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3rd Grade
Multiplication
2015-04-27
www.njctl.org
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Links to PARCC sample questions
Table of Contents
Relate addition to multiplication
Arrays
Multiply by 1 and 0
Multiply by 2
Multiply by 10
Multiply by 5
Multiplication Table Activity
Multiply by 3
Multiply by 4
Multiply by 6
Multiply by 7
Multiply by 8
Multiply by 9
Performance Based Assessment
click on the topic to go
to that section
Non-Calculator #1
Non-Calculator #8
Non-Calculator #9
Non-Calculator #14
End of Year
Non-Calculator #2
Non-Calculator #4
Non-Calculator #12
Non-Calculator #19
Non-Calculator #25
Square and Rectangles
Unit squares and tiling - Area of Squares
Area of rectangles
Area Word Problems
Non-Calculator #27
Non-Calculator #36
Non-Calculator #37
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There are 5 students. Each student is holding up both hands in
the air. How many hands are up in the air?
Relate Multiplication to Addition
click to return to
table of contents
What are all of the ways you could figure out this answer?
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The Greene brothers went for a bike ride. If all four went riding, how
many bicycle wheels would you see?
Teacher Notes
There are 5 students. Each student is holding up both hands in
the air. How many hands are up in the air?
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Teachers: choose 5
students
to stand
up.
What are all of the ways you could
figure out
this answer?
Have each student
raise both hands.
[This object is a pull tab]
What are all of the ways you could figure out this answer?
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Did you use addition? What would the number sentence look like?
Click
2+2+2+2=8
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Did you consider using multiplication?
How many bicycles were there?
This is called repeated addition. Why do you think it is called this?
How many wheels did each bicycle have?
What would the number sentence look like?
Click
4X2=8
Once you are able to memorize your multiplication facts, you will
realize that it is the quickest way to solve problems like the Greene
brothers' problem.
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Which number sentences match the picture of three flowers
with 7 petals each?
Repeated Addition
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There are five jars. In each jar, there are 3 insects.
Show all 5 jars with 3 insects in each jar in the space below.
How many insects are there all together?
Multiplication
7 + 7 + 7 + 7=
3 x 5=
6 x 3=
6+6+6=
3x7=
3+3+3=
7 + 7 + 7=
What is the repeated addition sentence?
What is the multiplication number sentence?
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How would you write 4 x 6 = in a repeated addition problem?
How would you write 2 x 8 = in a repeated addition problem?
What kind of picture could show these problems?
What kind of picture could show these problems?
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1
2 x 5 = 5 + 5?
True
False
Click to play Carl's Cookie Capers.
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2
What would the repeated addition number sentence
look like for the multiplication problem, 3 x 8 =?
A
8+8=
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3
What would the multiplication number sentence look
like for the repeated addition problem, 5 + 5 + 5 =?
A
10 + 5 =
B
3 + 3 + 3=
B
3 x 5=
C
8x3=
C
5x5=
D
8+8+8=
D
3x3=
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4
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What repeated addition number sentence would help
you figure out the number of petals in the picture
below?
5
What multiplication number sentence would help you
figure out the number of petals in the picture below?
A
2x7=
A
2x7=
B
7+7=
B
7+7=
C
7+7+7+ 7+7+7+7=
C
7+7+7+ 7+7+7+7=
D
10 + 4 =
D
10 + 4 =
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Arrays are rectangles made of organized rows and columns
of objects to represent a certain number.
An example, of the arrays for the number 6 are shown below.
Arrays
click to return to
table of contents
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Now you try! Drag and place 8 soccer balls in an array on the field.
How many different ways can you arrange the soccer balls so they
are arranged into organized rows and columns?
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When writing a multiplication number sentence for an array, write
the number of rows first. The second number should be the
number in each row, or the number of columns.
columns
columns
rows
rows
4x2
2x4
Click to reveal the multiplication number sentence for each array.
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Each array below is an example of 6. What would the
multiplication number sentence for each array be?
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Drag the stars into the rectangle to make an array showing 2 x 5.
How many stars will it take to complete the array?
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Circle the peanuts to show other ways to make arrays showing 10.
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6
Are the cats arranged in an array?
Yes
No
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7
This is an array for what number?
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8
Which array is a model for 3 x 2?
A
the mice
B
the frogs
C
the flowers
D
none of the above
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9
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The multiplication number sentence for this array of
shoes is 2 x 3.
True
False
What array is circled?
10
A
2x6
B
3+3+3
C
12 x 1
D
3x4
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When multiplying a number by 0, try to remember relating it to
addition.
Multiplying by 1 and 0
For example,
8x0
can be thought of as
0 + 0 + 0 + 0 + 0 + 0 + 0 + 0.
What would that equal?
