How many triangles? (basic linear pattern)

Topics: counting & combinatorics, symmetry, geometry, Linear patterns This activity focuses on the importance of counting things systematically. Why is it important to learn about counting/doing things systematically? Because counting systematically/being systematic: `\cdot`helps you not lose track of what you've counted `\cdot`helps make sure you count them all `\cdot`helps you generalize and count harder versions of the same problem `\cdot`And in today's age, things which are systematized can be automated by a computer Extension ideas: As you extend the diagram downwards the num of triangles scales linearly (as done in this activity). But if you extend the diagram outwards the num of triangles grows as a quadratic pattern (it turns out to basically be the triangular numbers). This is a good investigation for students studying quadratic patterns. If you liked this activity and found it useful, I would love to hear about it on twitter! @KenClarkson3

By Kenneth Clarkson