Practicing the **Bridges in Mathematics Grade 4 Home Connections Answer Key** **Unit 7 Module 2** will help students analyze their level of preparation.

## Bridges in Mathematics Grade 4 Home Connections Answer Key Unit 7 Module 2

**Bridges in Mathematics Grade 4 Home Connections Unit 7 Module 2 Session 1 Answer Key**

**Number Patterns**

For each pattern, fill in what comes next. Then makes each pattern.

ex: a. Pattern: 1, 4, 7, 10, 13, 16, 19

b. Rule: Add 3 each time.

Question 1.

a. Pattern: 3, 6, 12, _________, _________, _________

b. Rule: _________

Answer:

a. Pattern: 3, 6, 12, 24, 48, 96

b. Rule: Multiply 2 each time

Question 2.

a. Pattern: 16, 8, 4, _________, _________, _________

b. Rule: _________

Answer:

a. Pattern: 16, 8, 4, 2, 1, 0.5

b. Rule: Divide 2 each time.

Question 3.

a. Pattern: 10, 100, 1,000, _________, _________, _________

b. Rule: _________

Answer:

a. Pattern: 10, 100, 1,000, 10,000, 100,000, 1,000,000.

b. Rule: Multiply 10 each time

Question 4.

a. Pattern: 2\(\frac{1}{8}\), 3\(\frac{2}{8}\), 4\(\frac{3}{8}\), 5\(\frac{4}{8}\), _________, _________, _________

b. Rule: _________

Answer:

Pattern: 2\(\frac{1}{8}\), 3\(\frac{2}{8}\), 4\(\frac{3}{8}\), 5\(\frac{4}{8}\), 6\(\frac{5}{8}\), 7\(\frac{6}{8}\), 8\(\frac{7}{8}\)

b. Rule: Add 1\(\frac{1}{8}\) each time.

**CHALLENGE**

Question 5

a Pattern: \(\frac{18}{9}\), \(\frac{15}{9}\), 1\(\frac{3}{9}\), 1, _________, __________, ________

b Rule: ______________

Answer:

Pattern: \(\frac{18}{9}\), \(\frac{15}{9}\), 1\(\frac{3}{9}\), 1, \(\frac{6}{9}\), \(\frac{3}{9}\), 0.

b Rule: Subtract \(\frac{3}{9}\) each time

Question 6.

Fill in the missing numbers in each count-by sequence.

Answer:

Question 7.

Write a sentence to explain what the numbers in each sequence above have in common. Hint: Look at the numbers in the ones place.

a. All the count-by-2 numbers

Answer:

The count by 2 numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20,….

b. All the count-by-5 numbers

Answer:

The count by 5 numbers are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50,….

c. All the count-by-10 numbers

Answer:

The count by 10 numbers are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100,….

Question 8.

All the numbers in a count-by sequence are divisible by the same number. For example, all the numbers in the count-by-2 sequence are divisible by 2. Think about whether each number below is divisible by 2, 5, and 10.

Answer:

96 ÷ 2 = 48

96 is divisible by 2.

Any number having 5 or 0 in its ones place is divisible by 5.

Any number having 0 in its ones place is divisible by 10.

40 ÷ 2 = 20

40 ÷ 5 = 8

40 ÷ 10 = 4

75 is not divisible by 2.

75 ÷ 5 = 15

Any number having 0 in its ones place is divisible by 10.

75 is not divisible by 10.

37 is not divisible by 2, 5 and 10.

110 ÷ 2 = 55

Any number having 5 or 0 in its ones place is divisible by 5.

Any number having 0 in its ones place is divisible by 10.

110 is divisible by 2, 5 and 10.

364 ÷ 2 = 182

364 is not divisible by 5 and 10.

930 ÷ 2 = 465

Any number has 5 or 0 in its ones place is divisible by 5.

Any number having 0 in its ones place is divisible by 10.

361 is not divisible by 2, 5 and 10.

576 ÷ 2 = 288

576 is not divisible by 5 and 10.

Any number has 5 or 0 in its ones place is divisible by 5.

785 is divisible by 5.

**Bridges in Mathematics Grade 4 Home Connections Unit 7 Module 2 Session 4 Answer Key**

**Solving & Writing Equations**

For these problems, if an operation is in parentheses (), do it first. Otherwise, work from left to right.

Question 1.