Could you make an array using 8 x 0?
click to return to
table of contents
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Can you explain what happens every time a number is
multiplied by 0?
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When multiplying a number by zero, we call it
Any number x 0 = 0
This is called the Zero Property of Multiplication.
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Can you explain what happens every time a number is
multiplied by 1?
When multiplying a number by 1, try to remember relating it to
addition.
For example,
8x1
can be thought of as
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1.
What would that equal?
What would an array of 8 x 1 look like?
Use the
circles to
show the
array.
This is called the Identity Property of Multiplication.
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When multiplying a number by one, we call it
Any number x 1 = itself
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11
Click the tire to play a game.
The answer to 10 x 0 is 10.
True
False
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Sandra wants to buy prizes from the machines in
front of the store. She has to put in one coin in
each machine. If there are 5 machines, how many
coins will she need to buy a prize from each
machine?
12
A
1
B
5
C
0
D
4
13
What is the answer to any problem that involves
multiplying by 0?
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14
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6 x 1 is an example of the Identity Property?
Yes
No
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15
Greg gives each of his customers 2 coupons
when they visit his store. If he hasn't had any
customers today, how many coupons has he given
out?
A
2
B
1
C
0
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2 x 5 = 10
Factor Factor Product
Factors are the numbers we multiply together to get to an
answer which we call the product.
When you are asked to multiply a number by the factor 2,
what are some ways you could go about finding the answer?
Multiply by 2
click to return to
table of contents
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Think of some words that may mean 2.
Click the numbers to reveal some.
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Multiplying by 2 can be thought of as doubling your factor.
So, imagine that the problem 3 x 2 is 3 doubled, or 2 groups of 3.
Double each set of animals below and write the multiplication
number sentence to match.
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16
2x0=2
True
Click the pencil to play a game.
False
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17
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If you were to double 4, what would be your
answer?
18
When you multiply a number by 2, the answer is
always 2?
A
2
Yes
B
4
No
C
6
D
8
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19
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Which number sentence matches the following
word problem?
Mr. Blake asked his students to take off their shoes
for an activity and place them against the wall. If he
has 9 students, how many shoes were along the
wall?
A
9 + 1 = 10
B
9x2=9
C
9 x 9 = 81
D
9 x 2 = 18
20
Which picture below shows an array where 2 was a
factor?
A
peanuts
B
flowers
C
pigs
D
none of the pictures
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Fill in the chart below.
Fa ctor1
2
3
4
5
6
7
x5
Multiply by 5
What pattern do you see in the products of each factor?
Could this be a rule? What do you notice about the digits
in the ones place?
click to return to
table of contents
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Let's practice! Using what your remember from the table you
created in the last slide, practice multiplying 5 and the number
you roll on the 6-sided dice. Click the dice to roll again.
5x
What items do you think of when 5 is mentioned?
Click each box for some ideas.
=
Can you use one of these items in a multiplication number story?
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For example, here's a number story using a factor of five.
Now you try! Alone or with a partner, write and solve a
multiplication word problem using number 5.
Natalie is saving up for a new painting set for her artwork.
The new paint set costs $32. She can save $5 a week. If she
saves her money for 7 weeks, will Natalie have enough
money to purchase the new paint set?
What number sentence would you use to check your work?
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21
Click the beach ball to play a multiplication of 5 game.
9 x 5 = 40
True
False
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22
What number besides 5, could be in the ones place
of the multiples of 5?
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23
This wagon has 4 wheels. How many wheels
would there be if there were 5 wagons?
A
20
B
45
C
1
D
9
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24
It takes Jim 5 minutes to run one lap around the
track. How many minutes does it take for him to
run 8 laps?
A
58
B
3
C
40
D
45
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25
Yes
No
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26
Does knowing the multiples of 5
help you tell time?
If the big hand is on the 5, how many
minutes past the hour is it?
11
12
If the big hand is on the 2, how many
minutes past the hour is it?
11
2
3
9
4
8
6
27
1
10
7
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5
12
1
2
10
3
9
4
8
7
6
5
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28 Carol plays a ball game. She gets 7 points each time her ball
hits a target. If she hits the target at least 5 times in a row, she
gets an extra 25 points. What is the total number of points
Carol gets if she hits the target 5 times in a row?
Reminder: Nickels are worth 5 cents.
From PARCC sample test
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29
Four friends each have a nickel, what is
the total amount of money they have?
4 groups of 5
4 x 5 = 20 cents
click
click
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30
A piece of candy is five cents. If you buy
8 pieces, how much will it cost?
You find six nickels under the couch.
How many cents did you find?
A
6 cents
B
5 cents
C
65 cents
D
30 cents
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31
Your aunt gives you five cents for each
flower you help her plant. If you plant 3,
how many cents will she give you?
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32
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While cleaning out your dad's car you
find 9 nickels. How many cents is this?
