1. Distributive Property
Lesson 1.10:

2. Application Problem
A guitar has 6 strings. How many strings are there on 3 guitars?
Write a multiplication sentence to solve.
Solution

3. Guided Instruction Concept Development:
Draw an array to represent the total number of guitar strings. Let the number of strings on 1 guitar be one row.
Make a dotted line below the first row to show just 1 guitar.
Write and solve a multiplication
to describe each part of your array.
1 x 6 = 6 and 2 x 6 = 12
= 3 sixes Why is this true?
(1 x 6) + (2 x 6) = 3 sixes. How do you know the 2 number sentences on the board are equal?

4. Guided Instruction Concept Development:
1 × 6 is the same as 6, and 2 × 6 is the same as 12. You just rewrote 6 and 12 as multiplication facts.
(1x 6) + (2 x 6) = 6 +____ With your partner discuss what number completes the equation.
(1x 6) + (2 x 6) =
Notice the symbols around my multiplication expressions. They are called parentheses. Let’s say that word together.

5. Guided Instruction Concept Development:
(1x 6) + (2 x 6) = _____
(1 + 2) x 6 = ____
My parentheses show how I make groups. How did I rearrange the groups?
We added the number of rows. Then we multiplied by 6.
Look back at the array you drew. Do the 1 and 2 represent the number of groups or the size of groups?
The 1 and 2 represent the number of groups.
What does the 6 represent?
The size of groups

6. Guided Instruction Concept Development:
Use that language—the number of groups and the size of groups—to tell your partner about my second equation.
We added the number of groups first. That’s Then she multiplied the number of groups times the size of the groups, which is 6.
1 + 2 equals?
3 × 6 = _____ under the second equation. Look back at the work you did on today’s application problem. How does this equation compare with what you did?
It’s the number of groups times the size of groups, just like we did.

7. Guided Instruction Concept Development:
Rewrite each equation on your board and solve them. What is the answer to all 3 equations?
18 what?
18 strings
(1 × 6) + (2 × 6) = 3 × 6 True or false?

8. Guided Instruction Concept Development:
In your own words, tell your partner how we got 3 × 6 and why it’s equal to (1 × 6) + (2 × 6). Use the 3 equations you just solved to help you explain.

9. Guided Practice Problem 1, page 50
7 x 3 = (5 x 3) + (2 x 3) = _____
(5 x 3) + (2 x 3) =
____ + ____ = _____
5 x 3 = _____
2 x 3 = _____

10. Guided Practice Problem 2, page 50
8 x 3 = (4 x 3) + (4 x 3) = m
(4 x 3) + (4 x 3) = m
_____ + _____ = ____
4 x 3 = _____
4 x 3 = _____

11. Guided Practice Problem 3a, page 50
Ruby is making a photo album. She puts 3 pictures in each row.
Use the multiplication sentences on the left to show the photos on the upper and lower parts of Ruby’s album page.
= ---
___x 3 = 6
___x 3 = 9

12. Guided Practice Problem 3b, page 50
Ruby calculates the total number of pictures as show below. Use the array you drew from the previous slide to help explain her calculation.
5 x 3 = = 15