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## Bridges in Mathematics Grade 5 Student Book Answer Key Unit 6 Module 1

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 1 Session 1 Answer Key **

**Fraction & Decimal Story Problems**

**Solve each problem. Show your work using numbers, labeled sketches, or words.**

Question 1.

Josie is picking apples. She has 3 identical baskets that she is trying to fill. One basket is \(\frac{3}{5}\) full, another is \(\frac{7}{10}\) full, and the last is \(\frac{2}{3}\) full. What portion of the 3 baskets has Josie filled? Give your answer as a mixed number and as an improper fraction.

Answer: 1\(\frac{29}{30}\)

Number of baskets Josie fill = 3

First basket is \(\frac{3}{5}\) full.

second is \(\frac{7}{10}\) full and the last is \(\frac{2}{3}\) full.

The portion of the 3 baskets has Josie filled = first basket + second basket + last basket

= \(\frac{3}{5}\) + \(\frac{7}{10}\) + \(\frac{2}{3}\)

= \(\frac{18}{30}\) + \(\frac{21}{30}\) + \(\frac{20}{30}\)

= \(\frac{59}{30}\)

= 1\(\frac{29}{30}\)

Question 2.

Tommy picked 2 baskets full of apples. One basket weighed 18.63 kilograms. The other basket weighed 9.97 kilograms. How much more did the first basket weigh?

Answer: 8.66 kilograms

Total number of baskets Tommy picked = 2

First basket weighed = 18.63 kilograms

Second basket weighed = 9.97 kilograms

The first basket that weigh more than second = 18.63 – 9.97 = 8.66 kilograms

Question 3.

Kaya filled 3\(\frac{1}{4}\) baskets with apples. On her way home, the baskets spilled and she lost 2\(\frac{1}{3}\) baskets of apples. What portion of the apples did not spill?

Answer: \(\frac{11}{12}\)

Kaya filled 3\(\frac{1}{4}\) baskets with apples.

she lost 2\(\frac{1}{3}\) baskets of apples.

The portion of the apples did not spill = 3\(\frac{1}{4}\) – 2\(\frac{1}{3}\)

= \(\frac{13}{4}\) – \(\frac{7}{3}\)

= \(\frac{39}{12}\) – \(\frac{28}{12}\)

= \(\frac{11}{12}\)

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 1 Session 2 Answer Key **

**Zero Patterns Review**

Question 1.

Fill in the blanks.

a. 57 × 10 = _______________

Answer: 570

57 × 10 = 570

b. 57 × 100 = _______________

Answer: 5700

57 × 100 = 5700

c. 57 × 1000 = _______________

Answer: 57000

57 × 1000 = 57000

d. 57 × 10,000 = _______________

Answer: 570000

57 × 10,000 = 570000

e. 57 × _______________ = 5,700,000

Answer: 100000

57 x **100000** = 5700000

Question 2.

What do you notice about the problems above? Explain any patterns you see.

Answer:

The number 57 is multiplied from 10 to 100000, that is from 10, 100, 1000, 10000, 100000.

Question 3.

Fill in the blanks.

a. 570 ÷ 10 = _______________

Answer: 57

570 ÷ 10 = 57

b. 570 ÷ 100 = _______________

Answer: 5.7

570 ÷ 100 = 5.7

c. 570 ÷ 1,000 = _______________

Answer: 0.57

570 ÷ 1,000 = 0.57

d. 570 ÷ 10,000 = _______________

Answer: 0.0570

570 ÷ 10,000 = 0.0570

e. 570 ÷ _______________ = 0.0057

Answer: 100000

570 ÷ **100000** = 0.0057

Question 4.

What do you notice about the problems above? Explain any patterns you see.

Answer: when the number is multiplied by 10, 100, 1000, 10000, 100000 we place as number of zeroes after the number for the result.

Question 5.

Evaluate the following expressions.

a. 25 × (6 × 5) = _______________

Answer: 750

25 x (6 x 5) = 25 x 30 = 750

b. 67 × (28 – 9) = ________________

Answer: 1273

67 x (28 – 9) = 67 x 19 = 1273

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 1 Session 3 Answer Key**

**Graphing the Cube Sequence**

Question 1.

