One cut geometry is a fun challenge based on a theorem that every pattern (plane graph) of straight-line cuts can be made by folding and one complete straight cut. So it should be possible to make every single polygon from one cut on a folded piece of paper.
You need scissors and a LOT of paper for this challenge. The recommendation is that the paper is square but I think you could use a regular piece of paper. Draw a scalene triangle in the middle of the paper. Can you cut the triangle with one cut? What shapes did you cut? What mistakes did you make? Below are the directions for this activity taken from Youcubed:
We decided that this challenge would be a great problem for our Summer Math Camp students because it fosters a growth mindset. Students have to try multiple times (you can see above the mistakes poster) to figure how to make a shape. When students did figure out how to cut out a shape, other students wanted to know how they did it. We celebrated mistakes as well, realizing that they were learning to learn from them.
You can adapt this idea to younger grade levels by having them do a Fold and Cut Challenge (no one cut here). This idea comes from Games for Young Minds.
Students take a piece of paper and fold it in half. Can you cut a rectangle? Can you cut a square? Can you cut a triangle? Can you cut the letter X? This version is great for students who are learning their shapes and letters.
Where’s the math? For both versions, students have to persevere to solve the problem. For the version for younger students, students learn about symmetry and shapes. For the one cut activity, students learn about properties of different polygons.
What grade level? K-12+ (The two versions, Fold and Cut and One Cut Geometry, make this activity great for all ages.
Ideas for Remote Teaching
- Synchronous Technology – Give students the challenge and have them share what they made in the first 2 or 3 attempts. I would be cautious in using this in a synchronous meeting because I think it could use a lot of time.
- Asynchronous Technology – Give students this challenge and have them post photos of ones that worked and ones that did not. You could do a GoogleSheet with different shapes on different sheets and separate the sheet into two columns – worked and did not work. Have them post their photos in the correct column.
- Paper – Send this home with students to try with family members.
- Homework – I think this activity could go on and on and on…so not sure about homework for this one.
Did you try this activity? How did it go? Do you have some suggestions. Leave a note.
Mathematical Thinking In Wuttig's World 