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Transcript of Slide 1 / 234content.njctl.org/courses/math/3rd-grade-math/multiplication/... · Slide 1 / 234....

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3rd Grade

Multiplication

2015-12-30

www.njctl.org

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Relate addition to multiplicationArraysMultiply by 1 and 0Multiply by 2

Multiply by 4

Multiply by 10

Multiply by 6

Table of Contentsclick on the topic to go

to that section

Multiply by 7Multiply by 8Multiply by 9

Multiply by 3Multiplication Table Activity

Multiply by 5

Square and RectanglesUnit squares and tiling - Area of SquaresArea of rectanglesArea Word Problems

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Relate Multiplication to Addition

click to return to table of contents

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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?

What are all of the ways you could figure out this answer?

Relate Multiplication to Addition

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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?

What are all of the ways you could figure out this answer?

Relate Multiplication to Addition

[This object is a pull tab]

Teac

her N

otes

Teachers: choose 5 students to stand up. Have each student raise both hands.

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What are all of the ways you could figure out this answer?

The Greene brothers went for a bike ride. If all four went riding, how many bicycle wheels would you see?

Relate Multiplication to Addition

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Did you use addition? What would the number sentence look like?

2 + 2 + 2 + 2 = 8

This is called repeated addition. Why do you think it is called this?

Click

Relate Multiplication to Addition

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Did you consider using multiplication?

How many bicycles were there?How many wheels did each bicycle have?

What would the number sentence look like?

4 X 2 = 8Click

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.

Relate Multiplication to Addition

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Which number sentences match the picture of three flowers with 7 petals each?

Repeated Addition Multiplication

3 x 5=

6 x 3=

6 + 6 + 6 = 3 + 3 + 3 =

3 x 7 = 7 + 7 + 7=

7 + 7 + 7 + 7=

Relate Multiplication to 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?

What is the repeated addition sentence?

What is the multiplication number sentence?

Relate Multiplication to Addition

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How would you write 4 x 6 = in a repeated addition problem?

What kind of picture could show these problems?

Relate Multiplication to Addition

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How would you write 2 x 8 = in a repeated addition problem?

What kind of picture could show these problems?

Relate Multiplication to Addition

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Click to play Carl's Cookie Capers.

Multiplication Game

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1 ) 2 x 5 = 5 + 5?

True

False

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1 ) 2 x 5 = 5 + 5?

True

False

[This object is a pull tab]

Ans

wer

True

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2 What would the repeated addition number sentence look like for the multiplication problem, 3 x 8 =?

A 8 + 8 =

B 3 + 3 + 3=

C 8 x 3 =

D 8 + 8 + 8 =

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2 What would the repeated addition number sentence look like for the multiplication problem, 3 x 8 =?

A 8 + 8 =

B 3 + 3 + 3=

C 8 x 3 =

D 8 + 8 + 8 =

[This object is a pull tab]

Ans

wer

D

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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 x 5=

C 5 x 5 =

D 3 x 3 =

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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 x 5=

C 5 x 5 =

D 3 x 3 =

[This object is a pull tab]

Ans

wer

B

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4 What repeated addition number sentence would help you figure out the number of petals in the picture below?

A 2 x 7 =

B 7 + 7 =

C 7 + 7 + 7 + 7 + 7 + 7 + 7 =

D 10 + 4 =

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4 What repeated addition number sentence would help you figure out the number of petals in the picture below?

A 2 x 7 =

B 7 + 7 =

C 7 + 7 + 7 + 7 + 7 + 7 + 7 =

D 10 + 4 =

[This object is a pull tab]

Ans

wer

B

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5 What multiplication number sentence would help you figure out the number of petals in the picture below?

A 2 x 7 =

B 7 + 7 =

C 7 + 7 + 7 + 7 + 7 + 7 + 7 =

D 10 + 4 =

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5 What multiplication number sentence would help you figure out the number of petals in the picture below?

A 2 x 7 =

B 7 + 7 =

C 7 + 7 + 7 + 7 + 7 + 7 + 7 =

D 10 + 4 =

[This object is a pull tab]

Ans

wer

A

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Arrays

click to return to table of contents

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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.

What are Arrays?

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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?

Using Arrays

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rows

rows

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.

Click to reveal the multiplication number sentence for each array.

4 x 2 2 x 4

columns columns

Using Arrays

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Each array below is an example of 6. What would the multiplication number sentence for each array be?

Using Arrays

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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?

Using Arrays

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Circle the peanuts to show other ways to make arrays showing 10.Using Arrays

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6 Are the cats arranged in an array?

Yes

No

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6 Are the cats arranged in an array?