The picture below shows the first five arrangements in the cube sequence we’ve been working with this session. Record the number of cubes it takes to build each arrangement.

Answer:

Question 2.

Write an ordered pair to represent each cube arrangement. Use the arrangement number for the first number in the pair, and the number of cubes it takes to make the arrangement for the second number in the pair. So, for example, arrangement 1 would be written as (1, 2), and arrangement 2 would be written as (2, 6).

Answer:

Here x coordinate describes the arrangement number. And y coordinate describes the number of cubes.

Question 3.

Graph and label each of the ordered pairs.

Answer:

**Coordinate Dot-to-Dots**

Question 1.

On each of the grids below, draw and number a dot at each of the ordered pairs on the list. Connect the dots in order to make a picture. The first dot is drawn for you.

a.

Answer:

b.

Answer:

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 1 Session 4 Answer Key **

**Graphing Another Cube Sequence**

Question 1.

The picture below shows the first five arrangements in the new cube sequence we’ve been working with this session. Record the number of cubes it takes to build each arrangement.

Answer:

Question 2.

Write an ordered pair to represent each cube arrangement. Use the arrangement number for the first number in the pair, and use the number of cubes it takes to make the arrangement for the second number in the pair.

Answer:

Here x coordinate describes the arrangement number. And y coordinate describes the number of cubes.

Question 3.

Graph and label each of the ordered pairs.

Answer:

**Short & Tall Towers**

Question 1.

Here are the first three arrangements in the Short Tower sequence.

- Use your cubes to build the 4th and 5th arrangements in this sequence.
- In the table below, sketch and label the 4th and 5th arrangements you built. You don’t have to make your drawings look three-dimensional.
- Record the number of cubes it took to build each of the 5 arrangements.

Answer:

Question 2.

Write an ordered pair to represent each cube arrangement in the Short Tower Sequence. Use the arrangement number for the first number in the pair, and use the number of cubes it takes to make the arrangement for the second number in the pair.

Answer:

Here x coordinate describes the arrangement number. And y coordinate describes the number of cubes.

Question 3.

Here are the first three arrangements in the Tall Tower Sequence. Build, sketch, and label the 4th and 5th arrangements in this sequence. Then record the number of cubes it took to build each of the 5 arrangements.

Answer:

Question 4.

Write an ordered pair to represent each cube arrangement in the Tall Tower Sequence.

Answer:

Here x coordinate describes the arrangement number. And y coordinate describes the number of cubes.

Question 5.

Graph and label the ordered pairs for both cube sequences—the Short Towers and the Tall Towers. Use a different color for each sequence, and fill in the key to show which is which.

Answer:

Question 6.

Compare the graphs for the two cube sequences. How are they similar? How are they different? Describe any relationships you see between the patterns in the short tower sequence and the tall tower sequence.

Answer:

short tower and tall tower sequences are parallel lines. The difference between the arrangement numbers in x- axis is 1 and the difference between the number of cubes in y- axis is 5.

**Exploring a New Sequence**

Question 1.

What do you notice about the first three arrangements in the sequence above?

Answer: For every arrangement 4 cubes are adding. We are adding to the vertical cubes which are standing and two are adding to the horizontal cubes.

Question 2.

Sketch the 4th and 5th arrangements in this sequence.

Answer:

Question 3.

How many cubes would it take to build the 149th arrangement? Explain your answer using words, numbers, or a labeled sketch.

Answer: 596 cubes

Each arrangement is always 4 times the arrangement number.

4 x 149 = (4 x 150) – (4 x 1)

= 600 – 4

=596

Question 4.

A certain arrangement takes 124 cubes to build. Which arrangement is it? Explain your answer using words, numbers, or a labeled sketch.

Answer: Arrangement 31

SInce it always takes 4 times as many cubes as the arrangement number, you can find out which arrangement this is by dividing 124 by 4.

124 = 100 + 24

100 / 4 = 25

24 / 4 = 6

so, 124 / 4 =31

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 1 Session 5 Answer Key **

**Tile Pools**

Question 1.

