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## Bridges in Mathematics Grade 5 Student Book Answer Key Unit 8 Module 3

**Bridges in Mathematics Grade 5 Student Book Unit 8 Module 3 Session 1 Answer Key**

** Insulation Graph Questions**

**After you create your graph, answer the following questions.**

Question 1.

Once your house heated up, how efficient was it at maintaining its temperature? What was the temperature change from the highest temperature until your team stopped taking readings?

Answer:

Constant for few minutes,

Explanation:

Once my house heated up efficiently was it at maintaining its temperature the temperature change from the highest temperature until my team stopped taking readings is 74° F.

Question 2.

What would you do differently if you could insulate your house again? Record at least two changes you would make.

Answer:

Well design the house to cut cooling and heating bills,

Explanation:

If I could insulate my house again as insulation acts as a barrier to heat flow and is essential for keeping my home warm in winter and cool in summer. A well-insulated and well-designed home provides year-round comfort, cutting cooling and heating bills and reducing greenhouse gas emissions.

**Look at another team’s graph and your own together.**

Question 3.

What was the other team’s temperature change, from the highest temperature until they stopped taking readings? How does that compare with yours?

Answer:

My temperature with other teams is almost similar,

Explanation:

As my temperature is 74° F and other team’s temperature change from the highest temperature until they stopped taking readings is also 74° F so it is same only.

Question 4.

Look at your line’s slope and the other team’s line’s slope as the temperature decreases. Which one is steeper? What does this mean?

Answer:

Inside the class room other team’s line of slope is much steeper than mine,

Explanation:

Looking at my line’s slope and the other team’s line’s slope as the others team’s line of slope decreases so other team’s line of slope is much steeper than mine.

Question 5.

Examine the other team’s house. Look at the insulation they used, and compare it with yours. Write at least three reasons why there might be a difference in the insulation efficiency of the two houses.

Answer:

Reasons:

1. Due to fibreglass,

2. Cellulose,

3. Polystyrene,

Explanation:

Examined the other team’s house. Looking at the insulation they used and comparing it with mine. Three reasons why there might be a difference in the insulation efficiency of the two houses is due to because of difference between the materials used by both of them and quality 1. The most widely used insulating material is fibreglass now days, 2. Cellulose is made from recycled paper products and isn’t just an efficient insulator, it’s very environmentally friendly and 3. Materials of polystyrene.

**Using Energy**

Question 1.

Cole’s neighbors are interested in incorporating several solar energy features into their home. They gathered information and found that they can save approximately \(\frac{1}{5}\) on basic electricity costs and an additional \(\frac{1}{4}\) on heating costs.

a. What fraction of their utility bill will Cole’s neighbors save by using solar energy? Show your work.

Answer:

Fraction of their utility bill will Cole’s neighbors save by using solar energy is \(\frac{9}{20}\),

Explanation:

Given Cole’s neighbors are interested in incorporating several solar energy features into their home. They gathered information and found that they can save approximately \(\frac{1}{5}\) on basic electricity costs and an additional \(\frac{1}{4}\) on heating costs.

So fraction of their utility bill will Cole’s neighbors save by using solar energy is \(\frac{1}{5}\) + \(\frac{1}{4}\) = \(\frac{9}{20}\).

b. If Cole’s neighbors’ monthly utility bill is approximately $200, how much money can they save on their bill each month? Show your work.

Answer:

They can save on their bill each month is $90,

Explanation:

If Cole’s neighbors’ monthly utility bill is approximately $200 much money can they save on their bill each month is as fraction of their utility bill will Cole’s neighbors save by using solar energy is \(\frac{9}{20}\), So it is $200 X \(\frac{9}{20}\) = $10 X 9 = $90.

Question 2.

The graph below shows the sources of energy used throughout the world.

a. What fraction of the energy used is petroleum? Show your work.

Answer:

The energy used in petroleum is \(\frac{39}{100}\),

Explanation:

Given graph above shows the sources of energy used throughout the world it has fraction of

natural gas \(\frac{1}{5}\), Coal \(\frac{1}{4}\), Nuclear \(\frac{5}{100}\), Renewable Energy \(\frac{11}{100}\) and let the energy used in petroleum be x so the value of x is \(\frac{1}{5}\) + \(\frac{1}{4}\) + \(\frac{5}{100}\) + \(\frac{11}{100}\) + x= 1, \(\frac{1 X 20 + 1 X 25 + 5 X 1 + 11 X 1 + x X 1}{100}\) = \(\frac{20 + 25 + 5 + 11 + x}{100}\) = \(\frac{61 + x}{100}\) therefore x = \(\frac{100 – 61}{100}\) = \(\frac{39}{100}\).

b. How much more petroleum is used than renewable energy sources? Show your work.

