2
Rules that add and take away
Discover Mathematics P2: Term 2, Lessons 71–80
GoalUse rules that take away, and rules with two steps.
New words
take away · go down, written with a minus sign −two-step rule · a rule that does two things in turn, like +5 then −1extend · to keep a pattern going
Explanation
Some patterns go down. In 90, 80, 70 each number is 10 less, so the rule is minus 10, written −10, and the next numbers are 60 and 50. In 75, 66, 57 the rule is −9, and the next numbers are 48 and 39. Some patterns use two steps over and over. The rule +5, −1 starting at 34 gives 34, 39, 38, 43, 42, 47. Add 5, take away 1, add 5, take away 1. To find a rule, subtract the smaller number from the bigger number in the first pair, then check the second pair.
Worked examples
27, 24, 21: each number is 3 less. The rule is −3. Next: 18, 15.
66, 70, 74: the rule is +4. Next: 78, 82.
Rule +5, −1, start at 34: 34, 39, 38, 43, 42, 47, 46.
Class activity
Pattern cards. Write a start number and a rule on a card, for example 50 and −10, or 10 and +5, −1. Swap cards with a family member and write the first six numbers. Check each other's work.
Practice
1
Write the next two numbers: 100, 90, 80, 70, __, __
The rule is −10. Next: 60, 50.
2
What is the rule of 75, 66, 57? Write the next two numbers.
The rule is −9. Next: 48, 39.
3
Start at 66 and use the rule +4. Write the first five numbers.
66, 70, 74, 78, 82.
4
Use the rule +5, −1 and start at 10. Write five numbers.
10, 15, 14, 19, 18.
5
Does 12, 18, 24 follow the rule −6? Explain.
No. The numbers go up by 6 each time, so the rule is +6.