Engage NY Eureka Math 5th Grade Module 5 Lesson 2 Answer Key

Eureka Math Grade 5 Module 5 Lesson 2 Problem Set Answer Key

Question 1.
Shade the following figures on centimeter grid paper. Cut and fold each to make 3 open boxes, taping them so they hold their shapes. Pack each box with cubes. Write how many cubes fill each box.
a.

Number of cubes: ____________

Number of cubes = 8

b.

Number of cubes: ____________

Number of cubes =  16

c.

Number of cubes: ____________

Number of cubes = 48

Question 2.
Predict how many centimeter cubes will fit in each box, and briefly explain your predictions. Use cubes to find the actual volume. (The figures are not drawn to scale.)
a.

Prediction: _________________
Actual: ____________________

Prediction : 8 cubic centimetres

Actual : 8 cubic centemetre

2 rows by 4 colums

= 4 x 2 = 8 cubes of each 1 sq. cm

Therefore, the total number of cubes = 8 cubic centimeters

b.

Prediction: _________________
Actual: ____________________

Prediction : 16

Actual : 16

2 rows x 4 columns multiplied by 2

2 x 4 x 2 = 16

Therefore, number of cubes = 16

c.

Prediction: _________________
Actual: ____________________

Prediction : 40

Actual : 40

2 rows x 5 columns multiplied by 4

2 x 5 x 4 = 40

Therefore, total number of cubes = 40

Question 3.
Cut out the net in the template, and fold it into a cube. Predict the number of 1-centimeter cubes that would be required to fill it.
a. Prediction: ____________________
c. How many 1-centimeter cubes are used to fill the figure? Was your prediction accurate?

Prediction: 1 cube

I know that the net has 6 faces, When I folded the net it is in the shape of cube so, it cannot be a open box.

Eureka Math Grade 5 Module 5 Lesson 2 Exit Ticket Answer Key

Question 1.
If this figure were to be folded into a box, how many cubes would fill it?

Number of cubes: _____________

8

Question 2.
Predict how many centimeter cubes will fit in the box, and briefly explain your prediction. Use cubes to find the actual volume. (The figure is not drawn to scale.)

Prediction: _________________
Actual: ____________________

Prediction : 12

Rows = 2 and

Columns = 3

2 layers

Now, 2 x 3 x 2 =12

Therefore, total number of cubes = 12

Question 1.
Make the following boxes on centimeter grid paper. Cut and fold each to make 3 open boxes, taping them so they hold their shape. How many cubes would fill each box? Explain how you found the number.
a.

Number of cubes: _____________

b.

Number of cubes: _____________

c.

Number of cubes: _____________

Question 2.
How many centimeter cubes would fit inside each box? Explain your answer using words and diagrams on each box. (The figures are not drawn to scale.)
a.

Number of cubes: ____________________

Explanation:

2 rows and 3 columns ( Each cube measures 1 cm

So, 2 x 3 = 6

b.

Number of cubes: ____________________

Explanation:

2 rows x 3 columns multiplied by 2

6 x 2 = 12 cubes

c.

Number of cubes: ____________________
Explanation:

2 rows x 4 columns multiplies by 4

2 x 4 x 4 = 32

Question 3.
The box pattern below holds 24 1-centimeter cubes. Draw two different box patterns that would hold the same number of cubes.

Engage NY Eureka Math 6th Grade Module 4 Lesson 2 Answer Key

Eureka Math Grade 6 Module 4 Lesson 2 Problem Set Answer Key

Question 1.
Fill in each blank to make each equation true.
a. 132 ÷ 3 × 3 = __________
132

b. _______ ÷ 25 × 25 = 225
225

c. 56 × ______ ÷ 8 = 56
8

d. 452 × 12 ÷ ___ = 452
12

Question 2
How is the relationship of addition and subtraction similar to the relationship of multiplication and division?
Possible answer: Both relationships create identities.

