There are no other rectangles you can make with three counters. You can only make the same rectangle turned around a different way.
With 6 counters you can make another rectangle with 1 line of 6 counters.
Oliver said that with odd numbers of counters you can only make one rectangle with 1 line of counters.
Oliver, Amy and Izzy said that with even numbers of counters you can make a rectangle with 1 row of counters, or a different one with 2 rows because even numbers are in the 2 times table.
Molly pointed out that some odd numbers can make more than one rectangle; for example 9 counters can go into 3 rows of 3 counters and 15 counters can go into 3 rows of 5 counters. Izzy said that was because 9 and 15 are in the 3 times table.
Then we started to investigate different numbers of counters, starting with 1 and going up to 18. We realised that we were making arrays so we could write multiplication facts to go with our rectangles. Molly has crossed out two rectangles which she realised were similar to other ones she had already made.
We recorded our findings in a table and found that there were 31 rectangles altogether.
Number of Counters Multiplication facts for rectangles
1 1 x 1
2 1 x 2
3 1 x 3
4 1 x 4 2 x 2
5 1 x 5
6 1 x 6 2 x 3
7 1 x 7
8 1 x 8 2 x 4
9 1 x 9 3 x 3
10 1 x 10 2 x 5
11 1 x 11
12 1 x 12 2 x 6 3 x 4
13 1 x 13
14 1 x 14 2 x 7
15 1 x 15 3 x 5
16 1 x 16 2 x 8 4 x 4
17 1 x 17
18 1 x 18 2 x 9 3 x 6
We have predicted that some larger numbers of counters will be able to make more rectangles; for example 24 counters can be arranged into 4 different rectangles.