Transcript Applying the Distributive Property

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 Development
Problem 1
O How many threes?
O The dotted line shows a way to
7x3
break apart the array.
O The 7 threes are broken into
________ threes and ______ threes.
O Let’s draw a number bond.
Guided Instruction Concept Development
Problem 1
O Write the equation that shows how to add
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7x3
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).
5 threes
7 threes
2 threes
Guided Instruction Concept Development
Problem 1
O The number bond is another way to show
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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.
5x3
(___ x 3) + (__ x 3) = ____ x 3
____ + _____ = _____
Did you write……
(5 x 3) + (2 x 3) = 7 x 3
15 + 6 = 21
7x3
2x3
Guided Instruction Concept Development
Problem 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
7x3
5x3
2x3
Guided Instruction Concept Development
Problem 1
O 9x4
O Draw an array to show 9 x 4. Draw a line to
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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
O 5 x 4 = 20 and 4 x 4 = 16
O 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 Development
Problem 1
O Draw a second number bond using the
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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
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 Development
Problem 2
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 2
O 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 Development
Problem 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 threes
O Rewrite this as the addition of two products
using the equation.
Guided Instruction Concept Development
Problem 2
O (__ x 3) + ( __ x 3) = ___ x 3
____ + _____ = ______
O (6 x 3) + (4 x 3) = 10 x 3
18 + 12 = 30
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Guided Instruction Concept Development
Problem 2
O Repeat with 8 x 4
O 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 Development
Problem 2
O (__ x 4) + ( __ x 4) = ___ x 4
____ + _____ = ______
O Find someone who used a different
equation. Discuss the way you
worked the problem.
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