2 objects with numbers in speech bubbles – first one counts them separately, second counts all of them from 1 to 5", "block2_text": "**Transition to Counting On:** As a student gets comfortable with seeing a set number of objects, such as 2, 3, 4, or 5 of them, use that familiarity to start practicing adding with Counting On. When you have 3 objects and 2 objects, instead of counting “1, 2, 3, 4, 5” you can point at the 3 objects and say “3,” and then continue the counting to include the 2 objects with “4, 5.”\n\n< show 3 things, a space, then 2 things – speech bubbles – “3” for first group, and “4, 5” on second. >", - "block3_text": "Subtraction should be modeled as both “take away” and as “difference.”.\n\n**Take away:** Start with 5 objects, count them, and then take 2 away as you count “1, 2.” Count that there are 3 objects remaining. You can do this by counting down from 5 and keeping track of how many have been removed on your fingers: “5” (no fingers), “4” (1 finger, “3” (2 fingers).\n\n< 5 objects with 2 covered over (greyed out?) or moved slightly to the side with number bubble 1, 2 >\n\n**Difference:** Put 2 objects above 5 objects and count how many more objects the group of 5 has. You are finding how far apart they are, which is their difference. You can do this by Counting On from 2 and keeping track of the difference on your fingers: “2” (no fingers), “3” (1 finger), … “5” (3 fingers).\n\n< show what is described – 2 objects above 5 objects >", - "block4_accord": "Tip: Number lines and paths", - "block4_text": "A number line on a wall, or a number path, are useful environments for practicing adding and subtracting.\n\n**Addition:** On a number path, have the student start at 0 and then walk forward for the count of the first number. After that, have them walk forward counting out the second number. They are standing on the sum of the two numbers.\n\nThere are two ways to do subtraction on a number path. Let's use 7 - 3 as an example.\n\n**Take away:** Have a student stand at 7 and then walk back three steps to end on the 4.\n\n**Difference:** Have one student stand on 7 and another on 3, and then ask how many steps are between them.", - "block5_accord": "Tip: Fingers are a good manipulative", - "block5_text": "Fingers are a convenient set of objects to count for these small problems. One lovely thing about fingers is they are always available.\n\n**Addition:** Take 3 fingers on one hand and 2 fingers on another, then move the two hands together and count the 5 fingers.\n\n**Take away:** For 7 - 3, first put up 7 fingers and then count to 3 as you lower one finger at a time.\n\n**Difference:** For 7 - 3, first put up 3 fingers and then count \"1, 2, 3, 4\" as you raise one finger at a time until 7 fingers are raised." + "block3_text": "Subtraction should be modeled as both “take away” and as “difference.”.\n\n**Take away:** Start with 5 objects, count them, and then take 2 away as you count “1, 2.” Count that there are 3 objects remaining. You can do this by counting down from 5 and keeping track of how many have been removed on your fingers: “5” (no fingers), “4” (1 finger, “3” (2 fingers).\n\n< 5 objects with 2 covered over (greyed out?) or moved slightly to the side with number bubble 1, 2 >", + "block4_text": "**Difference:** Put 2 objects above 5 objects and count how many more objects the group of 5 has. You are finding how far apart they are, which is their difference. You can do this by Counting On from 2 and keeping track of the difference on your fingers: “2” (no fingers), “3” (1 finger), … “5” (3 fingers).\n\n< show what is described – 2 objects above 5 objects >", + "block5_accord": "Tip: Number lines and paths", + "block5_text": "A number line on a wall, or a number path, are useful environments for practicing adding and subtracting.\n\n**Addition:** On a number path, have the student start at 0 and then walk forward for the count of the first number. After that, have them walk forward counting out the second number. They are standing on the sum of the two numbers.\n\nThere are two ways to do subtraction on a number path. Let's use 7 - 3 as an example.\n\n**Take away:** Have a student stand at 7 and then walk back three steps to end on the 4.\n\n**Difference:** Have one student stand on 7 and another on 3, and then ask how many steps are between them.", + "block6_accord": "Tip: Fingers are a good manipulative", + "block6_text": "Fingers are a convenient set of objects to count for these small problems. One lovely thing about fingers is they are always available.\n\n**Addition:** Take 3 fingers on one hand and 2 fingers on another, then move the two hands together and count the 5 fingers.\n\n**Take away:** For 7 - 3, first put up 7 fingers and then count to 3 as you lower one finger at a time.\n\n**Difference:** For 7 - 3, first put up 3 fingers and then count \"1, 2, 3, 4\" as you raise one finger at a time until 7 fingers are raised." }, { "id": "NO_AS10_AS1and2", + "searching_for_this": false, "theme_id": "NO_AS10_", "strand_id": "NO", "prev_topic_1": "NO_AS10_QAS", + "next_topic_1": "NO_AS10_ASto5", "block1_type": "all_text", "block2_type": "accord_all_text", "block3_type": "accord_all_text", @@ -968,7 +1055,7 @@ "eng": "Add & Subtract 1, 2" }, "block1_text": { - "eng": "The ideas of One More and One Less are foundational steps for adding and subtracting.\n\n**Next and Previous:** One more and One Less are strongly connected to the ideas of the “next number” and “previous number” when you are counting up and down. Counting practice in both directions will help your child recognize which number comes next and which number was the previous one.\n\n< illustration showing part of a number line, maybe 3 to 8, with 5 circled and arrows to 4 and 6 marked with “one less” and “one more” on one side and “previous number” and “next number” on the other. >" + "eng": "The ideas of One More and One Less are foundational steps for adding and subtracting.\n\n**Next and Previous:** One more and One Less are strongly connected to the ideas of the “next number” and “previous number” when you are counting up and down. Counting practice in both directions will help a child recognize which number comes next and which number was the previous one.\n\n< illustration showing part of a number line, maybe 3 to 8, with 5 circled and arrows to 4 and 6 marked with “one less” and “one more” on one side and “previous number” and “next number” on the other. >" }, "block2_accord": { "eng": "Practicing: What If" @@ -986,81 +1073,90 @@ "eng": "Extending: 2 more or less" }, "block4_text": { - "eng": "When your child is ready, extend your child's understanding to what happens when you have “two more” or “two less.” There is no hurry to get to this, so please make sure your child thoroughly understands one more and one less first. If using two is very easy for a child to visualize, you can of course extend this to three." + "eng": "When the children are ready, extend their understanding to what happens when you have “two more” or “two less.” There is no hurry to get to this, so please make sure they thoroughly understand one more and one less first. If using two is very easy for a child to visualize, you can of course extend this to three." }, "block5_accord": { "eng": "Resources - Games" }, "block5_text": { - "eng": "With this simple bit of arithmetic, you can start playing some games with adding and subtracting. A very simple one is to play the game of Nim with 1 and 2 using either addition or subtraction. Other games are Get Out of My House and Within 1 or 2" + "eng": "With this simple bit of arithmetic, you can start playing some of the games with adding and subtracting. A very simple one is to play the game of Nim with 1 and 2 using either addition or subtraction. Other games are Get Out of My House and Within 1 or 2" } }, - "block1_text": "The ideas of One More and One Less are foundational steps for adding and subtracting.\n\n**Next and Previous:** One more and One Less are strongly connected to the ideas of the “next number” and “previous number” when you are counting up and down. Counting practice in both directions will help your child recognize which number comes next and which number was the previous one.