Egypt Primary 5 Mathematics, Week 14: Spotting the rule of a pattern

Numerical patterns and rules

Week 14 · Numerical patterns · 3 lessons

Spotting the rule of a pattern

Discover Mathematics P5: Term 1, Unit 6, Lessons 5–7

GoalFind the rule that makes a number pattern grow or shrink, and use it to write the next terms.

New words

pattern · numbers that follow a rulerule · what you do to one term to get the next, such as add 5 or multiply by 3term · one number in a pattern

Explanation

A number pattern starts at a number and uses a rule to get every next term. To find the rule, look at how one term becomes the next. If the gaps are always the same, the rule is add (or subtract) that gap: 4, 9, 14, 19 has gaps of 5, so the rule is add 5. If every term is a number of times the one before, the rule is multiply: 2, 6, 18, 54 uses multiply by 3. Test your rule on every pair of neighbours, not just the first pair. A pattern can use decimals too: 0.2, 0.7, 1.2 adds 0.5 each time.

Pattern	Rule	Next two terms
4, 9, 14, 19	add 5	24, 29
2, 6, 18, 54	multiply by 3	162, 486
80, 71, 62, 53	subtract 9	44, 35

Worked examples

Term	1	2	3	4	5	6
Value	4	9	14	19	24	29

Find the rule: 4, 9, 14, 19. The gaps are 9 − 4 = 5, 14 − 9 = 5 and 19 − 14 = 5. Rule: add 5. Next terms: 24 and 29.

Term	1	2	3	4	5
Value	2	6	18	54	162

Find the rule: 2, 6, 18, 54. 6 ÷ 2 = 3, 18 ÷ 6 = 3 and 54 ÷ 18 = 3. Rule: multiply by 3. The next term is 54 × 3 = 162.

Find the rule: 0.2, 0.7, 1.2, 1.7. Each gap is 0.5, so add 0.5. Next terms: 2.2 and 2.7.

Class activity

Rule cards. Write a start number and a rule on a card (for example start 3, add 8). The child writes the first six terms. Then the grown-up writes a pattern with a missing rule (for example 5, 15, 45, 135) and the child finds the rule. Swap roles.

Practice

Write the rule and the next two terms: 7, 13, 19, 25.

Write the rule and the next term: 3, 12, 48, 192.

Write the rule and the next two terms: 100, 92, 84, 76.

Write the rule and the next two terms: 1.5, 2, 2.5, 3.

Nour says 5, 10, 20, 25 follows the rule “add 5”. Is she right?