Growing Shapes - Polygonal Numbers #MTBoS30 - 16

We've been talking about patterns in class.  Today we explored "growing shapes."  We started with this one from Day 5, Week of Inspirational Math, YouCubed:

I asked students what they noticed ... and how they saw the shape growing. I gave them a few minutes to share with their partners.

Students shared numerous ideas ... they talked about columns, rows, colors, triangular shape, symmetry, and more.

Then I asked students to name the pattern. And that's where they had quite a bit of fun! Here are some of the suggestions ...

Space Invaders
Pyramid Effect
Hourglass
Growing Tree
Ant Pile
Power Pyramids
Cloudy with a Chance of Falling Blocks
Boomerang
Propagator
Quadratic Cascading
Stairs Squared
Roof Building
Tetris Mountain

Partners then explored typical figurate numbers, triangular, square, rectangular, and pentagonal numbers.  They discussed the patterns they saw and connections between the patterns.

Students are looking for the answers to these questions, "What 3-digit number is both triangular and pentagonal? What 4-digit number is both square and pentagonal? Can you find a number that is triangular, square, AND pentagonal?"  I overhead a couple of students talking about writing a program to find their answers.  I'm looking forward to our next class.