a
Geometry and Measurement Concepts: The student
is familiar with assorted two and threedimensional objects….
d
Geometry and Measurement Concepts: The student
determines and understands length, area, and volume (as well as
the differences among these measurements)….
h
Geometry and Measurement Concepts: The student
chooses appropriate units of measure and converts with ease between
like units….
j
Geometry and Measurement Concepts: The student
reasons proportionally with measurements…to make…larger
scale drawings.
The
student appropriately used the 1:10 scale to increase each of the
linear measurements. He converted to centimeters as appropriate,
for instance, stating that two enlarged walls are 15 cm long instead
of 150 mm long.
The student recognized that the halfcentimeter thickness of the
tagboard would be a factor in creating an accurate scale model,
sixteen centimeters on each side. The two fifteencentimeter walls
are each about two extra half centimeters where they touch the adjacent
walls.
The
student recognized, correctly, that the volume of the enlargement
is 10 x 10 x 10 = 1,000 times larger than the original. Some explanation
is in order, though. Here, since the measurements of the original
piece are stated, the smaller volume could have been computed and
shown to be onethousandth of the larger volume.
d
Mathematical Skills and Tools: The student measures length, area,
[and] volume…accurately.
f
Mathematical Skills and Tools: The student
uses…formulas…appropriately.
Standard formulas for volumes of rectangular prisms and of cylinders
are applied accurately here. The student recognized that the volume
of his creation is determined by adding the easily calculated volumes
of the standard geometric shapes that are component parts.
There are two errors in the units of measure in the calculation
of total volume. In the first line, “4 cm” should be
“4 cm²” since the 4 represents the square of the
2 cm radius. The student computed the volume of each of the four
cylindrical “bumps” as V = [r² x ]
x h. On the fifth line, “256 cc” should be “256
cm²” since it is the area of the prism’s square
base computed from the previous line’s “16 cm x 16 cm.”
The total volume determined is given with the correct units, cubic
centimeters.

c
Putting Mathematics to Work: The student
designs a physical structure, in which the student:
• generates a plan to build something….
The paragraph
describes the process of building the enlarged LEGO®. It also
describes the design issues that arose in creating the components.
• uses mathematics from Standard
2 to make the design realistic or appropriate, e.g., areas and volumes
in general and of specific geometric shapes.
• summarizes the important features
of the structure….
It would
be helpful to the reader, and more appropriate mathematical communication,
if the student had referred at least once to the “bumps”
as “cylindrical bumps” or “cylinders.” The
student appears to have recognized them as such when using the formula
for cylindrical volume in computing the total volume later in the
piece. The student observed that these cylindrical bumps could be
made from the same tagboard as the block by stacking four circular
halfinch thick disks to make each twoinch tall cylinder.
• prepares a presentation or report
that includes the question investigated, a detailed description
of how the project was carried out, and an explanation of the findings.
