Download INQUIRY: Distributive Property and Partial Products

Paramount Unified School District
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INQUIRY: Distributive Property and Partial Products
Grade 4 – Unit 4
Learning Outcome: Students will use area model, partial products and the distributive property to represent
multiplication of a 2-digit number by a 1-digit number. Through the discussion, students will see how partial
products and the distributive property represent the place value of the numbers that are multiplied in a
problem.
Standard: NBT.5
Skills: Multiply a number up to 4-digits by a 1-digit number using distributive property and partial products
Focus Question: What is the role of place value when using the distributive property and partial products to
multiply larger numbers? When multiplying multi-digit numbers, how do partial products and distributive property
relate to each other?
Time: 2 days
Investigation & Discussion (Day 1)
1)
Connect to Prior Knowledge: Yesterday we used an area model to solve this problem:
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?
Possible guiding questions to support students during the task

Prompt students to think about the steps they used to find the product—What did you do first?
Next? What operations did you use to find the answer?
2) Share: Select a student who uses the area model to solve and adds up the 30 + 18 = 48. The student
presents their solution. Ask the student, “How did you come up with your solution? What did you do first?
next? etc.?” As the student summarizes each step, the teacher records the step mathematically for all
students to see and rephrases each step.
Example
 Student shares. Teacher says, “So, first you multiplied the 3 rows by the ones, 6 ones in each row”
and teacher records (3 x 6) —teacher says, “you found the product of the ones.”
 Student shares. Teacher says, “Then, you multiplied the 3 rows by the tens, the 1 ten in each row”
and teacher records (3 x 10)—teacher says, “you found the product of the tens.”
 Student shares. Teacher says, “Then, you added these products together (3 x 6) + (3 x 10) = 48, which
is the total product.”
3) Ask the class, “What operations did _______ use to solve?” (multiplication and addition).
4) Instruct: This represents the distributive property of multiplication. We take a factor and we “distribute” it
by multiplying it by each place or the parts of a multi-digit number—first by the ones and then by the tens.
This gives us the product of the ones and the product of the tens and then we add the product of each part
to get our answer.
This idea of multiplying the parts using the distributive property is also referred to as partial products. First,
we find the product of the ones and then the product of the tens and we add these together to find the
total product. The distributive property is the process we use to find the partial products and when we add
these products, it gives us the final answer.
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INQUIRY: Distributive Property and Partial Products
Grade 4 – Unit 4
5) Task: Let’s take what we learned and see if we can apply it using the distributive property and partial
products to multiply. Look at Problem 1. Ask, “How can we use the distributive property to solve using
partial products?”
6) Task: Let’s take what we learned and see if we can apply it using the distributive property and partial
products to multiply. Look at Problem 2. Ask, “How can we use the distributive property to solve using
partial products?”
Checking for Understanding
Use distributive property/partial products to solve:
1) Show students an area model for 43 x 5. Ask them to enter the unknown numbers that make the
equation true.
43 x 5 = (5 x ___) + (5 x 3).
2) Show students an area model for 4 x 28. Ask them to enter the unknown numbers that make the
equation true.
4 x 28 = (4 x ___) + (4 x ___)
3) Without an area model, ask students to enter the unknown numbers that make the equation true and
solve.
32 x 3= (3 x ___) + (3 x ___) = ____
4) Without an area model, ask students to enter the unknown numbers that make the equation true and
solve.
2 x 43= (___ x ___) + (___ x ___) = ____
Guided Practice & Independent Practice options:
1) Additional problems—pg. 239-40 #1, #3, #5, #7, #14
2) Explain to a friend how you would multiply 18 x 3 using the distributive property.
--------------------------------------------------------------------------------------------------------------------------------------------------------Investigation & Discussion (Day 2)
1) Discuss: Ask, “The past few days we have been working with area model, distributive property and partial
products. Question for you---when we multiply, do we have to use an area model or is there a quicker way to
solve? ”
2) Model: Model how the area model represents the multiplication in a multiplication problem that is set up in
a traditional format. Show students the area model they worked on for the Ms. Jenkin’s problem. Remind
students how they multiplied using the distributive property and partial products.
10
6
3
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INQUIRY: Distributive Property and Partial Products
Grade 4 – Unit 4
Now show students the multiplication problem set up like the problem below and ask, “How can we use
distributive property and partial products to solve a multiplication problem that looks like this?”
16
x 3
First, refer to the area model to show how they multiply the ones (3 x 6=18) and then show this very same
process using the traditional multiplication format (3 x 6=18). Record the 18 under the line. Then, use the area
model to show how they multiply the tens (3 x 10=30) and then show this same process using the traditional
multiplication problem (3 x 10=30)—remind students that the 1 represents one ten. Record the 30 under the
18 and add the partial products of the ones and the tens to get the solution of 48.
16
x 3
18
+ 30
48
Students should see that the process they use to solve multiplication using the area model is the same process
they can use to solve a multiplication problem in a traditional format without the area model.
3) Task: Refer to the area model in Problem 1. Show the students the multiplication problem set up like this
and ask them to solve using distributive property and partial products:
26
x 2
Checking for Understanding
1) 17
x3
Use distributive property and partial products to solve:
2)
12
x4
3) 2 x 26
Guided Practice & Independent Practice options:
1)Additional problems—pg. 234 #2, #3, #4, #7
2)Explain how you can use partial products to multiply 3 x 15.
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INQUIRY: Distributive Property and Partial Products
Grade 4 – Unit 4
Problem 1
20
6
2
(__ x __) + (__ x __)
_____ + _____ =
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INQUIRY: Distributive Property and Partial Products
Grade 4 – Unit 4
Problem 2
30
7
3
(__ x __) + (__ x __)
_____ + _____ =
5