MATH 613—S Explorations Math Tasks
Geometry and Measurement: K - 8 Learning and Teacher Practices
S Math Task 1: Quilt Patch Designs
For this activity, you will need another person. Ideally this should be a child (elementary school
student or your child), but another adult is acceptable if no children are available for you to
work with.
Task With a partner, play at least one round (#1 - #5) of the Quilt Design game and record all
four of the quilt images (sketches or photos).
(Secret) QUILT DESIGN GAME Adapted from ideas in NCTM’s
“Navigating Through Geometry in Grade 3 – 5”
Materials: Pattern Blocks
Directions
1. Using 10 – 20 pattern blocks in a contiguous arrangement,
one person designs a "secret quilt patch" (for example, see the diagram) from
pattern blocks without their partner seeing it.
2. The creator of the secret design gives directions out loud to their partner so the
partner can recreate the design without looking at it. There are no restrictions on
these verbal directions.
3. The re-creator now verbally describes to the designer what the quilt patch looks
like.
4. The partners compare the designs visually and answer questions a-e.
a. What words or phrases helped you recreate the design?
b. What words or phrases confused you? Why?
c. Can you think of better ways to explain the directions for making the
design?
d. What are the names of the pattern block pieces?
e. How many sides does your quilt block have?
5. Repeat 1 – 4 with partners switching roles.
Questions for you (please answer)
1. Our images are … (include at least four images – you/partner, partner/you)
2. Record your (you with partner) answers to questions 4a-e in the game.
3. Feel free to discuss these questions with your partner. Kid answers are more interesting!
a. How many ways can you make a quadrilateral by putting different pattern block pieces
together? Show at least four examples.
b. What are the names for the quadrilaterals you made?
c. Which quadrilaterals are the same size and shape (congruent)? How can you tell?
d. Can you make a five-sided shape with pattern blocks? A six–sided shape? A seven-sided
shape?
MATH 613—S Explorations Math Tasks
Geometry and Measurement: K - 8 Learning and Teacher Practices
S Math Task 2: Decomposing and Composing Shapes with Geoboards
Use geoboards to explore these ideas. Use actual boards (photograph your work) and take
photos or use virtual geoboards. Other displays that make sense, such as sketches on dot paper
are also OK.
Task
Explore composing and decomposing shapes as described below.
Questions for you (please answer)
1. Divide this shape into three triangles that are all the same. Explain how you
know they are the same triangle. Can you do this in more than one way? If so,
give another example.
2. Divide this shape into four triangles that are all the same. Explain how you know
they are the same triangle. Can you do this in more than one way? If so, give
another example.
3. What is the fewest number of triangles that will fill this shape? Explain how you
know. Can you do this in more than one way? If so, give another example.
4. Divide this shape into three rectangles that are all the same. Explain how you
know they are the same rectangle. Can you do this in more than one way? If so,
give another example.
5. Make a shape on a 5 pin × 5 pin geoboard using six triangles that are all the same and then redivide your shape in a different way using six triangles that are all the same. Use a shape that can
be composed of six triangles in at least two ways.
6. Make a shape on 5 pin × 5 pin geoboard using four rectangles that are all the same and then redivide your shape in a different way using four rectangles that are all the same. Use a shape that
can be composed of four rectangles in at least two ways.
MATH 613—S Explorations Math Tasks
Geometry and Measurement: K - 8 Learning and Teacher Practices
S Math Task 3: Solids and Nets
I.
II.
III.
Base
Cirlce
Square
Cirlce
IV.
Rectangle
V.
Equilateral
triangle
VI.
Square
VII.
Right scalene
triangle
VIII.
Regular
hexagon
IX.
Equilateral
triangle
Task
By hand or with technology, sketch and clearly label a net for each shape I - IX. Try really hard
to do it without looking it up or asking someone else. If you look it up, please mention this in
your write up. You aren’t given measurements, but sketch congruent faces so they look
congruent and include angle and congruence marks so a reader can tell which sides you mean
to be congruent, and which angles you mean to be right, etc.
Questions for you (please answer)
Include the net sketches with #1 and #2 in an organized way
1. Precisely name each of the three-dimensional shapes I – IX.
2. Precisely name the two-dimensional shapes components (polygons and circles) that make
up the net for each of the three-dimensional shapes I – IX.
3. Do all prisms have the same polygonal pieces in their net? Explain.
4. Do all pyramids have the same polygonal pieces in their net? Explain.
5. Do all cylinders have the same polygonal pieces in their net? Explain.
6. Do all cones have the same polygonal pieces in their net? Explain.