Terrific Tiles

If students are unsure how to begin these problems, ask them first how many tiles there are in a one-person pattern. Then ask how many extra tiles they will need for each extra person. Suggest that they record the number of tiles needed in a table.

Students should see that each time another person is added, they need five extra tiles. To find out how many tiles they need to make the pattern with 10 people, students can extend their table until they get to 10 people.

Although students are not asked to find a general rule or formula for the pattern, as an extension exercise, you could work with students to find the general rule for the pattern.
You could ask students whether they can see a quick way to count the number of tiles needed for 10 people. They know that five extra tiles are needed for each extra person, so they may say “5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 2 = 52, which is five tiles for each of the 10 people and two more needed to make the first person”.
You could use this to show them that a shorter way of writing this is 10 x 5 + 2 = 52. So if n stands for the number of people, the general rule is: number of tiles needed for n people = n x 5 + 2.
This can also be developed further in a table:

Students can follow the same procedure to answer the other questions on this page.

Answers to Activity

1. 52 tiles
2. 21 rhombuses
3. 31 triangles
4. 42 trapezia