Eureka Math Grade 6 Module 4 Lesson 2 Exit Ticket Answer Key

Question 1.
Fill In the blanks to make each equation true.
a. 12 ÷ 3 × __________ = 12
3

b. f × h ÷ h = __________
f

c. 45 × _________ ÷ 15 = 45
15

d. __________ ÷ r × r = p
p

Question 2.
Draw a series of tape diagrams to represent the following number sentences.
a. 12 ÷ 3 × 3 = 12

b. 4 × 5 ÷ 5 = 4

Eureka Math Grade 6 Module 4 Lesson 2 Opening Exercise Answer Key

Draw a pictorial representation of the division and multiplication problems using a tape diagram.

a. 8 ÷ 2

b. 3 × 2

Eureka Math Grade 6 Module 4 Lesson 2 Exploratory Challenge Answer Key

Work in pairs or small groups to determine equations to show the relationship between multiplication and division. Use tape diagrams to provide support for your findings.

Question 1.
Create two equations to show the relationship between multiplication and division. These equations should be identities and Include variables. Use the squares to develop these equations.

Question 2.
Write your equations on large paper. Show a series of tape diagrams to defend each of your equations.
Only one number sentence is shown there; the second number sentence and series of tape diagrams are included in the optional Discussion.
Possible answer: a × b ÷ b = a

Possible answer: a ÷ b × b = a

Use the following rubric to critique other posters.
1. Name of the group you are critiquing
2. Equation you are critiquing
3. Whether or not you believe the equations are true and reasons why

Eureka Math Grade 6 Module 4 Lesson 2 Division of Fractions Answer Key

Divisions of Fractions – Round 1

Question 1.
9 ones ÷ 3 ones
$$\frac{9}{3}$$ = 3

Question 2.
9 ÷ 3
$$\frac{9}{3}$$ = 3

Question 3.
9 tens ÷ 3 tens
$$\frac{9}{3}$$ = 3

Question 4.
90 ÷ 30
$$\frac{9}{3}$$ = 3

Question 5.
9 hundreds ÷ 3 hundreds
$$\frac{9}{3}$$ = 3

Question 6.
900 ÷ 300
$$\frac{9}{3}$$ = 3

Question 7.
9 halves ÷ 3 halves
$$\frac{9}{3}$$ = 3

Question 8.
$$\frac{9}{2} \div \frac{3}{2}$$
$$\frac{9}{3}$$ = 3

Question 9.
9 fourths ÷ 3 fourths
$$\frac{9}{3}$$

Question 10.
$$\frac{9}{4} \div \frac{3}{4}$$
$$\frac{9}{3}$$ = 3

Question 11.
$$\frac{9}{8} \div \frac{3}{8}$$
$$\frac{9}{3}$$ = 3

Question 12.
$$\frac{2}{3} \div \frac{1}{3}$$
$$\frac{2}{1}$$ = 2

Question 13.
$$\frac{1}{3} \div \frac{2}{3}$$
$$\frac{1}{2}$$

Question 14.
$$\frac{6}{7} \div \frac{2}{7}$$
$$\frac{6}{2}$$ = 3

Question 15.
$$\frac{5}{7} \div \frac{2}{7}$$
$$\frac{5}{2}=2 \frac{1}{2}$$

Question 16.
$$\frac{3}{7} \div \frac{4}{7}$$
$$\frac{3}{4}$$

Question 17.
$$\frac{6}{10} \div \frac{2}{10}$$
$$\frac{6}{2}$$ = 3

Question 18.
$$\frac{6}{10} \div \frac{4}{10}$$
$$\frac{6}{4}=1 \frac{1}{2}$$

Question 19.
$$\frac{6}{10} \div \frac{8}{10}$$
$$\frac{6}{8}=\frac{3}{4}$$

Question 20.
$$\frac{7}{12} \div \frac{2}{12}$$
$$\frac{7}{2}=3 \frac{1}{2}$$

Question 21.
$$\frac{6}{12} \div \frac{9}{12}$$
$$\frac{6}{9}=\frac{2}{3}$$

Question 22.
$$\frac{4}{12} \div \frac{11}{12}$$
$$\frac{4}{11}$$

Question 23.
$$\frac{6}{10} \div \frac{4}{10}$$
$$\frac{6}{4}=1 \frac{1}{2}$$

Question 24.
$$\frac{6}{10} \div \frac{2}{5}=\frac{6}{10} \div \frac{ }{10}$$
$$\frac{6}{4}=1 \frac{1}{2}$$

Question 25.
$$\frac{10}{12} \div \frac{5}{12}$$
$$\frac{10}{5}=2$$

Question 26.
$$\frac{5}{6} \div \frac{5}{12}=\frac{ }{12} \div \frac{5}{12}$$
$$\frac{10}{5}=2$$

