M1 L7 Powerpoint

1. Multiplication and
the Meaning
of Commutativity
Module 1: Lesson 7
Demonstrate the commutativity of
multiplication and practice related facts by
skip-counting objects in array models.

2. Fluency Practice
Group Counting
(4 minutes)

3. Fluency Practice
Divide Equal Groups
(5 minutes)

4. Fluency Practice
Divide Equal Groups
(continued)
Now write a division
sentence for 8
divided into 4 equal
groups.

5. Fluency Practice: Multiply with Twos
(4 minutes)
• Put your Twos Array Template into your personal
white board and turn your board so that it’s vertical
(going up and down.)
• Use your blank paper to cover all but the first row of
dots. How many twos show?
• Say the multiplication sentence to represent the array
shown and solve it.
• Uncover another row and say the multiplication
sentence for the array shown.
• Continue this for 3 rows, 10 rows, 5 rows, 6 rows, 7
rows, 9 rows, and 8 rows.

6. Application Problem
( 5 minutes)
Anna picks 24 flowers. She makes equal bundles of
flowers and gives 1 bundle to each of her 7 friends.
She keeps a bundle for herself, too. How many
flowers does Anna put in each bundle?
Use the RDW process to show your solution,
Drawing a division array or a number bond.

7. Concept Development
(32 minutes)
Problem 1: Rotate arrays 90 degrees.
Turn your personal white board so it’s horizontal (wider
than it is tall.)
Draw a line down the middle to make 2 sides.
On the left side skip-count by two 4 times and write each
number. (2, 4, 6, 8)
On the right side skip-count by four 2 times and write the
numbers. (4, 8)
How are the count-bys related?

8. Concept Development
Under each count-by draw an array to match it.
2, 4, 6, 8
4 x 2 =
4, 8
2 x 4 =

9. Concept Development
(32 minutes)
What do you notice about the arrays?
Do they both have 4 groups of 2?
Do they both have 2 groups of 4?
Turn to a partner and discuss it.

10. Concept Development
• It’s the same array turned different ways!
• When rows are vertical, they have a special name.
We call them columns.
• When the arrays are rotated, the factors switch
places.
• Discuss with a partner how you know that
4 x 2 = 2 x 4.
• Depending on how we look at an array, columns or
rows can be the number of groups.
• Discuss with your partner how you know that’s true.

11. Concept Development
(32 minutes)
Problem 2: Interpreting rows and columns in rotated arrays.
Turn your board so it’s vertical. Draw an array that shows
8 equal groups of two.
How many rows of 2 did you draw?
How many columns of 8 did you draw?
Write a multiplication sentence to match the array.
Don’t solve it yet!

12. Concept Development
(32 minutes)
Rotate your board so that it’s horizontal.
How many rows of 8 do you have now?
How many columns of 2?
Write a multiplication sentence to match the array.
Don’t solve it yet!
Explain to your partner using the words columns and rows
why your multiplication sentence changed.
Will 8 x 2 and 2 x 8 have the same total?
How do you know?

13. Concept Development
• When we multiply, changing the order of the
factors doesn’t change the total. We say the
factors are commutative. That means they
can switch around.
• Tell your partner what commutative means.
• Draw arrays to show that 6 x 2 = 2 x 6 and
that 2 x 9 = 9 x 2.
• What we’ve explored today is called the
commutative property!

14. Problem Set (10 minutes)
Do your personal best to complete the Problem Set
in 10 minutes!
Debrief (10 minutes)
Turn to your partner and compare answers!
Let’s review your solutions for the problem set.

15. Exit Ticket
(3 minutes)
This is where you are going to show
us that you understand what we learned today!
We will learn if you are ready for the next lesson!

16. Homework
The homework sheet for
3.1 – Lesson 7
is due tomorrow!