33
In your piggy bank you have 7 nickels.
How many cents is this?
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Fill in the chart below.
Fa ctor1
2
3
4
5
6
7
x 10
Multiply by 10
What pattern do you see in the products of each factor?
Could this be a rule? What do you notice about the digits in
the ones place?
click to return to
table of contents
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Let's practice! Using what your remember from the table you
created in the last slide, practice multiplying 10 and the number
you roll on the 6-sided dice. Click the dice to roll again.
10 x
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What items do you think of when 10 is mentioned?
Click each box for some ideas.
=
Can you use one of these items in a multiplication number story?
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For example, here is a multiplication number story using a factor
of 10.
Now you try! Alone or with a partner, write and solve a
multiplication word problem using the number 10.
Melissa is in a beginner's typing class. At the end of her first day
she could type 10 words in one minute. How many words could
she type if the teacher gave her 7 minutes to finish?
What is the number sentence you would use to check your work?
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When multiplying by 10, the rule is you are basically "adding a
place value" to that number. So in the case of 10 x 5 = 50, we
are "adding a place value" to 5 making it 50. This works for all
numbers! Let's practice. Pop the balloons to check your
answers.
150
320
480
Click to play a multiplication of 10 game.
210
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34
Multiples of 10 have _____ in the ones place?
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35
The product below is 10?
A
10
Yes
B
1
No
C
0
D
Both B and C
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36
This bouquet has 3 flowers. How many flowers
would there be if there were 10 bouquets?
A
13
B
103
C
7
D
30
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37
You charge $10 for raking leaves. If you
rake 7 yards, how much money will you
earn?
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38
While cleaning out your mom's car you
find 9 dimes. How many cents is this?
A
9
B
19
C
90
D
900
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39
While shopping you buy five new shirts.
Each one is $10. How much did you
spend?
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40
You can use the rule for 10 for numbers larger than
10. (for example, 13 x 10)
True
False
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41
What is 21 x 10?
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42 Which two ways show how to find the value of 7 x 40?
Select two correct answers.
43
3 x 80 =
A 7x4
B 4 x 10
C 7 x 4 x 10
D 7 groups of 4 ones
E 7 groups of 4 tens
From PARCC sample test
From PARCC sample test
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Multiplication Table Activity
Multiplication Table Activity
click to return to
table of contents
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Teacher Notes
Multiplication Table Activity
Distribute a multiplication table to each
student. Discuss with them which facts
they have memorized or can count by
quickly. (i.e. zeros, ones, twos, fives, and
tens) Highlight these facts or cross them
out. The facts that
are left, are ones
that the children
should focus on
( i.e. play games,
make flash cards,
etc.).
Multiply by 3
[This object is a teacher notes pull tab]
click to return to
table of contents
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Slide 101 (Answer) / 235
When given the multiplication problem of 6 x 3, you can picture 6
groups of 3. It can be helpful to use the circles as your groups.
Make 6 groups with 3 pigs in each.
Teacher Notes
When given the multiplication problem of 6 x 3, you can picture 6
groups of 3. It can be helpful to use the circles as your groups.
Make 6 groups with 3 pigs in each.
The circles
and pigs are
infinitely
cloned
[This object is a teacher notes pull tab]
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Slide 102 (Answer) / 235
3, 6, 9...
Counting by threes and creating arrays may also help you with
your 3 times tables.
3, 6, 9...
6x3
Teacher Notes
Counting by threes and creating arrays may also help you with
your 3 times tables.
Teachers: this is a good opportunity to
get kids up and moving for practice. If
you have access to an outside or open
area with jump ropes, soft balls to toss or
bounce, or even sidewalk chalk students
6x3
can practice counting by threes each
time they jump, toss, bounce, or step.
[This object is a teacher notes pull tab]
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Fill out the multiplication chart below.
Factors
1
2
3
4
5
6
7
x3
Is there a pattern?
What else do you notice about the products?
8
9
10
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44
Click on the dinosaur to play a multiplication game.
The products of multiplication problems with 3 in
them are all odd.
True
False
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45
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46
In Fairytale Town, there are 9 cottages that have 3
bears in each. How many bears are there in all?
What number was 3 multiplied by to make the array
below?
A
3
A
12
B
12
B
27
C
4
C
6
D
15
D
3
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47
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48
Can a 3 times table have even numbersas
products?
Yes
No
Factors
x3
1
2
3
4
5
6
7
8
9
10
What is 3 x 8?
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Multiply by 4
click to return to
table of contents
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When given the multiplication of 3 x 4, you can picture 3 groups of
four. It can be helpful to use the circles as your groups. Make 3
groups with 4 quarters in each.
Teacher Notes
When given the multiplication of 3 x 4, you can picture 3 groups of
four. It can be helpful to use the circles as your groups. Make 3
groups with 4 quarters in each.