\n\n< illustration showing part of a number line, maybe 3 to 8, with 5 circled and arrows to 4 and 6 marked with “one less” and “one more” on one side and “previous number” and “next number” on the other. >", + "block1_text": "The ideas of One More and One Less are foundational steps for adding and subtracting.\n\n**Next and Previous:** One more and One Less are strongly connected to the ideas of the “next number” and “previous number” when you are counting up and down. Counting practice in both directions will help a child recognize which number comes next and which number was the previous one.\n\n< illustration showing part of a number line, maybe 3 to 8, with 5 circled and arrows to 4 and 6 marked with “one less” and “one more” on one side and “previous number” and “next number” on the other. >", "block2_accord": "Practicing: What If", "block2_text": "Gradually combine these ideas with “adding” and “subtracting” by asking questions such as: \"How many pebbles do you have now? If I add 1 more, how many would you have? If I took 1 away so you had 1 less, how many would you have?\" These are very easy and natural questions to fit into everyday conversation, and your child can talk about them without noticing at first that they are doing addition and subtraction.", "block3_accord": "Practicing: Comparing Nearby Quantities", "block3_text": "If you have 3 of something and your child has four of that thing, you can discuss various possibilities. Would you have the same amount if you had one more? Would you have the same amount if your child has one less. Be playful with the idea. If your numbers are 3 and 5, you can talk about getting one more twice, or about one of you getting one more and the other getting one less.", "block4_accord": "Extending: 2 more or less", - "block4_text": "When your child is ready, extend your child's understanding to what happens when you have “two more” or “two less.” There is no hurry to get to this, so please make sure your child thoroughly understands one more and one less first. If using two is very easy for a child to visualize, you can of course extend this to three.", + "block4_text": "When the children are ready, extend their understanding to what happens when you have “two more” or “two less.” There is no hurry to get to this, so please make sure they thoroughly understand one more and one less first. If using two is very easy for a child to visualize, you can of course extend this to three.", "block5_accord": "Resources - Games", - "block5_text": "With this simple bit of arithmetic, you can start playing some games with adding and subtracting. A very simple one is to play the game of Nim with 1 and 2 using either addition or subtraction. Other games are Get Out of My House and Within 1 or 2" + "block5_text": "With this simple bit of arithmetic, you can start playing some of the games with adding and subtracting. A very simple one is to play the game of Nim with 1 and 2 using either addition or subtraction. Other games are Get Out of My House and Within 1 or 2" }, { "id": "NO_AS10_ASto5", + "searching_for_this": false, "theme_id": "NO_AS10_", "strand_id": "NO", "prev_topic_1": "NO_AS10_QAS", + "prev_topic_2": "NO_AS10_AS1and2", "block1_type": "all_text", - "block2_type": "accord_all_text", + "block2_type": "all_text", "block3_type": "accord_all_text", "block4_type": "accord_all_text", + "block5_type": "accord_all_text", "name": "Add & Subtract to 5", "_translations": { "name": {}, "block1_text": {}, - "block2_accord": {}, "block2_text": {}, "block3_accord": {}, "block3_text": {}, "block4_accord": {}, - "block4_text": {} + "block4_text": {}, + "block5_accord": {}, + "block5_text": {} }, "_translatedFields": { "name": { "eng": "Add & Subtract to 5" }, "block1_text": { - "eng": "Your child has been doing adding problems by counting everything. If asked to add two things to three things, that was done by counting all five things. As your child mastered Counting On, some of that counting was replaced by starting with one of the numbers, say 3 in this example, and then counting the two remaining things (“4, 5”). This experience with counting has also allowed your child to visualize and master the ideas of 1 more and 2 more, which has made adding 1 and 2 much easier.\n\n**Five Frames:** Start using five frames to provide a structured environment for learning these math facts, as well as to lead into learning number bonds and ten frames. Play up the connection of five frames with having five fingers on one hand.\n\n**Equation Symbols:** Start using “+” and “–” and “=” when you write down this material for your children. Also, don’t always write equalities with the “result” on the right. Writing “=” just means that the two sides are equal, not that the left side produces the right side. So, 5 – 1 = 4, 3 = 5 – 2, and 1 + 3 = 5 – 1 are all good things to write and should be intermixed.\n\n< illustration of a five frame with 3 dots in it >\n\n**Zero is Important:** Mix in adding 0 sometimes. It is easy to do, and it is important conceptually. Similarly, mix in questions where you subtract 0 and questions where you subtract everything. For example, if you have three bits of food and you eat all of them, how many do you have left?" - }, - "block2_accord": { - "eng": "Tip: Manipulatives and Fingers" + "eng": "Your children have been doing adding problems by counting each individual item. If asked to add two things to three things, that was done by counting all five things. As they master Counting On, some of that counting is replaced by starting with one of the numbers, say 3 in this example, and then counting the two remaining things (“4, 5”). This experience with counting also allows a child to visualize and master the ideas of 1 more and 2 more, which has made adding 1 and 2 much easier.\n\n**Five Frames and Ten Frames:** Start using five frames and ten frames to provide a structured environment for learning these math facts, as well as to lead into learning number bonds. Play up the connection of five frames with having five fingers on one hand.\n\n< illustration of a five frame with 3 dots in it >" }, "block2_text": { - "eng": "Children of this age benefit greatly from having manipulatives to use when doing addition and subtraction. It cements their understanding of the numbers in terms of quantities.\n\nThe manipulative that is always available is their fingers. When doing the example of adding two to three, they can put up two fingers on one hand, three fingers on the other hand, and bring the two hands together. Another way to do it is to raise two fingers on one hand, raise three more fingers on that same hand, and then see a total of five fingers raised.\n\nThe ideas behind practicing subtraction are similar to those for addition. If your child is going to subtract three from five, have your chid raise five fingers and then lower three of them. Their familiarity with one less and two less will probably make subtracting one and two very easy." + "eng": "**Equation Symbols:** Start using “+” and “–” and “=” when you write down this material for your children. Also, don’t always write equalities with the “result” on the right. Writing “=” just means that the two sides are equal, not that the left side produces the right side. So, 5 – 1 = 4, 3 = 5 – 2, and 1 + 3 = 5 – 1 are all good things to write and should be intermixed.\n\n**Zero is Important:** Mix in adding 0 sometimes. It is easy to do, and it is important conceptually. Similarly, mix in questions where you subtract 0 and questions where you subtract everything. For example, if you have three bits of food and you eat all of them, how many do you have left?" }, "block3_accord": { - "eng": "Tip: Be patient with Memorizing" + "eng": "Tip: Manipulatives and Fingers" }, "block3_text": { - "eng": "As you ask your student to do various adding and subtracting problems, your child will become more and more familiar with them and will eventually memorize them. While it is desirable to eventually make the recall of these facts automatic and easy, there is no hurry." + "eng": "Children of this age benefit greatly from having manipulatives to use when doing addition and subtraction. It cements their understanding of the numbers in terms of quantities.