1. 4th Grade Math Mini-Lesson 10
Multiplication
MA.A.3.2.3

2. MA.A.3.2.3
The student adds, subtracts, and multiplies whole numbers, decimals, and fractions, including mixed numbers, and divides whole numbers to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

3. Part 1
Explicit Instruction

4. Explicit Instruction (about 15 minutes)
For this Mini-Lesson, we are going to review multiplication.

5. Explicit Instruction (about 15 minutes)
Multiplication is a shortcut
for adding same-size groups!
That is correct!
You just won
ONE MILLION dollars!
“…And now, for the ONE MILLION DOLLAR question…”
What is
multiplication?

6. Explicit Instruction (about 15 minutes)
Multiplication is a shortcut for adding same-size groups. Imagine that today you are going to recycle all of the cans you have been collecting. There are 869 cans waiting to be turned in for 5 cents each. You certainly don’t want to add 5 cents 869 times, so you will be really glad you know how to multiply!

7. Explicit Instruction (about 15 minutes)
Two terms that you may hear used in multiplication are factor and product.
7 X 8 = 56
factor factor
product

8. Explicit Instruction (about 15 minutes)
If you know how to multiply 1-digit numbers, such as 6 x 7, you can also multiply larger numbers, such as 6 x 77.
One way to multiply larger numbers is by finding partial products.
Let’s check out
partial products!

9. Explicit Instruction (about 15 minutes)
You can multiply without listing every partial product. Let’s solve 15 x 9 without listing every partial product. 15
x 9
So, 15 x 9 = 13 tens
and 5 ones, or 135. 4
9 x 10 = 90,
but we can’t
forget about the
4 tens.
= 130
45 is
4 tens and
5 ones.
We are not
listing every
partial product, so
130 equals 13 tens.
Let’s multiply
by the ones.
9 x 5 = 45
Let’s multiply
by the tens.
9 x 10 = 90 13 5

10. Explicit Instruction (about 15 minutes)
We have our partial
products, 45 and 90.
Let’s add our
partial products.
So, 15 x 9 = 135!
Explicit Instruction (about 15 minutes)
Let’s solve 15 x 9 using partial products. 15
x 9 45
15 is 1 ten
and 5 ones.
15 is 1 ten
and 5 ones.
9 x 1 ten = 90
Now, multiply
the tens.
9 x 5 ones = 45
First, let’s
multiply the ones.
+___
135 90

11. Explicit Instruction (about 15 minutes)
Another way to multiply larger numbers is to think of an area model.
The area model for multiplication is a pictorial way of representing multiplication.
In the area model, the length and width of a rectangle represent factors, and the area of the rectangle represents their product.
I remember area
from 3rd grade!
Area is the number of
square units needed
to cover a figure.
That’s right!
You have a great memory!

12. Explicit Instruction (about 15 minutes)
Let’s look at an example of an area model for 7 x 8 = 56. 8
(factor)
7 x 8 means
7 groups of 8,
or 7 rows of 8.
In this area model, we
have 7 rows with
8 squares in each row. 56
(product) 7
(factor)

13. Explicit Instruction (about 15 minutes)
We broke our original
area model into two
rectangles.
Now, we have
factors for each rectangle.
All we have to do is
find the products
and add them up!
= 135
15 x 9 = 135 9
Let’s solve 15 x 9 using an area model.
5 x 9 = 45
10 x 9 = 90 10
Let’s decompose 15 into
10 and 5.
Both of these numbers are
easy to work with.
15 and 9 are factors.
Let’s label our area model. 90 15 45 5

14. Explicit Instruction (about 15 minutes)
Let’s see other ways to think about 15 x 9.
I think about 15 x 10, which is easy
because working with multiples of 10
is like skip counting by 10.
So, 15 groups of 10 is 150.
since I only had to multiply 15 x 9,
150 is one group of 15 too much.
150 – 15 = 135.
I think about breaking
up 15 into 10 and 5.
I know 10 x 9 equals 90.
5 is half of 10, so 5 x 9 is half of 90,
or 45.
= 135

15. Explicit Instruction (about 15 minutes)
Before we move on, I have a
question about the area model
for multiplication. I really like it, but
what happens when you have a 2 digit
number multiplied by a 2 digit
number? For example, if we wanted
to use the area model for
24 x 32, would we have to draw this…

16. Explicit Instruction (about 15 minutes)
GREAT QUESTION!
No, we don’t have to draw
that to multiply 2 digit
numbers. Let’s look at
an open array!
PHEW! That would
take a long time to
draw!