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The circles and
quarters are
infinitely cloned.
[This object is a teacher notes pull tab]
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Counting by fours and creating arrays may also help you with your
4 times tables.
Fill out the multiplication chart below.
4, 8, 12...
But have you heard of double doubling? You've
been taught that multiplying by two can be done
by doubling. If you double that one more time,
you've multiplied by four.
For example, 4 x 5 can be thought of as
doubling 5. That will equal 10. Then double
that, and you will have 20. So, 4 x 5 = 20.
Factors
1
2
3
4
5
6
7
x4
Is there a pattern?
What else do you notice?
8
9
10
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Another way to quickly recall
multiplication facts is to think of your 2
times table and double that.
Notice how the 4 times tables are
double the 2 times tables.
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Let's multiply by 4. Roll the 6-sided dice to see by which factor
you are multiplying the 4. Can you double the double? Once you
find a product, you may pop that balloon. Play until all balloons
have been popped.
x
Click on the snow to play a multiplication game.
=
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50
The products of multiplication problems with 4 in
them are all odd.
True
False
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51
What is 4 x 8?
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52
The waitress gave us 4 packs of crayons when we
sat down to eat. There were 4 crayons in each pack.
How many crayons are there?
A
8
B
0
C
16
D
44
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54
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53
The number 36 has 4 as a factor. What is the other
factor?
A
9
B
32
C
40
D
0
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Does the picture show a multiple of 4?
Yes
No
Multiply by 6
click to return to
table of contents
When given the multiplication of 6 x 4, you can picture 6 groups of
four. It can be helpful to use the circles as your groups. Make 6
groups with 4 x's in each.
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When given the multiplication of 6 x 4, you can picture 6 groups of
four. It can be helpful to use the circles as your groups. Make 6
groups with 4 x's in each.
Teacher Notes
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The circles
and x's are
infinitely
cloned.
[This object is a teacher notes pull tab]
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Counting by six and creating arrays may also help you with your 6
times tables.
Fill out the multiplication chart below.
6, 12, 18...
Factors
6x3
1
2
3
4
5
6
7
8
9
x6
Is there a pattern?
What else do you notice?
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Let's play a game of multiplication by 6 tic-tac-toe.
o
x
6
Teacher Notes
6
Let's play a game of multiplication by 6 tic-tac-toe.
x
12
6
18
24
30
36
6
12
30
o
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x
12
6
18
24
30
36
6
12
30
[This object is a teacher notes pull tab]
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55
Click on the fish to play a multiplication game.
x
Directions: choose 2 volunteers to play
or elect to play class vs. teacher, boys vs.
girls, or half the class against half the
class. Roll the 6-sided dice and find the
product. Find the product on the tic-tactoe board on the right. The first player
places an x over that product. Player 2
rolls the dice and they place an o over
their product. If the x is already on that
product, you cannot play. Play until
winner is determined. Clear the board if a
round ends in a tie.
The products of multiplication problems with 6 in
them are all odd.
True
False
10
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56
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I rolled 4 dice. Each die landed on 6. What was the
product of all of the dice?
57
What is not a multiple of 6?
A
6
A
10
B
16
B
2
C
24
C
16
D
42
D
24
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58
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Does the picture below show a multiple of 6?
59
What is 6 x 8?
Yes
No
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If the seven swans a swimming decide to become seven swans a
laying. How many eggs will there be after each lays six eggs?
Multiply by 7
click to return to
table of contents
Use the nests and the eggs to show a picture to match the story
problem.
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Teacher Notes
If the seven swans a swimming decide to become seven swans a
laying. How many eggs will there be after each lays six eggs?
Creating arrays may also help you with your 7 times tables. Use the
pen to trace around the squares to make arrays with 7 as a factor.
The nests and the
eggs infinitely
cloned.
[This object is a teacher notes pull tab]
Use the nests and the eggs to show a picture to match the story
problem.
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Fill out the multiplication chart below.
Factors
1
2
3
4
5
6
7
8
9
10
x7
Is there a pattern?
What else do you notice?
The baker has several birthdays coming up. If each cake receives 7
candles, how many candles will he need to order for the 9 cakes he
has baked? The cake is infinitely cloned.
What is your multiplication number sentence?
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60
The products of multiplication problems with 7 in
them are all odd.
True
Click on the rocking horse to play a multiplication game.
False
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61
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The seven dwarves were getting ready to go to work.
Each carried two pick axes. How many axes were
there?
62
When in a word problem, what word could mean 7?
A
meter
A
9
B
Half dozen
B
5
C
week
C
72
D
octagon
D
14
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63
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If I had 5 of the following cards, would I have 35
hearts?
64
What is 7 x 8?