Here are the first five arrangements in the tile pool sequence. In the box below each arrangement, write the number of gray tiles it took to build the border for each.

Answer:

Question 2.

Write an ordered pair to represent each of the pool borders in the sequence. Use the arrangement number for the first number in the pair, and the number of gray tiles it took to make the border around the pool for the second number in the pair.

Answer:

Here x coordinate describes the arrangement number. And y coordinate describes the number of cubes.

Question 3.

Here is another picture of the first five arrangements in the tile pool sequence. In the box below each arrangement, write the number of white tiles it took to build the water.

Answer:

Question 4.

Write an ordered pair to represent each of the water areas in the sequence. Use the arrangement number for the first number in the pair, and the number of white tiles it took to make the water in the pool for the second number in the pair.

Answer:

Here x coordinate describes the arrangement number. And y coordinate describes the number of cubes.

Question 5.

Graph and label the ordered pairs for both parts of each pool—the borders, and the water. Use a different color for each sequence, and fill in the key to show which is which.

Answer:

Question 6.

In your journal, describe the shape of each graph, and tell why you think the two are so different.

Answer: Both the lines in the graph are straight lines.

But the pool border is more linear compare to pool water.

**Here are the first five arrangements in the tile pool sequence.**

Question 1.

How many tiles would it take to build the water for the 10th arrangement in this sequence? Use numbers, words, or labeled sketches to explain how you got your answer.

Answer: 100

The number of tiles would it take to build the water for the 10th arrangement in this sequence is 100.

Question 2.

How many tiles would it take to build the border for the 10th arrangement in this sequence? Use numbers, words, or labeled sketches to explain how you got your answer.

Answer: 45

The number of tiles would it take to build the border for the 10th arrangement in this sequence is 45.

Question 3.

What do you have to do to figure out how many tiles it takes to build the water for any arrangement in this sequence? Include a labeled sketch in your explanation.

Answer: Arrangement number is required and also first arrangement is required for the reference.

Question 4.

What do you have to do to figure out how many tiles it takes to build the border for any arrangement in this sequence? Include a labeled sketch in your explanation.

Answer: Arrangement number is required and also first arrangement is required for the reference.

Question 5.

It takes exactly 196 tiles to build both the water and the border for a certain arrangement in this sequence. Which arrangement is it? Use numbers, words, or labeled sketches to explain how you got your answer.

Answer: arrangement 16

It takes exactly 196 tiles to build both the water and the border for a 16 arrangement in this sequence

**More Coordinate Dot-to-Dots**

Question 1.

On the grid below, draw and number a dot at each of the ordered pairs on the list. Connect the dots in order to make a picture. The first dot is drawn for you.

Answer:

Question 2.

Make up your own dot-to-dot picture on the grid below. Use at least 12 points for your picture. List the coordinates for your picture in order.

Answer:

points:

1) (1, 1)

2) (2, 2)

3) (3, 3)

4) (4, 4)

5) (5, 5)

6) (5, 1)

7) (4, 1)

8) (2, 4)

9) (2, 1)

10) (3, 1)

11) (1, 3)

12) (1, 1)

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 1 Session 6 Answer Key**

**Anthony’s Problem**

Anthony is a junior in high school. He decided to get a job this summer so he could put some money in his college savings account. His goal was to put $1,000 into his account, but still have time to rest up before school started again. He is a very good math student who loves computers, and he was lucky to be offered a summer job with two different software companies.

Company 1 offered to pay Anthony $1 on the first day and double the amount each day ($1 the first day, $2 the next day, $4 the third day, $8 the fourth day, and so on).

in

Company 2 offered to pay Anthony $75 every day.

Which job should Anthony accept if he wants to reach his goal of earning $1,000 as quickly as possible?

If Anthony accept company 1 then he will earn $1000 quickly. He will earn $1000 in 10days if he joins in first company. But if he joins in second company then he will earn $1000 in 13 days. So, if he wants to earn $1000 quickly its better to join in first company.

Question 1.