Answer:

More petroleum is used than renewable energy sources is \(\frac{28}{100}\),

Explanation:

Much more petroleum is used than renewable energy sources is as petroleum is \(\frac{39}{100}\) and renewable energy sources is \(\frac{11}{100}\) s it is \(\frac{39}{100}\) – \(\frac{11}{100}\) as denominators are the same it is

\(\frac{39 -11}{100}\) = \(\frac{28}{100}\).

**Bridges in Mathematics Grade 5 Student Book Unit 8 Module 3 Session 2 Answer Key **

**Solar Devices**

Question 1.

Set up your house to test the efficiency of your solar collector.

- Place the thermometer in the slot and line it up with the 0° F line.
- Read the temperature, and record the temperature and time in the table below.

- Figure out the time 20 minutes from now, and record the end time in the table.

Answer:

Explanation:

Set up my house to test the efficiency of my solar collector. Placed the thermometer in the slot and lined it up with the 0° F line. Read the temperature and recorded the temperature and time in the table above starting at 8:20 am as 73° F and figured out the time 20 minutes from now and recorded the end time at 8:40 am in the table as 73° F.

Question 2.

After 20 minutes, remove the thermometer and record the temperature. What is the change in temperature?

Answer:

Not much change same 73° F,

Explanation:

After 20 minutes removing the thermometer and recording the temperature the change in temperature is not much difference same as before 20 minutes which is 73° F.

Question 3.

Photovoltaic (PV) cells absorb solar energy and convert it to electricity. A motor converts electricity into motion. Follow these directions to see how a PV cell can run a fan for your model house.

- Place the motor stem in the slot you made on the roof (where the thermometer usually goes).
- Open up your house and carefully attach the binder clip to the stem of the motor inside your house. This will serve as a fan. Make sure the clip is not touching the top of your ceiling.
- Close the house and place the PV panel on top.
- Carefully connect the PV panel to the motor by attaching the black and red clips to each metal piece on the motor.
- Look through a window. What happens?
- Cover the PV cell with your hand. What happens?

Answer:

Fan will rotate or run,

Explanation:

As Photovoltaic (PV) cells absorb solar energy and convert it to electricity. A motor converts electricity into motion. Following these directions to see how a PV cell can run a fan for my model house. Placing the motor stem in the slot I made on the roof (where the thermometer usually goes). Opening up my house and carefully attaching the binder clip to the stem of the motor inside your house. This will serve as a fan. Making sure the clip is not touching the top of my ceiling. Closing the house and placing the PV panel on top. Carefully connecting the PV panel to the motor by attaching the black and red clips to each metal piece on the motor. Looking through the window and covering the PV cell with my hand the fans starts rotating or moving it means cells absorbed solar energy and generated electricity which makes fan to rotate.

Question 4.

Now that your house is set up for testing, follow these directions to conduct experiments with your PV cells and record your observations.

a. Place the PV cell in bright sunlight. Write at least two observations about the rate of spin of the fan.

Answer:

300 to 350 rotations per minute in morning, 380 to 400 rotations per minute in afternoon,

Explanation:

Now that my house is set up for testing following these directions to conduct experiments with my PV cells and recorded my observations placed the PV cell in bright sunlight. Wrote at least two observations about the rate of spin of the fan in morning as 300 to 350 rotations per minute and in the afternoon 380 to 400 rotations per minute.

b. Have a team member cover half of the PV cell with a piece of paper. Write at least two observations about the rate of spin of the fan.

Answer:

300 to 320 rotations per minute in morning, 350 to 380 rotations per minute in afternoon,

Explanation:

With a team member covered half of the PV cell with a piece of paper, the least two observations about the rate of spin of the fan is 300 to 320 rotations per minute in morning,

350 to 380 rotations per minute in afternoon.

c. Now try covering \(\frac{3}{4}\) of the PV cell with the paper. Write at least two observations about the rate of spin of the fan.