Yes
No
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If 7 itsy bitsy spiders crawl up to the top of a wall, how many spider
legs will there be in all?
Multiply by 8
click to return to
table of contents
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Teacher Notes
If 7 itsy bitsy spiders crawl up to the top of a wall, how many spider
legs will there be in all?
Creating arrays may also help you with your 8 times tables. Use the
pen to trace around the squares to make arrays with 8 as a factor.
Use the spider to
show a picture to
match the story
problem. It is infinitely
cloned.
[This object is a teacher notes pull tab]
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Fill out the multiplication chart below.
Factors
1
2
3
4
5
6
7
8
Mario is the head chef at Tony's Pizza House. He makes sure
each pizza is cut into 8 slices. How many slices of pizza will
there be if Mario serves 5 pizzas during his lunch rush? The
pizzas are infinitely cloned.
9
10
x8
Is there a pattern?
What is the multiplication number sentence you could use?
What else do you notice?
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65
Click on the bear to play a multiplication game.
The products of multiplication problems with 8 in
them are all even.
True
False
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66
Most jobs ask you to work 8 hours a day for 5 days
each week. How many hours is that in all?
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67
When in a word problem, what word could mean 8?
A
ate
A
13
B
Half dozen
B
3
C
week
C
40
D
octagon
D
85
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68
This is an array that shows 8 x 4.
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69
What is 9 x 8?
Yes
No
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70 Which two statements can be represented by the
expression 4x8?
A A teacher puts 8 chairs at each of 4 tables.
B Tom buys 4 red markers and 8 black markers.
C Marie shares her 8 marbles equally among 4 friends.
D There are 4 rows of flowers. There are 8 flowers
in each row.
E There are 8 ducks in the pond. Then, 4 more
ducks join them.
From PARCC sample test
Multiply by 9
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table of contents
Slide 160 / 235
A cat is said to have 9 lives. If there were six cats, how many
"lives" would they have altogether?
Teacher Notes
A cat is said to have 9 lives. If there were six cats, how many
"lives" would they have altogether?
Slide 160 (Answer) / 235
Use the cat to show
a picture to match the
story problem. It is
infinitely cloned.
[This object is a teacher notes pull tab]
Slide 161 / 235
Creating arrays may also help you with your 9 times tables. Use the
pen to trace around the squares to make arrays with 9 as a factor.
Slide 162 / 235
There is also a strategy for your 9 times tables using your hands.
Place your hands in front of you like so. If you put
down your left pinky, how many fingers do you have
up?
If you put down your next finger, how many fingers
do you have to the left of that finger? How many
fingers do you have to the right?
If you put down your next finger, how many fingers
do you have to the left of that finger? How many
fingers do you have to the right?
Slide 163 / 235
Slide 164 / 235
Fill out the multiplication chart below.
Factor
x9
1
2
3
4
5
6
7
8
9
10
Is there a pattern?
What else do you notice?
Slide 165 / 235
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71
The products of multiplication problems with 9 in
them are all even.
True
Click on the window to play a multiplication game.
False
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72 Nine teachers each have 4 computers in their
classrooms. How many computers is that in all?
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73
What number is not a multiple of 9?
A
9
A
13
B
19
B
5
C
27
C
36
D
90
D
94
Slide 169 / 235
74
If there are 9 starfish, there would be 45 legs?
Yes
No
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75
What is 9 x 8?
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76 Cade has 4 boxes. He puts 9 model cars in each
box. What is the total number of model cars Cade
put in these boxes?
Squares & Rectangles
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table of contents
From PARCC sample test
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A square is a shape where all four sides are the same
length. The four corners are all right angles.
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A rectangle is a four sided shape. All four corners are
right angles.
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A square is a shape where all four sides are the same
length. The four corners are all right angles.
A rectangle is a four sided shape. All four corners are
right angles.
It is important to remember that because of the definition of
a RECTANGLE, all squares are in fact rectangles. They
meet the definition in that they have four sides and all four
corners are right angles. A rectangle is only a SQUARE
when all four sides are the same length and all four corners
are right angles.
Slide 177 / 235
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77
Choose all of the below that are squares.
B
A
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78
C
D
E
F
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79
Choose all of the below that are
rectangles.
Is a square a rectangle?
Yes
No
A
B
C
D
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80
E
F
Slide 182 / 235
Is a rectangle a square?
Yes
No
Unit Squares and Tiling Area of Squares
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table of contents
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Area is the space inside of an object.
For example, in a backyard the grass inside the fence makes up
the area of the yard.
fence = perimeter
grass = area
A unit square, is a square
that has side lengths of one.
1 unit
1 unit
Slide 185 (Answer) / 235
On grid paper,
make a square
that has sides
of 3 units.
On grid paper,
make a square
that has sides
of 3 units.