Question 27.
$$\frac{10}{12} \div \frac{3}{12}$$
$$\frac{10}{3}=3 \frac{1}{3}$$

Question 28.
$$\frac{10}{12} \div \frac{1}{4}=\frac{10}{12} \div \frac{ }{12}$$
$$\frac{10}{3}=3 \frac{1}{3}$$

Question 29.
$$\frac{5}{6} \div \frac{3}{12}=\frac{ }{12} \div \frac{3}{12}$$
$$\frac{10}{3}=3 \frac{1}{3}$$

Question 30.
$$\frac{5}{10} \div \frac{2}{10}$$
$$\frac{5}{2}=2 \frac{1}{2}$$

Question 31.
$$\frac{5}{10} \div \frac{1}{5}=\frac{5}{10} \div \frac{ }{10}$$
$$\frac{5}{2}=2 \frac{1}{2}$$

Question 32.
$$\frac{1}{2} \div \frac{2}{10}=\frac{ }{10} \div \frac{2}{10}$$
$$\frac{5}{2}=2 \frac{1}{2}$$

Question 33.
$$\frac{1}{2} \div \frac{2}{4}$$
$$\frac{2}{2}=1$$

Question 34.
$$\frac{3}{4} \div \frac{2}{8}$$
3

Question 35.
$$\frac{1}{2} \div \frac{3}{8}$$
$$\frac{4}{3}=1 \frac{1}{3}$$

Question 36.
$$\frac{1}{2} \div \frac{1}{5}=\frac{1}{10} \div \frac{ }{10}$$
$$\frac{5}{2}=2 \frac{1}{2}$$

