We set out to see what shapes we could "cut" from other shapes using only a single straight cut.
Here's how we went.
1. Can you make a rhombus from a parallelogram?
2. Can you make a parallelogram from a rhombus?
That bottom shape looks a bit uneven.
3. Can you make a rectangle from a square?
Yep - not too hard
4. Can you make a trapezium from a hexagon?
Nice work. Cutting from corner to opposite corner
5. Can you make a triangle form a rhombus? Can it be an equilateral triangle?
Hmm, I can do the triangle bit but I don't think they're equilateral are they? Might need to tweek the angles and cut on the other diagonal.
6. Can you make a triangle from a trapezium? Can it be an equilateral triangle?
7. Can you make an irregular pentagon from a regular pentagon?
Careful to cut from one of the corners so that the remaining shape still has 5 corners and an extra one isn't added. Great move!
8. Can you make an equilateral triangle from a square?
Like a rabbit in the headlights, we hit a problem and froze - can't go forward, can't go backward. What do I do? Nothing - I just leave the square as it is.
Some interesting thinking revealed in this exercise. Students showed understanding of the properties of 2D shapes. Most found solutions without having to resort to cheating (cutting multiple lines, cutting lines that weren't straight etc).
The activity was designed to culminate in an impossible problem. You cannot cut a line through a square that will result in an equilateral triangle because wherever you cut you will include a right angle.
So how did the kids handle this? How did they respond?
Stay tuned for the next post, "Asking Impossible Questions"
Thanks to Mr Richard Black (@CapitanoAmazing), colleague and author of the blog "When 4th Grade Kids Ask The Big Questions?" http://4thgradebigquestions.blogspot.com.au/, for his inspiration, creation and initiation of the activity described above.