Terrific tiles
This is a level 3 algebra strand activity from the Figure It Out series. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
Find and apply rules for sequential patterns.
Terrific tiles
Achievement objectives
NA3-8: Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
Required materials
- Figure It Out, Level 3, Algebra, "Terrific Tiles", page 1
- pattern blocks (optional)
See Materials that come with this resource to download:
- Terrific tiles activity (.pdf)
Activity
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.
Number of people |
Number of tiles |
|---|---|
1 |
7 |
2 |
12 |
3 |
17 |
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.
Number of people |
Number of tiles |
|---|---|
1 |
7 |
2 |
12 |
3 |
17 |
4 |
22 |
5 |
27 |
: |
: |
10 |
52 |
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:
Number of people |
1 |
2 |
3 |
4 |
: |
10 |
n |
|---|---|---|---|---|---|---|---|
Number of tiles |
7 |
7 + 5 = 12 |
12 + 5 = 17 |
17 + 5 = 22 |
: |
|
|
Using rule |
1 x 5 + 2 = 7 |
2 x 5 + 2 = 12 |
3 x 5 + 2 = 17 |
4 x 5 + 2 = 22 |
: |
10 x 5 + 2 = 52 |
n x 5 + 2 |
Students can follow the same procedure to answer the other questions on this page.
1.
52 tiles
2.
21 rhombuses
3.
31 triangles
4.
42 trapezia
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