1. Multiply using the Distributive Property
Go Math!
Chapter 2
Lesson 2.5
Multiply using the Distributive Property
Materials needed:
- Lesson 2-5 homework sheet (teacher created)
Optional:
dry erase boards, markers, erasers for students to write answers to review questions
Lesson 2.5 classwork riddle sheets

2. Multiply by 1-Digit Numbers
Last week we started our new chapter all about multiplication.
Since you had a long weekend…

3. Let’s Review! …let’s start with a review.
The first question we answered in our unit was this… 3

4. How can multiplication be used as a comparison?
Can someone remind us?
We learned to write comparison sentences and equations.

5. 42 = 7 x 6 3 x 4 = 12 42 is 7 times as many as ___ 6
What would be the missing number in this comparison sentence? *
What equation would I write to match this sentence? *
What would be the missing number in * this comparison sentence? *
Now let’s go the opposite way…
3 times as many as ___ is 12 4
3 x 4 = 12

6. 63 = 7 x 9
63 is 7 times as many as 9
Can someone give me the comparison sentence to go with this equation? *
How about * this one? *
When it is two times as many, there is another special way I can say it. What is it? *
We also made wrote comparison sentences and equations to go with models…
2 x 9 = 18
2 times as many as 9 is 18
twice as many as 9 is 18

7. ___ times as many as ___ is ___24 4 4 4 4 4 4 4
___ times as many as ___ is ___ 6 4 24
Can you complete the * comparison sentence? *
What would the matching equation be? *
The next question we answered was…
6 x 4 = 24

8. How does a model help you solve a comparison problem?
Can someone remind us?
Let’s see if you remember how to solve one of those types of problems….

9. Julie has 3 times as many stickers as Ray
Julie has 3 times as many stickers as Ray. Together they have 20 stickers. How many stickers does Julie have?
Can someone read this problem?
What am I comparing? I need a row for *Julie and * Ray.
What should I put behind Ray? * Julie? *
What else do I need? *
What equation can I write for n? *
What would n equal? *
N is how much Ray has. I need to find Julie.
Can you give me an equation to find how many Julie has? *
Since n is 5, I need to find * 3 x 5.
What would that equal? *
How many stickers does Julie have? *
The next big question we answered was… n n n
Julie
4 x n = 20 20
n = 5 n
Ray
Julie = 3 x n
= 3 x 5
= 15
Julie has 15 stickers.

10. How can you use place value to multiply tens, hundreds, and thousands?
Can someone remind us?
We learned that you can use your basic facts to help you multiply by 10s, 100s, and 1,000s.
After solving the basic fact, you have to add the correct number of zeroes.
Let’s see what you remember….

11. 80 x 3 =
80 x 3 =
240
If I wanted to solve this problem, what basic fact should I solve? *
How many zeroes will I need to add to my answer?
What is the product? *
If I wanted to solve…

12. 6,000 x 5 =
6,000 x 5 =
30,000
…this problem, what basic fact should I solve? *
How many zeroes will I need to add to my answer?
What is the product? *
If I wanted to solve…

13. 9 x 800 =
9 x 800 =
7,200
…this problem, what basic fact should I solve? *
How many zeroes will I need to add to my answer?
What is the product? *
On Friday, we answered one last big question…

14. How can you estimate products?
Can someone remind us?
We learned two ways to estimate products.
One way was by rounding…

15. 50
x 9
= 450
52 x 9 =
Raise your hand when you can tell me what our rounded problem should be. *
Raise your hand when you know the estimated product. *
Would the exact answer be greater or less than my estimate? Why?

16. 9 x 3,000
= 27,000
9 x 2,565 =
Raise your hand when you can tell me what our rounded problem should be. *
Raise your hand when you know the estimated product. *
Would the exact answer be greater or less than my estimate? Why?