17. Explicit Instruction (about 15 minutes)
We can take the idea of an area model and apply it to double digit multiplication. We can use rectangles to represent our factors. Let’s look at 24 x 32 on an open array model.

18. Explicit Instruction (about 15 minutes)
There are now four small arrays that have two factors. Let’s start multiplying!
Now let’s decompose our factors into easy numbers to work with.
24 =
32 =
We can now break our large rectangle into smaller arrays. This will help us find products.
We have products for all four arrays!
Let’s add them up!
= 768
First, let’s draw a rectangle and label our factors.
24 x 32 means 24 groups of 32, or 24 rows of 32.
24 x 32 = 768
24 x 32 32 30 2
20 x 30 = 600
20 x 2 = 40 20 24
4 x 30 = 120 4
4 x 2 = 8

19. Explicit Instruction (about 15 minutes)
Let’s multiply by the tens.
30 x 24.
30 x 4 = 120
30 x 20 = 600
hundred = 700
So, 30 x 24 = 720
24 x 34 = 816
Let’s add!
= 816
Let’s start by multiplying by the ones.
4 x 24.
4 x 4 = 16
4 x 20 = 80
ten = 90
So, 4 x 24 = 96 1
First, we will solve by not listing all of the partial products.
We can also use partial products to answer 2 digit multiplication problems. Let’s look at 24 x 34. 1 24
x 34 9 6
+ ____
816 7 20

20. Explicit Instruction (about 15 minutes)
We can now add our partial products!
= 816
Now, let’s multiply by the tens.
30 x 20 = 600
Let’s start by multiplying by the ones.
4 x 20 = 80
Let’s start by multiplying by the ones.
4 x 4 = 16
We can also use partial products to answer 2 digit multiplication problems. Let’s look at 24 x 34.
Now, we will solve by listing all of the partial products, and adding them up to get the product.
Now, let’s multiply by the tens.
30 x 4 = 120 24
x 34 16 80
120
+ ____
816
600

21. Part 2
Guided Practice

22. Guided Practice (5 – 7 minutes)
Let’s review: Multiplication is a shortcut for adding same-size groups. We can solve problems using partial products and area models.

23. Guided Practice (5 – 7 minutes)
Let’s look at some word problems that can be solved using multiplication.

24. Guided Practice (5 – 7 minutes)
Wanda has 6 pages of math problems to do for homework. There are 28 problems on each page. How many math problems does Wanda have to do?
I am going to use partial products, and I am going to list my partial products that I need to add up.
I’m a gentleman, so ladies first!
I’m glad I know multiplication! Imagine adding 28 six times? Even worse, 6 twenty-eight times! I bet I would make a lot of mistakes that way.
I am going to use partial products, but I am not going to list every partial product.

25. Guided Practice (5 – 7 minutes)
Wanda has 6 pages of math problems to do for homework. There are 28 problems on each page. How many math problems does Wanda have to do?
First, I am going to multiply
6 x 8 ones.
6 x 8 = 48
Then, I am going to multiply
6 x 2 tens.
6 x 20 = 120
= 168
Wanda has 168 math problems to do.
Since I have my partial products, all I have to do now is add them up!
I am going to use partial products, and I am going to list my partial products that I need to add up. 28
x 6 48
+ ____
168
120

26. Guided Practice (5 – 7 minutes)
Now I am going to multiply 6 x 2 tens.
6 x 20 = 120
I can’t forget about the 4 tens from 48.
= 160
160 = 16 tens
Wanda has 168 math problems to do.
Wanda has 6 pages of math problems to do for homework. There are 28 problems on each page. How many math problems does Wanda have to do?
First I am going to multiply
6 x 8.
6 x 8 = 48, and 48 is 4 tens and 8 ones.
I am going to use partial products, but I am not going to list every partial product. 4
Cool!
We got the same answer! 28
x 6 16 8

27. Guided Practice (5 – 7 minutes)
Wanda has 6 pages of math problems to do for homework. There are 28 problems on each page. How many math problems does Wanda have to do?
Wanda has 168 math problems to do.
Almost done!
= 168
Let’s use our factors to find products!
Now we can divide our large rectangle into smaller arrays.
We can decompose 28 into friendlier numbers, like
20 and 8.
First, we’ll draw a rectangle and label the factors.
Let’s try the area model for this problem! 28 20 8
6 x 20 = 120 6
6 x 8 = 48