\n\nThe manipulative that is always available is their fingers. When doing the example of adding two to three, they can put up two fingers on one hand, three fingers on the other hand, and bring the two hands together. Another way to do it is to raise two fingers on one hand, raise three more fingers on that same hand, and then see a total of five fingers raised.\n\nThe ideas behind practicing subtraction are similar to those for addition. If your child is going to subtract three from five, have your chid raise five fingers and then lower three of them. Their familiarity with one less and two less will probably make subtracting one and two very easy." }, "block4_accord": { - "eng": "Extending: Larger Numbers" + "eng": "Tip: Be patient with Memorizing" }, "block4_text": { + "eng": "As your student does various adding and subtracting problems, your child will become more and more familiar with them and will eventually memorize them. While it is desirable to eventually make the recall of these facts automatic and easy, there is no hurry." + }, + "block5_accord": { + "eng": "Extending: Larger Numbers" + }, + "block5_text": { "eng": "During this time your student's exposure to adding won't be restricted to those whose sum is 5 or less, and that is fine. For example, your student will probably have learned to add 1 or 2 to all the numbers up to 10. Your child may also have begun to learn the adding twin facts, such as 3 + 3 or 4 + 4." } }, - "block1_text": "Your child has been doing adding problems by counting everything. If asked to add two things to three things, that was done by counting all five things. As your child mastered Counting On, some of that counting was replaced by starting with one of the numbers, say 3 in this example, and then counting the two remaining things (“4, 5”). This experience with counting has also allowed your child to visualize and master the ideas of 1 more and 2 more, which has made adding 1 and 2 much easier.\n\n**Five Frames:** Start using five frames to provide a structured environment for learning these math facts, as well as to lead into learning number bonds and ten frames. Play up the connection of five frames with having five fingers on one hand.\n\n**Equation Symbols:** Start using “+” and “–” and “=” when you write down this material for your children. Also, don’t always write equalities with the “result” on the right. Writing “=” just means that the two sides are equal, not that the left side produces the right side. So, 5 – 1 = 4, 3 = 5 – 2, and 1 + 3 = 5 – 1 are all good things to write and should be intermixed.\n\n< illustration of a five frame with 3 dots in it >\n\n**Zero is Important:** Mix in adding 0 sometimes. It is easy to do, and it is important conceptually. Similarly, mix in questions where you subtract 0 and questions where you subtract everything. For example, if you have three bits of food and you eat all of them, how many do you have left?", - "block2_accord": "Tip: Manipulatives and Fingers", - "block2_text": "Children of this age benefit greatly from having manipulatives to use when doing addition and subtraction. It cements their understanding of the numbers in terms of quantities.\n\nThe manipulative that is always available is their fingers. When doing the example of adding two to three, they can put up two fingers on one hand, three fingers on the other hand, and bring the two hands together. Another way to do it is to raise two fingers on one hand, raise three more fingers on that same hand, and then see a total of five fingers raised.\n\nThe ideas behind practicing subtraction are similar to those for addition. If your child is going to subtract three from five, have your chid raise five fingers and then lower three of them. Their familiarity with one less and two less will probably make subtracting one and two very easy.", - "block3_accord": "Tip: Be patient with Memorizing", - "block3_text": "As you ask your student to do various adding and subtracting problems, your child will become more and more familiar with them and will eventually memorize them. While it is desirable to eventually make the recall of these facts automatic and easy, there is no hurry.", - "block4_accord": "Extending: Larger Numbers", - "block4_text": "During this time your student's exposure to adding won't be restricted to those whose sum is 5 or less, and that is fine. For example, your student will probably have learned to add 1 or 2 to all the numbers up to 10. Your child may also have begun to learn the adding twin facts, such as 3 + 3 or 4 + 4." + "block1_text": "Your children have been doing adding problems by counting each individual item. If asked to add two things to three things, that was done by counting all five things. As they master Counting On, some of that counting is replaced by starting with one of the numbers, say 3 in this example, and then counting the two remaining things (“4, 5”). This experience with counting also allows a child to visualize and master the ideas of 1 more and 2 more, which has made adding 1 and 2 much easier.\n\n**Five Frames and Ten Frames:** Start using five frames and ten frames to provide a structured environment for learning these math facts, as well as to lead into learning number bonds. Play up the connection of five frames with having five fingers on one hand.\n\n< illustration of a five frame with 3 dots in it >", + "block2_text": "**Equation Symbols:** Start using “+” and “–” and “=” when you write down this material for your children. Also, don’t always write equalities with the “result” on the right. Writing “=” just means that the two sides are equal, not that the left side produces the right side. So, 5 – 1 = 4, 3 = 5 – 2, and 1 + 3 = 5 – 1 are all good things to write and should be intermixed.\n\n**Zero is Important:** Mix in adding 0 sometimes. It is easy to do, and it is important conceptually. Similarly, mix in questions where you subtract 0 and questions where you subtract everything. For example, if you have three bits of food and you eat all of them, how many do you have left?", + "block3_accord": "Tip: Manipulatives and Fingers", + "block3_text": "Children of this age benefit greatly from having manipulatives to use when doing addition and subtraction. It cements their understanding of the numbers in terms of quantities.\n\nThe manipulative that is always available is their fingers. When doing the example of adding two to three, they can put up two fingers on one hand, three fingers on the other hand, and bring the two hands together. Another way to do it is to raise two fingers on one hand, raise three more fingers on that same hand, and then see a total of five fingers raised.\n\nThe ideas behind practicing subtraction are similar to those for addition. If your child is going to subtract three from five, have your chid raise five fingers and then lower three of them. Their familiarity with one less and two less will probably make subtracting one and two very easy.", + "block4_accord": "Tip: Be patient with Memorizing", + "block4_text": "As your student does various adding and subtracting problems, your child will become more and more familiar with them and will eventually memorize them. While it is desirable to eventually make the recall of these facts automatic and easy, there is no hurry.", + "block5_accord": "Extending: Larger Numbers", + "block5_text": "During this time your student's exposure to adding won't be restricted to those whose sum is 5 or less, and that is fine. For example, your student will probably have learned to add 1 or 2 to all the numbers up to 10. Your child may also have begun to learn the adding twin facts, such as 3 + 3 or 4 + 4." }, { "id": "NO_AS10_AT", + "searching_for_this": false, "theme_id": "NO_AS10_", "strand_id": "NO", "next_topic_1": "NO_AS10_ANT", @@ -1084,7 +1180,7 @@ "eng": "Adding Twins to 10" }, "block1_text": { - "eng": "**Adding Twins** are when you add a number to itself. Children generally enjoy Adding Twins, so these facts are easily learned and make a good part of a foundation for learning addition." + "eng": "**Adding Twins** are when you add a number to itself. Children generally enjoy Adding Twins, so these facts are easily learned and make a good part of a foundation for