Printable ResourcesDig Up the VolumeAppendix A - Pre/Post TestAppendix B - Pre/Post Test Answer KeyAppendix C - Volume Discovery ActivityAppendix D - Engineering Design ChallengeAppendix E - Sample Data TableAppendix F - Percent Accuracy Practice PageAppendix G - Rubric

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Dig Up the Volume

Appendix A: Pre/Post TestName _____________________________

1. Plot the following points on the coordinate grid below. After you plot each point, draw a line segment to connect it to the last point you plotted. Reminder: Use your straightedge!

(-5,1); (1,3); (3,3); (3,-1); (-3,-3); (-5,-3); (-5,1); (-3,1)

Draw a line segment connecting (-3,1) and (-3,-3).Draw a line segment connecting (-3,1) and (3,3).

2. What 3-dimensional shape could this drawing represent?

________________________

3. What missing ordered pair would name the missing vertex to represent a prism?

________________________

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4. Draw the missing vertex, and then add dashed lines for the missing edges.

5. Record the following dimensions for the prism in the grid above. Use your ruler to measure in centimeters to the nearest half centimeter.

Length: _____________ Height: _____________

Width: ______________ Volume: ____________

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Appendix B: Pre/Post Test Key

1. Plot the following points on the coordinate grid below. After you plot each point, draw a line segment to connect it to the last point you plotted. Reminder: Use your straightedge!

(-5,1); (1,3); (3,3); (3,-1); (-3,-3); (-5,-3); (-5,1); (-3,1)

Draw a line segment connecting (-3,1) and (-3,-3).Draw a line segment connecting (-3,1) and (3,3).

2. What 3-dimensional shape could this drawing represent? rectangular prism

3. What missing ordered pair would name the missing vertex to represent a prism? (1, -1)

4. Draw the missing vertex, and then add dashed lines for the missing edges.

5. Record the following dimensions for the prism in the grid above. Use your ruler to measure in centimeters to the nearest half centimeter.

Length: ____3 cm___ Height: ____ 2 cm ___

Width: _____1 cm___ Volume: __3 cubic cm__

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Appendix C: Volume Discovery Activity

Name ___________________________

Discovering VolumeVolume is the measure of space inside a solid object or the amount of space an object takes up. Volume is measured in cubic units, such as cubic inches or cubic centimeters. The volume or capacity of a container is a measure of how much the container will hold or how much space it takes up.

You can calculate volume by counting the number of cubes it takes to fill up the rectangular prism.

What is the length of your box? _____________________________

What is the width of your box? _____________________________

What is the height of your box? _____________________________

Use one of the methods described above to find the volume of your box. What is it?

_________________________________

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Or… you can calculate volume by multiplying length * width* height. Be sure to label with cubic units.

Dig Up the Volume

Find a classmate with a similar volume. Compare your boxes. Are they similar? Are any of the measurements the same? Can you find anyone with a similar volume but different measurements? _______________________________________________________

_______________________________________________________

_______________________________________________________

Find the volume of the following prisms.

volume = _____ cm3

volume = _____ cm3

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Appendix D: Engineering Design Challenge

Dig Up the VolumeEngineering Design Challenge

Your challenge is to design a process to calculate the volume of a hidden rectangular prism. You will receive a box with a hidden prism and a set of sensors. You will need to utilize a coordinate grid and your knowledge of volume to correctly calculate the prism’s volume with the greatest amount of accuracy. You will be inserting your sensors into the coordinate grid on the top of the box. You will use these sensors to determine the object’s length, width, and height. Each time you receive a new box you will have one less sensor available.

You may use the following tools to help you with your challenge: ruler, sensors, graph paper, stopwatch, and a pencil. As you work through each box you should be developing a strategy to become more accurate and efficient in your calculations.

You will need to create a data table and record the following data in that table: length (cm), width (cm), height (cm), time it took your group (seconds) to determine length, width, and height, volume (cubic cm), coordinates, number of sensors used, and your percent accuracy. You will also create a line graph and plot each of your percent accuracy amounts on the graph.

Your engineer teams will be divided into the following roles. You should rotate roles for each box.

Data Recorder – your job is to record all the required data in your group’s data table and create the line graph of your percent accuracy.

Sensor Operator – your job is to “drill” with the sensors during the challenge. Process Engineer – your job is to take the information from your engineering

team and determine which coordinate you will drill next. Industrial Engineer – Your job is to keep your group working efficiently and

record the amount of time it takes the group to identify the length, width, and height of the prism.

**Remember your challenge is to create an efficient and accurate process to discover the volume of the object. Use the knowledge you discover with each sensor to help determine your next move. Think, discuss, and analyze as a team.

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Dig Up the Volume

Appendix E: Sample Data Table

Sample Data Table

Box Lette

r

Length (cm)

Width (cm)

Height (cm)

Time (seconds

)

Volume(cubic cm)

# sensors used

Coordinates Percent accuracy

A15

B14

C13

D12

E11

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Appendix F: Percent Accuracy Practice Page

Percent Accuracy

The accuracy of a measurement tells us how correct the measurement is.

You will use the following formula to express as a percent how accurate your measurements are to the actual measurements. Remember to use order of operations.

100% - (difference of measurements / actual measurement) x100%

Let’s look at an example……

Calculated measurement = 6 inches Actual measurement = 10 inches

100% - (4/10) x 100%100% - 0.4 x 100%100% - 40% = 60%

Practice… Find the degree of accuracy for the following measurements.

1. calculated- 12 inches actual – 14 inches

2. calculated- 8 cm actual – 5 cm

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Appendix G: Rubric

4 3 2 1Volume Accuracy

Within 10% Within 20% Within 30% Between 0-69% accurate or no answer

Identified coordinate points

Identified all coordinate points correctly

Identified 85-99% of coordinate points correctly

Identified 70-84% of coordinate points correctly

Identified less than 70% of coordinate points correctly

Process Design and Explanation

Designed a detailed process and explained it so that anyone could follow the process

Designed a detailed process but left out 1-2 steps when explaining

Did not have a consistent process but did explain some step used

Developed no process

Number of sensors used

Used less than 10 sensors

Used 10-11 sensors

Used 12-13 sensors

Used 14-15 sensors

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