Yes

No

[This object is a pull tab]

Ans

wer

No

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7 This is an array for what number?

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7 This is an array for what number?

[This object is a pull tab]

Ans

wer

12

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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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8 Which array is a model for 3 x 2?

A the mice

B the frogs

C the flowers

D none of the above

[This object is a pull tab]

Ans

wer

B

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9 The multiplication number sentence for this array of shoes is 2 x 3.

True

False

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9 The multiplication number sentence for this array of shoes is 2 x 3.

True

False

[This object is a pull tab]

Ans

wer

False

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10 What array is circled?

A 2 x 6

B 3 + 3 + 3

C 12 x 1

D 3 x 4

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10 What array is circled?

A 2 x 6

B 3 + 3 + 3

C 12 x 1

D 3 x 4

[This object is a pull tab]

Ans

wer

D

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Multiplying by 1 and 0

click to return to table of contents

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When multiplying a number by 0, try to remember relating it to addition.

For example, 8 x 0

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?

Multiplying by 0

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Can you explain what happens every time a number is multiplied by 0?

This is called the Zero Property of Multiplication.

Multiplying by 0

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When multiplying a number by zero, we call it

Any number x 0 = 0

Multiplying by 0

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When multiplying a number by 1, try to remember relating it to addition.

For example, 8 x 1

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.

Multiplying by 1

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Can you explain what happens every time a number is multiplied by 1?

This is called the Identity Property of Multiplication.

Multiplying by 1

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When multiplying a number by one, we call it

Any number x 1 = itself

Multiplying by 1

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Click the tire to play a game.

Multiplying by 1 and 0 Game

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11 The answer to 10 x 0 is 10.

True

False

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11 The answer to 10 x 0 is 10.

True

False

[This object is a pull tab]

Ans

wer

False

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12 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?

A 1

B 5

C 0

D 4

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12 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?

A 1

B 5

C 0

D 4

[This object is a pull tab]

Ans

wer

B

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13 What is the answer to any problem that involves multiplying by 0?

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13 What is the answer to any problem that involves multiplying by 0?

[This object is a pull tab]

Ans

wer

0

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14 ) 6 x 1 is an example of the Identity Property?

Yes

No

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14 ) 6 x 1 is an example of the Identity Property?

Yes

No

[This object is a pull tab]

Ans

wer

Yes

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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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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

[This object is a pull tab]

Ans

wer

C

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Multiply by 2

click to return to table of contents

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2 x 5 = 10Factor 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?

Multiplying by 2

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Think of some words that mean 2. Click the numbers to reveal some.

Multiplying by 2

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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.

Multiplying by 2

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Click the pencil to play a game.

Multiplying by 2 Game

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16 ) 2 x 0 = 2

True

False

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16 ) 2 x 0 = 2

True

False

[This object is a pull tab]

Ans

wer

False

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17 If you were to double 4, what would be your answer?

A 2

B 4

C 6

D 8

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17 If you were to double 4, what would be your answer?

A 2

B 4

C 6

D 8

[This object is a pull tab]

Ans

wer

D

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18 When you multiply a number by 2, the answer is always 2?

Yes

No

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18 When you multiply a number by 2, the answer is always 2?

Yes

No

[This object is a pull tab]

Ans

wer

No

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19 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 9 x 2 = 9

C 9 x 9 = 81

D 9 x 2 = 18

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19 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 9 x 2 = 9

C 9 x 9 = 81

D 9 x 2 = 18 [This object is a pull tab]

Ans

wer

D

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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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20 Which picture below shows an array where 2 was a factor?A peanuts

B flowers

C pigs

D none of the pictures

[This object is a pull tab]

Ans

wer

D

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Multiply by 5

click to return to table of contents

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Factor 1 2 3 4 5 6 7

x 5

Fill in the chart below.

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?

Multiplying by 5

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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.

5 x =

Let's Practice!

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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?

Multiplying by 5

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For example, here's a number story using a factor of five.

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?

Multiplying by 5

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Now you try! Alone or with a partner, write and solve a multiplication word problem using number 5.

Practice Multiplying by 5

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Click the beach ball to play a multiplication of 5 game.

Multiplying by 5 Game

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21 ) 9 x 5 = 40

True

False

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21 ) 9 x 5 = 40

True

False

[This object is a pull tab]

Ans

wer

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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22 What number besides 5, could be in the ones place of the multiples of 5?

[This object is a pull tab]

Ans

wer

0

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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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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

[This object is a pull tab]

Ans

wer

20

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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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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

[This object is a pull tab]

Ans

wer

C

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25 Does knowing the multiples of 5 help you tell time?

Yes

No

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25 Does knowing the multiples of 5 help you tell time?

Yes

No

[This object is a pull tab]

Ans

wer

Yes

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26 If the big hand is on the 5, how many minutes past the hour is it?

12

3

4567

8

9

10

1211

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26 If the big hand is on the 5, how many minutes past the hour is it?

12

3

4567

8

9

10

1211

[This object is a pull tab]

Ans

wer

25 minutes

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27 If the big hand is on the 2, how many minutes past the hour is it?

12

3

4567

8

9

10

1211

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27 If the big hand is on the 2, how many minutes past the hour is it?

12

3

4567

8

9

10

1211

[This object is a pull tab]

Ans

wer

10 minutes

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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?

From PARCC EOY sample test #12

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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?

From PARCC EOY sample test #12

[This object is a pull tab]

Ans

wer

60 points

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Reminder: Nickels are worth 5 cents.

Multiplying by 5

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Four friends each have a nickel, what is the total amount of money they have?

4 groups of 5

4 x 5 = 20 centsclick

click

Multiplying by 5

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29 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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29 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

[This object is a pull tab]

Ans

wer

D

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30 A piece of candy is five cents. If you buy 8 pieces, how much will it cost?

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30 A piece of candy is five cents. If you buy 8 pieces, how much will it cost?

[This object is a pull tab]

Ans

wer

40 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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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?

[This object is a pull tab]

Ans

wer

15 cents

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32 While cleaning out your dad's car you find 9 nickels. How many cents is this?

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32 While cleaning out your dad's car you find 9 nickels. How many cents is this?

[This object is a pull tab]

Ans

wer

45 cents

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33 In your piggy bank you have 7 nickels. How many cents is this?

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33 In your piggy bank you have 7 nickels. How many cents is this?

[This object is a pull tab]

Ans

wer

35 cents

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Multiply by 10

click to return to table of contents

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Factor 1 2 3 4 5 6 7

x 10

Fill in the chart below.

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?

Multiplying by 10

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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 =

Multiplying by 10

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Slide 82 / 234

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?

Multiplying by 10

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For example, here is a multiplication number story using a factor of 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?

Multiplying by 10

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Now you try! Alone or with a partner, write and solve a multiplication word problem using the number 10.

Practice Multiplying by 10

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150

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.

320 480 210

Practice Multiplying by 10

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Click to play a multiplication of 10 game.

Multiplying by 10 Game

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34 Multiples of 10 have _____ in the ones place?

A 10

B 1

C 0

D Both B and C

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34 Multiples of 10 have _____ in the ones place?

A 10

B 1

C 0

D Both B and C

[This object is a pull tab]

Ans

wer

C

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35 The product below is 10?

Yes

No

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35 The product below is 10?

Yes

No

[This object is a pull tab]

Ans

wer

No

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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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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

[This object is a pull tab]

Ans

wer

D

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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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37 You charge $10 for raking leaves. If you rake 7 yards, how much money will you earn?

[This object is a pull tab]

Ans

wer

$70

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38 While cleaning out your mom's car you find nine dimes. How many cents is this?

A 9

B 19

C 90

D 900

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38 While cleaning out your mom's car you find nine dimes. How many cents is this?

A 9

B 19

C 90

D 900

[This object is a pull tab]

Ans

wer

C

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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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39 While shopping you buy five new shirts. Each one is $10. How much did you spend?

[This object is a pull tab]

Ans

wer

$50

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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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40 You can use the rule for 10 for numbers larger than 10. (for example, 13 x 10)

True

False

[This object is a pull tab]

Ans

wer

True

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41 What is 21 x 10?

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41 What is 21 x 10?

[This object is a pull tab]

Ans

wer

210

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42 Which two ways show how to find the value of 7 x 40? Select two correct answers.

A 7 x 4

B 4 x 10

C 7 x 4 x 10

D 7 groups of 4 ones

E 7 groups of 4 tens

From PARCC EOY sample test #4

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42 Which two ways show how to find the value of 7 x 40? Select two correct answers.

A 7 x 4

B 4 x 10

C 7 x 4 x 10

D 7 groups of 4 ones

E 7 groups of 4 tens

From PARCC EOY sample test #4

[This object is a pull tab]

Ans

wer

C,E

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43 ) 3 x 80 =

From PARCC EOY sample test #36

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43 ) 3 x 80 =

From PARCC EOY sample test #36

[This object is a pull tab]

Ans

wer

240

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Multiplication Table Activity

click to return to table of contents

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Multiplication Table

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Slide 98 (Answer) / 234

Multiplication Table

Teac

her N

otes

[This object is a teacher notes pull tab]

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.).

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Multiply by 3

click to return to table of contents

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Slide 100 / 234

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.

Multiplying by 3

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Slide 100 (Answer) / 234

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.

Multiplying by 3

Teac

her N

otes

[This object is a teacher notes pull tab]

The circles and pigs are

infinitely cloned.

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Slide 101 / 234

Counting by threes and creating arrays may also help you with your 3 times tables.

3, 6, 9...

6 x 3

Multiplying by 3

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Slide 101 (Answer) / 234

Counting by threes and creating arrays may also help you with your 3 times tables.

3, 6, 9...

6 x 3

Multiplying by 3

Teac

her N

otes

[This object is a teacher notes pull tab]

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 can practice counting by threes each time they jump, toss, bounce, or step.

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Fill out the multiplication chart below.

Factors

x3

1 2 3 4 5 6 7 8 9 10

Is there a pattern?

What else do you notice about the products?

Multiplying by 3

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Multiplying by 3

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Click on the dinosaur to play a multiplication game.

Multiplication by 3 Game

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44 The products of multiplication problems with 3 in them are all odd.

True

False

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Slide 105 (Answer) / 234

44 The products of multiplication problems with 3 in them are all odd.

True

False

[This object is a pull tab]

Ans

wer

False

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45 In Fairytale Town, there are 9 cottages that have 3 bears in each. How many bears are there in all?

A 12

B 27

C 6

D 3

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45 In Fairytale Town, there are 9 cottages that have 3 bears in each. How many bears are there in all?

A 12

B 27

C 6

D 3

[This object is a pull tab]

Ans

wer

B

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46 What number was 3 multiplied by to make the array below?

A 3

B 12

C 4

D 15

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Slide 107 (Answer) / 234

46 What number was 3 multiplied by to make the array below?

A 3

B 12

C 4

D 15

[This object is a pull tab]

Ans

wer

C

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47 Can a 3 times table have even numbers as products?

YesNo

Factors

x3

1 2 3 4 5 6 7 8 9 10

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47 Can a 3 times table have even numbers as products?

YesNo

Factors

x3

1 2 3 4 5 6 7 8 9 10[This object is a pull tab]

Ans

wer

Yes

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48 What is 3 x 8?

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Slide 109 (Answer) / 234

48 What is 3 x 8?

[This object is a pull tab]

Ans

wer

24

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Slide 110 / 234

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Slide 110 (Answer) / 234

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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.

Multiplying by 4

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Slide 112 (Answer) / 234

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.

Multiplying by 4

Teac

her N

otes

[This object is a teacher notes pull tab]

The circles and quarters are

infinitely cloned.

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Counting by fours and creating arrays may also help you with your 4 times tables.

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.

Multiplying by 4

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Fill out the multiplication chart below.

Factors

x4

1 2 3 4 5 6 7 8 9 10

Is there a pattern?

What else do you notice?

Multiplying by 4

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Another way to quickly recall multiplication facts is to think of your 2 times table and double that.

Multiplying by 4

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Notice how the 4 times tables are double the 2 times tables.

Multiplying by 4

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x

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.

=

Practice Multiplying by 4

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Click on the snow to play a multiplication game.

Multiplication by 4 Game

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50 The products of multiplication problems with 4 in them are all odd.

True

False

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Slide 119 (Answer) / 234

50 The products of multiplication problems with 4 in them are all odd.

True

False

[This object is a pull tab]

Ans

wer

False

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51 What is 4 x 8?

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51 What is 4 x 8?

[This object is a pull tab]

Ans

wer

32

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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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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

[This object is a pull tab]

Ans

wer

C

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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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Slide 122 (Answer) / 234

53 The number 36 has 4 as a factor. What is the other factor?

A 9

B 32

C 40

D 0

[This object is a pull tab]

Ans

wer

A

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54 Does the picture show a multiple of 4?

Yes

No

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Slide 123 (Answer) / 234

54 Does the picture show a multiple of 4?

Yes

No

[This object is a pull tab]

Ans

wer

Yes

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Multiply by 6

click to return to table of contents

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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.

Multiplying by 6

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Slide 125 (Answer) / 234

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.

Multiplying by 6

Teac

her N

otes

[This object is a teacher notes pull tab]

The circles and x's are infinitely cloned.

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Counting by six and creating arrays may also help you with your 6 times tables.

6, 12, 18...

6 x 3

Multiplying by 6

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Fill out the multiplication chart below.

Factors

x6

Is there a pattern?

What else do you notice?

1 2 3 4 5 6 7 8 9 10

Multiplying by 6

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Let's play a game of multiplication by 6 tic-tac-toe.

x

o x12 6 18

24 30 36

6 12 30

6

Multiplication by 6 Game

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Slide 128 (Answer) / 234

Let's play a game of multiplication by 6 tic-tac-toe.

x

o x12 6 18

24 30 36

6 12 30

6

Multiplication by 6 Game

Teac

her N

otes

[This object is a teacher notes pull tab]

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-tac-toe 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.

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Slide 129 / 234

Click on the fish to play a multiplication game.

Multiplication by 6 Game

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55 The products of multiplication problems with 6 in them are all odd.

True

False

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Slide 130 (Answer) / 234

55 The products of multiplication problems with 6 in them are all odd.

True

False

[This object is a pull tab]

Ans

wer

False

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56 I rolled 4 dice. Each die landed on 6. What was the product of all of the dice?

A 10

B 2

C 16

D 24

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56 I rolled 4 dice. Each die landed on 6. What was the product of all of the dice?

A 10

B 2

C 16

D 24

[This object is a pull tab]

Ans

wer

D

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57 What is not a multiple of 6?

A 6

B 16

C 24

D 42

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57 What is not a multiple of 6?

A 6

B 16

C 24

D 42

[This object is a pull tab]

Ans

wer

B

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58 Does the picture below show a multiple of 6?

Yes

No

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58 Does the picture below show a multiple of 6?

Yes

No

[This object is a pull tab]

Ans

wer

Yes

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Slide 134 / 234

59 What is 6 x 8?

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59 What is 6 x 8?

[This object is a pull tab]

Ans

wer

48

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Multiply by 7

click to return to table of contents

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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?

Use the nests and the eggs to show a picture to match the story problem.

Multiplying by 7

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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?

Use the nests and the eggs to show a picture to match the story problem.

Multiplying by 7

Teac

her N

otes

[This object is a teacher notes pull tab]

The nests and the eggs are infinitely

cloned.

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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.

Multiplying by 7

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Fill out the multiplication chart below.

Factors

x7

Is there a pattern?

What else do you notice?

1 2 3 4 5 6 7 8 9 10

Multiplying by 7

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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?

Multiplying by 7

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Click on the rocking horse to play a multiplication game.

Multiplication by 7 Game

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60 The products of multiplication problems with 7 in them are all odd.True

False

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60 The products of multiplication problems with 7 in them are all odd.True

False

[This object is a pull tab]

Ans

wer

False

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61 The seven dwarves were getting ready to go to work. Each carried two pick axes. How many axes were there?

A 9

B 5

C 72

D 14

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61 The seven dwarves were getting ready to go to work. Each carried two pick axes. How many axes were there?

A 9

B 5

C 72

D 14

[This object is a pull tab]

Ans

wer

D

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62 When in a word problem, what word could mean 7?

A meter

B Half dozen

C week

D octagon

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62 When in a word problem, what word could mean 7?

A meter

B Half dozen

C week

D octagon

[This object is a pull tab]

Ans

wer

C

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63 If I had 5 of the following cards, would I have 35 hearts?

Yes

No

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63 If I had 5 of the following cards, would I have 35 hearts?

Yes

No

[This object is a pull tab]

Ans

wer

Yes

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64 What is 7 x 8?

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64 What is 7 x 8?

[This object is a pull tab]

Ans

wer

56

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Multiply by 8

click to return to table of contents

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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?

Multiplying by 8

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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?

Multiplying by 8

Teac

her N

otes

[This object is a teacher notes pull tab]

Use the spider to show a picture to match the story

problem. It is infinitely cloned.

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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.

Multiplying by 8

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Fill out the multiplication chart below.

Factors

x8

Is there a pattern?

What else do you notice?

1 2 3 4 5 6 7 8 9 10

Multiplying by 8

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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.

What is the multiplication number sentence you could use?

Multiplying by 8

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Click on the bear to play a multiplication game.

Multiplication by 8 Game

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65 The products of multiplication problems with 8 in them are all even.

True

False

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65 The products of multiplication problems with 8 in them are all even.

True

False

[This object is a pull tab]

Ans

wer

True

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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?

A 13

B 3

C 40

D 85

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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?

A 13

B 3

C 40

D 85

[This object is a pull tab]

Ans

wer

C

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67 When in a word problem, what word could mean 8?

A ate

B Half dozen

C week

D octagon

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67 When in a word problem, what word could mean 8?

A ate

B Half dozen

C week

D octagon

[This object is a pull tab]

Ans

wer

D

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68 This is an array that shows 8 x 4.

Yes

No

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68 This is an array that shows 8 x 4.

Yes

No

[This object is a pull tab]

Ans

wer

Yes

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69 What is 9 x 8?

