Circles, Circles

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?

As another route to being creative consider these four arrangements. What could they lead you to creating and share?


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.

You may assume that but you may explore other similar ideas, as this is a creative exploration.

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 .

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.

I've used "Reveal" here because this comment perhaps show too much, so only reveal if you've got a solution and you want to look at others

Rectangle number Number of counters Counters added
1 12 N/A
2 30 18
3 56 26
4 90 34
5 132 42
6 182 50

Our idea of the next size up is that each time, the old rectangle gets surrounded by another rectangle of counters .The rule is to add 8 more to the new layer than the old layer. For example in size number 2 there are 18 counters added, whereas in size 3 there are 26 counter added which is 18 + 8. Esti , Hiral , Karina, Rhiya and Roshni Year 4

We have investigated building up triangles made of circles. • Finding the meaning of the next size up • Finding pattern to get the next size up Our definition for the next size up on a triangle is to add a border round the original triangle and to keep on doing it to get the additional size up.
Triangle No. No. counters added Total of counters
1 9 10
2 18 20
3 27 30
4 36 40

The rule used is: multiply the triangle number by 9 then add the size/border number. Algebraically it was: n x 9 +n which is 9n + n which is 10 n. by Rali, Shreya, Gracie and Avril Chloe, Year 5

For the triangle you need 15 as the next size

For the triangle you need 15 as the next size

For the hexagons you need 24 counters

For the rectangle you need thirty rings all to gether

I found that to make the triangle next size up i had to add 15 and that made my shape bigger in total i had 25 pieces of circles together.
I made some mistakes but i had my teacher to help me but I think that at the end thought that it was not challenging enough for me and I did not enjoy it as much as I thought.