Tasks for exploring math that are likely outside the school curriculum
Task 1. What can you do with 4 identical isosceles right triangles?
Go here: Mathigon Polypad.
Add four identical isosceles right triangles to the work space:
Explore what you can create when you place the triangles in such a way that they have a side in common.
For example, this is a hexagon:
Sketch your results. How many different designs can you make?
Did you make a single triangle? a square? a non-square rectangle? a non-special parallelogram? a trapezoid?
Task 2. Sharing a cake
Go here: 25-pin geoboard
Jessica pretended to make a cake in this shape on her geoboard:
Show all the ways she can "cut" the cake into two equal shares for herself and her brother James.
Task 3. Towers
Go here: Unifix
Here are some examples of a unifix tower 5 cubes tall:
Find all the ways you can make a tower 3 unifix cubes tall when you have two colors, brown and yellow, available.
Then write a letter to a student who was unable to attend this session. Describe all of the different towers that you built that are three cubes tall, when you had brown and yellow cubes available to work with. Why were you sure that you had made every possible tower and had not left any out?
Task 4. Tetris and beyond
Explore the shapes you get when you put squares together in such a way that they have a whole side in common. The figure below shows two blue TRIOMINOES (composed of 3 squares) and two examples of green QUADRIMINOES (composed of 4 squares). Two shapes are the SAME if you can slide, flip, or turn one of them so it fits exactly on top of the other.
Can you make any DIFFERENT triominoes from the two shown? What about quadriminoes? Sketch your findings.
Challenge: Make all the different PENTOMINOES that are possible. (Hint: There are more than 10.) Sketch your findings.
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