Growing and shrinking patterns

Patterns that change

Not all patterns repeat. Some get bigger each time, and some get smaller.

• A growing pattern increases: 2, 4, 6, 8, 10 …
• A shrinking pattern decreases: 20, 17, 14, 11, 8 …

Each number or picture in a pattern is called a term.

Growing patterns with shapes

Picture towers of blocks:

Each new term has 2 more blocks. The rule is "start at 1 and add 2 each time". Term 5 would have 9 blocks.

Shrinking patterns

A staircase going down:

Rule: "start at 10 and take away 2 each time". Next comes 2, then 0.

Finding the rule

1. Look at the first two terms. What changed?
2. Check the next pair. Is it the same change?
3. Describe the rule in words: "start at … and add (or subtract) … each time".

Writing the change between terms helps:

5 → 8 → 11 → 14, adding 3 each time.

Real-life growing and shrinking patterns

• Saving $2 every week: 2, 4, 6, 8 …
• Candles on birthday cakes: 1, 2, 3, 4 …
• A countdown: 10, 9, 8, 7 …
• Juice left in a jug as each person pours a cup.

Worked examples

Example 1: What is the next term? 3, 6, 9, 12, __

Each term goes up by 3. Next is 15.

Example 2: What is the rule? 30, 25, 20, 15

Start at 30 and subtract 5 each time.

Example 3: Is 1, 4, 7, 10 growing or shrinking?

The terms increase: growing.

Common mistakes

• Checking only the first two terms. Make sure the change is the same all the way along.
• Mixing up adding and subtracting in a shrinking pattern.
• Forgetting the start number when describing the rule.

Try it yourself

1. Next term: 4, 8, 12, 16, __
2. Next term: 50, 40, 30, __
3. Write the rule for 7, 9, 11, 13.
4. Is 12, 10, 8, 6 growing or shrinking?

Answers: 1) 20 2) 20 3) Start at 7 and add 2 each time. 4) shrinking

Quick recap

• Growing patterns increase; shrinking patterns decrease.
• A rule tells how to get from one term to the next.
• Check that the change is the same every time.