Here are some circles which are coins, counters, and rings. I used 10 coins, 19 counters, and 12 rings.

**I wonder how many coins, counters, and rings I would need to make the next size up for each?**

**What is your idea of the 'next size up'?**

My shapes are a triangle, a hexagon, and a rectangle.

**What shapes could you make by putting circles together?**

**How many would you use?**

**How many would you need for the next size up?**

## Comments

### What shapes could you make by putting circles together?

Are we assuming that the circles are packed in a hexagonal packing arrangement? Because if we are not, then we could make any shape we want with integral sides whose angles are between sixty and three-hundred degrees.

### answer

To make the triangle the next size I put the counters on top of each other to make it higher. I doubled the counters.

Then I made it longer. Each time I added on more counter to the bottom row. First I added 5, then 6, then 7 and then 8 .

### My answers

I added 5 coins to the bottom of the triangle to make it the next size up.

I added 6 counters to make the next size up on the Hexagon.

I added 8 rings to the rectangle to make it the next size up.