17. 500 x 7
= 3,500
486 x 7 =
Raise your hand when you can tell me what our rounded problem should be. *
Raise your hand when you know the estimated product. *
Would the exact answer be greater or less than my estimate? Why?
We also learned that we could estimate products by finding two numbers that the product can be between…

18. 60
x 7
= 420
63 x 7 =
I have to think what two tens 63 is between. What two tens is it between?
So I can solve * 60 x 7. What would I get? *
I can solve * 70 x 7. What would I get? *
I know the exact answer must be between 420 and 490.
Which one would the exact answer be closer to?
How do you know? 70
x 7
= 490

19. 4 x 7,000
= 28,000
4 x 7,237 =
4 x 8,000
I have to think what two thousands 7,237 is between. What two thousands is it between?
So I can solve * 4 x 7,000. What would I get? *
I can solve * 4 x 8,000. What would I get? *
I know the exact answer must be between 28,000 and 32,000.
Which one would the exact answer be closer to?
How do you know?
Finally, on Friday, we answered this big question…
= 32,000

20. How can you use estimation to check if an answer is reasonable?
Can someone remind us?
Let’s check out one of those problems…

21. John has a baseball card collection
John has a baseball card collection. He keeps his cards in a special album. He can fit 9 cards on each page, and he has filled 33 pages. John says he has 396 cards. Is this answer reasonable?
9 x 30
= 270
9 x 33 =
Can someone read it?
To find an exact answer, John would have to solve * 9 x 33.
Let’s think…what two tens is 33 between?
I can solve * 9 x 30. What would that be? *
I can also solve * 9 x 40. What would that be? *
Is John’s answer reasonable?
Let’s check out our new problem for today…
9 x 40
= 360

22. Ian has his books on 3 shelves. Sixteen books can fit on each shelf
Ian has his books on 3 shelves. Sixteen books can fit on each shelf. How many total books can Ian fit on his shelves?
Would someone like to read it for us?
What problem would I need to solve to find out how many books Ian has? *
I don’t see the word “about” so I am not estimating. This time I need an exact answer.
So our new big question for today is…
3 x 16

23. How can you multiply a 2-digit number by a 1-digit number?
Can someone read it?
This week, I am going to teach you three different methods that you can use to find the product of two numbers.
Several of the methods use another important property of multiplication.
We have been talking a lot about the commutative property.
Today, we’ll use another property called the distributive property.
Let’s look at our problem to figure out how many books Ian can fit on his bookshelves…

24. 3 x 16 = 16
We know that Ian has 3 bookshelves, and each one can hold 16 books, so I need to solve 3 x 16.
I can model this problem on * grid paper. I know that the multiplication sign can say “rows of,” so to model 3 x 16, I would need * 3 rows of 16. I will label my * 3 here and my * 16 here.
3 x 16 is not an easy problem for me to solve in my head, so I am going to break apart my 16 to see if I can make some easier problems.
If I break 16 apart into tens and ones, I know that I can write 16 as * What do you call this form of a number? (expanded form)
I am going to draw a line to show that on my rectangle… 3
16 =

25. 3 x 16 = 48
Now I’ll re-label this top part. I have * 10 on this side, and * 6 on this side.
Can you give me a multiplication problem that will tell me how many squares I have in * this section? *
How many is that? *
I know how many squares are in the blue part and how many are in the green part, but I still don’t know how many that is altogether. What do I still need to do? * The 30 and 18 are called partial products. They are just part of the final product.
What would I get if I add ? (you can write it vertically for the kids) *
So the product of 3 x 16 is * 48.
I broke apart my 16 into the sum of , and then I used the... 10 16 6 3
(3 x 10)
(3 x 6) + 30 + 18 48

26. Distributive Property
Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
…distributive property of multiplication to solve the problem.
Here is * what the distributive property says.
Can someone read it?
Let’s see what that means with our problem…

27. 3 x 16 = 48 10 6
Since I broke my 16 into , I had to solve 3 x (10 + 6).
The distributive property says I just multiply the 3 times each addend – so 3 x 10 and 3 x 6 and just add the products together.
Let’s look at another problem and use the distributive property to solve it… 3
3 x (10 + 6)
(3 x 10)
(3 x 6) + 30 + 18 48