How many unit squares would you need to
cover the area of the square?
Teacher Notes
Slide 185 / 235
Area is the number of square units it takes to cover the
surface of a unit.
Unit square is
infinitely
cloned.
How many unit squares would you need to
cover the area of the square? [This object is a teacher notes pull tab]
unit square
Slide 186 / 235
unit square
Slide 186 (Answer) / 235
Now make a square that
has sides of 4 units.
How many unit squares would you need to
cover the area of the square?
How many unit squares would you need to
cover the area of the square? [This object is a teacher notes pull tab]
Teacher Notes
Now make a square that
has sides of 4 units.
unit square
Unit square is
infinitely
cloned.
unit square
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Slide 188 / 235
81 The area is the part around the outside of a shape.
82
True
How many unit squares will it take to
cover this square?
False
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83
Slide 190 / 235
84
How many unit squares will it take to
cover this square?
If a square has side lengths of 7, how many unit
squares do you think it will take to cover it? (Do
not draw this example.)
Slide 191 / 235
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Area can be found by counting the unit squares on a grid. It is
also found by multiplying the length and the width of a square.
Because of the definition of a square, we know that each side has
the same length. Sometimes, length and width are called base
and height. These two measurements are also called the
dimensions.
Identify the parts of the rectangle below. Drag words from the
bubble to show where they belong.
length
AREA
or
or
width
base
height
Square Side
Lengths
Number of Unit
Squares to
Cover
2
4
3
9
4
16
5
25
6
7
49
Teacher Notes
Finding the area of a square:
Slide 193 / 235
85
Slide 194 / 235
86
What is the area of a square with side
lengths of 9 units?
_______ units
_______ square units
Slide 195 / 235
87
What is the area of a square with side
lengths of 10 units?
2
Slide 196 / 235
What is the area of a square with side
lengths of 1 inch?
_______ square inches
Area of Rectangles
click to return to
table of contents
Slide 197 / 235
Slide 197 (Answer) / 235
How many unit squares would you
need to cover the rectangle?
On grid paper,
make a rectangle
that has sides
of 3 units by 2 units.
Teacher Notes
On grid paper,
make a rectangle
that has sides
of 3 units by 2 units.
unit square
Unit square is
infinitely
cloned.
How many unit squares would you
need to cover the rectangle?
unit square
[This object is a teacher notes pull tab]
Slide 198 / 235
Slide 198 (Answer) / 235
How many unit squares would you
need to cover the rectangle?
On grid paper,
make a rectangle
that has sides
of 3 units by 6 units.
Teacher Notes
On grid paper,
make a rectangle
that has sides
of 3 units by 6 units.
unit square
Unit square is
infinitely
cloned.
How many unit squares would you
need to cover the rectangle?
unit square
[This object is a teacher notes pull tab]
Slide 199 / 235
Slide 199 (Answer) / 235
How many unit squares would you
need to cover the rectangle?
On grid paper,
make a rectangle
that has sides
of 4 units by 5 units.
Teacher Notes
On grid paper,
make a rectangle
that has sides
of 4 units by 5 units.
unit square
Unit square is
infinitely
cloned.
How many unit squares would you
need to cover the rectangle?
unit square
[This object is a teacher notes pull tab]
Slide 200 / 235
Slide 200 (Answer) / 235
How many unit squares would you
need to cover the rectangle?
On grid paper,
make a rectangle
that has sides
of 5 units by 3 units.
Teacher Notes
On grid paper,
make a rectangle
that has sides
of 5 units by 3 units.
unit square
Unit square is
infinitely
cloned.
How many unit squares would you
need to cover the rectangle?
unit square
[This object is a teacher notes pull tab]
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Slide 202 / 235
Finding the area of a rectangle:
Sometimes, you are given the length and width of a rectangle.
Multiply them together to find the area.
Area is found by counting the unit squares taken up by a grid. It
can also be found by multiplying the length and the width of a
rectangle. Sometimes, length and width are called base and
height. These two measurements are also called the dimensions.
Identify the parts of the rectangle below. Drag words from the
bubble to show where they belong.
3
length x width = area
8 x 3 = 24
length
8
width
or
AREA
base
the area is 24
height
or
Slide 203 / 235
Slide 204 / 235
Rectangle
Length
Rectangle
Width
2
3
6
3
6
18
4
5
20
5
3
15
6
2
Slide 205 / 235
In other cases, you may only know the measure of one side and
the total area. Your job is to find the length of the remaining side.
Teacher Notes
Number of
Unit
Squares
to
Cover
?
Think: length x ________
= area
Use what you already know about multiplication and fact families
to help you find the missing width.
? = 45
5 x ____
For example,
?
5
The length must be 9
because 5 x 9 = 45
Slide 206 / 235
Let's help solve a problem!
