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4th grade foundations (Eureka Math/EngageNY)

Course: 4th grade foundations (Eureka Math/EngageNY)  > Unit 3

Lesson 2: Topic B & C: Foundations
Math
4th grade foundations (Eureka Math/EngageNY)
Module 3: Foundations
Topic B & C: Foundations
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Intro to commutative property of multiplication

Google Classroom
Practice changing the order of factors in a multiplication problem and see how it affects the product.

Comparing totals

This array shows start color #1fab54, 2, end color #1fab54 rows of dots with start color #7854ab, 4, end color #7854ab dots in each row. We can use the expression start color #1fab54, 2, end color #1fab54, times, start color #7854ab, 4, end color #7854ab, equals, start color #e07d10, 8, end color #e07d10 to represent the array.
This array shows start color #7854ab, 4, end color #7854ab rows of dots with start color #1fab54, 2, end color #1fab54 dots in each row. We can use the expression start color #7854ab, 4, end color #7854ab, times, start color #1fab54, 2, end color #1fab54, equals, start color #e07d10, 8, end color #e07d10 to represent the array.
In both examples we get a total of start color #e07d10, 8, end color #e07d10 dots.
start color #1fab54, 4, end color #1fab54, times, start color #7854ab, 2, end color #7854ab, equals, start color #e07d10, 8, end color #e07d10 and start color #7854ab, 2, end color #7854ab, times, start color #1fab54, 4, end color #1fab54, equals, start color #e07d10, 8, end color #e07d10
When we change the order of the numbers that we are multiplying the product stays the same.
start color #1fab54, 5, end color #1fab54, times, start color #7854ab, 4, end color #7854ab, equals, start color #e07d10, 20, end color #e07d10
start color #7854ab, 4, end color #7854ab, times, start color #1fab54, 5, end color #1fab54, equals, start color #e07d10, 20, end color #e07d10
start color #1fab54, 5, end color #1fab54, times, start color #7854ab, 4, end color #7854ab, equals, start color #7854ab, 4, end color #7854ab, times, start color #1fab54, 5, end color #1fab54
start color #1fab54, 7, end color #1fab54, times, start color #7854ab, 10, end color #7854ab, equals, start color #e07d10, 70, end color #e07d10
start color #7854ab, 10, end color #7854ab, times, start color #1fab54, 7, end color #1fab54, equals, start color #e07d10, 70, end color #e07d10
start color #1fab54, 7, end color #1fab54, times, start color #7854ab, 10, end color #7854ab, equals, start color #7854ab, 10, end color #7854ab, times, start color #1fab54, 7, end color #1fab54
Practice problem 1a
Match the expressions that are equal to each other.

Practice problem 1b
Which two expressions will give us the same answer?
Choose all answers that apply:

Commutative property

The math rule that says the order in which we multiply the factors does not change the product is the commutative property.
Let's use an array to help explain why this works. This array shows start color #e07d10, 5, end color #e07d10 rows with start color #11accd, 2, end color #11accd dots in each row.
We can find the total number of dots by multiplying the number of rows by the number of dots in each row.
start color #e07d10, 5, end color #e07d10, times, start color #11accd, 2, end color #11accd, equals, start color #1fab54, 10, end color #1fab54
If we turned the array on its side we have an array that shows start color #11accd, 2, end color #11accd rows with start color #e07d10, 5, end color #e07d10 dots in each row.
All we did was tip the array over. The total number of dots did not change.
If we multiply the number of rows by the number of dots in each row we get:
start color #11accd, 2, end color #11accd, times, start color #e07d10, 5, end color #e07d10, equals, start color #1fab54, 10, end color #1fab54
The order in which we multiply the numbers start color #11accd, 2, end color #11accd and start color #e07d10, 5, end color #e07d10 does not matter.
start color #e07d10, 5, end color #e07d10, times, start color #11accd, 2, end color #11accd, equals, start color #11accd, 2, end color #11accd, times, start color #e07d10, 5, end color #e07d10

Let's try a few problems

This array shows 8 rows with 4 dots in each row.
Problem 2, part A
What would the array look like if we tipped it on its side?
Choose 1 answer:

Problem 2, part B
8 rows with 4 dots equals 4 rows with
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
dots.

Problem 2, part C
8, times, 4, equals
Choose 1 answer:

Using the commutative property

Describing an array

The commutative property says that the order of the numbers doesn't matter in multiplication.
So the order of the numbers doesn't matter when describing an array.
We can use the expression 5, times, 3 to show 5 groups of 3.
Or the expression 3, times, 5 to show 3 groups of 5.
Both expressions equal 15.

Another problem

Practice problem 3
Which two expressions can be used to represent the array?
Choose all answers that apply:

Why is the commutative property helpful?

The commutative property can make multiplying more than two numbers easier.
Let's look at an example:
We can multiply 7, times, 2, times, 5 in two steps:
7, times, 2, equals, 14
14, times, 5, equals, 70
We got the right answer, but 14, times, 5 is a little tricky to multiply!
Remember that the commutative property lets us change the order of the numbers without changing the answer.
We can switch the 7 and 5 and change the problem to 5, times, 2, times, 7. Let's see how this makes it easier to multiply:
5, times, 2, equals, 10
10, times, 7, equals, 70
Multiplying by 10 in the second step made it easier to find the product.
Practice problem 4A
Which expressions are the same as 4, times, 3, times, 5?
Choose all answers that apply:

Practice problem 4B
Use the commutative property to rearrange the numbers and solve.
5, times, 3, times, 6, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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