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Learn how to model and obtain the value of multiplication.

1.
Modeling Multiplication

“A critical area of instruction is to develop student understanding of the meanings of multiplication and

division of whole numbers through activities and problems involving equal- sized groups, arrays, and area

models (NGA/CCSSO 2010c).”

-Grade Three, California Mathematics Framework

“In grade four, students extend multiplication and division to include whole numbers greater than 100. The

standards (4.NBT.5-6) call for students to use visual representations such as area and array models that

students draw and connect to equations…With larger numbers, such array models become too difficult to

draw, so students can make sketches of rectangles and then label the resulting product as the number of

things or square units.”

- Grade Four, California Mathematics Framework

“In previous grades, students built a conceptual understanding of multiplication with whole numbers as they

applied multiple strategies to compute and solve problems. Students can continue to use different strategies

and methods learned previously-as long as the methods are efficient- but they must also understand and be

able to use the standard algorithm.”

-Grade Five, California Mathematics Framework

“A critical area of instruction is to develop student understanding of the meanings of multiplication and

division of whole numbers through activities and problems involving equal- sized groups, arrays, and area

models (NGA/CCSSO 2010c).”

-Grade Three, California Mathematics Framework

“In grade four, students extend multiplication and division to include whole numbers greater than 100. The

standards (4.NBT.5-6) call for students to use visual representations such as area and array models that

students draw and connect to equations…With larger numbers, such array models become too difficult to

draw, so students can make sketches of rectangles and then label the resulting product as the number of

things or square units.”

- Grade Four, California Mathematics Framework

“In previous grades, students built a conceptual understanding of multiplication with whole numbers as they

applied multiple strategies to compute and solve problems. Students can continue to use different strategies

and methods learned previously-as long as the methods are efficient- but they must also understand and be

able to use the standard algorithm.”

-Grade Five, California Mathematics Framework

2.
Groups (3.OA.1, 3.OA.3)

4 x 3 is 4 groups of 3.

Step 1: Create 4 groups. Draw a circle.

Step 2: Put 3 blocks or objects in each group.

Step 3: Find the total number of objects using different strategies: skip counting, adding repeatedly, etc.

4 x 3 is 4 groups of 3.

Step 1: Create 4 groups. Draw a circle.

Step 2: Put 3 blocks or objects in each group.

Step 3: Find the total number of objects using different strategies: skip counting, adding repeatedly, etc.

3.
Array and Area Model (3.OA.1, 3.OA.3)

4 x 3 is 4 rows of 3 or 4 rows and 3 columns

Step 1: Identify the number of rows and columns. Use the Multiplication Mat.

columns

rows

Step 2: Put the right number of rows and columns as guide.

Step 3: Fill in the area with blocks.

Step 4: Remove the guide and find the total number of blocks on the mat.

4 x 3 is 4 rows of 3 or 4 rows and 3 columns

Step 1: Identify the number of rows and columns. Use the Multiplication Mat.

columns

rows

Step 2: Put the right number of rows and columns as guide.

Step 3: Fill in the area with blocks.

Step 4: Remove the guide and find the total number of blocks on the mat.

4.
Area Model and Partial Products (4.NBT.5)

4 x 13 is 4 rows of 13 or 4 rows and 13 columns

Step 1: Identify the number of rows and columns. Use the Multiplication Mat.

columns

rows

Step 2: Put the right number of rows and columns as guide.

c c

Step 3: Fill in the area with blocks.

c c

c c

c c

c c

c c

Step 4: Remove the guide and find the total number of blocks on the mat.

Find the total value of the tens and the

c c total value of the ones using previously

c c learned strategies. Add the partial products.

c c

c c

4 x 13 is 4 rows of 13 or 4 rows and 13 columns

Step 1: Identify the number of rows and columns. Use the Multiplication Mat.

columns

rows

Step 2: Put the right number of rows and columns as guide.

c c

Step 3: Fill in the area with blocks.

c c

c c

c c

c c

c c

Step 4: Remove the guide and find the total number of blocks on the mat.

Find the total value of the tens and the

c c total value of the ones using previously

c c learned strategies. Add the partial products.

c c

c c

5.
Open Area Model (4.NBT.5)

22 x 13

Step 1: Decompose each number by place value: (20 + 2) x (10 + 3).

Step 2: Draw a rectangle large enough to write numbers inside. Leave space outside to write decomposition of

given numbers.

Step 3: Draw a vertical and horizontal line on the rectangle. Modeling ….

Step 4: Write the decomposition of numbers as dimensions of the rectangles.

10 3

20

2

Step 5: Find the area of each section of the largest rectangle.

10 3

20 20 x 10 = 200 20 x 3 = 60

2 2 x 10 = 20 2x3=6

Step 6: Add the partial areas to find the area of the whole rectangle.

200 + 60 + 20 + 6 = 286

22 x 13

Step 1: Decompose each number by place value: (20 + 2) x (10 + 3).

Step 2: Draw a rectangle large enough to write numbers inside. Leave space outside to write decomposition of

given numbers.

Step 3: Draw a vertical and horizontal line on the rectangle. Modeling ….

Step 4: Write the decomposition of numbers as dimensions of the rectangles.

10 3

20

2

Step 5: Find the area of each section of the largest rectangle.

10 3

20 20 x 10 = 200 20 x 3 = 60

2 2 x 10 = 20 2x3=6

Step 6: Add the partial areas to find the area of the whole rectangle.

200 + 60 + 20 + 6 = 286

6.
Multiplication Algorithm and Partial Products (4.NBT.5)

123 x 4

1 2 3

X 4

1 2 3x4 1. Multiply the value of the digit in each place value by

the multiplier. Ex. 3 x 4, 20 x 4, 100 x 4

+ 8 0 20 x 4 2. Write the product from each place value (partial

products). Ex. 12, 80, 400

4 0 0 100 x 4 3. Add the partial products to find the product of the

given problem.

4 9 2

22 x 13

2 2

X 1 3

6 2x3 1. Multiply the value of the digits in each place value by

the value of each digit in the multiplier.

6 0 20 x 3

2. Write the product from each place value (partial

+ 2 0 2 x 10 products).

3. Add the partial products to find the product of the

2 0 0 20 x 10 given problem.

2 8 6

123 x 4

1 2 3

X 4

1 2 3x4 1. Multiply the value of the digit in each place value by

the multiplier. Ex. 3 x 4, 20 x 4, 100 x 4

+ 8 0 20 x 4 2. Write the product from each place value (partial

products). Ex. 12, 80, 400

4 0 0 100 x 4 3. Add the partial products to find the product of the

given problem.

4 9 2

22 x 13

2 2

X 1 3

6 2x3 1. Multiply the value of the digits in each place value by

the value of each digit in the multiplier.

6 0 20 x 3

2. Write the product from each place value (partial

+ 2 0 2 x 10 products).

3. Add the partial products to find the product of the

2 0 0 20 x 10 given problem.

2 8 6