Tyler is a home painter. He knows he will need enough paint to
cover a wall area of 80 square feet. The wall is 10 feet wide.
What is the length of a wall?
What do we already know? We know the width and the area.
Let's use our fact families to figure out the length of the wall.
______ feet x 10 feet = 80 square feet
8 feet x 10 feet = 80 square feet
Click the button to play a game.
Slide 207 / 235
88
Slide 208 / 235
How many unit squares will it take to cover this
rectangle?
89
How many unit squares will it take to cover this
rectangle?
______ square units
______ square units
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Slide 209 (Answer) / 235
4 feet
1
4 feet
6 feet
A
B
C
D
2
3
3 feet
90 Look at the shaded rectangles below. Which area would you
drag to label below Rectangle Number 3?
4 feet
9 feet
7 feet
6 feet
A
B
C
D
20 square feet
24 square feet
27 square feet
28 square feet
From PARCC sample test
Answers are infinitely cloned so
students can come to the board
2 the areas into the 3
and drag
9 feet
correct
box. They can input
the
7 feet
letter that matches with the area
of Rectangle Number 3 into their
responders.
4 feet
20 square feet
24 square feet
27 square feet
28 square feet
3 feet
[This object is a teacher notes pull tab]
From PARCC sample test
Slide 210 / 235
91
1
Teacher Notes
90 Look at the shaded rectangles below. Which area would you
drag to label below Rectangle Number 3?
If a rectangle has side length of 7 and a side width
of 3, how many unit squares do you think it will
take to cover it? (Do not draw this example.)
______ units
2
Slide 211 / 235
92
If a rectangle has side length of 5 and a side width
of 8, how many unit squares do you think it will
take to cover it? (Do not draw this example.)
______ units
2
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93
Slide 213 / 235
What is the area of a rectangle with a
side length of 10 feet and a side width of
3 feet?
94
What is the area of a rectangle with a
side length of 1 inch and a side width of
3 inch?
______ square feet
______ in
Slide 214 / 235
Slide 214 (Answer) / 235
95 Which rectangle has an area of 24 square units?
C
95 Which rectangle has an area of 24 square units?
C
A
Answer
A
2
B
D
B
C
D
[This object is a pull tab]
From PARCC sample test
From PARCC sample test
Slide 215 / 235
Slide 216 / 235
As with any word problems, read each carefully to make sure you
understand the problem.
You may draw pictures and use multiplication to solve each
problem.
Area Word Problems
click to return to
table of contents
The units are important. Do not forget to include them in your
answer.
Slide 217 / 235
96 A rectangular field measures 10 ft by 4ft.
What is the area of this field?
_____ feet
2
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97 Cooper wants new carpeting for his
bedroom.
His room is 5 yd by 8 yd. How
much carpeting
does he need to buy to
cover his bedroom floor?
_____ square yards
Slide 219 / 235
98 Mrs. Clark decided to change the tile in
her classroom. Her classroom has a
length of 7 m
and the width of 10 m. If
each tile is 1 square meter, how many
tiles would she need to cover
the floor?
Slide 220 / 235
99 There is a square garden with the side
length of 7 m. What is the area of the
garden?
_____ m
2
_____ tiles
Slide 221 / 235
100 The area of a square photo is 25 square
inches.
What is the length of one of the
sides of the
photo?
_____ inches
Slide 222 / 235
101 Mr. George is building square platforms
for students to reach their SMARTboards.
Can he build one with the area of 56
square inches?
Yes
No
Slide 223 / 235
102 Janie is covering a bulletin board for the school
talent show. The board is 9 ft by 5 ft. How many
square feet of paper will she need to cover the
board?
Slide 224 / 235
103 Each side of our kitchen TV is 9 inches long.
What is the area of the TV screen?
_______ inches2
_____ feet2
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104 I counted the squares that were inside the
rectangle I drew. There were 48 squares.
What are the side lengths of my rectangle
(dimensions)?
A
7x7
B
8+6
C
6x8
D
48 x 2
Slide 226 / 235
105 A room has an area of 24 square feet.
Its length is 3 feet long. What is the width?
_____ feet
Slide 227 / 235
106 Jenny is making a box garden in her backyard. The
length of her box garden is 8 yards. The area inside
where she will fill dirt is 72 square yards. What is
the width of her box garden in yards?
Slide 228 / 235
107 Ken draws a rectangle with an area of 35-square
inches. The width of the rectangle is 5 inches. What
is the length of Ken's rectangle?
From PARCC sample test
Slide 229 / 235
108 Mr. James is covering his bulletin boards with paper
to start the new school year. His bulletin board is 7
feet wide, and he has already cut 56 square feet of
red paper. Determine the length of his bulletin
board.
