arrays area models and repeated addition · 2020-01-14 · arrays • this represents 3 x 6 as an...
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Arrays, Area Models, and Repeated Addition
Some Extra Help for Those Who Are Still Struggling with One or
More of These Concepts
Created by Dr. Peggy L. MochOctober 2010
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MORE HELP WITH ARRAYS
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Arrays• This represents 3 x 6 as an array of
forks• Rows are horizontal (3)• Columns are vertical (6)• Some folks use “RC Cola” to
remember the order• Some folks use “RCMP” (Royal
Canadian Mounted Police)
Rows
Columns
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Arrays• This represents 6 x 3 as
an array of forks• Rows are horizontal (6)• Columns are vertical
(3)• This concept of rows
and columns is used in– Arrays– Area Models– Repeated Addition– Matrices
Rows
Columns
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Arrays• Your Turn!• Provide arrays for each
of the following using O:– 4 x 3– 5 x 2– 2 x 3– 3 x 2– 2 x 5– 3 x 4
• Do the arrays on your own paper
• Label each array with the problem it represents
• Answers are provided on the next slide
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Array Answers• 4 x 3
• 5 x 2
• 2 x 3
• 3 x 2
• 2 x 5
• 3 x 4
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MORE HELP WITH AREA MODELS
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Area Models• Uses place value of two
linear measures to create areas
• Areas are summed together
• Sum of areas is the product of the two linear measures
• Follows rows then columns idea of arrays for set up purposes– 12 x 37 is a short wide
rectangle– 37 x 12 is a tall narrow
rectangle
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Area Models• Modeling 37 x 12
– 37 units (u) is the length of the left side of the rectangle (red)
– 12 units (u) is the length of the top of the rectangle (blue)37 u
12 u
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Area Models• Modeling 37 x 12
– The rest of the rectangle is constructed by adding the congruent parallel parts (green)
37 u
12 u
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Area Models• Modeling 37 x 12
– Next divide the rows by place value (estimate the size – it should be reasonable)
– Rows will break apart 37 into 30 units + 7 units
– The 30 unit length will be much larger than the 7 unit length
37 u
12 u
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Area Models• Modeling 37 x 12
– Next divide the columns by place value (estimate the size – it should be reasonable)
– Rows will break apart 12 into 10 units + 2 units
– The 10 unit length will be much larger than the 2 unit length
37 u
12 u
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Area Models• Modeling 37 x 12
– At this point the areas of each of the internal rectangles is calculated mentally and written into the their respective areas
• 30 x 10 for the top left rectangle• 30 x 2 for the top right rectangle• 7 x 10 for the bottom left rectangle• 7 x 2 for the bottom right rectangle
37 u
12 u
300 u2 60 u2
70 u2 14 u2
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Area Models• Modeling 37 x 12
– The last step is to sum up the areas, which will equal the product of 37 units x 12 units
37 u
12 u
300 u2 60 u2
70 u2 14 u2
300 u2 + 60 u2 + 70 u2 + 14 u2 = 444 u2
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Area Models• Your Turn!• Provide area models for
each of the following using an appropriately sized rectangle:– 14 x 35– 53 x 27– 32 x 177– 43 x 239
• Do the area models on your own paper
• Label each area model with the problem it represents
• Answers are provided on the next slides
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Area Model Answers• 14 x 35
300 u2 + 50 u2 + 120 u2 + 20 u2 = 490 u2
14 u
35 u
300 u2
120 u2
50 u2
20 u2
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Area Model Answers• 53 x 27
1000 u2 + 350 u2 + 60 u2 + 21 u2 = 1431 u2
53 u
27 u
1000 u2 350 u2
60 u2 21 u2
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Area Model Answers• 32 x 177
3000 u2 + 200 u2 + 2100 u2 + 140 u2 + 210 u2 + 14 u2 = 490 u2
32 u
177 u
3000 u2
200 u2
2100 u2
140 u2 14 u2
210 u2
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Area Model Answers• 43 x 239
8000 u2 + 1200 u2 + 360 u2 + 600 u2 + 90 u2 + 27 u2 = 10277 u2
43 u
239 u
8000 u2
600 u2
1200 u2
90 u2 27 u2
360 u2
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MORE HELP WITHREPEATED ADDITION
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Repeated Addition• Repeated addition is an
alternate way of defining multiplication
• The first factor tells how many sets or addends that will be needed (5)
• The second factor tells the cardinality of each set (3)
5 Sets
3 elementsin each set
5 x 3
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Repeated Addition• In terms of Vygotsky
self-talk repeated addition (n x m) is thought of as “n sets of m each” (5 sets of 3 each)
• Repeated addition is usually written horizontally
• 3 + 3 + 3 + 3 + 3 = 15
3+3+3+3+3=15
5 x 3
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Repeated Addition• Your Turn!• Provide repeated
addition models for each of the following:– 4 x 3– 5 x 2– 2 x 3– 3 x 2– 2 x 5– 3 x 4
• Do the repeated addition models on your own paper
• Label each model with the problem it represents
• Answers are provided on the next slide
![Page 24: Arrays Area Models and Repeated Addition · 2020-01-14 · Arrays • This represents 3 x 6 as an array of forks • Rows are horizontal (3) • Columns are vertical (6) • Some](https://reader033.vdocuments.mx/reader033/viewer/2022042012/5e7303ecf51a550f7d6a8a38/html5/thumbnails/24.jpg)
Repeated Addition Answers• 4 x 3
3 + 3 + 3 + 3 = 12
• 5 x 22 + 2 + 2 + 2 + 2 = 10
• 2 x 33 + 3 = 6
• 3 x 22 + 2 + 2 = 6
• 2 x 55 + 5 = 10
• 3 x 44 + 4 + 4 = 12
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The End