Answer:

280 to 300 rotations per minute in morning,

310 to 330 rotations per minute in afternoon,

Explanation:

Now covered \(\frac{3}{4}\) of the PV cell with the paper. The least two observations about the rate of spin of the fan is reduced to 280 to 300 rotations per minute in morning,

310 to 330 rotations per minute in afternoon.

d. How much of the PV cell can you cover before the motor stops?

Answer:

250 miles in 5 hours,

Explanation:

As the rate of spin of fan is 43 to 50 miles per hour so much of the PV cell can I cover before the motor stops is if motor works for at least 5 hours then the total rate of spin of fan is 50 miles X 5 hours = 250 miles in 5 hours.

e. Hold the PV cell at different angles to the sun. Write at least two observations about the rate of spin of the fan.

Answer:

The least two observations about the rate of spin of the fan is at 30° it is 40 to 48 miles per hour and at 90° it is 45 to 53 miles per hour,

Explanation:

Holding the PV cell at different angles to the sun. The least two observations about the rate of spin of the fan is at 30° it is 40 to 48 miles per hour and at 90° it is 45 to 53 miles per hour.

f. What do you think is the best angle to point the PV cell? Explain your reasoning.

Answer:

At 90°,

Explanation:

The best angle to point the PV cell is at 90° because the rate of spin of the fan is 45 to 53 miles per hour which is the maximum number of spins.

Question 5.

When the sunlight hits the PV cell, it produces watts of electricity. The more surface area exposed, the more watts the PV cell generates. One PV cell can generate 0.18 watts per square inch of surface area. How many watts can your PV cell generate? (Hint: the dimensions are 1\(\frac{1}{2}\) inches by 3 inches.)

Answer:

0.81 watts,

Explanation:

Given when sunlight hits the PV cell, it produces watts of electricity. The more surface area exposed, the more watts the PV cell generates. One PV cell can generate 0.18 watts per square inch of surface area. Number of watts can my PV cell generate is as the dimensions are 1\(\frac{1}{2}\) inches by 3 inches so it is 0.18 wats X 1\(\frac{1}{2}\) inches X 3 inches = 0.18 watts X \(\frac{3}{2}\) inches X 3 inches = 0.81 watts.

Question 6.

If you connect PV cells together, they can generate more electricity than one alone. If 1 PV cell can generate 0.18 watts per square inch, how many watts could 5 PV cells like yours generate?

Answer:

0.9 watts,

Explanation:

If I connect PV cells together they can generate more electricity than one alone. If 1 PV cell can generate 0.18 watts per square inch, Number of watts could 5 PV cells like my generate is 5 X 0.18 watts = 0.9 watts.

Question 7.

**CHALLENGE** When you covered \(\frac{3}{4}\) of your PV cell with paper, how many watts was it generating?

Answer:

0.135 watts,

Explanation:

If I covered \(\frac{3}{4}\) of my PV cell with paper then number of watts was it generating is 0.18 watts X \(\frac{3}{4}\) = 0.135 watts.

**Solar PV Cells**

Question 1.

Sage’s team added 8 photovoltaic (PV) cells to the roof of their model house. Each PV cell has dimensions of 2 × 3\(\frac{1}{2}\) inches. If each PV cell can provide 0.18 watts per square inch, how many total watts can these 8 PV cells produce? Show your work.

Answer:

10.08 watts,

Explanation:

Given Sage’s team added 8 photovoltaic (PV) cells to the roof of their model house. Each PV cell has dimensions of 2 X 3\(\frac{1}{2}\) inches. If each PV cell can provide 0.18 watts per square inch, Number of total watts can these 8 PV cells produce is 8 X 0.18 watts X 2 X 3\(\frac{1}{2}\) = 8 X 0.8 watts X 7 = 10.08 watts.

Question 2.

Satellites use PV cells to run their instruments. The cells are attached to the outer surface of the satellite.

a. Look at the picture of the satellite below. The PV cells on the surface of the satellite can provide 0.18 watts per square inch, and the satellite needs 580 watts. Is there enough surface area to meet this satellite’s electrical needs? Show your work.