28. Guided Practice (5 – 7 minutes)
Isn’t that great! You all had a different way of multiplying 28 x 6, but you all got the same answer!
I thought of one more way to solve 6 x 28!
I thought about 6 x 30, which is Then, I realized I was two groups of 6 over, so I subtracted 12.
180 – 12 = 168

29. Guided Practice (5 – 7 minutes)
One level of a parking garage holds 75 cars. There are 16 levels in the parking garage. How many cars can the parking garage hold?
I went first last time, so you can go first this time.
I am going to use partial products, and I am going to list my partial products that I need to add up.
Imagine adding 75
sixteen times?
I am going to use partial products, but I am not going to list every partial product.

30. Guided Practice (5 – 7 minutes)
Let’s add!
= 1200
Let’s multiply by the tens.
10 x 75.
10 x 5 = 50
10 x 70 = 700
So, 10 x 75 = 750
The parking garage holds 1200 cars.
75 x 16 = 1200
Guided Practice (5 – 7 minutes)
Let’s start by multiplying by the ones.
6 x 75.
6 x 5 = 30
6 x 70 = 420
tens = 450
So, 4 x 24 = 450
One level of a parking garage holds 75 cars. There are 16 levels in the parking garage. How many cars can the parking garage hold?
I am going to use partial products, but I am not going to list every partial product. 3 75
x 16 45
+ ____
1200 7 50

31. Guided Practice (5 – 7 minutes)
The parking garage holds 1200 cars.
One level of a parking garage holds 75 cars. There are 16 levels in the parking garage. How many cars can the parking garage hold?
Let’s start by multiplying by the ones.
6 x 5 = 30
Let’s start by multiplying by the ones.
6 x 70 = 420
Now, let’s multiply by the tens.
10 x 70 = 700
We can now add our partial products.
= 1200
Now, let’s multiply by the tens.
10 x 5 = 50
I am going to use partial products, and I am going to list my partial products that I need to add up. 75
x 16 30
420 50
+ ____
1200
700

32. Guided Practice (5 – 7 minutes)
The parking garage holds 1200 cars.
Guided Practice (5 – 7 minutes)
One level of a parking garage holds 75 cars. There are 16 levels in the parking garage. How many cars can the parking garage hold?
We are ready to multiply!
Let’s add up all our areas!
= 1200
We can decompose our factors.
75 is 70 and 5.
16 is 10 and 6.
Let’s divide up our rectangle into 4 smaller arrays.
I have been waiting to try another area model with double digit numbers!
First, let’s draw our rectangle and label our factors. 75 70 5 10
10 x 70 = 700
10 x 5 = 50 16 6
6 x 70 = 420
6 x 5 = 30

33. Part 3
Independent Practice

34. Independent Practice (5 - 7 minutes)
Mrs. Robinson planted 17 rows of palmetto palm trees. There are 9 trees in each row. How many trees did Mrs. Robinson plant?
A. 963
B. 153
C. 93
D. 26
Adam bought 45 packs of gum. Each pack has 6 pieces of gum. How many pieces of gum did Adam buy?
A. 51
B. 240
C. 270 D

35. Independent Practice (5 - 7 minutes)
4. Mr. Sinnott has taught fourth grade for 24 years. Each year, he has had 27 students in his class. How many fourth graders has Mr. Sinnott taught? A. 51 B. 216 C. 628 D. 648
Tim has 19 boxes of baseball cards. There are 81 cards in each box. How many baseball cards does Tim have in all?
A. 1,719
B. 1,629
C. 1,539
D. 1,459

36. Independent Practice (5 - 7 minutes)
5. The fourth grade classes are having a food drive. There are 84 students in the fourth grade. The goal is for each student to collect 16 cans of food. How many cans will be collected in all if each fourth grader achieves the goal? A. 1,464 B. 1,344 C. 100 D. 48

37. Independent Practice (5 - 7 minutes)
The answers to the Independent Practice questions appear on the next 3 slides.

38. Independent Practice (5 - 7 minutes)
Mrs. Robinson planted 17 rows of palmetto palm trees. There are 9 trees in each row. How many trees did Mrs. Robinson plant?
A. 963
B. 153
C. 93
D. 26
Adam bought 45 packs of gum. Each pack has 6 pieces of gum. How many pieces of gum did Adam buy?
A. 51
B. 240
C. 270 D

