Applying the Distributive Property

Lesson 1.18

Application Problem O A parking structure has 10 levels. There

are 3 cards parked on each level. How many cars are parked in the structure?

O Solution

Guided Instruction Concept DevelopmentProblem 1O How many threes?O The dotted line shows a way to break apart the array. O The 7 threes are broken into ________ threes and ______ threes.O Let’s draw a number bond.

7 x 3

O Write the equation that shows how to add the two parts.

O 5 threes + 2 threes = 7 threesO Tell you partner the 2 multiplication

sentences you used to help you solve 7 x 3.

O 5 x 3 = 15 and 2 x 3 = 6O Draw a second number bond using

the expressions (5 x 3) and (2 x 3).

7 x 3

7 threes

5 threes 2 threes

Guided Instruction Concept DevelopmentProblem 1

O The number bond is another way to show decomposition. This shows how we partitioned the array and wrote the number bond using our number sentences.

O Let’s write this as the addition of two products using the equation.

O (___ x 3) + (__ x 3) = ____ x 3O ____ + _____ = _____O Did you write……O (5 x 3) + (2 x 3) = 7 x 3O 15 + 6 = 21

7 x 3

5 x 3 2 x 3

Guided Instruction Concept DevelopmentProblem 1

O How does the number sentence show the number bond?

O It shows the 7 broken into 5 and 2.O The threes are shared with both

parts.O 5 threes and 2 threes

7 x 3

5 x 3 2 x 3

Guided Instruction Concept DevelopmentProblem 1

O 9 x 4O Draw an array to show 9 x 4. Draw a

line to break apart the array. Remember that we know our fives so we will draw the dotted line after the 5th row.

O What are the 2 parts of the array?O 5 fours + 4 fours = 9 foursO Let’s draw our number bonds.O Tell your partner the two

multiplication sentences you used to solve 9 x 4.

Guided Instruction Concept DevelopmentProblem 1

O 5 x 4 = 20 and 4 x 4 = 16O Write the equation that shows how to

add the two parts.O Whisper to a partner the 2

multiplication sentences you used to help you solve 9 x 4.

Guided Instruction Concept DevelopmentProblem 1

O Draw a second number bond using the

expressions (5 x 4) and (4 x 4).O Let’s write this as the addition of two

products using the equation.O (___ x 4) + (__ x 4) = ____ x 4O ____ + _____ = _____O Did you write……O (5 x 4) + (4 x 4) = 36O 20 + 16 = 16

Guided Instruction Concept DevelopmentProblem 1

O Let’s call it the break apart and distribute strategy. The number bond helps us see that we can find the total by adding two smaller parts together.

Guided Instruction Concept DevelopmentProblem 1

O 10 x 3 O How many threes?O What are some ways we can break apart

10?O 5 and 5, 6 and 4, 7 and 3, 8 and 2O If we were counting apples that would be 5

apples and 5 apples or 6 apples and 4 apples.

O But, we aren’t counting apples. What are we counting?

O Threes

Guided Instruction Concept DevelopmentProblem 2

O So that would be 6 threes and ____ threes.

O Let’s draw our number bonds.O Write the equation that shows how to add the two parts. Start with 6 threes and 4 threes.O 6 threes + 4 threes = 10 threesO Rewrite this as the addition of two

products using the equation.

Guided Instruction Concept DevelopmentProblem 2

O(__ x 3) + ( __ x 3) = ___ x 3O ____ + _____ = ______O(6 x 3) + (4 x 3) = 10 x 3 18 + 12 = 30

Guided Instruction Concept DevelopmentProblem 2

O Repeat with 8 x 4O How many fours?O What are some ways we can break apart 8?O This time, you decide how you want to break

apart the 8.O Draw a number bond showing the 2 parts of

fours.O Write the equation that shows how to add the

two parts. Start with ___ fours and ____ fours.O Rewrite this as the addition of two products

using the equation.

Guided Instruction Concept DevelopmentProblem 2

O(__ x 4) + ( __ x 4) = ___ x 4O ____ + _____ = ______OFind someone who used a

different equation. Discuss the way you worked the problem.

Guided Instruction Concept DevelopmentProblem 2