learning all the single-digit addition facts." }, "block2_accord": { "eng": "Practicing: 2 Rows of Dots" @@ -1105,7 +1201,7 @@ "eng": "Look at the numbers that result from adding twins. These are exactly the numbers that can be split into two equal whole parts – e.g. 6 is 3 + 3. These are the even numbers. Numbers that cannot be split into two equal whole parts are the odd numbers. Children relate to this splitting naturally if you describe it in terms of sharing fairly some resource (food, toys, stones) among two people." } }, - "block1_text": "**Adding Twins** are when you add a number to itself. Children generally enjoy Adding Twins, so these facts are easily learned and make a good part of a foundation for learning addition.", + "block1_text": "**Adding Twins** are when you add a number to itself. Children generally enjoy Adding Twins, so these facts are easily learned and make a good part of a foundation for learning all the single-digit addition facts.", "block2_accord": "Practicing: 2 Rows of Dots", "block2_text": "Practicing: Put out two rows of dots or objects and count them. Count them by 2’s sometimes to get the child used to skip counting by 2’s. \n\n< illustration of two rows of 3 dots >", "block3_accord": "Extending: New Words - Doubling, Multiplying", @@ -1115,27 +1211,51 @@ }, { "id": "NO_AS10_ANT", + "searching_for_this": false, "theme_id": "NO_AS10_", "strand_id": "NO", "prev_topic_1": "NO_AS10_AT", "block1_type": "all_text", + "block2_type": "accord_all_text", + "block3_type": "accord_all_text", "name": "Adding Near Twins", "_translations": { "name": {}, - "block1_text": {} + "block1_text": {}, + "block2_accord": {}, + "block2_text": {}, + "block3_accord": {}, + "block3_text": {} }, "_translatedFields": { "name": { "eng": "Adding Near Twins" }, "block1_text": { - "eng": "This combines addition twins with the idea of adding and subtracting one. This mental juggling may take some getting used to for some children. \n\nTake 3 + 4 as an example. Lay out a row of 3 things above a row of 4 things. Cover over the last of the four things and say that 3 + 3 is 6 – then uncover the last item and say that adding one more is 7. Summarize by saying 3 + 4 is 7. With practice, this can become automatic.\n\n< show what was described – 3 things in one row, 4 things directly below with the 3 and 3 lined up and the fourth thing in the bottom row grayed out or otherwise shown to be temporarily ignored >\n\nSimilarly, 3 + 4 can be thought of one less than 4 + 4. For example, with two rows of 4 things, the sum is 8, but then when you take 1 away you get 7 is 3 + 4.\n\n< Show what was described >" + "eng": "This topic combines addition twins with the idea of adding and subtracting one. This mental juggling may take some getting used to for some children, and they may resist using this method – and that is okay." + }, + "block2_accord": { + "eng": "Example: One More" + }, + "block2_text": { + "eng": "For 3 + 4, lay out a row of 3 things above a row of 4 things. Cover over the last of the four things and say that 3 + 3 is 6 – then uncover the last item and say that adding one more is 7. Summarize by saying 3 + 4 is 7. With practice, this can become automatic.\n\n< show what was described – 3 things in one row, 4 things directly below with the 3 and 3 lined up and the fourth thing in the bottom row grayed out or otherwise shown to be temporarily ignored >" + }, + "block3_accord": { + "eng": "Example: One Less" + }, + "block3_text": { + "eng": "3 + 4 can also be thought of as one less than 4 + 4. For example, with two rows of 4 things, the sum is 8, but then when you take 1 away you get 7 is 3 + 4.\n\n< Show what was described >" } }, - "block1_text": "This combines addition twins with the idea of adding and subtracting one. This mental juggling may take some getting used to for some children. \n\nTake 3 + 4 as an example. Lay out a row of 3 things above a row of 4 things. Cover over the last of the four things and say that 3 + 3 is 6 – then uncover the last item and say that adding one more is 7. Summarize by saying 3 + 4 is 7. With practice, this can become automatic.\n\n< show what was described – 3 things in one row, 4 things directly below with the 3 and 3 lined up and the fourth thing in the bottom row grayed out or otherwise shown to be temporarily ignored >\n\nSimilarly, 3 + 4 can be thought of one less than 4 + 4. For example, with two rows of 4 things, the sum is 8, but then when you take 1 away you get 7 is 3 + 4.\n\n< Show what was described >" + "block1_text": "This topic combines addition twins with the idea of adding and subtracting one. This mental juggling may take some getting used to for some children, and they may resist using this method – and that is okay.", + "block2_accord": "Example: One More", + "block2_text": "For 3 + 4, lay out a row of 3 things above a row of 4 things. Cover over the last of the four things and say that 3 + 3 is 6 – then uncover the last item and say that adding one more is 7. Summarize by saying 3 + 4 is 7. With practice, this can become automatic.\n\n< show what was described – 3 things in one row, 4 things directly below with the 3 and 3 lined up and the fourth thing in the bottom row grayed out or otherwise shown to be temporarily ignored >", + "block3_accord": "Example: One Less", + "block3_text": "3 + 4 can also be thought of as one less than 4 + 4. For example, with two rows of 4 things, the sum is 8, but then when you take 1 away you get 7 is 3 + 4.\n\n< Show what was described >" }, { "id": "NO_AS10_NBFF", + "searching_for_this": false, "theme_id": "NO_AS10_", "strand_id": "NO", "block1_type": "all_text", @@ -1163,10 +1283,10 @@ "eng": "Number Bonds & Fact Families" }, "block1_text": { - "eng": "Seeing a whole thing as being made up of its parts is an important developmental step for a child. This is the part-whole concept, and it can take time.\n\nThe number bonds for a number, say 6, are all pairs of numbers that add up to 6. It is all the ways of taking the whole of 6 and breaking it into two parts. This reinforces an understanding of the connection between addition and subtraction as forming groups of fact families\n\nThe number bonds for 6 are: 0 + 6, 1 + 5, 2 + 4, and 3 + 3. A child who has learned these well will then have little trouble answering the question: \"What do I need to add to 2 to get 6?\" They will know that 2 + 4 is a number bond for 6, so 4 is the part of 6 that is missing. This strengthens seeing 4 + 2 = 6, 2 + 4 = 6, 6 – 2 = 4, and 6 – 4 = 2 as a family of facts that are tied together.\n\n< show picture of 2 things, space, 4 things >" + "eng": "Seeing a whole thing as being made up of its parts is an important developmental step for a child. This is the **part-whole concept,** and it can take time.\n\nThe **number bonds** for a number, say 6, are all pairs of numbers that add up to 6. It is all the ways of taking the whole of 6 and breaking it into two parts. This reinforces an understanding of the connection between addition and subtraction in forming groups of fact families\n\nThe number bonds for 6 are: 0 + 6, 1 + 5, 2 + 4, and 3 + 3. A child who has learned these well will then have little trouble answering the question: \"What do I need to add to 2 to get 6?\" They will know that 2 + 4 is a number bond for 6, so 4 is the part of 6 that is missing. This strengthens seeing 4 + 2 = 6, 2 + 4 = 6, 6 – 2 = 4, and 6 – 4 = 2 as a family of facts that are tied together.\n\n< show picture of 2 things, space, 4 things >" }, "block2_text": { - "eng": "If you haven’t done so already, start pointing out that addition is commutative, that 2 + 4 = 4 + 2. This aligns nicely with the idea of a fact family. Show this by taking a group of 2 things on the left and another group of 4 things slightly to the right, and then either redraw them or move them around the opposite order – you have the same things, so you must have the same total.\n\n< show (2 dots and 4 dots) two-headed arrow (4 dots and 2 dots) >" + "eng": "If you haven’t done so already, start pointing out that addition is commutative, that 2 + 4 = 4 + 2. This aligns nicely with the idea of a fact family. \n\nShow this by taking a group of 2 things on the left and another group of 4 things slightly to the right, and then either redraw them or move them around to the opposite order – you have the same things, so you must have the same total.