On the next page, fill in the table for each company’s payment plan. You can stop as soon as the total amount of money reaches or goes over $1,000 for a plan, and then do the other one.

Answer:

Question 2.

On the next page, graph the running totals for each day. Graph each plan in a different color, and mark the key at the bottom of the sheet to show which is which.

Answer:

Question 3.

Which company’s plan turned out to be best? Why?

Answer:

**Graphing the Two Payment Plans**

Answer:

**Miranda’s Number Patterns**

Question 1.

Miranda made a number pattern. She started with 4 and added 3 several times. Continue Miranda’s pattern: 4, 7, 10, _______, _______, _______, _______.

Answer: 13, 16, 19, 22

The numbers are in the ascending order with difference 3

Question 2.

Miranda made another number pattern. She started at 30 and subtracted 3 each time. Continue Miranda’s new pattern: 30, 27, 24, _______, _______, _______, _______.

Answer: 21, 18, 15, 12

The numbers are in the descending pattern with difference 3.

Question 3.

Compare Miranda’s patterns. Write two observations about how her number patterns are alike, and two observations about how her number patterns are different.

Answer: In the first pattern the numbers are in the ascending order with difference 3 whereas in the second pattern the numbers are in the descending pattern with difference 3.

Question 4.

Miranda graphed one of her patterns on the coordinate grid below.

- Did Miranda graph her first or her second pattern?
- Label the ordered pairs that Miranda graphed.
- Graph and label the ordered pairs in Miranda’s other pattern.

Answer: Miranda graph her second pattern

**Bridges in Mathematics Grade 5 Student Book Unit 6 Module 1 Session 7 Answer Key **

**Work Place Instructions 6A Dragon’s Treasure**

Each pair of players needs:

- 1 Dragon’s Treasure Record Sheet to share
- 1 red and 1 blue game marker
- 1 die numbered 1-6
- scratch paper

1. Each player rolls the die once to determine who gets to start. Player 1 chooses whether to play for red or for blue.

2. Player 1 places his game marker on the coordinate grid at point (1, 0) and rolls the die. He chooses the best move, and then records his path, his score, and the coordinates of the point on which he landed.

- A player moves his marker the number of spaces he rolled, forward, backward, or sideways, but not diagonally.
- A player collects the value of any gold pieces he lands on along the way.
- If there is one star along the path the player takes, he gets to multiply his total for that turn by 10.
- If there are two stars along the path the player takes, he gets to multiply his total for that turn by 100.
- Once the player has decided on the path he will take, he must record it, using numbers and arrows. He must also record the coordinates for the point on which he lands at the end of his path as the Start Point for his next turn.

Player 1 OK, I rolled a 4.1 tried some different paths, and I decided to go 2 up and 2 over to the right. On that path, I landed on a gold piece worth $18.25, a star, and another gold piece worth $24.00. I added $18.25 and $24.00 on my scratch paper. I got $42.25, and if you multiply that by 10, you get $422.50.

3. Player 2 places her game marker on the coordinate grid at point (1, 0) and takes her turn.

4. Players take turns until they’ve each had five turns.

- Each time a player takes her next turn, she must start at the coordinate point she landed on at the end of her previous turn.

5. Players add their scores for all five turns. The player with the higher score wins the game.

Game Variations

A. Use a calculator to check your addition and multiplication.

B. Use a copy of the Challenge Record Sheet, and before the game begins, work with your partner to fill in your own values on the dragon’s gold pieces.

C. Multiply by numbers that are more interesting than 10 and 100. If you decide to use this variation, you and your partner have to agree on the numbers. The second number must be 10 times the first number.

D. Use a die numbered 4-9 instead of a die numbered 1-6.

**Rita’s Robot**

Pirate Rita built a robot to go out and collect treasure for her. She needs to program the robot so it knows where to go on the map.

The robot can collect only 90 gold coins before it has to come back, and it can travel only along the grid lines (not on the diagonals). It can travel only 30 spaces before it runs out of fuel.

Help Pirate Rita program the robot to collect as much treasure as it can carry and return to the starting point before it runs out of fuel. Draw on the map at right, and keep track of the robot’s moves on the table below.

Answer: