We included **HMH Into Math Grade 3 Answer Key**** PDF** **Module 8 Lesson 2 Find Unknown Factors and Numbers** to make students experts in learning maths.

## HMH Into Math Grade 3 Module 8 Lesson 2 Answer Key Find Unknown Factors and Numbers

I Can use multiplication and division equations with unknown numbers to solve problems.

**Spark Your Learning**

Jon is building a rectangle-shaped koi pond. He uses 24 one-foot square tiles to cover the bottom of the pond. He sets the same number of tiles in each row. How many rows of tiles can he set if he uses all the tiles?

Make a visual model of the problem to show the rows of tiles.

Answer:

He could set 4×6 rows of tiles.

Explanation:

Given that Jon is building a rectangle-shaped koi pond and he uses 24 one-foot square tiles to cover the bottom of the pond then he sets the same number of tiles in each row. So the number of rows of tiles can he set if he uses all the tiles is 4×6 = 24.

**Turn and Talk** How could you use a related multiplication or division fact to solve the problem?

**Build Understanding**

1. Jon has 4 aquariums that hold a total of 32 gallons of water. Each aquarium holds the same amount of water. How much water is in each aquarium?

A. Show your work using a visual model.

Answer:

Each aquarium can hold 8 gallons of water.

Explanation:

Given that Jon has 4 aquariums that hold a total of 32 gallons of water and each aquarium holds the same amount of water. So each aquarium can hold 32÷4 which is 8 gallons of water.

B. How many equal groups did you draw? Explain.

__________________

Answer:

4 equal number of groups.

Explanation:

The number of equal groups can we draw is 4 equal numbers.

C. What is the total number of gallons shown in your visual model? __________________

Answer:

32 gallons.

Explanation:

The total number of gallons shown in the visual model is 32 gallons.

D. How can you use your visual model to write a multiplication equation with an unknown factor to represent the problem? Use to represent the unknown factor. __________________

Answer:

4 × s = 32,

s = 8 gallons.

Explanation:

The multiplication equation for the visual model with an unknown factor is 4 × s = 32 where s is 32÷4 = 8 gallons.

E. Find the unknown factor. How much water is in each aquarium? __________________

Answer:

8 gallons.

Explanation:

The unknown factor that how much water in each aquarium is 8 gallons.

**Turn and Talk** How could the problem be rewritten so that 4 is the unknown factor?

2. Jon buys 35 new fish. He wants to place the fish into aquariums in groups of 7. How many aquariums does he need?

A. Show the problem using a visual model.

Answer:

He needs 5 aquariums.

Explanation:

Given that Jon bought 35 new fish and he wants to place the fish into aquariums in groups of 7. So the number of aquariums does he need is 35÷7 which is 5 aquariums.

B. What is the total number of fish shown in your visual model? ______________

Answer:

35 fishes.

Explanation:

The total number of fish shown in the visual model is 35 fish.

C. How many fish are in each equal group? __________

Answer:

7 fish.

Explanation:

The number of fish in each equal group is 7 fish.

D. How can you use your visual model to write a division equation with an unknown to represent the problem? Use to represent the unknown factor. _______

Answer:

35÷7 = ,

is 5.

Explanation:

The division equation to represent the problem is 35÷7 = where is 5.

E. What related multiplication equation with an unknown factor can you write to solve the problem? ____________

Answer:

7×=35.

Explanation:

The related multiplication equation is 7×=35.

F. Find the unknown factor. How many aquariums does Jon need? ____________

Answer:

5 aquariums.

Explanation:

The unknown factor will be 5. So Jon needs 5 aquariums.

**Turn and Talk** How can you tell that your answer is reasonable?

**Step It Out**

3. Nan buys 18 plants to place in aquariums for her betta fish. She places 3 plants in each aquarium. If Nan places all the plants, how many aquariums does she have?

A. Write the division equation with an unknown.

18 ÷ __ =

Answer:

18 ÷ 3 = 6.

Explanation:

The division equation is 18 ÷ 3 = where is 6.

B. Write the related multiplication equation.

× ___ = 18

Answer:

× 3 = 18.

Explanation:

The related multiplication equation is × 3 = 18

C. Solve. = ___; Nan has ___ aquariums.

Answer:

6 aquariums.

Explanation:

The are 6 and Nan has 6 aquariums.

4. Nan has 8 packs of treats for her fish. She has a total of 40 treats. If each pack has the same number of treats, how many treats are in each pack?

A. Write a multiplication equation with an unknown and the related division equation to represent the problem.

___ × = 40 40 ÷ ___ =

Answer:

8 × = 40 and 40 ÷ 8 = .

Explanation:

The multiplication equation with an unknown and the related division equation to represent the problem is

8 × = 40 and 40 ÷ 8 = .

B. Solve. = ___; Each pack has ___ treats.

Answer:

5.

Explanation:

The is 5 and each pack has 5 treats.

**Check Understanding Math Board**

Question 1.

Sami has some boxes of pens. Each box has 6 pens. Sami has 54 pens. How many boxes does Sami have? Write a multiplication equation and a division equation with an unknown to represent the problem. Solve.

Sami has ___ boxes.

Answer:

Sami has 9 boxes.

Explanation:

Given that Sami has some boxes of pens and each box has 6 pens and Sami has 54 pens. So the multiplication equation and a division equation with an unknown to represent the problem is 6 × = 54 and 54 ÷ 6 = . So Sami has 9 boxes.