\n\n< show (2 dots and 4 dots) two-headed arrow (4 dots and 2 dots) >" }, "block3_accord": { "eng": "Tip: Use ten frames" @@ -1193,8 +1313,8 @@ "eng": "Play Splat! Activities. Have some objects covered and some uncovered. Tell how many there are altogether and ask how many are covered. There are lots of variations of this." } }, - "block1_text": "Seeing a whole thing as being made up of its parts is an important developmental step for a child. This is the part-whole concept, and it can take time.\n\nThe number bonds for a number, say 6, are all pairs of numbers that add up to 6. It is all the ways of taking the whole of 6 and breaking it into two parts. This reinforces an understanding of the connection between addition and subtraction as forming groups of fact families\n\nThe number bonds for 6 are: 0 + 6, 1 + 5, 2 + 4, and 3 + 3. A child who has learned these well will then have little trouble answering the question: \"What do I need to add to 2 to get 6?\" They will know that 2 + 4 is a number bond for 6, so 4 is the part of 6 that is missing. This strengthens seeing 4 + 2 = 6, 2 + 4 = 6, 6 – 2 = 4, and 6 – 4 = 2 as a family of facts that are tied together.\n\n< show picture of 2 things, space, 4 things >", - "block2_text": "If you haven’t done so already, start pointing out that addition is commutative, that 2 + 4 = 4 + 2. This aligns nicely with the idea of a fact family. Show this by taking a group of 2 things on the left and another group of 4 things slightly to the right, and then either redraw them or move them around the opposite order – you have the same things, so you must have the same total.\n\n< show (2 dots and 4 dots) two-headed arrow (4 dots and 2 dots) >", + "block1_text": "Seeing a whole thing as being made up of its parts is an important developmental step for a child. This is the **part-whole concept,** and it can take time.\n\nThe **number bonds** for a number, say 6, are all pairs of numbers that add up to 6. It is all the ways of taking the whole of 6 and breaking it into two parts. This reinforces an understanding of the connection between addition and subtraction in forming groups of fact families\n\nThe number bonds for 6 are: 0 + 6, 1 + 5, 2 + 4, and 3 + 3. A child who has learned these well will then have little trouble answering the question: \"What do I need to add to 2 to get 6?\" They will know that 2 + 4 is a number bond for 6, so 4 is the part of 6 that is missing. This strengthens seeing 4 + 2 = 6, 2 + 4 = 6, 6 – 2 = 4, and 6 – 4 = 2 as a family of facts that are tied together.\n\n< show picture of 2 things, space, 4 things >", + "block2_text": "If you haven’t done so already, start pointing out that addition is commutative, that 2 + 4 = 4 + 2. This aligns nicely with the idea of a fact family. \n\nShow this by taking a group of 2 things on the left and another group of 4 things slightly to the right, and then either redraw them or move them around to the opposite order – you have the same things, so you must have the same total.\n\n< show (2 dots and 4 dots) two-headed arrow (4 dots and 2 dots) >", "block3_accord": "Tip: Use ten frames", "block3_text": "Fluency with number bonds for all numbers up to about 10 is very useful for doing adding and subtracting, The number bonds that arise most often are those for 10. Ten frames are designed to help visualize number bonds for 10. A ten frame with 7 dots in it makes it visually obvious that 7 + 3 is a number bond for 10.\n\n< illustration with a ten frame with 7 dots in it >", "block4_accord": "Requirement: Counting to 20", @@ -1206,6 +1326,7 @@ }, { "id": "NO_ASSD_PVto19", + "searching_for_this": false, "theme_id": "NO_ASSD_", "strand_id": "NO", "block1_type": "all_text", @@ -1225,7 +1346,7 @@ "eng": "Place Value to 19" }, "block1_text": { - "eng": "Use a bundle of 10 or a ten frame to help your child unitize the 10 and be able to reason with it. The ability to consider a group of 10 as one thing is a surprisingly big step. \n\nDo lots of practice counting out numbers between 10 and 19 and seeing how a group of 10 objects can be split off. Also frequently represent these numbers in expanded form, as 10 plus some more." + "eng": "Use a bundle of 10 or a ten frame to help your child see the 10 as a unit and be able to reason with it. This is called **unitizing** the 10. The ability to consider a group of 10 as one thing is a surprisingly big step. \n\nDo lots of practice counting out quantities of object between 10 and 19 and seeing how a group of 10 objects can be split off. Also frequently represent these numbers in expanded form, as 10 plus some more." }, "block2_accord": { "eng": "Tip: Use two ten frames" @@ -1240,7 +1361,7 @@ "eng": "At these early stages, do not use a coin to represent ten things. This is too abstract a representation at this point." } }, - "block1_text": "Use a bundle of 10 or a ten frame to help your child unitize the 10 and be able to reason with it. The ability to consider a group of 10 as one thing is a surprisingly big step. \n\nDo lots of practice counting out numbers between 10 and 19 and seeing how a group of 10 objects can be split off. Also frequently represent these numbers in expanded form, as 10 plus some more.", + "block1_text": "Use a bundle of 10 or a ten frame to help your child see the 10 as a unit and be able to reason with it. This is called **unitizing** the 10. The ability to consider a group of 10 as one thing is a surprisingly big step. \n\nDo lots of practice counting out quantities of object between 10 and 19 and seeing how a group of 10 objects can be split off. Also frequently represent these numbers in expanded form, as 10 plus some more.", "block2_accord": "Tip: Use two ten frames", "block2_text": "Use a filled in ten frame plus a partially filled in ten frame as one way to show these numbers.", "block3_accord": "Tip: Coins are too abstract", @@ -1248,8 +1369,11 @@ }, { "id": "NO_ASSD_AS10", + "searching_for_this": false, "theme_id": "NO_ASSD_", "strand_id": "NO", + "next_topic_1": "NO_ASSD_10BA", + "next_topic_2": "NO_ASSD_10BS", "block1_type": "all_text", "block2_type": "accord_all_text", "name": "Add & Subtract 10", @@ -1264,7 +1388,7 @@ "eng": "Add & Subtract 10" }, "block1_text": { - "eng": "If you show two dots and you add a ten frame of 10 dots, then you have the standard representation for 12 dots. Similarly, if you represent 15 as 5 dots plus a ten frame (or a bundle of 10), then removing the 10 is easily seen as leaving 5 dots." + "eng": "If you show two dots and you add a ten frame of 10 dots, then you have the standard representation for 12 dots. Similarly, if you represent 15 as 5 dots plus a ten frame (or a bundle of 10), then removing the 10 is easily seen as leaving 5 dots.\n\nThis topic and the next topic form a gateway to the topics where 10 is used as a bridge for doing addition and subtraction." }, "block2_accord": { "eng": "Required topics" @@ -1273,14 +1397,17 @@ "eng": "Make sure that place value and expanded form are well understood first. Then this step is fairly easy." } }, - "block1_text": "If you show two dots and you add a ten frame of 10 dots, then you have the standard representation for 12 dots. Similarly, if you represent 15 as 5 dots plus a ten frame (or a bundle of 10), then removing the 10 is easily seen as leaving 5 dots.", + "block1_text": "If you show two dots and you add a ten frame of 10 dots, then you have the standard representation for 12 dots. Similarly, if you represent 15 as 5 dots plus a ten frame (or a bundle of 10), then removing the 10 is easily seen as leaving 5 dots.\n\nThis topic and the next topic form a gateway to the topics where 10 is used as a bridge for doing addition and subtraction.", "block2_accord": "Required topics", "block2_text": "Make sure that place value and expanded form are well understood first. Then this step is fairly easy." }, { "id": "NO_ASSD_ASto10", + "searching_for_this": false, "theme_id": "NO_ASSD_", "strand_id": "NO", + "next_topic_1": "NO_ASSD_10BA", + "next_topic_2": "NO_ASSD_10BS", "block1_type": "all_text", "name": "Add & Subtract to 10", "_translations": { @@ -1292,15 +1419,18 @@ "eng": "Add & Subtract to 10" }, "block1_text": { - "eng": "This combines all the steps learned so far: 1) adding and subtracting 1 and 2; 2) addition twins; 3) addition near twins; 4) number bonds for numbers up to 10; 5) commutativity; and 6) fact families. Take time and ensure these facts have been solidly mastered.