Find the answer to each problem below. Show your work.

ex: 25 + (2 × 6) = 37

2 × 6 = 12

25 + 12 = 37

(20 ÷ 4) × 3 = _______________

6 + (15 ÷ 3) = ______________

12 × (2 + 3) = ______________

(12 + 16) ÷ 7= _____________

(14 × 3) ÷ 6 = ______________

63 ÷ (9 × 1) = ______________

Answer:

(20 ÷ 4) × 3 = _______________

5 × 3 = 15

6 + (15 ÷ 3) = ______________

6 + 5 = 11

12 × (2 + 3) = ______________

12 × 5 = 60

(12 + 16) ÷ 7= _____________

(28) ÷ 7 = 4

(14 × 3) ÷ 6 = ______________

42 ÷ 6 = 7

63 ÷ (9 × 1) = ______________

63 ÷ 9 = 7

Question 2.

Evaluate each equation to see if it makes sense. Add parentheses to those equations that need them.

Answer:

(5 × 3) + 10 = 15 + 10 = 25

12 – (6 × 2) = 12 – 12 = 0

9 × (6 ÷ 2) = 9 × 3 = 27

(5 × 4) × 3 = 20 × 3 = 60

100 ÷ (2 + 3) = 100 ÷ 5 = 20

3 + (5 × 8) = 3 + 40 = 43

Question 3.

Find the values of the variables.

z × 10 = 700

z = __________

18 = 3x

x = ____________

15 + (3 × 3) = 6y

y = ____________

120 ÷ m = 20

m = ______________

Answer:

z × 10 = 700

z = 700/10

z = 70

18 = 3x

x = 18/3

x = 6

15 + (3 × 3) = 6y

15 + 9 = 6y

24 = 6y

y = 24/6

y = 4

120 ÷ m = 20

120/20 = m

m = 6

Question 4.

Write and solve an equation for each of the word problems below:

ex: Ebony had 45 stickers. She got 3 times that many stickers for her birthday. She gave some of the stickers to her sister. Now Ebony has 120 stickers. How many stickers did Ebony give to her sister?

(45 + (3 × 45)) – s = 120

180 – s = 120

180 – 120 = s

s = 60

Ebony gave 60 stickers to her sister.

a. Mrs. Grace had 75 erasers. She divided the erasers evenly among all of her students. Each student got 3 erasers and there were 6 erasers left over. How many students are there in Mrs. Grace’s class?

Answer:

Given,

Mrs. Grace had 75 erasers. She divided the erasers evenly among all of her students. Each student got 3 erasers and there were 6 erasers left over.

(75 ÷ 3) = 25 students

25 – 2 = 23

There are 23 students in Mrs. Grace’s class.

b. Bottled water is on sale for $13 a case. Jon and his mom got several cases for the soccer team. They also got a new soccer ball for Jon that cost $19. They spent $84 in all. How many cases of bottled water did they buy?

Answer:

Given,

Bottled water is on sale for $13 a case. Jon and his mom got several cases for the soccer team. They also got a new soccer ball for Jon that cost $19. They spent $84 in all.

19 + (13 × x) = 84

13x = 84 – 19

13x = 65

x = 65/13

x = 5

Thus they buy 5 cases of bottled water.

c. Mrs. Jones brought 3 of the cases of bottled water to the soccer tournament. There were 24 bottles in each case. When they packed up to go home, there were still 16 bottles of water left. How many of the bottles of water did the team drink at the tournament?

Answer:

Given,

Mrs. Jones brought 3 of the cases of bottled water to the soccer tournament. There were 24 bottles in each case. When they packed up to go home, there were still 16 bottles of water left.

(3 × 24) – 16 = b

72 – 16 = b

b = 56 bottles

Thus the team drinks 56 bottles of water at the tournament.

Question 5.

**CHALLENGE** Solve these algebra puzzles.

Answer:

3 × x = 27

x = 27/3

x = 9

36 ÷ 9 = 4

(9 + x) × 36 = 360

9 + x = 360/36

9 + x = 10

x = 1

200 ÷ x = 20

200 ÷ 20 = x

x = 10

10 × y = 600

10 × 60 = 600

(60 – 10) + z = 58

50 + z = 58

z = 58 – 50

z = 8

Question 6.

Circle the word to show whether each equation below is true or false.

47 = 3n + 2 if the value of n is 15.

True

False

Answer:

47 = 3n + 2

47 – 2 = 3n

45 = 3n

n = 45/3

n = 15

The equation is true.

4z ÷ (3 + 3) = 10 if the value of z is 12.

True

False

Answer:

4z ÷ (3 + 3) = 10

4z ÷ 6 = 10

2z ÷ 3 = 10

2z = 10/3

2z = 3.3

z = 3.3 × 2

z = 6.6

The equation is false.