**On Your Own**

**Model with Mathematics** Write a multiplication equation and a division equation with an unknown. Solve.

Question 2.

Laurence goes to the aquarium shop 5 days in a row and sees 15 new fish. He sees the same number of new fish each day. How many new fish does he see each day?

Answer:

Laurence will see 3 new fish each day.

Explanation:

Given that Laurence goes to the aquarium shop 5 days in a row and sees 15 new fish. As he sees the same number of new fish each day, the new fish does he see each day is 5 × = 15 and 15 ÷ 5 = where is 3. So Laurence will see 3 new fish each day.

Question 3.

Liam is making sandwiches for a family picnic. He uses 18 slices of bread. Each sandwich uses 2 slices of bread. How many sandwiches does Liam make?

Answer:

Liam makes 9 sandwiches.

Explanation:

Given that Liam uses 18 slices of bread and each sandwich uses 2 slices of bread. So the number of sandwiches does Liam make is 2 × = 18 and 18 ÷ 2 = . The unknown value is 9, Liam makes 9 sandwiches.

Question 4.

A mountain lion has a litter of cubs. Her litter has 24 paws. If each cub has 4 paws, how many cubs are in her litter?

Answer:

The number of cubs in her litter is 6.

Explanation:

Given that a mountain lion has a litter of cubs as her litter has 24 paws and if each cub has 4 paws. So the number of cubs are in her litter is 4 × = 24 and 24 ÷ 4 = where the unknown value is 6. So the number of cubs in her litter is 6.

Question 5.

Tamara wants to give each of her 7 friends an equal number of friendship bracelets. She gives out 28 friendship bracelets. How many bracelets does each friend get?

Answer:

The number of bracelets are 4.

Explanation:

Given that Tamara wants to give each of her 7 friends an equal number of friendship bracelets and she gives out 28 friendship bracelets. So the number of braclets does each friend get is 7 × = 28 and 28 ÷ 7 = where the unknown value is 4. So the number of bracelets are 4.

**Find the unknown number.**

Question 6.

12 ÷ ___ = 4

Answer:

12 ÷ 3 = 4.

Explanation:

Let the missing digit be X, the equation will be 12 ÷ X = 4. So X will be

X = 12 ÷ 4

X = 3.

Question 7.

27 ÷ __ = 9

Answer:

27 ÷ 3 = 9.

Explanation:

Let the missing digit be X, the equation will be 27 ÷ X = 9. So X will be

X = 27 ÷ 9

X = 3.

Question 8.

24 = 3 × ___

Answer:

24 = 3 × 8.

Explanation:

Let the missing digit be X, the equation will be 24 = 3 × X. So X will be

X = 24 ÷ 3

X = 8.

Question 9.

___ ÷ 7 = 7

Answer:

49 ÷ 7 = 7.

Explanation:

Let the missing digit be X, the equation will be X ÷ 7 = 7. So X will be

X ÷ 7 = 7,

X = 7 × 7

= 49.

Question 10.

___ × 9 = 18

Answer:

2 × 9 = 18.

Explanation:

Let the missing digit be X, the equation will be X × 9 = 18. So X will be

X × 9 = 18,

X = 18 ÷ 9,

X = 2.

Question 11.

8 = 48 ÷ __

Answer:

8 = 48 ÷ 6.

Explanation:

Let the missing digit be X, the equation will be 8 = 48 ÷ X. So X will be

8 = 48 ÷ X,

X = 48 ÷ 8,

X = 6.

Question 12.

__ ÷ 9 = 5

Answer:

45 ÷ 9 = 5.

Explanation:

Let the missing digit be X, the equation will be X ÷ 9 = 5. So X will be

X ÷ 9 = 5,

X = 5 × 9

= 45.

Question 13.

9 × __ = 36

Answer:

9 × 4 = 36.

Explanation:

Let the missing digit be X, the equation will be 9 × X = 36. So X will be

9 × X = 36,

X = 36 ÷ 9

= 4.

**On Your Own**

**Solve.**

Question 14.

Jack has $18 to spend on fish for an aquarium. He buys 6 fish. Each fish costs the same amount. How much does each fish cost?

Answer:

The cost of each fish is $3.

Explanation:

Given that Jack has $18 to spend on fish for an aquarium and he bought 6 fish. As each fish costs the same amount. So the cost of each fish is 18÷6 which is $3.

Question 15.

Nykeba is assigning tour guides for people going on museum tours. Each guide leads 4 people around the museum. There are 20 people going on a tour. How many tour guides does Nykeba assign?

Answer:

The number of tour guides does Nykeba assigned is 5 people.

Explanation:

Given that Nykeba is assigning tour guides for people going on museum tours and each guide leads 4 people around the museum as there are 20 people going on a tour. So the number of tour guides does Nykeba assign is 20÷4 = 5.

Question 16.

**Open Ended** Write a word problem that could be solved using these related multiplication and

division equations.

12 ÷ = 3 and 3 × = 12

Answer:

The unknown value is 4.

Explanation:

Given the equation is 12 ÷ = 3 and 3 × = 12 where the unknown value is 4.

**I’m in a Learning Mindset!**

What strategies do I have to solve multiplication and division problems with unknown numbers?

______________________________

______________________________