\n\nA few of the adding 3 facts (and their subtraction counterparts) are the only ones that do not immediately fall under the steps covered so far: 3 + 5; 3 + 6; and 3 + 7." + "eng": "This combines all the steps learned so far: 1) adding and subtracting 1 and 2; 2) addition twins; 3) addition near twins; 4) number bonds for numbers up to 10; 5) commutativity; and 6) fact families. Take time and ensure these previous topics have been solidly mastered.\n\nA few of the adding 3 facts (and their subtraction counterparts) are the only ones not covered in the topics discussed so far: 3 + 5; 3 + 6; and 3 + 7." } }, - "block1_text": "This combines all the steps learned so far: 1) adding and subtracting 1 and 2; 2) addition twins; 3) addition near twins; 4) number bonds for numbers up to 10; 5) commutativity; and 6) fact families. Take time and ensure these facts have been solidly mastered.\n\nA few of the adding 3 facts (and their subtraction counterparts) are the only ones that do not immediately fall under the steps covered so far: 3 + 5; 3 + 6; and 3 + 7." + "block1_text": "This combines all the steps learned so far: 1) adding and subtracting 1 and 2; 2) addition twins; 3) addition near twins; 4) number bonds for numbers up to 10; 5) commutativity; and 6) fact families. Take time and ensure these previous topics have been solidly mastered.\n\nA few of the adding 3 facts (and their subtraction counterparts) are the only ones not covered in the topics discussed so far: 3 + 5; 3 + 6; and 3 + 7." }, { "id": "NO_ASSD_10BA", + "searching_for_this": false, "theme_id": "NO_ASSD_", "strand_id": "NO", + "prev_topic_1": "NO_ASSD_AS10", + "prev_topic_2": "NO_ASSD_ASto10", "block1_type": "all_text", "block2_type": "all_text", "block3_type": "accord_all_text", @@ -1317,7 +1447,7 @@ "eng": "10 as a Bridge for Adding" }, "block1_text": { - "eng": "**Compensation** is a useful tool for simplifying addition and subtraction calculations of all sizes. Understanding it also increases number sense for addition and subtraction. It is simpler than it sounds.\n\nThe idea is to give or take some small amount to make one of the numbers easier to work with. We will typically be making one of the numbers into a multiple of 10 – the earlier practice with number bonds for 10 pays off here. Suppose you are adding 8 + 7. The 8 just needs 2 more to become 10, so take that 2 away from the 7. This turns 8 + 7 into 10 + 5, which is easy. We could also have done this problem by giving 3 to the 7 to make it 10. In that case, we'd turn 8 + 7 into 5 + 10.\n\n< show a stack of 8 blocks next to a stack of 7 blocks – indicate that 2 of the 7 blocks get moved on top of the 8 blocks >" + "eng": "**Compensation** simplifies addition and subtraction calculations of all sizes. Understanding it also increases number sense for addition and subtraction. It is simpler than it sounds.\n\nThe idea is to give or take some small amount to make one of the numbers easier to work with. We will typically be making one of the numbers into a multiple of 10 – the earlier practice with number bonds for 10 pays off here. Suppose you are adding 8 + 7. The 8 just needs 2 more to become 10, so take that 2 away from the 7. This turns 8 + 7 into 10 + 5, which is easy. We could also have done this problem by giving 3 to the 7 to make it 10. In that case, we'd turn 8 + 7 into 5 + 10.\n\n< show a stack of 8 blocks next to a stack of 7 blocks – indicate that 2 of the 7 blocks get moved on top of the 8 blocks >" }, "block2_text": { "eng": "**10 as a Bridge:** Single-digit compensation can also be thought of as using 10 as a bridge or intermediate stopping point. Although equivalent to the compensation model, this model may resonate better with some children. When adding 7 to 8, it takes 2 of the 7 to get from 8 to 10, and then there are 5 more left from the 7 to take 10 to 15.\n\n< show 8 → 10 → 15 with 2 and 5 annotated above the arrows - perhaps have 10 on top of a bridge with 8 on the left side and 15 on the right side of the bridge>" @@ -1329,15 +1459,18 @@ "eng": "There are often other possibilities for using compensation in a given addition problem. Consider 6 + 8 for example. The 6 could give 2 to the 8 to make this problem 4 + 10. However, the 8 could give 1 to the 6 to make this 7 + 7, an adding twin problem. Challenge each other to think of different ways for doing a given adding problem." } }, - "block1_text": "**Compensation** is a useful tool for simplifying addition and subtraction calculations of all sizes. Understanding it also increases number sense for addition and subtraction. It is simpler than it sounds.\n\nThe idea is to give or take some small amount to make one of the numbers easier to work with. We will typically be making one of the numbers into a multiple of 10 – the earlier practice with number bonds for 10 pays off here. Suppose you are adding 8 + 7. The 8 just needs 2 more to become 10, so take that 2 away from the 7. This turns 8 + 7 into 10 + 5, which is easy. We could also have done this problem by giving 3 to the 7 to make it 10. In that case, we'd turn 8 + 7 into 5 + 10.\n\n< show a stack of 8 blocks next to a stack of 7 blocks – indicate that 2 of the 7 blocks get moved on top of the 8 blocks >", + "block1_text": "**Compensation** simplifies addition and subtraction calculations of all sizes. Understanding it also increases number sense for addition and subtraction. It is simpler than it sounds.\n\nThe idea is to give or take some small amount to make one of the numbers easier to work with. We will typically be making one of the numbers into a multiple of 10 – the earlier practice with number bonds for 10 pays off here. Suppose you are adding 8 + 7. The 8 just needs 2 more to become 10, so take that 2 away from the 7. This turns 8 + 7 into 10 + 5, which is easy. We could also have done this problem by giving 3 to the 7 to make it 10. In that case, we'd turn 8 + 7 into 5 + 10.\n\n< show a stack of 8 blocks next to a stack of 7 blocks – indicate that 2 of the 7 blocks get moved on top of the 8 blocks >", "block2_text": "**10 as a Bridge:** Single-digit compensation can also be thought of as using 10 as a bridge or intermediate stopping point. Although equivalent to the compensation model, this model may resonate better with some children. When adding 7 to 8, it takes 2 of the 7 to get from 8 to 10, and then there are 5 more left from the 7 to take 10 to 15.\n\n< show 8 → 10 → 15 with 2 and 5 annotated above the arrows - perhaps have 10 on top of a bridge with 8 on the left side and 15 on the right side of the bridge>", "block3_accord": "Practicing: Multiple ways", "block3_text": "There are often other possibilities for using compensation in a given addition problem. Consider 6 + 8 for example. The 6 could give 2 to the 8 to make this problem 4 + 10. However, the 8 could give 1 to the 6 to make this 7 + 7, an adding twin problem. Challenge each other to think of different ways for doing a given adding problem." }, { "id": "NO_ASSD_10BS", + "searching_for_this": false, "theme_id": "NO_ASSD_", "strand_id": "NO", + "prev_topic_1": "NO_ASSD_AS10", + "prev_topic_2": "NO_ASSD_ASto10", "block1_type": "all_text", "block2_type": "all_text", "block3_type": "all_text", @@ -1353,7 +1486,7 @@ "eng": "10 as a Bridge for Subtracting" }, "block1_text": { - "eng": "**Compensation:** Add the same amount or subtract the same amount from both numbers. This will keep the distance between the two numbers the same, but will make them easier to work with. Typically that will mean turning the number we're subtracting in the original problem into a multiple of 10. \n\n**Example:** Suppose we are subtracting 13 – 8. If we add 2 to both numbers, then the distance between them stays the same, but now we are subtracting 15 – 10. Similarly, if we were asked to do 17 – 13, we could subtract 3 from both numbers and turn it into 14 – 10. Alternatively, we could subtract 10 from both numbers and turn it into 7 – 3.