Mystery Blocks
Connecting Geometry, Algebra
and Science
Lenny VerMaas
ESU #6
210 5 Street P.O. Box 748
Milford, NE 68405
402-761-3341
th
Residence
205 South Washington Ave
Cortland, NE 68331
402-798-7453
lvermaas@esu6.org
http://manila.esu6.org/lvermaas
Grade level 6-10 Students calculate the surface area and volume of various
sized blocks of wood. They measure the mass, water displaced when floating,
and water displaced when submerged of the blocks. Several important
concepts are discovered as well as a “surprise” about the blocks.
Agenda






Lenny VerMaas
lvermaas@esu6.org
Overview of the mystery blocks activity.
Relate to Nebraska State Standards
Learning Strategies
Complete part of the activity.
o Estimation is important
o Measure a block and fill in the chart
o Plot point on graph paper
Processing and analyzing the data
Alternative assessment idea
o The Nebraska Hot Tub
page -1http://manila.esu6.org/lvermaas
Mystery Blocks
Materials needed:










6 pieces of wood block cut to fit inside graduated cylinder
6 pieces of wood blocks cut from another type of wood
1 piece of wood could be fixed with a plug to change the density of the block (add lead)
Cedar and oak block work well. The shape of the blocks is dependent on the level of students.
Rectangular and triangular blocks work well to start with. The blocks can be number and
painted to help disguise the type of wood and plugs.
Graduated cylinders
Gram scales
Paper towels
Scissors of some other tool to get blocks from cylinders
Calculators and rulers
Chart paper for graphing points with the volume on the horizontal and mass on the vertical.
Guided practice (depth depending on level and experience of teachers)






Review how to find the volume of a rectangular prism (triangular, pyramid, or others)
Measure in cm but use accuracy of mm
Volume is measured in cm cubed
Find the mass of the objects using the scales
Work in groups
o Blocks may be rotated to confirm measurements and check for accuracy
Plot the mass and the volume of each block and place the number of block by the point.
Sample graph
X
X
X
Mass
X
X
X
X
Volume
As students plot points look for blocks with the same number being placed at different points. Drawing
a line between numbers that are the same will highlight these points. Most of these lines will be
horizontal because the masses will be similar and volumes will vary. Volumes will differ due to
rounding or calculation mistakes. Have students reconcile differences.
Lenny VerMaas
lvermaas@esu6.org
page -2http://manila.esu6.org/lvermaas
After data is collected and plotted.
Ask for observations from the data collected and graphed. Depending on the group some will quickly
observe the following while others will need some guidance. Help them to discover the following:
 There are different types of wood. Why? Same volume different weight. Float in water
differently.
 Discuss how water displacement can be used to confirm the volume
o Block must be completely under the water
o Accuracy will vary depending on graduated cylinders used
 The density of a block can be determined by
o Mass/volume
o The percent of the block that floats under water
o The slope of the line that goes through points from the same type of wood.
 Have students estimate the density and compare with calculated density.
 Show how the points of the graph are related be a line. (could use best fit)
o (0,0) is a point on both lines
o slope of the line will be the average density of the wood.
 Using the gram stackers the smallest cube is 1 cm cubed, has a weight of 1 gram and a density of
1 so it will just float in water. (actually it should remain suspended in the water at any level)
 If using the wood with the plug its point will be off of the line
 What is the difference between mass and weight? Mass remains the same weight changes due to
gravity.
Estimate the density of blocks by observing the percent of the block under water while floating.
Have students calculate the density of their blocks.
Use a yard stick to draw a line through the points that come from the same type of wood. Pick two
points from different places on the line and find the slope of the line. Compare this slope with the
density of the blocks.
Checking the density of an object is a way to check for purity. If an object is hollow or not pure the
point would be above or below the line.
Other explorations
What changes would occur if the liquid was not water or salt water?
What is the density of objects that float or sink?
How can something that weights a lot not sink?
Literature connections “Mr. Archimedes’ Bath by Pamela Allen.
Assessments
The California Hot Tub
Lenny VerMaas
lvermaas@esu6.org
page -3http://manila.esu6.org/lvermaas
Mystery Blocks
1.
2.
3.
4.
Pick a block and complete the information requested in the table.
Measure the length to the nearest millimeter but write as centimeters.
Measure mass to the nearest gram.
When the measurements are completed, plot and label the points on the graph with the mass on
the vertical axis and volume on the horizontal axis. Put the block number and group ID by the
point.
5. If another group has measured the same block compare your measurements. If your
measurements are significantly different from another group check with that group to see how
they arrived at their numbers.
Block # Estimated Estimated
Measured volume
Measured
ml of water
ml of water
volume in
mass in
in cubic cm (show
mass in
displaced
displaced when
cubic cm.
grams
work)
grams
when floating
submerged
Lenny VerMaas
lvermaas@esu6.org
page -4http://manila.esu6.org/lvermaas
Mystery Block Worksheet
Make a graph of the following information.
Block #
Volume
1
45ml
2
18 ml
3
33 ml
4
88 ml
5
55 ml
Mass
9.5 grams
4.2 grams
6.6 grams
19.2 grams
11.6 grams
Density
Find the equation of the best fit line through the above points.
What does the slope of the line represent? Explain why.
If a block of wood was made of the same material with a volume of 160 cubic centimeters, how much
would the block weigh?
If a block of wood was made of the same material with a weight of 45 grams what would be the volume
of the block?
Another piece of wood weighs 60 grams and has a volume of 195 ml. Is this block made out of the
same type of wood? Explain.
Measure the trapezoid below. Find the area of the trapezoid in as many ways as possible. Give the
answer in square cm.
Lenny VerMaas
lvermaas@esu6.org
page -5http://manila.esu6.org/lvermaas
Mystery Block Quiz
Name ___________________
Score __________
1. Find one of the rectangular blocks. Find the volume and weight. Sketch a picture of the block and
show measurements. Show your work.
Block # ______
Volume ______
Weight _______
Density _______
2. Find one of the triangular blocks. Find the volume and weight. Sketch a picture of the block and
show measurements. Show your work.
Block # ______
Volume ______
Weight _______
Density _______
3. Find the area of the trapezoid shown below. Show your measurements and work. Give your answer
in square cm.
Lenny VerMaas
lvermaas@esu6.org
page -6http://manila.esu6.org/lvermaas
Mystery Block Quiz
Name ___________________
Score __________
1. The mass of an object can be found by weighing the object or by observing what with water?
Explain
2. The volume of an object can be calculated by measuring with a ruler or by observing what with
water? Explain
3. The density of a piece of wood can be calculated or it can be found by observing what in water?
Explain and draw a diagram.
4. On the back of this sheet make a graph of the information
Block #
Volume
Mass
1
40 ml
28 grams
2
15 ml
10 grams
3
33 ml
24 grams
4
82 ml
59 grams
5
51 ml
35 grams
5. Find the equation of the best fit line through the above points.
Density
6. What does the slope of the line represent? Explain why.
7. If a block of wood was made of the same material with a weight of 88 grams what would be the
volume of the block?
8. If a block of wood was made of the same material with a volume of 185 cubic centimeters, how
much would the block weigh?
9. Another piece of wood weighs 126 grams and has a volume of 210 ml. Is this block made out of the
same type of wood? Explain.
Lenny VerMaas
lvermaas@esu6.org
page -7http://manila.esu6.org/lvermaas
The Nebraska Hot Tub
Depth of water
Time
What’s the story??? Write a story that will fully explain the graph above.
Lenny VerMaas
lvermaas@esu6.org
page -8http://manila.esu6.org/lvermaas