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Growing Patterns: Two Variables

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Growing Patterns: Two Variables

Look for how the number of objects changes as the term number increases. Complete each pattern and explain the relationship between the two variables.

Tile Pattern

The table shows a growing tile pattern. The term number and the number of tiles are two variables.

Term number

1

2

3

4

5

Number of tiles

4

7

10

?

?

1.Complete the tile pattern table. How many tiles belong in Term 4 and Term 5?
2.Which statement describes the tile pattern’s growth?
  • Add 2 tiles each term.
  • Add 3 tiles each term.
  • Add 4 tiles each term.
  • Multiply the number of tiles by 3 each term.
3.Write a rule connecting the term number, n, and the number of tiles, T. Use your rule to find the number of tiles in Term 8.
Draw exactly 13 square tiles in any arrangement.

Stick Pattern

A stick pattern starts with 5 sticks in Term 1, then has 9 sticks in Term 2 and 13 sticks in Term 3.

4.How many sticks are in Term 4 and Term 5 if the pattern keeps growing at the same rate?
5.Explain how the number of sticks changes between consecutive terms.
6.Choose the rule for the stick pattern, where n is the term number and S is the number of sticks.
  • S = 4n + 1
  • S = 5n
  • S = 4n − 1
  • S = n + 4

Counter Pattern

A counter pattern has 8 counters in Term 1, 13 in Term 2 and 18 in Term 3.

7.Complete the counter sequence for Terms 4 and 5, then state the number of counters added at each step.
8.Write an equation for the number of counters C in Term n. How many counters will be in Term 10?
9.A different pattern follows the rule A = 2n + 6, where n is the term number and A is the number of objects. How many objects are in Term 1, Term 2 and Term 3?

2 printable pages

  • Growing Patterns: Two Variables, page 1 of 2: Tile Pattern

    Page 1

  • Growing Patterns: Two Variables, page 2 of 2: Stick Pattern, Counter Pattern

    Page 2

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