Paramount Unified School District
Educational Services
INQUIRY: Arrays and Area Model
Grade 4 – Unit 4
Learning Outcome: Students will use unifix cubes, arrays and area model to represent multiplication of a 2-digit
number by a 1-digit number. Through the discussion, students will see how the cubes and arrays model place
value within multiplication.
Standard: NBT.5
Skills: Illustrate multiplication problems using place value, rectangular arrays and area models
Focus Questions: How do rectangular arrays and the area model represent multiplication of larger numbers? What is
the role of place value when using arrays and area model to multiply larger numbers?
Time: 2 days
Investigation & Discussion (Day 1)
Materials: Unifix cubes, grid paper
Math Task #1:
Ms. Jenkins wants to buy a rug for her classroom. She finds a rug that is 16 feet long and 3 feet wide.
What is the area of the rug?
1) Task: Students solve alone and then come to consensus.
2) Share: Select students to share solutions and strategies (e.g., repeated addition, multiplication, Commutative
Property, etc.).
3) Task: Ask students to represent the problem using cubes.
4) Discuss: Ask, “Now, how can you arrange the cubes into a rectangle?” Students share.
5) Instruct: Tell students to look at one of their rows and to count ten cubes, snapping them together. Students
proceed to make groups of ten in the remaining two rows.
6) Task: Using grid paper, students draw the model.
7) Discuss: Ask, “How many rows of tens are there? How many rows of ones are there?”
8) Instruct: Tell students to label their drawings with the factors—(3 on the side and the 16 decomposed into 10 and
the 6, representing the groups of ten and the ones).
9) Discuss: Ask, “How many tens are there altogether? How many ones are there altogether? What is the total of
ones and tens?”
10) Discuss: Ask, “How does this model relate to area? How does this area model represent multiplication?”
Math Task #2:
At the pet store, there are 4 female dogs. They each have 13 puppies. How many puppies are there?

Arrange the cubes in a rectangle.

Make groups of ten in each row.

Draw the array on grid paper.
1) Discuss: Ask, “How many rows of tens are there? How many rows of ones are there?”
2) Instruct: Tell students to label their drawings with the factors—(4 on the side and the 13 decomposed into 10 and
the 3, representing the groups of ten and the ones).
3) Discuss: Ask, “How many tens are there altogether? How many ones are there altogether? What is the total of
ones and tens?”
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INQUIRY: Arrays and Area Model
Grade 4 – Unit 4
4) Discuss: Say to students, “This is a lot of work to do to—work with cubes and then the array and then drawcouldn’t we just draw an area model without drawing all the cubes?”
5) Model: Model for students how you can replace the cubes with the product of the ones and the product of the
tens.
10
3
4
Remind students that this is an example of an area model of multiplication which shows that when you multiply
factors with more than one digit, you need to multiply each place, or digit—so in the case of 16, by the 6 ones
and by the 1 ten.
Checking for Understanding
Solve using area model:
1) 17 x 4
2) 5 x 13
3) 19 x 3
Guided Practice & Independent Practice options:
1) Additional problems—pg. 213 #4, #7, #9 (use area model to solve)
2) Explain how to draw an area model to represent 4 x 15.
3) Explain to a friend how you would multiply 18 x 3 using an area model.
---------------------------------------------------------------------------------------------------------------------------------------------------------------Investigation & Discussion (Day 2)
1) Connect to Prior Knowledge: Yesterday we used an area model to multiply problems. Ask students what they
recall about an area model.
2) Task: Show students Problem 1 Model A and ask, “What multiplication problem do you think this area model
represents?” (26 x 2 or 2 x 26).
Possible guiding questions to support students during the task:
 What can you recall about multiplying factors with 2-digits?
 How can you use what you we learned yesterday to help us think about this problem?
3) Task: Direct students to Problem 1 Model B. Ask students to solve the problem using the area model.
4) Task: Show students Problem 2 Model A and ask, “What multiplication problem do you think this area model
represents?” (37 x 3 or 3 x 37).
5) Task: Direct students to Problem 2 Model B. Ask students to solve the problem using the area model.
6) Discuss: Ask, “So, if a factor has more than 1 ten, can we still use an area model to solve?”
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INQUIRY: Arrays and Area Model
Grade 4 – Unit 4
7) Task: Now let’s practice solving a problem using area with larger numbers.
Barbara has 3 bags of candy. Inside each bag, she has 24 candies.
How many candies does she have? Solve using the area model.
Possible guiding questions for whole-class discussion:
 How is multiplying a factor with more than one ten similar to multiplying a factor with just one ten?
 What do you observe about the area when multiplying by a larger number?
Checking for Understanding
Solve using area model:
1) 27 x 4
2) 5 x 23
3) 32 x 4
Guided Practice & Independent Practice options:
1) Additional problems—pg. 213 #1, #2, #5, #8, #10 (use area model to solve)
2) Explain how to draw an area model to represent 2 x 25.
3) Explain to a friend how you would multiply 28 x 3 using area model.
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INQUIRY: Arrays and Area Model
Grade 4 – Unit 4
Problem 1 Model A
_____ x _____ = ?
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INQUIRY: Arrays and Area Model
Grade 4 – Unit 4
Problem 1 Model B
20
6
2
5
INQUIRY: Arrays and Area Model
Grade 4 – Unit 4
Problem 2 Model A
_____ x _____ = ?
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INQUIRY: Arrays and Area Model
Grade 4 – Unit 4
Problem 2 Model B
30
7
3
7
INQUIRY: Arrays and Area Model
Grade 4 – Unit 4
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