Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using
strategies based on place value and the properties of operations.

Illustrate and explain the product of two factors using equations, rectangular arrays, and area models.

Arkansas Academic Standards:
4.NBT.B.5

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations

Illustrate and explain the calculation by using equations, rectangular arrays, and area models

Note: Properties of operations need to be referenced.

Common Core State Standards:
Math.4.NBT.5 or 4.NBT.B.5

Georgia Standards of Excellence (GSE):
MGSE4.NBT.5

Multiply a whole number of up to four digits by a one-digit whole
number, and multiply two two-digit numbers, using strategies based
on place value and the properties of operations. Illustrate and explain
the calculation by using equations, rectangular arrays, and/or area
models.

North Carolina - Standard Course of Study:
4.NBT.5

Multiply a whole number of up to three digits by a one-digit whole number, and multiply up to two two-digit numbers with place value understanding using area models, partial products, and the properties of operations. Use models to make connections and develop the algorithm.

New York State Next Generation Learning Standards:
4.NBT.5

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Note on and/or: Students should be taught to use equations, rectangular arrays, and area models; however, when illustrating and explaining any calculation, students can choose any strategy.

Tennessee Academic Standards:
4.NBT.B.5

Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Wisconsin Academic Standards:
4.NBT.B.5

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Illustrate and
explain the calculation by using equations, rectangular arrays, or area models.

Pennsylvania Core Standards:
CC.2.1.4.B.2

Use place-value understanding and properties of operations to perform multi-digit arithmetic

Pennsylvania Core Standards:
M04.A-T.2.1.2

Multiply a whole number of up to four digits by a one-digit whole number and multiply 2 two-digit numbers

4th Grade Math - Multiplication Lesson

One way to multiply a one-digit number by a number with more than one digit is by using partial products.

Example:

Step 1: Write the second number under the first number so that the corresponding places are lined up.

443

×

8

Step 2: Expand the top number by place value.

443

400 + 40 + 3

×

8

Step 3: Multiply the bottom number by each number in the expansion.

443

400 + 40 + 3

×

8

3,200

8 × 400

320

8 × 40

24

8 × 3

Step 4: Add the products.

443

×

8

3,200

320

+

24

3,544

So, 443 × 8 = 3,544.

An area model can also be used to multiply using partial products.

Example:

Step 1: Set up the area model using place value.

400

40

3

8

Step 2: Multiply 8 by each number in the top row.

400

40

3

8

3,200

320

24

Step 3: Add the products.

3,200 + 320 + 24 = 3,544

So, 443 × 8 = 3,544.

One way to multiply two numbers that each have more than one digit is by using partial products.

Example:

Step 1: Write the second number under the first number so that the corresponding places are lined up.

26

×

95

Step 2: Expand both numbers by place value.

26

20 + 6

×

95

90 + 5

Step 3: Multiply each number on the bottom by each number on the top.

26

20 + 6

×

95

90 + 5

1,800

90 × 20

540

90 × 6

100

5 × 20

30

5 × 6

Step 4: Add the products.

26

×

95

1,800

540

100

+

30

2,470

So, 26 × 95 = 2,470.

An area model can also be used to multiply using partial products.

Example:

Step 1: Set up the area model using place value.

20

6

90

5

Step 2: Multiply each number on the left by each number in the top row.

20

6

90

1,800

540

5

100

30

Step 3: Add the products.

1,800 + 540 + 100 + 30 = 2,470

So, 26 × 95 = 2,470.

To multiply a multi-digit number by a one-digit number, multiply each digit in the multi-digit number by the one-digit number.

Example:

Step 1: Write the second number under the first number so that the corresponding places are lined up.

Step 2: Multiply the bottom number by the ones digit in the top number (9 × 8 = 72). Since 72 has two digits, both digits won't fit in the ones place. So, write the 2 in the ones place of the product, and carry the 7 to the tens column.

Step 3: Multiply the bottom number by the tens digit in the top number (9 × 8 = 72). Then, add the 7 that was carried to the tens column in the previous step (72 + 7 = 79).
Since 79 has two digits, both digits won't fit in the tens place. So, write the 9 in the tens place of the product, and carry the 7 to the hundreds column.

Step 4: Multiply the bottom number by the hundreds digit in the top number (9 × 1 = 9). Then, add the 7 that was carried to the hundreds column in the previous step (9 + 7 = 16). Write the 6 in the hundreds place and the 1 in the thousands place of the sum.

To multiply a two-digit number by a two-digit number, multiply each digit in one of the numbers by each digit in the other number.

Example:

Step 1: Write the second number under the first number so that the corresponding places are lined up.

Step 2: Multiply the ones digit in the bottom number by the ones digit in the top number (9 × 8 = 72). Since 72 has two digits, both digits won't fit in the ones place. So, write the 9 in the ones place, and carry the 7 to the tens column.

Step 3: Multiply the ones digit in the bottom number by the tens digit in the top number (9 × 8 = 72). Then, add the 7 that was carried to the tens column in the previous step (72 + 7 = 79). Write the 9 in the tens place and the 7 in the hundreds place.

Step 4: Start a new line, and add a placeholder zero to the ones column. Then, multiply the tens digit in the bottom number by the ones digit in the top number (3 × 8 = 24). Since 24 has two digits, both digits won't fit in the tens place. So, write the 4 in the tens place, and carry the 2 to the tens column.

Step 5: Multiply the tens digit in the bottom number by the tens digit in the top number (3 × 8 = 24). Then, add the 2 that was carried to the hundreds column (24 + 2 = 26). Write the 6 in the hundreds place and the 2 in the thousands place.

Step 6: Add to find the product (792 + 2,640 = 3,432).