\n\n< show a number line with 8 and 13 and how that pair of numbers can be slid to 10 and 15>" + "eng": "**Compensation:** Add the same amount or subtract the same amount from both numbers. This will keep the distance between the two numbers the same, but can make them easier to work with. Typically that will mean turning the number we're subtracting in the original problem into a multiple of 10. \n\n**Example:** Suppose we are subtracting 13 – 8. If we add 2 to both numbers, then the distance between them stays the same, but now we are subtracting 15 – 10. Similarly, if we were asked to do 17 – 13, we could subtract 3 from both numbers and turn it into 14 – 10. Alternatively, we could subtract 10 from both numbers and turn it into 7 – 3.\n\n< show a number line with 8 and 13 and how that pair of numbers can be slid to 10 and 15>" }, "block2_text": { "eng": "**10 as a Bridge:** Just as we did for addition, we can use 10 as a bridge subtraction problems. Your child should have a strong command of the number bonds for 10 to take full advantage of these methods.\n\nLet's use 12 – 7 as our example. We can do this as a take away or a difference problem.\n\nAs a take away problem, we'll use 2 of the 7 to get 12 down to 10. We then have 5 of the 7 left to take the 10 down to 5. We broke 7 into 2 and 5 to be able to use 10 as a bridge along the way.\n\n< show 12 blocks, 10 blocks, and 5 blocks – with annotations going down by 2 and then 5 >" @@ -1362,12 +1495,13 @@ "eng": "As a difference problem, the total distance between 12 and 7 is the distance between 12 and 10 plus the distance between 10 and 7. The distance between 12 and 10 is 2, and the distance from 10 and 7 is 3, so the total distance is 2 plus 3, which is 5.\n\n< show stacks of 7 blocks, 10 blocks, and 12 blocks. Annotate that there is 3 between 7 and 10 and another 2 between 10 and 12>" } }, - "block1_text": "**Compensation:** Add the same amount or subtract the same amount from both numbers. This will keep the distance between the two numbers the same, but will make them easier to work with. Typically that will mean turning the number we're subtracting in the original problem into a multiple of 10. \n\n**Example:** Suppose we are subtracting 13 – 8. If we add 2 to both numbers, then the distance between them stays the same, but now we are subtracting 15 – 10. Similarly, if we were asked to do 17 – 13, we could subtract 3 from both numbers and turn it into 14 – 10. Alternatively, we could subtract 10 from both numbers and turn it into 7 – 3.\n\n< show a number line with 8 and 13 and how that pair of numbers can be slid to 10 and 15>", + "block1_text": "**Compensation:** Add the same amount or subtract the same amount from both numbers. This will keep the distance between the two numbers the same, but can make them easier to work with. Typically that will mean turning the number we're subtracting in the original problem into a multiple of 10. \n\n**Example:** Suppose we are subtracting 13 – 8. If we add 2 to both numbers, then the distance between them stays the same, but now we are subtracting 15 – 10. Similarly, if we were asked to do 17 – 13, we could subtract 3 from both numbers and turn it into 14 – 10. Alternatively, we could subtract 10 from both numbers and turn it into 7 – 3.\n\n< show a number line with 8 and 13 and how that pair of numbers can be slid to 10 and 15>", "block2_text": "**10 as a Bridge:** Just as we did for addition, we can use 10 as a bridge subtraction problems. Your child should have a strong command of the number bonds for 10 to take full advantage of these methods.\n\nLet's use 12 – 7 as our example. We can do this as a take away or a difference problem.\n\nAs a take away problem, we'll use 2 of the 7 to get 12 down to 10. We then have 5 of the 7 left to take the 10 down to 5. We broke 7 into 2 and 5 to be able to use 10 as a bridge along the way.\n\n< show 12 blocks, 10 blocks, and 5 blocks – with annotations going down by 2 and then 5 >", "block3_text": "As a difference problem, the total distance between 12 and 7 is the distance between 12 and 10 plus the distance between 10 and 7. The distance between 12 and 10 is 2, and the distance from 10 and 7 is 3, so the total distance is 2 plus 3, which is 5.\n\n< show stacks of 7 blocks, 10 blocks, and 12 blocks. Annotate that there is 3 between 7 and 10 and another 2 between 10 and 12>" }, { "id": "NO_DD_P", + "searching_for_this": false, "theme_id": "NO_DD_", "strand_id": "NO", "block1_type": "all_text", @@ -1388,6 +1522,7 @@ }, { "id": "NO_MSD_P", + "searching_for_this": false, "theme_id": "NO_MSD_", "strand_id": "NO", "block1_type": "all_text", @@ -1408,6 +1543,7 @@ }, { "id": "FEP_EPW_NEP", + "searching_for_this": false, "theme_id": "FEP_EPW_", "strand_id": "FP", "block1_type": "all_text", @@ -1421,13 +1557,14 @@ "eng": "~~Naming Equal Parts~~" }, "block1_text": { - "eng": "Understanding and naming equal parts of a whole. Name at least halves, thirds, and quarters." + "eng": "Understanding and naming equal parts of a whole. Name at least halves, thirds, and quarters. \n\nIllustrate with cut up circles and rectangles." } }, - "block1_text": "Understanding and naming equal parts of a whole. Name at least halves, thirds, and quarters." + "block1_text": "Understanding and naming equal parts of a whole. Name at least halves, thirds, and quarters. \n\nIllustrate with cut up circles and rectangles." }, { "id": "FEP_EPW_MEPS", + "searching_for_this": false, "theme_id": "FEP_EPW_", "strand_id": "FP", "block1_type": "all_text", @@ -1448,6 +1585,7 @@ }, { "id": "FEP_EPS_NEP", + "searching_for_this": false, "theme_id": "FEP_EPS_", "strand_id": "FP", "block1_type": "all_text", @@ -1468,6 +1606,7 @@ }, { "id": "FEP_EPS_MEPS", + "searching_for_this": false, "theme_id": "FEP_EPS_", "strand_id": "FP", "block1_type": "all_text", @@ -1488,6 +1627,7 @@ }, { "id": "Data_CO_P", + "searching_for_this": false, "theme_id": "Data_CO_", "strand_id": "Data", "block1_type": "all_text", @@ -1508,6 +1648,7 @@ }, { "id": "Data_Rep_P", + "searching_for_this": false, "theme_id": "Data_Rep_", "strand_id": "Data", "block1_type": "all_text", @@ -1528,6 +1669,7 @@ }, { "id": "Data_Graph_P", + "searching_for_this": false, "theme_id": "Data_Graph_", "strand_id": "Data", "block1_type": "all_text", @@ -1548,6 +1690,7 @@ }, { "id": "Data_Anal_P", + "searching_for_this": false, "theme_id": "Data_Anal_", "strand_id": "Data", "block1_type": "all_text", @@ -1568,6 +1711,7 @@ }, { "id": "Meas_Dist_CL", + "searching_for_this": false, "theme_id": "Meas_Dist_", "strand_id": "Meas", "block1_type": "all_text", @@ -1588,6 +1732,7 @@ }, { "id": "Meas_Dist_MLNS", + "searching_for_this": false, "theme_id": "Meas_Dist_", "strand_id": "Meas", "block1_type": "all_text", @@ -1608,6 +1753,7 @@ }, { "id": "Meas_Dist_MLS", + "searching_for_this": false, "theme_id": "Meas_Dist_", "strand_id": "Meas", "block1_type": "all_text", @@ -1628,6 +1774,7 @@ }, { "id": "Meas_Wt_CW", + "searching_for_this": false, "theme_id": "Meas_Wt_", "strand_id": "Meas", "block1_type": "all_text", @@ -1648,6 +1795,7 @@ }, { "id": "Meas_Wt_MWNS", + "searching_for_this": false, "theme_id": "Meas_Wt_", "strand_id": "Meas", "block1_type": "all_text", @@ -1668,6 +1816,7 @@ }, { "id": "Meas_Wt_MWS", + "searching_for_this": false, "theme_id": "Meas_Wt_", "strand_id": "Meas", "block1_type": "all_text", @@ -1688,6 +1837,7 @@ }, { "id": "Meas_Vol_CV", + "searching_for_this": false, "theme_id": "Meas_Vol_", "strand_id": "Meas", "block1_type": "all_text", @@ -1708,6 +1858,7 @@ }, { "id": "Meas_Vol_CVNS", + "searching_for_this": false, "theme_id": "Meas_Vol_", "strand_id": "Meas", "block1_type": "all_text", @@ -1728,6 +1879,7 @@ }, { "id": "Meas_Vol_CVS", + "searching_for_this": false, "theme_id": "Meas_Vol_", "strand_id": "Meas", "block1_type": "all_text", @@ -1748,6 +1900,7 @@ }, { "id": "Meas_Time_PofD", + "searching_for_this": false, "theme_id": "Meas_Time_", "strand_id": "Meas", "block1_type": "all_text", @@ -1768,6 +1921,7 @@ }, { "id": "Meas_Time_Cal", + "searching_for_this": false, "theme_id": "Meas_Time_", "strand_id": "Meas", "block1_type": "all_text", @@ -1788,6 +1942,7 @@ }, { "id": "Meas_Time_TTH", + "searching_for_this": false, "theme_id": "Meas_Time_", "strand_id": "Meas", "block1_type": "all_text", @@ -1809,6 +1964,9 @@ ], "_xlsxPath": "EFM_topics_high_level_sheets.xlsx", "_metadata": { + "searching_for_this": { + "type": "boolean" + }, "block2_illust_flex": { "type": "number" }, diff --git a/app_data/sheets/data_list/test_list.json b/app_data/sheets/data_list/test_list.json new file mode 100644 index 0000000..9f962e5 --- /dev/null +++ b/app_data/sheets/data_list/test_list.json @@ -0,0 +1,21 @@ +{ + "flow_type": "data_list", + "flow_name": "test_list", + "status": "released", + "rows": [ + { + "id": "id_1", + "torf": false + }, + { + "id": "id_2", + "torf": false + } + ], + "_xlsxPath": "EFM_high_level_sheets.xlsx", + "_metadata": { + "torf": { + "type": "boolean" + } + } +} \ No newline at end of file diff --git a/app_data/sheets/template/efm_pow_start.json b/app_data/sheets/template/efm_pow_start.json index 11f857a..20f4cd2 100644 --- a/app_data/sheets/template/efm_pow_start.json +++ b/app_data/sheets/template/efm_pow_start.json @@ -49,6 +49,26 @@ ], "_nested_name": "dg_top_of_page" }, + { + "type": "display_group", + "name": "dg_info", + "rows": [ + { + "type": "text", + "name": "help_button", + "value": "These puzzles are separated into increasing levels of difficulty and not by grade level. With each increase in level there will tend to be more difficult puzzles and the mathematics is more advanced.", + "_translations": { + "value": {} + }, + "parameter_list": { + "icon_src": "help", + "style": "navigation" + }, + "_nested_name": "dg_info.help_button" + } + ], + "_nested_name": "dg_info" + }, { "name": "now", "value": "@calc(timestamp())", @@ -85,328 +105,754 @@ "_nested_name": "pow_click_history" }, { - "type": "display_group", - "name": "dg_powlist", + "type": "accordion", + "name": "accordion_for_pows", "parameter_list": { - "style": "column" + "open_multiple": "TRUE" }, "rows": [ { - "type": "items", - "name": "activity_buttons", - "value": "@data.efm_pows", + "type": "accordion_section", + "name": "level_a", + "value": "Level A", + "parameter_list": { + "text_align": "center", + "style": "large emphasised" + }, "rows": [ { - "name": "pow_id", - "value": "@item.id", - "_translations": { - "value": {} - }, - "type": "set_variable", - "_nested_name": "dg_powlist.activity_buttons.pow_id", - "_dynamicFields": { - "value": [ - { - "fullExpression": "@item.id", - "matchedExpression": "@item.id", - "type": "item", - "fieldName": "id" - } - ] - }, - "_dynamicDependencies": { - "@item.id": [ - "value" - ] - } - }, - { - "name": "click_history_field_name", - "value": "@local.pow_id@local.pow_click_history", - "_translations": { - "value": {} + "type": "display_group", + "name": "dg_powlist_a", + "parameter_list": { + "style": "column" }, - "exclude_from_translation": true, - "type": "set_variable", - "_nested_name": "dg_powlist.activity_buttons.click_history_field_name", - "_dynamicFields": { - "value": [ - { - "fullExpression": "@local.pow_id@local.pow_click_history", - "matchedExpression": "@local.pow_id", - "type": "local", - "fieldName": "pow_id" + "rows": [ + { + "type": "items", + "name": "activity_buttons_a", + "value": "@data.efm_pows", + "parameter_list": { + "filter": "@item.level==\"A\"" }, - { - "fullExpression": "@local.pow_id@local.pow_click_history", - "matchedExpression": "@local.pow_click_history", - "type": "local", - "fieldName": "pow_click_history" - } - ] - }, - "_dynamicDependencies": { - "@local.pow_id": [ - "value" - ], - "@local.pow_click_history": [ - "value" - ] - } - }, - { - "name": "pows_click_history", - "value": "@fields.@local.click_history_field_name ; @local.now", - "_translations": { - "value": {} - }, - "condition": "!!(@fields.@local.click_history_field_name)", - "exclude_from_translation": true, - "type": "set_variable", - "_nested_name": "dg_powlist.activity_buttons.pows_click_history", - "_dynamicFields": { - "value": [ - { - "fullExpression": "@fields.@local.click_history_field_name ; @local.now", - "matchedExpression": "@local.click_history_field_name", - "type": "local", - "fieldName": "click_history_field_name" + "rows": [ + { + "name": "pow_id", + "value": "@item.id", + "_translations": { + "value": {} + }, + "type": "set_variable", + "_nested_name": "accordion_for_pows.level_a.dg_powlist_a.activity_buttons_a.pow_id", + "_dynamicFields": { + "value": [ + { + "fullExpression": "@item.id", + "matchedExpression": "@item.id", + "type": "item", + "fieldName": "id" + } + ] + }, + "_dynamicDependencies": { + "@item.id": [ + "value" + ] + } + }, + { + "name": "click_history_field_name", + "value": "@local.pow_id@local.pow_click_history", + "_translations": { + "value": {} + }, + "exclude_from_translation": true, + "type": "set_variable", + "_nested_name": "accordion_for_pows.level_a.dg_powlist_a.activity_buttons_a.click_history_field_name", + "_dynamicFields": { + "value": [ + { + "fullExpression": "@local.pow_id@local.pow_click_history", + "matchedExpression": "@local.pow_id", + "type": "local", + "fieldName": "pow_id" + }, + { + "fullExpression": "@local.pow_id@local.pow_click_history", + "matchedExpression": "@local.pow_click_history", + "type": "local", + "fieldName": "pow_click_history" + } + ] + }, + "_dynamicDependencies": { + "@local.pow_id": [ + "value" + ], + "@local.pow_click_history": [ + "value" + ] + } + }, + { + "name": "pows_click_history", + "value": "@fields.@local.click_history_field_name ; @local.now", + "_translations": { + "value": {} + }, + "condition": "!!(@fields.@local.click_history_field_name)", + "exclude_from_translation": true, + "type": "set_variable", + "_nested_name": "accordion_for_pows.level_a.dg_powlist_a.activity_buttons_a.pows_click_history", + "_dynamicFields": { + "value": [ + { + "fullExpression": "@fields.@local.click_history_field_name ; @local.now", + "matchedExpression": "@local.click_history_field_name", + "type": "local", + "fieldName": "click_history_field_name" + }, + { + "fullExpression": "@fields.@local.click_history_field_name ; @local.now", + "matchedExpression": "@local.now", + "type": "local", + "fieldName": "now" + } + ], + "condition": [ + { + "fullExpression": "!!(@fields.@local.click_history_field_name)", + "matchedExpression": "@local.click_history_field_name", + "type": "local", + "fieldName": "click_history_field_name" + } + ] + }, + "_dynamicDependencies": { + "@local.click_history_field_name": [ + "value", + "condition" + ], + "@local.now": [ + "value" + ] + } + }, + { + "name": "pows_click_history", + "value": "@local.now", + "_translations": { + "value": {} + }, + "condition": "!(@fields.@local.click_history_field_name)", + "exclude_from_translation": true, + "type": "set_variable", + "_nested_name": "accordion_for_pows.level_a.dg_powlist_a.activity_buttons_a.pows_click_history", + "_dynamicFields": { + "value": [ + { + "fullExpression": "@local.now", + "matchedExpression": "@local.now", + "type": "local", + "fieldName": "now" + } + ], + "condition": [ + { + "fullExpression": "!(@fields.@local.click_history_field_name)", + "matchedExpression": "@local.click_history_field_name", + "type": "local", + "fieldName": "click_history_field_name" + } + ] + }, + "_dynamicDependencies": { + "@local.now": [ + "value" + ], + "@local.click_history_field_name": [ + "condition" + ] + } + }, + { + "type": "button", + "name": "button_pow_@item.id", + "value": "@item.name", + "_translations": { + "value": {} + }, + "action_list": [ + { + "trigger": "click", + "action_id": "set_field", + "args": [ + "current_pow", + "data.efm_pows.@item.id" + ], + "_raw": "click | set_field:current_pow: data.efm_pows.@item.id", + "_cleaned": "click | set_field:current_pow: data.efm_pows.@item.id" + }, + { + "trigger": "click", + "action_id": "go_to", + "args": [ + "efm_pow_template" + ], + "_raw": "click | go_to: efm_pow_template", + "_cleaned": "click | go_to: efm_pow_template" + }, + { + "trigger": "click", + "action_id": "set_field", + "args": [ + "@local.click_history_field_name", + "@local.pows_click_history" + ], + "_raw": "click | set_field:@local.click_history_field_name: @local.pows_click_history", + "_cleaned": "click | set_field:@local.click_history_field_name: @local.pows_click_history" + } + ], + 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