Printable Resources
Dig Up the Volume
Appendix A - Pre/Post Test
Appendix B - Pre/Post Test Answer Key
Appendix C - Volume Discovery Activity
Appendix D - Engineering Design Challenge
Appendix E - Sample Data Table
Appendix F - Percent Accuracy Practice Page
Appendix G - Rubric
www.daytonregionalstemcenter.org
Dig Up the Volume
Appendix A: Pre/Post Test
Name _____________________________
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?
________________________
Draft: 2/9/2016
Page 2
Dig Up the Volume
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: ____________
Draft: 2/9/2016
Page 3
Dig Up the Volume
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___
Draft: 2/9/2016
Volume: __3 cubic cm__
Page 4
Dig Up the Volume
Appendix C: Volume Discovery Activity
Name ___________________________
Discovering Volume
Volume 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.
Or… you can calculate volume by
multiplying length * width* height. Be
sure to label with cubic units.
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?
_________________________________
Draft: 2/9/2016
Page 5
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
Draft: 2/9/2016
Page 6
Dig Up the Volume
Appendix D: Engineering Design Challenge
Dig Up the Volume
Engineering 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.
Draft: 2/9/2016
Page 7
Dig Up the Volume
Appendix E: Sample Data Table
Sample Data Table
Box Length Width Height
Time
Volume
#
Coordinates
Letter (cm)
(cm)
(cm) (seconds) (cubic sensors
cm)
used
Percent
accuracy
15
A
14
B
13
C
12
D
11
E
Draft: 2/9/2016
Page 8
Dig Up the Volume
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
2. calculated- 8 cm
Draft: 2/9/2016
actual – 14 inches
actual – 5 cm
Page 9
Dig Up the Volume
Appendix G: Rubric
4
3
2
Volume
Accuracy
Within 10%
Within 20%
Within 30%
Identified
coordinate
points
Identified all
coordinate
points
correctly
Identified 8599% of
coordinate
points
correctly
Designed a
detailed
process but
left out 1-2
steps when
explaining
Identified 7084% of
coordinate
points
correctly
Did not have
a consistent
process but
did explain
some step
used
Used 10-11
sensors
Used 12-13
sensors
Designed a
detailed
process and
explained it
so that
anyone
could follow
the process
Used less
Number of
sensors used than 10
sensors
Process
Design and
Explanation
Draft: 2/9/2016
1
Between 069% accurate
or no answer
Identified less
than 70% of
coordinate
points
correctly
Developed
no process
Used 14-15
sensors
Page 10