Answer:

Yes, almost enough surface area to meet this satellite’s electrical needs,

Explanation:

Given the PV cells on the surface of the satellite can provide 0.18 watts per square inch and the satellite needs 580 watts. Looking at the picture of the satellite above the total surface area is 15.5 inches X 45 inches + 40 inches X 46.5 inches + 15.5 inches X 45 inches = 697.5 square inches + 1,860 square inches + 697.5 square inches = 3,255 square inches so satellite’s electrical needs is 3,255 square inches X 0.18 watts = 585.9 watts therefore almost enough surface area to meet this satellite’s electrical needs.

b. This satellite has two holes that do not have PV cells. The remaining PV cells on the surface of the satellite can provide 0.18 watts per square inch, and the satellite needs 600 watts. Is there enough surface area to meet this satellite’s electrical needs? Show your work.

Answer:

Yes, There is enough surface area to meet this satellite’s electrical needs,

Explanation:

Given this satellite has two holes that do not have PV cells. The remaining PV cells on the surface of the satellite can provide 0.18 watts per square inch and the satellite needs 600 watts. So total area of the surface excluding the two holes is (40 inches x 90 inches) – ((10 inches X 9 inches) + (12 inches X 15 inches)) = 3,600 square inches – ( 90 square inches + 180 square inches) = 3,600 square inches – 270 square inches = 3,300 square inches as the surface of the satellite can provide 0.18 watts per square inches so it is 3,300 square inches X 0.18 watts = 599.4 watts which is almost equal to 600 watts therefore yes there is enough surface area to meet this satellite’s electrical needs.

**Bridges in Mathematics Grade 5 Student Book Unit 8 Module 3 Session 3 Answer Key **

**Collector Experiment**

Mr. Ivy’s class tested their model houses with the added solar collectors. The class data is in the table shown here.

Question 1.

Plot the data on a graph, then answer the questions. Title and label the graph.

Answer:

Explanation:

Plotted the data on a graph with title as temperature and time solar collector on x – axis taken time and on y – axis as temperature as shown above.

Question 2.

Which team had the most efficient solar collector? Explain your reasoning.

Answer:

Team 3,

Explanation:

If we see the graph among the teams that had the most efficient solar collector is team 3 as it has some common and constant growth than the other teams.

Question 3.

Based on the data and your own experiments, what type of solar collector did Team 3 build? Explain your reasoning.

Answer:

Evacuated tube solar collectors,

Explanation:

Based on the data and my own experiments the type of solar collector did Team 3 build would be evacuated tube solar collectors as it has most productive and are most efficient.

**Bridges in Mathematics Grade 5 Student Book Unit 8 Module 3 Session 4 Answer Key **

**Choosing Our Materials**

Question 1.

Determine the minimum amount of cardboard you need for the house, and list the size of each piece you’ll need to cut.

Answer:

14” wide by 17\(\frac{1}{2}\)” long by 10” tall,

1 door of size 4” wide by 6” long,

2 windows of size 3” wide by 4” long,

Explanation:

The minimum amount of cardboard I need for the house is 14” wide by 17\(\frac{1}{2}\)” long by 10” tall and size of 1 door of size 4” wide by 6” long, 2 windows of size 3” wide by 4” long respectively.

Question 2.

Determine the minimum size of the piece of window material you need for the windows, and list the size of each piece you’ll need to cut. Remember that you need to make each piece \(\frac{1}{8}\)” larger than the window opening, all the way around.

Answer:

Each size of piece 3” wide by 4” long,

Explanation:

The minimum size of the piece of window material I need for the windows is 3” wide by 4” long each.

Question 3.

Determine the materials you need for any solar collection devices you are incorporating and list them below.

Answer:

Explanation:

Determined the materials I need for solar collection devices that are incorporating and list them above.

Question 4.

Determine the insulation you need.

- As a team, determine the type and amount of the materials you want to use.
- Record the amount and cost of each insulation material on the cost sheet below.
- Calculate the total cost for all the materials and write it below the table.
- Check your calculations to make sure you have enough of every material you need.
- When you have completed the cost sheet, send a team member to buy the materials from your teacher.

Answer:

Explanation:

Determined the insulation I need, As a team, determined the type and amount of the materials I want to use, Recorded the amount and cost of each insulation material on the cost sheet above, Calculated the total cost for all the materials and wrote it above in the table. Checked my calculations to make sure I have enough of every material I need.

**Another Solar House**

Question 1.

One team in Mr. Ivy’s class made a model house with dimensions 12” wide by 13\(\frac{1}{2}\)” long by 8” tall. What is the volume of their model house? Show your work.

