## Everyday Mathematics 3rd Grade Answer Key Unit 8 Multiplication and Division

Measuring Fingers

Family Note Today your child measured objects to the nearest $$\frac{1}{4}$$ inch by using $$\frac{1}{8}$$ -inch markings on a ruler to determine which $$\frac{1}{4}$$ -inch mark was closer to the end of the object. When measuring an item, if one end is lined up with the 0 mark and the other end is to the right of the $$\frac{1}{8}$$ -inch mark, the measure is rounded to the next larger $$\frac{1}{4}$$ inch. If the end of the item is to the left of the $$\frac{1}{8}$$ -inch mark, the measure is rounded to the next smaller $$\frac{1}{4}$$ inch. Help your child trace his or her hand and use the $$\frac{1}{8}$$ -inch marks on the ruler to measure finger lengths to the nearest $$\frac{1}{4}$$ inch.

Question 1.
Cut out the ruler below. Carefully trace around one of your hands in the space below. Measure the length of each traced finger to the nearest $$\frac{1}{4}$$ inch. Write the measurement on each finger. Remember to record the unit.

Question 2.
Have someone at home trace his or her hand on the back of this page. Measure the lengths of the traced fingers to the nearest $$\frac{1}{4}$$ inch. Write the measurements above each finger.

Extended Facts: Multiplication and Division

Family Note Today your child learned to use basic multiplication facts, such as 4 × 6 = 24, to solve extended multiplication facts, such as 4 × 60, by thinking of groups of ten. For example, 4 × 60 can be thought of as 4 × 6 [10s]. If you know that 4 × 6 = 24, then you also know that 4 × 6 [10s] = 24 [10s] or 240. The same approach works for extended division facts like 120 ÷ 3 = 40. If you know that 12 ÷ 3 = 4, then you also know that 12 [10s] ÷ 3 = 4 [10s] or 40. The extended Fact Triangles below work the same way as the basic Fact Triangles.

Fill in the extended Fact Triangles. Write the extended fact families .
Question 1.

________ × ________ = ________
________ × ________ = ________
________ ÷ ________ = ________
________ ÷ ________ = ________

20 x 8 = 160.
8 x 20 = 160.
160 ÷ 8 = 20.
160 ÷  80 = 2.

Explanation:
In the above-given question,
given that,
160 and 8.
I used basic multiplication facts to solve extended multiplication facts.
20 x 8 = 160.
8 x 20 = 160.
160 ÷ 8 = 20.
160 ÷  80 = 2.

Question 2.

________ × ________ = ________
________ × ________ = ________
________ ÷ ________ = ________
________ ÷ ________ = ________

9 x 30 = 270.
30 x 9 = 270.
270 ÷ 9 = 30.
270 ÷  30 = 9.

Explanation:
In the above-given question,
given that,
30 and 9.
I used basic multiplication facts to solve extended multiplication facts.
9 x 30 = 270.
30 x 9 = 270.
270 ÷ 9 = 30.
270 ÷  30 = 9.

Question 3.

________ × ________ = ________
________ × ________ = ________
________ ÷ ________ = ________
________ ÷ ________ = ________

6 x 40 = 240.
40 x 6 = 240.
240 ÷ 6 = 40.
240/40 = 6.

Explanation:
In the above-given question,
given that,
240 and 6.
I used basic multiplication facts to solve extended multiplication facts.
6 x 40 = 240.
40 x 6 = 240.
240 ÷ 6 = 40.
240/40 = 6.

Question 4.

________ × ________ = ________
________ × ________ = ________
________ ÷ ________ = ________
________ ÷ ________ = ________

9 x 30 = 270.
30 x 9 = 270.
270 ÷ 9 = 30.
270 ÷  30 = 9.

Explanation:
In the above-given question,
given that,
30 and 9.
I used basic multiplication facts to solve extended multiplication facts.
9 x 30 = 270.
30 x 9 = 270.
270 ÷ 9 = 30.
270 ÷  30 = 9.

Factor Pairs

Family Note Today your child found factor pairs for numbers by using basic facts, pictures, and arrays. For example, 2 and 8 are a factor pair for 16 because 2 × 8 = 16.

Question 1.
The third-grade class is putting on a play. They have 18 chairs for the audience. Jayla and Kevin are in charge of arranging the chairs in equal rows with no chairs left over.
Describe ways that Jayla and Kevin can arrange the chairs.
___________________________
Listtwo factor pairs for 18:
________ × ________ = 18
________ × ________ = 18
How does knowing ways to arrange 18 chairs in equal rows help you find factors of 18?

3 x 6 = 18.
6 x 3 = 18.

Explanation:
In the above-given question,
given that,
The third-grade class is putting on a play.
They have 18 chairs for the audience.
6 rows and 3 columns.
6 x 3 = 18.
3 rows and 6 columns.
3 x 6 = 18.
The factors of 18 = 1, 2, 9, 3, 6, 18.

Question 2.
40 = ________ × ________
40 = ________ × ________

5 x 8 = 40.
8 x 5 = 40.
2 x 20 = 40.
20 x 2 = 40.

Explanation:
In the above-given question,
given that,
the number is 40.
so i used basic multiplication facts to solve the extended multiplication facts.
5 x 8 = 40.
8 x 5 = 40.
2 x 20 = 40.
20 x 2 = 40.

Question 3.
72 = ________ × ________
72 = ________ × ________

1 x 72 = 72.
72 x 1 = 72.
8 x 9 = 72.
9 x 8 = 72.

Explanation:
In the above-given question,
given that,
the number is 72.
so i used basic multiplication facts to solve the extended multiplication facts.
1 x 72 = 72.
72 x 1 = 72.
8 x 9 = 72.
9 x 8 = 72.

Try This
Question 4.
150 = ________ × ________
150 = ________ × ________

3 x 50 = 150.
50 x 3 = 150.
150 x 1 = 150.
1 x 150 = 150.

Explanation:
In the above-given question,
given that,
the number is 150.
so i used basic multiplication facts to solve the extended multiplication facts.
3 x 50 = 150.
50 x 3 = 150.
150 x 1 = 150.
1 x 150 = 150.

Making Conjectures and Arguments

Family Note Today your child learned how conjectures and arguments are related. In mathematics, a conjecture is a statement that is thought to be true, and an argument is the mathematical reasoning used to show whether a conjecture is true or false. In the problem below, children are asked to find two different ways band members can be arranged for marching. Then they are asked to choose which arrangement they think is better. When children are asked to explain the reasoning for their choice, they are being asked to make an argument. Encourage your child to show the mathematical reasoning he or she used in the explanation for which arrangement is better.

Question 1.
There are 24 members in the school band. The band director wants them to march in rows with the same number of band members in each row. Find two different ways that the band members can be arranged. Draw a sketch that shows each arrangement.

The two different ways are 6 x 4 = 24.
4 x 6 = 24.

Explanation:
In the above-given question,
given that,
There are 24 members in the school band.
The band director wants them to march in rows with the same number of band members in each row.
so the two different ways are 6 x 4 = 24.
4 x 6 = 24.

Question 2.
Which way do you think is better? Explain your reasoning.

I think the two ways are better.

Explanation:
In the above-given question,
given that,
There are 24 members in the school band.
The band director wants them to march in rows with the same number of band members in each row.
so the two different ways are 6 x 4 = 24.
4 x 6 = 24.

Factor Bingo

Family Note Today your child learned to play Factor Bingo to practice identifying factors of products. When the circled products on the game mat form a row, column, or diagonal, your child can call Bingo!

Look for a product for each factor in the table below on the Factor Bingo game mat. Circle the product on the game mat and record it next to the factor in the table. You can only use each product on the game mat one time. Explain to someone at home how you chose that product. For example, 2 is a factor of 6 because 2 × 3 equals 6. Call out Bingo! if you get five products in a row, column, or diagonal.
Question 1.

Factors of 5 = 10, 3 = 9, 10 = 60, 4 = 8, 7 = 21, 3 = 12, 2 = 16, 9 = 18, 5 = 15, 4 = 20, 8 = 24.

Explanation:
In the above-given question,
given that,
2 is a factor of 6.
2 x 3 = 6.
5 x 2 = 10.
3 x 3 = 9.
10 x 6 = 60.
4 x 2 = 8.
7 x 3 = 21.
3 x 4 = 12.
2 x 8 = 16.
9 x 2 = 18.
5 x 3 = 15.
4 x 5 = 20.
8 x 3 = 24.

