Number Patterns
Primary 4 · Mathematics
Number Patterns
Lesson 4 of 4
20 min
Let's begin
On Monday, Umutoni tells a funny story to 2 friends. On Tuesday, each of them tells it to 2 more children. On Wednesday, each of those children tells 2 more ...
2, 4, 8, 16 ... The numbers grow faster and faster!
Today you will learn about patterns where you multiply by the same number each time.
In this pattern each term is 2 times the one before. A pattern where you multiply (or divide) by the same number every time is called a geometric progression. The number you multiply by is the common ratio.
Worked example 1
5, 20, 80, 320, …
Step 1 Divide each term by the one before it: 20 ÷ 5 = 4, 80 ÷ 20 = 4, 320 ÷ 80 = 4.
Step 2 The ratio is always 4. The rule is: start at 5, multiply by 4.
Step 3 Next term: 320 × 4 = 1 280.
Worked example 2
640, 320, 160, 80, …
Each term is half of the one before. The rule is: divide by 2. Next terms: 40, 20.
| Add 2 each time | 2 | 4 | 6 | 8 | 10 |
|---|---|---|---|---|---|
| Multiply by 2 each time | 2 | 4 | 8 | 16 | 32 |
Both patterns start 2, 4, but then they go different ways. The multiplying pattern grows much faster.
Careful! Two terms are not enough to know the rule. 2, 4 could go on 6, 8 (add 2) or 8, 16 (multiply by 2). Always look at three or more terms.
Worked example 3
3, ?, 48, 192. The last two terms are neighbours: 192 ÷ 48 = 4. So the rule is multiply by 4, and the missing term is 3 × 4 = 12. Check: 12 × 4 = 48.
Tip
Divide neighbours. Divide each term by the one before it. If you get the same answer every time, that is the common ratio. Multiply by it to continue the pattern.
Work each one in your exercise book first. Then tap Show answer to check.
Write the next two terms: 4, 12, 36, …
Answer: 108, 324. The pattern multiplies by 3.
What is the rule for 5, 50, 500, 5 000, …?
Answer: Start at 5 and multiply by 10.
Write the next two terms: 800, 400, 200, …
Answer: 100, 50. The pattern divides by 2.
Which pattern adds and which multiplies: 7, 14, 21, 28 or 7, 14, 28, 56?
Answer: 7, 14, 21, 28 adds 7. 7, 14, 28, 56 multiplies by 2.
Find the missing term: 2, ?, 18, 54
Answer: 6. 54 ÷ 18 = 3, so multiply by 3: 2 × 3 = 6.
What you learned today
Sources and credits
The stories, Rwandan examples, drawings and practice questions were written by Ganzaa.
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