Answer:

1,296 cubic inches,

Explanation:

Given one team in Mr. Ivy’s class made a model house with dimensions 12” wide by 13\(\frac{1}{2}\)” long by 8” tall. The volume of their model house 12” X

13\(\frac{1}{2}\)” X 8” = 1,296 cubic inches.

Question 2.

What is the total surface area of the model house’s four walls? Show your work.

Answer:

Total surface area of the model house four walls 162 square inches,

Explanation:

As Mr. Ivy’s class made a model house with dimensions 12” wide by 13\(\frac{1}{2}\)” long by 8” tall so total surface area is 12 inches X 13\(\frac{1}{2}\)” = 162 square inches.

Question 3.

The team needs to cut out windows that take up \(\frac{1}{6}\) of the surface area of the four walls. How many square inches of windows do they need to cut out? Show your work.

Answer:

27 square inches,

Explanation:

As the total surface area of the model house four walls 162 square inches and the team needs to cut out windows that take up \(\frac{1}{6}\) of the surface area of the four walls is 162 square inches X \(\frac{1}{6}\) = 27 square inches.

Question 4.

Find and list at least three more sets of dimensions a team could use to make a model house with the same volume as the team in problem 1 above. Show your work.

Answer:

12” wide by 18” long by 6” tall,

16” wide by 9” long by 9” tall,

8” wide by 18” long by 9” tall,

Explanation:

Listed three more sets of dimensions a team could use to make a model house with the same volume as the team in 12” wide by 18” long by 6” tall, 16” wide by 9” long by 9” tall, 8” wide by 18” long by 9” tall.

Question 5.

Which house dimensions would you choose to make? Explain your reasoning.

Answer:

12” wide by 18” long by 6” tall,

Explanation:

I would choose to make house dimensions of 12” wide by 18” long by 6” tall the area is same for all as 12” wide X 18” long X 6” tall = 1,296 cubic inches.

**Bridges in Mathematics Grade 5 Student Book Unit 8 Module 3 Session 5 Answer Key **

**Determining House Materials**

One team in Mr. Ivy’s class made a model house with dimensions 12″ wide by 18″ long by 6″ tall. They want to buy some insulation materials. The costs are in the table below.

Question 1.

The team decided to buy foam sheeting for the floor, ceiling, and one of the small walls without windows. How much foam sheeting do they need to buy? Show your work.

Answer:

5,832 square inches,

Explanation:

Given the team decided to buy foam sheeting for the floor, ceiling and one of the small walls without windows. Much foam sheeting do they need to buy is as foam sheet costs 8.5 inches X 5.5 inches X $0.20 = $9.35 as Mr. Ivy’s class made a model house with dimensions 12″ wide by 18″ long by 6″ tall so it is 12 inches X 18 inches X 6 inches = 1,296 cubic inches, As area of each window is 4\(\frac{1}{2}\) square inches so foam sheeting required is 1,296 cubic inches X 4\(\frac{1}{2}\) square inches = 5,832 square inches.

Question 2.

The house has 8 windows that each have an area of 4\(\frac{1}{2}\) square inches, and 1 more window with an area of 24 square inches. Ava says they only need half of one transparency film for storm windows. Is she correct? Explain your reasoning.

Answer:

Yes Ava is correct,

Explanation:

As the house has 8 windows that each have an area of 4\(\frac{1}{2}\) square inches, and 1 more window with an area of 24 square inches. Ava says they only need half of one transparency film for storm windows so the total area of windows is 8 X 4\(\frac{1}{2}\) square inches + 24 square inches = 36 square inches + 24 square inches = 60 square inches, As Ava a says they only need half of one transparency film of storm windows it is 8.5″ X 11″ = 93.5 square inches so Ava is correct as 60 square inches is less than 93.5 square inches.

Question 3.

The team decided to use weather stripping. How many inches of weather stripping will each of their small windows get if 2 windows share \(\frac{1}{2}\) yard equally? Show your work. If you need more room, write in your math journal.

Answer:

36 inches,

Explanation:

As the team decided to use weather stripping. Many inches of weather stripping will each of their small windows get if 2 windows share \(\frac{1}{2}\) yard equally 2 X \(\frac{1}{2}\) yard = 1 yard, Area of weather stripping is \(\frac{1}{2}\) yard as 1 yard is equal to 36 inches so it is 36 inches.

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