Math Curiosity: Magic Triangles

Objective

Students will find several solutions for magic triangles of various sizes.

I'd recommend working through the Magic Squares tasks first.

Note that solutions can be rotated, reflected, and (in some cases) rearranged but still count as the same solution if the sides have the same numbers.

Steps

1. First, students find a solution that adds up to 9 for an order-3 magic triangle.
2. Next, they find a solution that equals 17 for an order-4 magic triangle.
3. They revisit the order-3 triangle and find the remaining three solutions.
4. Finally, your students will return to the order-4 triangle to find as many solutions as possible. (There are 18 unique solutions).

Resources

• Worksheet for Part 1 (PDF) Students can make many attempts at finding the solution.
• Worksheet for Part 2 (PDF)
• Worksheet for Part 3 (PDF) Find all four solutions to the Order-3 triangle.
• Worksheet for Part 4 (PDF) Find as many solutions as possible for an Order-4 triangle. (Students will need two copies).
• All Solutions for Part 4