Sharing Money with Friends

Family Note Today your child modeled equal sharing by distributing money amounts into equal groups. Equal sharing is one way to think about division. Work with more formal division algorithms will begin in Fourth Grade Everyday Mathematics. In the meantime, encourage your child to solve the following problems in his or her own way and to explain the strategy to you. Have your child model these problems with play money or with slips of paper labeled $10 and$1.

Question 1.
Four friends share $76. They have seven$10 bills and six $1 bills. They can go to the bank to get smaller bills . The letter ___________ represents ___________ Use numbers or pictures to show how you solved the problem: Each friend gets a total of$ ___________.

The number of dollars each friend gets = $19. Explanation: In the above-given question, given that, Four friends share$76.
They have seven $10 bills and six$1 bills.
76 / 4 = 19.
so the number of dollars each friend gets = $19. Model each sharing problem below. Record your answer. Question 2.$48 ÷ 3 = $_________ Answer:$48 / 3 = $16. Explanation: In the above-given question, given that, divide. 48 / 3 =$16.

Question 3.
$56 ÷ 4 =$ __________

$56 / 4 =$14.

Explanation:
In the above-given question,
given that,
divide.
56 / 4 = $14. Try This Question 4. Without calculating, explain how you know that$90 ÷ 5 would be larger than $90 ÷ 6. Answer: Yes,$90/5 is larger than $90/6. Explanation: In the above-given question, given that, divide. 90 / 5 =$18.
90/6 = \$15.

Locating Fractions

Family Note Today your child located and plotted fractions on a number line. To plot fractions accurately, children applied their understanding of fraction locations as a distance from 0 to an end point. They also made comparisons to 0, $$\frac{1}{2}$$, and 1 and used equivalence to place fractions. Ask your child to explain how he or she placed the fractions below on the number line.

Question 1.
Fill in the missing fractions on the number line. Choose from the fractions in the box below.

The missing fractions are 1/4 and 7/8.

Explanation:
In the above-given question,
given that,
the fractions in the box below.
the missing fractions are 1/4 and 7/8.
they are in order.
The distance from each and every fraction is the same.

Question 2.
Explain how you placed fraction A on the number line.

The distance from the fraction is the same.

Explanation:
In the above-given question,
given that,
the distance from fraction A to 1 was about the same distance as 0 to 1/8.
so I knew fraction A was 7/8.
I know that 3/4 is equivalent to 6/8.
so the next point is 7/8.

Practice
Question 3.
4 × 7 = _______

4 x 7 = 28.

Explanation:
In the above-given question,
given that,
multiply.
4 x 7 = 28.

Question 4.
________ = 6 × 8

6 x 8 = 48.

Explanation:
In the above-given question,
given that,
multiply.
6 x 8 = 48.

Question 5.
49 ÷ 7 = ________

49 ÷ 7 = 7.

Explanation:
In the above-given question,
given that,
Divide.
49 ÷ 7 = 7.

Question 6.
________ = 56 ÷ 7

56 ÷ 7 = 8.

Explanation:
In the above-given question,
given that,
Divide.
56 ÷ 7 = 8.

Making a Prism

Family Note Today your child explored attributes of prisms. The pattern on this page can be used to make a prism. Prisms are named for the shape of their bases.

Cut on the dashed lines. Fold on the dotted lines. Tape or paste each TAB inside or outside the shape.
Discuss the following questions with someone at home.
Question 1.
What shapes are the bases?

The bases are triangles.

Explanation:
In the above-given question,
given that,
cut on the dashed lines.
Fold on the dotted lines.
Tape or paste each tab inside or outside the shape.
so the shape formed on bases is triangles.

Question 2.
What shapes are the other faces?

The other faces are Rectangles.

Explanation:
In the above-given question,
given that,
cut on the dashed lines.
Fold on the dotted lines.
Tape or paste each tab inside or outside the shape.
so the shape formed on faces is rectangles.

Question 3.
How many faces are there that are not bases?

The faces that are not bases = 3.

The bases are triangles.

Explanation:
In the above-given question,
given that,
cut on the dashed lines.
Fold on the dotted lines.
Tape or paste each tab inside or outside the shape.
there are 3 faces that are not forming the bases.

Question 4.
What is this 3-dimensional shape called? Remember that prisms are named for the shape of their bases. ___________