28. At the market, there were 4 baskets of apples left
At the market, there were 4 baskets of apples left. Each basket had 24 apples. How many total apples were in the baskets?
Would someone like to read this problem for us?
What problem would I need to solve to find out how many total apples were in the baskets? *
Let’s model our problem on grid paper…
4 x 24

29. 4 x 24 = 24 = 20 + 4 24 4 I would need * 4 rows of 24.
4 x 24 is not an easy problem for me to solve in my head, so I am going to break apart my 24 to make two easier problems.
If I break 24 apart into tens and ones, I know that I can write 24 as *
I am going to draw a line to show that on my rectangle… 4
24 =

30. 4 x 24 = 96 20 24 4
Now I’ll re-label this top part. I have * 20 on this side, and * 4 on this side.
Can you give me a multiplication problem that will tell me how many squares I have in * this section? *
How many is that? *
I know my partial products. What do I still need to do to find the final product of 4 x 24? *
What would I get if I add ? (you can write it vertically for the kids) *
So the product of 4 x 24 is * 96.
I broke apart my 24 into the sum of , and then I used the distributive property, which says that I can multiply 4 x 20 and 4 x 4 and then add the products together. 4
(4 x 20)
(4 x 4) + 80 + 16 96

31. Patrick has a stamp collection
Patrick has a stamp collection. He has stamps from 5 different countries. If he has 32 stamps from each country, how many total stamps does he have?
Here is another problem. Would someone like to read it for us?
What problem would I need to solve to find out how many total stamps he has? *
Hmm…32 is a pretty big number. I would need a lot of squares on my grid paper to make my rectangle this exact size. I am not sure I can fit that on my screen.
Instead of using an array, I can use a model to help me break apart my factor and use the distributive property.
To solve…
5 x 32

32. 5 x 32 =
160 30 + 2
150
+ 10
…5 x 32, instead of drawing the exact size rectangle on grid paper, I can just draw a * rectangle.
On the side, I can put my *single digit factor.
On the top, I can break apart my other factor into tens and ones. How could I break my 32 apart? *
I need to make a * line to separate my rectangle into two parts.
Now I can use the distributive property. I can multiply * 5 x 30 first. What would I get? *
I can multiply * 5 x 2 next. What would I get? *
These are my partial products. What do I still need to do? *
What would be my final product? *
So, the product of 5 x 32 is * 160.
Patrick has 160 total stamps.
This model that we used is called an * area model.
Let’s use an area model to solve another problem…
5 x 30 =
5 x 2 = 5
150 10
160
area model

33. 8 x 53 =
424 50 + 3
400
+ 24
8 x 50 =
8 x 3 =
I want to solve 8 x 53.
First I need to draw a * rectangle.
On the side, I can put my * single digit factor.
On the top, I can break apart my other factor into tens and ones. How could I break my 53 apart? *
I need to draw a * line to separate my rectangle into two parts.
Now I can use the distributive property. I can multiply * 8 x 50 first. What would I get? *
I can multiply * 8 x 3 next. What would I get? *
These are my partial products. What do I still need to do? *
What would be my final product? *
So, the product of 8 x 53 is * 424.
Let’s do another one… 8
400 24
424

34. 3 x 64 =
192 60 + 4
180
+ 12
I want to solve 3 x 64.
First I need to draw a * rectangle.
What should I write on the side? *
What should I write on the top? *
What else do I need in my rectangle? *
What problem should I write in the first box? *
What does that equal? *
What problem should I write in the second box? *
These are my partial products. What do I still need to do? *
What would be my final product? *
So, the product of 3 x 64 is * 424.
Tonight for homework, you are going to practice this method of multiplication.
Let’s take a look at your homework sheet…
3 x 60 =
3 x 4 = 3
180 12
192

35. I did not learn this method of multiplication when I was in school, and neither did your parents. That means they won’t be able to help you..
Let’s do two examples that you can use if you get stuck. Perhaps you can even teach your parents how to do this method!
(do top 2 problems on board while kids do on their paper)
If time permits, have students work on the classwork riddle.