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69 What is 9 x 8?

[This object is a pull tab]

Ans

wer

72

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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 EOY sample test #2

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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 EOY sample test #2

[This object is a pull tab]

Ans

wer

A,D

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Multiply by 9

click to return to table of contents

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A cat is said to have 9 lives. If there were six cats, how many "lives" would they have altogether?

Multiplying by 9

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A cat is said to have 9 lives. If there were six cats, how many "lives" would they have altogether?

Multiplying by 9

Teac

her N

otes

[This object is a teacher notes pull tab]

Use the cat to show a picture to match the

story problem. It is infinitely cloned.

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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.

Multiplying by 9

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There is also a strategy for your 9 times tables using your hands.

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?

Place your hands in front of you like so. If you put down your left pinky, how many fingers do you have up?

Multiplying by 9

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Multiplying by 9

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Fill out the multiplication chart below.

Is there a pattern?

What else do you notice?

1

2

3

4

5

6

7

8

9

10

Factor x 9

Multiplying by 9

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Click on the window to play a multiplication game.

Multiplying by 9 Game

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71 The products of multiplication problems with 9 in them are all even.

True

False

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71 The products of multiplication problems with 9 in them are all even.

True

False

[This object is a pull tab]

Ans

wer

False

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72 Nine teachers each have 4 computers in their classrooms. How many computers is that in all?

A 13

B 5

C 36

D 94

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72 Nine teachers each have 4 computers in their classrooms. How many computers is that in all?

A 13

B 5

C 36

D 94

[This object is a pull tab]

Ans

wer

C

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73 What number is not a multiple of 9?

A 9

B 19

C 27

D 90

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73 What number is not a multiple of 9?

A 9

B 19

C 27

D 90

[This object is a pull tab]

Ans

wer

B

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74 If there are 9 starfish, there would be 45 legs?

Yes

No

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74 If there are 9 starfish, there would be 45 legs?

Yes

No

[This object is a pull tab]

Ans

wer

Yes

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75 What is 9 x 8?

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75 What is 9 x 8?

[This object is a pull tab]

Ans

wer

72

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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?

From PARCC EOY sample test #25

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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?

From PARCC EOY sample test #25

[This object is a pull tab]

Ans

wer

36 model cars

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Squares & Rectangles

click to return to table of contents

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A square is a shape where all four sides are the same length. The four corners are all right angles.

Squares

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A rectangle is a four sided shape. All four corners are right angles.

Rectangles

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A rectangle is a four sided shape. All four corners are right angles.

A square is a shape where all four sides are the same length. The four corners are all 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.

Squares & Rectangles

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77 Choose all of the below that are squares.

A B C D E F

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77 Choose all of the below that are squares.

A B C D E F

[This object is a pull tab]

Ans

wer

B,D

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78 Choose all of the below that are rectangles.

A B C D E F

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78 Choose all of the below that are rectangles.

A B C D E F

[This object is a pull tab]

Ans

wer

B, D, E

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79 Is a square a rectangle?

Yes

No

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79 Is a square a rectangle?

Yes

No

[This object is a pull tab]

Ans

wer

Yes

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80 Is a rectangle a square?

Yes

No

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80 Is a rectangle a square?

Yes

No

[This object is a pull tab]

Ans

wer

No

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Unit Squares and Tiling - Area of Squares

click to return to 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

What is Area?

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A unit square, is a square that has side lengths of one.

1 unit

1 unit

Area is the number of square units it takes to cover the surface of a unit.

What is Area?

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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?

unit square

Area

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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?

unit square

Area

Teac

her N

otes

[This object is a teacher notes pull tab]

Unit square is infinitely cloned.

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How many unit squares would you need to cover the area of the square?

unit square

Now make a square that has sides of 4 units.

Area

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How many unit squares would you need to cover the area of the square?

unit square

Now make a square that has sides of 4 units.

Area

Teac

her N

otes

[This object is a teacher notes pull tab]

Unit square is infinitely cloned.

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81 The area is the part around the outside of a shape.

True

False

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81 The area is the part around the outside of a shape.

True

False

[This object is a pull tab]

Ans

wer

False

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82 How many unit squares will it take to cover this square?

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82 How many unit squares will it take to cover this square?

[This object is a pull tab]

Ans

wer

4 square units

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83 How many unit squares will it take to cover this square?

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83 How many unit squares will it take to cover this square?

[This object is a pull tab]

Ans

wer

25 square units

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84 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.)

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84 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.)