A 9 feet
B 8 feet
C 7 feet
Welcome
to Mr. J's Class
D 6 feet
Slide 230 / 235
109 Cathy purchased a new tablecloth for her birthday
party. The area of the tablecloth is 24 square feet.
What are possible dimensions of the tablecloth?
Choose all that apply.
A 12 ft x 12 ft
B 8 ft x 3 ft
C 5 ft x 8 ft
D 6 ft x 4 ft
Slide 231 / 235
110 Gina's bedroom floor is in the shape of a rectangle.
It is 10 feet long and 9 feet wide. What is the area of
Gina's bedroom floor?
Slide 231 (Answer) / 235
110 Gina's bedroom floor is in the shape of a rectangle.
It is 10 feet long and 9 feet wide. What is the area of
Gina's bedroom floor?
A 19 square feet
B 38 square feet
B 38 square feet
C 90 square feet
C 90 square feet
D 109 square feet
D 109 square feet
From PARCC sample test
111 Part A
Tori and Leo set up their clubhouse with four tables.
These rectangles represent the tabletops.
C
D
From PARCC sample test
[This object is a pull tab]
Slide 232 (Answer) / 235
Enter the two tabletops
with the same area, in
square feet, and explain
how you know that the
areas are equal.
Student response includes each of the following
Tori and
Leo set up their clubhouse with four tables.
2 elements:
These rectangles
thestudent
tabletops.
· Computationrepresent
component: The
A
Answer
111 Part A
B
C
From PARCC sample test
Slide 232 / 235
A
Answer
A 19 square feet
B
C
D
identifies Table B and Table D as having the
same area.
Enter the two tabletops
· Reasoning component: The
student
explainsarea, in
with
the same
that the areas are the same because 3 x 4 =
square feet, and explain
4 x 3.
how you know that the
Notes:
areas
are equal.
· Use of the term"commutative
property"
is not
required.
· Full credit for both computation and
reasoning is awarded if student states
"Tables B and D are both 4 x 3 = 12 square
[This object is a pull tab]
feet."
From PARCC sample test
Slide 233 / 235
112 Part B
The grid shows Table C and Table D placed end to
end to make a new, larger tabletop.
Tori uses the expression 3 x (2 + 4) to find the total
area of the new, larger tabletop. Leo uses the
expression (3 x 2) + (3 x 4) to find the total area of the
new, larger tabletop.
· Enter the total area, in square feet, of the new,
larger tabletop.
· Use a grid to explain why both Tori's expression
and Leo's expression are correct.
From PARCC sample test
The grid shows Table C and Table D placed end to
Student response includes each of the
end to make
a new,
larger tabletop.
following
2 elements:
· Computation component: The student
indicates that the total area of the
combined tabletop is 18 square feet.
· Reasoning component: The student
explains why both expressions are correct
such as, "The diagram shows you can
Tori useseither
the expression
x (2table
+ 4)and
to find
find the area of3each
add the total
them
together,
(3x2)
+ (3x4), or
since
they the
area of the
new,
larger
tabletop.
Leo
uses
both have the same length, you can just
expression
(3 x 2) + (3 x 4) to find the total area of the
add the 2 widths together and then
new, larger
tabletop.
multiply
by the length, 3 x (2+4)."
Answer
112 Part B
Slide 233 (Answer) / 235
· EnterNote:
the total
area,
in square feet,
of the new,
Use of [This
the object
term is"distributive
property"
a pull tab]
largeristabletop.
not required.
· Use a grid to explain why both Tori's expression
and Leo's expression are correct.
From PARCC sample test
Slide 234 / 235
113 Adam needs to put 19 pictures from Classroom A
and 23 pictures from Classroom B on a bulletin
board. He wants to display the pictures in an array.
Slide 234 (Answer) / 235
113 Adam needs to put 19 pictures from Classroom A
and 23 pictures from Classroom B on a bulletin
board. He wants to display the pictures in an array.
Part A
Select a box for each pictures to create an array to
represent the pictures on the bulletin board.
Select a box for each pictures to create an array to
represent the pictures on the bulletin board.
Answer
Part A
Modeling component:
Student shades a 6 x 7 array.
[This object is a pull tab]
From PARCC sample test
From PARCC sample test
Slide 235 / 235
114 Part B (continued from previous slide)
114 Part B (continued from previous slide)
Find the area Student
of the array.
Explain your answer
response includes each of
using an equation
or
equations.
the following 2 elements:
Answer
Find the area of the array. Explain your answer
using an equation or equations.
Slide 235 (Answer) / 235
From PARCC sample test
From PARCC sample test
· Computation component: 42
· Modeling component: Student
writes an equation showing how
to find the area of the array.
Sample Student Response: I
shaded in an array of 6 x 7. I know
6 x 7 = 42, so the area of the array
is 42.
[This object is a pull tab]