39. Independent Practice (5 - 7 minutes)
4. Mr. Sinnott has taught fourth grade for 24 years. Each year, he has had 27 students in his class. How many fourth graders has Mr. Sinnott taught? A. 51 B. 216 C. 628 D. 648
Tim has 19 boxes of baseball cards. There are 81 cards in each box. How many baseball cards does Tim have in all?
A. 1,719
B. 1,629
C. 1,539
D. 1,459

40. Independent Practice (5 - 7 minutes)
5. The fourth grade classes are having a food drive. There are 84 students in the fourth grade. The goal is for each student to collect 16 cans of food. How many cans will be collected in all if each fourth grader achieves the goal? A. 1,464 B. 1,344 C. 100 D. 48

41. Mini-Assessment Form A
Part 4
Mini-Assessment Form A

42. Mini-Assessment Form A (5 - 7 minutes)
Test ID #9114

43. Mini-Assessment Form A (5 - 7 minutes)
At a school concert, the student singers stand in 4 rows. There are 16 students in each row. What is the total number of students in the 4 rows?
A.  64       
B.  54
C.  44
D.  20

44. Mini-Assessment Form A (5 - 7 minutes)
On Monday, 3 school buses take students to Miller School. Each bus carries 34 students. How many students take the bus to Miller School on Monday?
A.  92       
B.  97       
C.  102       
D.  112

45. Mini-Assessment Form A (5 - 7 minutes)
3. A cornfield contains 46 rows of corn. There are 32 corn stalks in each row. How many total corn stalks are there in the cornfield?
A.  1,362       
B.  1,372
C.  1,462  
D.  1,472

46. Mini-Assessment Form A (5 - 7 minutes)
Each student in Mrs. Kirk’s class sold 18 magazine subscriptions. There are 22 students in the class.  How many subscriptions did the class sell in all?
A.  386      
B.  396     
C.  406     
D.  416

47. Mini-Assessment Form A (5 - 7 minutes)
For 31 days, Willa collected bottles to recycle.  She collected 36 bottles each day.  How many total bottles did Willa collect?
A.  1,016       
B.  1,116       
C.  1,216       
D.  1,316

48. Mini-Assessment Form A (5 - 7 minutes)
The answers to the Mini-Assessment appear on the following slide.

49. Mini-Assessment Form A (5 - 7 minutes)C D B

50. Mini-Assessment Form A (5 - 7 minutes)
Provide reteaching to students who do not receive 60% or better on the Mini-Assessment.

51. Part 5
Reteach/ Enrich

52. Mini-Assessment Form B

53. Mini-Assessment Form B (5 - 7 minutes)
Test ID #9115

54. Mini-Assessment Form B (5 - 7 minutes)
A flower garden has 8 rows of rose bushes. There are 13 rose bushes in each row. How many rose bushes are there in all?
A.  114 rose bushes      
B.  104 rose bushes       
C.  94 rose bushes       
D.  21 rose bushes

55. Mini-Assessment Form B (5 - 7 minutes)
Ms. Keller’s students have a goal to collect a total of 48 cans of food each day during their food drive. The food drive lasts 8 days. If they meet their goal, what will be the total number of cans Ms. Keller’s students collect?
A.  324     
B.  334      
C.  366     
D.  384

56. Mini-Assessment Form B (5 - 7 minutes)
At a school concert, the student singers stand in 16 rows. There are 27 students in each row. What is the total number of students in the 16 rows?
A.  422       
B.  432       
C.  522       
D.  532

57. Mini-Assessment Form B (5 - 7 minutes)
4. There are 20 juice packs on a store shelf. Each juice pack contains 12 juice boxes.  What is the total number of juice boxes on the shelf?
A.  24       
B.  32      
C.  200       
D.  240       

58. Mini-Assessment Form B (5 - 7 minutes)
Each student in Mr. Pool’s class brought in 49 soup can labels. There are 18 students in the class. How many labels did the class collect in all?
A.  882       
B.  812       
C.  441       
D.  67

59. Mini-Assessment Form B (5 - 7 minutes)
The answers to the Mini-Assessment appear on the following slide.

60. Mini-Assessment Form B (5 - 7 minutes)D A