[This object is a pull tab]

Ans

wer

49 square units

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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.

or

or

lengthwidth

baseheight

AREA

Finding the Area of a Square

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Square Side Lengths

Number of Unit Squares to

Cover

2 4

3 9

4 16

5 25

6

7 49

Area of a Square

Teac

her N

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85 What is the area of a square with side lengths of 9 units?

_______ square units

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85 What is the area of a square with side lengths of 9 units?

_______ square units

[This object is a pull tab]

Ans

wer

81

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86 What is the area of a square with side lengths of 10 units?

_______ units 2

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Slide 193 (Answer) / 234

86 What is the area of a square with side lengths of 10 units?

_______ units 2

[This object is a pull tab]

Ans

wer

100

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87 What is the area of a square with side lengths of 1 inch?

_______ square inches

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87 What is the area of a square with side lengths of 1 inch?

_______ square inches

[This object is a pull tab]

Ans

wer

1

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Area of Rectangles

click to return to table of contents

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On grid paper, make a rectangle that has sides of 3 units by 2 units.

How many unit squares would you need to cover the rectangle? unit square

Area of Rectangles

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On grid paper, make a rectangle that has sides of 3 units by 2 units.

How many unit squares would you need to cover the rectangle? unit square

Area of Rectangles

Teac

her N

otes

[This object is a teacher notes pull tab]

Unit square is infinitely cloned.

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On grid paper, make a rectangle that has sides of 3 units by 6 units.

How many unit squares would you need to cover the rectangle?

unit square

Area of Rectangles

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Slide 197 (Answer) / 234

On grid paper, make a rectangle that has sides of 3 units by 6 units.

How many unit squares would you need to cover the rectangle?

unit square

Area of Rectangles

Teac

her N

otes

[This object is a teacher notes pull tab]

Unit square is infinitely cloned.

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On grid paper, make a rectangle that has sides of 4 units by 5 units.

How many unit squares would you need to cover the rectangle?

unit square

Area of Rectangles

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Slide 198 (Answer) / 234

On grid paper, make a rectangle that has sides of 4 units by 5 units.

How many unit squares would you need to cover the rectangle?

unit square

Area of Rectangles

Teac

her N

otes

[This object is a teacher notes pull tab]

Unit square is infinitely cloned.

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On grid paper, make a rectangle that has sides of 5 units by 3 units.

How many unit squares would you need to cover the rectangle?

unit square

Area of Rectangles

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Slide 199 (Answer) / 234

On grid paper, make a rectangle that has sides of 5 units by 3 units.

How many unit squares would you need to cover the rectangle?

unit square

Area of Rectangles

Teac

her N

otes

[This object is a teacher notes pull tab]

Unit square is infinitely cloned.

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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.

or

or

length

width

baseheight

AREA

Finding the Area of a Rectangle

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Sometimes, you are given the length and width of a rectangle. Multiply them together to find the area.

8

3 length x width = area

8 x 3 = 24

the area is 24

Area of Rectangles

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RectangleLength

Rectangle Width

Number of Unit

Squares to Cover

2 3 6

3 6 18

4 5 20

5 3 15

6 2

Area of Rectangles

Teac

her N

otes

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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.

Think: length x ________ = area

Use what you already know about multiplication and fact families to help you find the missing width.

For example,

?

5

? 5 x ____ = 45?

The length must be 9 because 5 x 9 = 45

Area of Rectangles

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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

Practice

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Click the button to play a game.

Area of Rectangles Game

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88 How many unit squares will it take to cover this rectangle?

______ square units

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88 How many unit squares will it take to cover this rectangle?

______ square units

[This object is a pull tab]

Ans

wer

24

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89 How many unit squares will it take to cover this rectangle?

______ square units

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89 How many unit squares will it take to cover this rectangle?

______ square units

[This object is a pull tab]

Ans

wer

18

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90 Look at the shaded rectangles below. Which area would you drag to label below Rectangle Number 3?

ABCD

6 feet

4 feet 4 feet

7 feet9 feet

3 feet1 2 3

From PARCC EOY sample test #19

20 square feet24 square feet27 square feet28 square feet

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90 Look at the shaded rectangles below. Which area would you drag to label below Rectangle Number 3?

ABCD

6 feet

4 feet 4 feet

7 feet9 feet

3 feet1 2 3

From PARCC EOY sample test #19

20 square feet24 square feet27 square feet28 square feet

Teac

her N

otes

[This object is a teacher notes pull tab]

Answers are infinitely cloned so students can come to the board and drag the areas into the correct box. They can input the letter that matches with the area of Rectangle Number 3 into their responders.

C

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91 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

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91 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

[This object is a pull tab]

Ans

wer

21

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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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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

[This object is a pull tab]

Ans

wer

40

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93 What is the area of a rectangle with a side length of 10 feet and a side width of 3 feet?

