Scaling Up

There are many ways that students can count the number of square tiles in each fish. Most will use one-by-one counting if you do not encourage them to explore other interesting ways to count.

Methods might include:
• using symmetry:

There are four tiles on this line of symmetry;
2 x 5 = 10 tiles are not on the line of symmetry.
Total: 10 + 4 = 14 tiles.

• using composite blocks:

4 + 4 + 6 = 14 tiles
• multiplication:

(3 x 3) + 3 + 2 = 14 tiles (or 4 x 3 + 2)

• using the larger enclosing square and noting the missing and additional tiles:

 (4 x 4) + 2 – 4 = 14 tiles
Students should try to use equal additions or multiplication to simplify the task of counting the scales (square tiles). A table using multiplication is illustrated in the Answers section.
A grandparent fish will build on the pattern of body, fins, and tail shown in the other fish.

The total number of scales on a grandparent fish is 25 + 6 + 6 + 10 = 47.

Answers to Activity

1. Baby fish have 5 scales, teenage fish have 14 scales, and adult fish have 28 scales.
2. There are 137 scales. Students could work this out in a table using multiplication:

3.