Applying the Distributive Property Lesson 1.18

Application Problem A parking structure has 10 levels. There are 3 cards parked on each level. How many cars are parked in the structure? Solution

Guided Instruction Concept Development Problem 1 How many threes? The dotted line shows a way to break apart the array. The 7 threes are broken into ________ threes and ______ threes. Let’s draw a number bond. 7 x 3

Guided Instruction Concept Development Problem 1 7 x 3 Write the equation that shows how to add the two parts. 5 threes + 2 threes = 7 threes Tell you partner the 2 multiplication sentences you used to help you solve 7 x 3. 5 x 3 = 15 and 2 x 3 = 6 Draw a second number bond using the expressions (5 x 3) and (2 x 3). 7 threes 5 threes 2 threes

Guided Instruction Concept Development Problem 1 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. Let’s write this as the addition of two products using the equation. (___ x 3) + (__ x 3) = ____ x 3 ____ + _____ = _____ Did you write…… (5 x 3) + (2 x 3) = 7 x 3 15 + 6 = 21 7 x 3 5 x 3 2 x 3

Guided Instruction Concept Development Problem 1 How does the number sentence show the number bond? It shows the 7 broken into 5 and 2. The threes are shared with both parts. 5 threes and 2 threes 7 x 3 5 x 3 2 x 3

Guided Instruction Concept Development Problem 1 9 x 4 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. What are the 2 parts of the array? 5 fours + 4 fours = 9 fours Let’s draw our number bonds. Tell your partner the two multiplication sentences you used to solve 9 x 4.

Guided Instruction Concept Development Problem 1 5 x 4 = 20 and 4 x 4 = 16 Write the equation that shows how to add the two parts. Whisper to a partner the 2 multiplication sentences you used to help you solve 9 x 4.

Guided Instruction Concept Development Problem 1 Draw a second number bond using the expressions (5 x 4) and (4 x 4). Let’s write this as the addition of two products using the equation. (___ x 4) + (__ x 4) = ____ x 4 ____ + _____ = _____ Did you write…… (5 x 4) + (4 x 4) = 36 20 + 16 = 16

Guided Instruction Concept Development Problem 1 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 Development Problem 2 10 x 3 How many threes? What are some ways we can break apart 10? 5 and 5, 6 and 4, 7 and 3, 8 and 2 If we were counting apples that would be 5 apples and 5 apples or 6 apples and 4 apples. But, we aren’t counting apples. What are we counting? Threes

Guided Instruction Concept Development Problem 2 So that would be 6 threes and ____ threes. Let’s draw our number bonds. Write the equation that shows how to add the two parts. Start with 6 threes and 4 threes. 6 threes + 4 threes = 10 threes Rewrite this as the addition of two products using the equation.

Guided Instruction Concept Development Problem 2 (__ x 3) + ( __ x 3) = ___ x 3 ____ + _____ = ______ (6 x 3) + (4 x 3) = 10 x 3 18 + 12 = 30

Guided Instruction Concept Development Problem 2 Repeat with 8 x 4 How many fours? What are some ways we can break apart 8? This time, you decide how you want to break apart the 8. Draw a number bond showing the 2 parts of fours. Write the equation that shows how to add the two parts. Start with ___ fours and ____ fours. Rewrite this as the addition of two products using the equation.

Guided Instruction Concept Development Problem 2 (__ x 4) + ( __ x 4) = ___ x 4 ____ + _____ = ______ Find someone who used a different equation. Discuss the way you worked the problem.