______ square feet

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93 What is the area of a rectangle with a side length of 10 feet and a side width of 3 feet?

______ square feet

[This object is a pull tab]

Ans

wer

30

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94 What is the area of a rectangle with a side length of 1 inch and a side width of 3 inch?

______ in2

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94 What is the area of a rectangle with a side length of 1 inch and a side width of 3 inch?

______ in2

[This object is a pull tab]

Ans

wer

3

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95 Which rectangle has an area of 24 square units?

A

B

C

D

From PARCC PBA sample test #14

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95 Which rectangle has an area of 24 square units?

A

B

C

D

From PARCC PBA sample test #14

[This object is a pull tab]

Ans

wer

C

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Area Word Problems

click to return to table of contents

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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.

The units are important. Do not forget to include them in your answer.

Area Word Problems

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96 A rectangular field measures 10 ft by 4ft. What is the area of this field?

_____ feet 2

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96 A rectangular field measures 10 ft by 4ft. What is the area of this field?

_____ feet 2

[This object is a pull tab]

Ans

wer

40

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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

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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

[This object is a pull tab]

Ans

wer

40

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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?

_____ tiles

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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?

_____ tiles

[This object is a pull tab]

Ans

wer

70

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99 There is a square garden with the side length of 7 m. What is the area of the garden?

_____ m 2

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99 There is a square garden with the side length of 7 m. What is the area of the garden?

_____ m 2

[This object is a pull tab]

Ans

wer

49

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100 The area of a square photo is 25 square inches. What is the length of one of the sides of the photo?

_____ inches

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100 The area of a square photo is 25 square inches. What is the length of one of the sides of the photo?

_____ inches

[This object is a pull tab]

Ans

wer

5

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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

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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

[This object is a pull tab]

Ans

wer

No

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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?

_____ feet2

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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?

_____ feet2

[This object is a pull tab]

Ans

wer

45

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103 Each side of our kitchen TV is 9 inches long. What is the area of the TV screen?

_______ inches2

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103 Each side of our kitchen TV is 9 inches long. What is the area of the TV screen?

_______ inches2

[This object is a pull tab]

Ans

wer

81

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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 7 x 7

B 8 + 6

C 6 x 8

D 48 x 2

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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 7 x 7

B 8 + 6

C 6 x 8

D 48 x 2

[This object is a pull tab]

Ans

wer

C

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105 A room has an area of 24 square feet. Its length is 3 feet long. What is the width?

_____ feet

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105 A room has an area of 24 square feet. Its length is 3 feet long. What is the width?

_____ feet

[This object is a pull tab]

Ans

wer

8

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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?

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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?

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9 yards

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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 EOY sample test #27

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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 EOY sample test #27

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7 inches

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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

D 6 feet

Welcome

to Mr. J's Class

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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

D 6 feet

Welcome

to Mr. J's Class

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B

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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

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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

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B, D

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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

C 90 square feet

D 109 square feet

From PARCC PBA sample test #1

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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

C 90 square feet

D 109 square feet

From PARCC PBA sample test #1

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C

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111 Part A

Tori and Leo set up their clubhouse with four tables. These rectangles represent the tabletops.

A

B

C

D

From PARCC PBA sample test #8

Enter the two tabletops with the same area, in square feet, and explain how you know that the areas are equal.

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111 Part A

Tori and Leo set up their clubhouse with four tables. These rectangles represent the tabletops.

A

B

C

D

From PARCC PBA sample test #8

Enter the two tabletops with the same area, in square feet, and explain how you know that the areas are equal.

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Student response includes each of the following 2 elements:· Computation component: The student

identifies Table B and Table D as having the same area.

· Reasoning component: The student explains that the areas are the same because 3 x 4 = 4 x 3.

Notes:· 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 feet."

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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 PBA sample test #8

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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 PBA sample test #8

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Student response includes each of the 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 either find the area of each table and add them together, (3x2) + (3x4), or since they both have the same length, you can just add the 2 widths together and then multiply by the length, 3 x (2+4)."

Note: Use of the term "distributive property" is not required.

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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.

From PARCC PBA sample test #9

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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.

From PARCC PBA sample test #9

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wer Modeling component:

Student shades a 6 x 7 array.

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114 Part B (continued from previous slide)

Find the area of the array. Explain your answer using an equation or equations.

From PARCC PBA sample test #9

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114 Part B (continued from previous slide)

Find the area of the array. Explain your answer using an equation or equations.

From PARCC PBA sample test #9

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Student response includes each of the following 2 elements:· 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.