Question 37.
$$\frac{2}{4} \div \frac{1}{3}$$
$$\frac{6}{4}=1 \frac{1}{2}$$

Question 38.
$$\frac{1}{4} \div \frac{4}{6}$$
$$\frac{3}{8}$$

Question 39.
$$\frac{3}{4} \div \frac{2}{6}$$
$$\frac{9}{4}=2 \frac{1}{4}$$

Question 40.
$$\frac{5}{6} \div \frac{1}{4}$$
$$\frac{10}{3}=3 \frac{1}{3}$$

Question 41.
$$\frac{2}{9} \div \frac{5}{6}$$
$$\frac{4}{15}$$

Question 42.
$$\frac{5}{9} \div \frac{1}{6}$$
$$\frac{15}{3}$$ = 5

Question 43.
$$\frac{1}{2} \div \frac{1}{7}$$
$$\frac{7}{2}=3 \frac{1}{2}$$

Question 44.
$$\frac{5}{7} \div \frac{1}{2}$$
$$\frac{10}{7}=1 \frac{3}{7}$$

Divisions of Fractions – Round 2

Question 1.
12 ones ÷ 2 ones
$$\frac{12}{2}$$ = 6

Question 2.
12 ÷ 2
$$\frac{12}{2}$$ = 6

Question 3.
12 tens ÷ 2 tens
$$\frac{12}{2}$$ = 6

Question 4.
120 ÷ 20
$$\frac{12}{2}$$ = 6

Question 5.
12 hundreds ÷ 2 hundreds
$$\frac{12}{2}$$ = 6

Question 6.
1,200 ÷ 200
$$\frac{12}{2}$$ = 6

Question 7.
12 halves ÷ 2 halves
$$\frac{12}{2}$$ = 6

Question 8.
$$\frac{12}{2} \div \frac{2}{2}$$
$$\frac{12}{2}$$ =6

Question 9.
12 fourths ÷ 3 fourths
$$\frac{12}{3}$$ = 4

Question 10.
$$\frac{12}{4} \div \frac{3}{4}$$
$$\frac{12}{3}$$ = 4

Question 11.
$$\frac{12}{8} \div \frac{3}{8}$$
$$\frac{12}{3}$$ = 4

Question 12.
$$\frac{2}{4} \div \frac{1}{4}$$
$$\frac{2}{1}$$ = 2

Question 13.
$$\frac{1}{4} \div \frac{2}{4}$$
$$\frac{1}{2}$$

Question 14.
$$\frac{4}{5} \div \frac{2}{5}$$
$$\frac{4}{2}$$ = 2

Question 15.
$$\frac{2}{5} \div \frac{4}{5}$$
$$\frac{2}{4}=\frac{1}{2}$$

Question 16.
$$\frac{3}{5} \div \frac{4}{5}$$
$$\frac{3}{4}$$

Question 17.
$$\frac{6}{8} \div \frac{2}{8}$$
$$\frac{6}{2}$$ = 3

Question 18.
$$\frac{6}{8} \div \frac{4}{8}$$
$$\frac{6}{4}=1 \frac{1}{2}$$

Question 19.
$$\frac{6}{8} \div \frac{5}{8}$$
$$\frac{6}{5}=1 \frac{1}{5}$$

Question 20.
$$\frac{6}{10} \div \frac{2}{10}$$
$$\frac{6}{2}$$ = 3

Question 21.
$$\frac{7}{10} \div \frac{8}{10}$$
$$\frac{7}{8}$$

Question 22.
$$\frac{4}{10} \div \frac{7}{10}$$
$$\frac{4}{7}$$

Question 23.
$$\frac{6}{12} \div \frac{4}{12}$$
$$\frac{6}{4}=1 \frac{1}{2}$$

Question 24.
$$\frac{6}{12} \div \frac{2}{6}=\frac{6}{12} \div \frac{ }{12}$$
$$\frac{6}{4}=1 \frac{1}{2}$$

Question 25.
$$\frac{8}{14} \div \frac{7}{14}$$
$$\frac{8}{7}=1 \frac{1}{7}$$

Question 26.
$$\frac{8}{14} \div \frac{1}{2}=\frac{8}{14} \div \frac{ }{14}$$
$$\frac{8}{7}=1 \frac{1}{7}$$

Question 27.
$$\frac{11}{14} \div \frac{2}{14}$$
$$\frac{11}{2}=5 \frac{1}{2}$$

Question 28.
$$\frac{11}{14} \div \frac{1}{7}=\frac{11}{14} \div \frac{ }{14}$$
$$\frac{11}{2}=5 \frac{1}{2}$$

Question 29.
$$\frac{1}{7} \div \frac{6}{14}=\frac{ }{14} \div \frac{6}{14}$$
$$\frac{2}{6}=\frac{1}{3}$$

Question 30.
$$\frac{7}{18} \div \frac{3}{18}$$
$$\frac{7}{3}=2 \frac{1}{3}$$

Question 31.
$$\frac{7}{18} \div \frac{1}{6}=\frac{7}{18} \div \frac{ }{18}$$
$$\frac{7}{3}=2 \frac{1}{3}$$

Question 32.
$$\frac{1}{3} \div \frac{12}{18}=\frac{ }{18} \div \frac{12}{18}$$
$$\frac{6}{12}=\frac{1}{2}$$

Question 33.
$$\frac{1}{6} \div \frac{4}{18}$$
$$\frac{3}{4}$$

Question 34.
$$\frac{4}{12} \div \frac{8}{6}$$
$$\frac{4}{16}=\frac{1}{4}$$

Question 35.
$$\frac{1}{3} \div \frac{3}{15}$$
$$\frac{5}{3}=1 \frac{2}{3}$$

Question 36.
$$\frac{2}{6} \div \frac{1}{9}=\frac{1}{18} \div \frac{ }{18}$$
$$\frac{6}{2}$$

Question 37.
$$\frac{1}{6} \div \frac{4}{9}$$
$$\frac{3}{8}$$

Question 38.
$$\frac{2}{3} \div \frac{3}{4}$$
$$\frac{8}{9}$$

Question 39.
$$\frac{1}{3} \div \frac{3}{5}$$
$$\frac{5}{9}$$

Question 40.
$$\frac{1}{7} \div \frac{1}{2}$$
$$\frac{2}{7}$$

Question 41.
$$\frac{5}{6} \div \frac{2}{9}$$
$$\frac{15}{4}=3 \frac{3}{4}$$

Question 42.
$$\frac{5}{9} \div \frac{2}{6}$$
$$\frac{10}{6}=1 \frac{2}{3}$$
$$\frac{5}{6} \div \frac{4}{9}$$
$$\frac{15}{8}=1 \frac{7}{8}$$
$$\frac{1}{2} \div \frac{4}{5}$$
$$\frac{5}{8}$$