Understand the idea.
Order matters
A step-by-step rule is a set of instructions in order. Read the whole rule, then complete its first action before moving to the next. Keep the intermediate result because the next action uses that changed number.
“Add three, then double” differs from “double, then add three”. Starting at four, the first gives fourteen while the second gives eleven. The same operations can produce different answers when their order changes.
Repeat the whole rule
When a rule has two actions, finish both before recording a round's result. “Double and add one” means the result is found after doubling and then adding one, not halfway through the round.
For repeated rounds, use the previous result as the new starting number. Keep a small record of the start, the intermediate value and the finished result. Restarting from the original number would repeat the first round instead of continuing.
| Round | Start | Double | Add 1: result |
|---|---|---|---|
| 1 | 2 | 4 | 5 |
| 2 | 5 | 10 | 11 |
| 3 | 11 | 22 | 23 |
See the method in action.
Two instructions
Start at 4. Add 3, then double.
Worked solution
- 1
Complete the first instruction.
The rule says to add three before doubling.
- 2
Double the new number.
Doubling uses seven, the result of the first instruction.
14.
Two rounds
Start at 1. Each round, add 2 then double. Find the first 2 results.
Worked solution
- 1
Start the first round by adding two.
One is the first starting number.
- 2
Finish the first round by doubling.
The first complete result is six.
- 3
Begin the second round from six.
The previous finished result becomes the next starting number.
- 4
Finish the second round by doubling.
The first two round results are six and sixteen.
6, then 16.
Try it yourself.
Check your understanding
Start at 5. Double, then subtract 1.
Show answer & reasoning
9.
Double the starting five: . Then use that result for the second instruction: .
Keep practising
6 worksheet questions
Read the questions online
- Start at 3. Add 4, then subtract 2.
- Start at 6. Double, then add 3.
- Start at 6. Add 3, then double. Compare with the previous answer.
- Start at 10. Subtract 2 each round. Give the first 3 results.
- Start at 2. Each round, double then add 1. Find the second result.
- Change 7 into 15 using add 1 and double, each once. Give the order.
Read the worked solutions
- Start at 3. Add 4, then subtract 2.
; .
5. - Start at 6. Double, then add 3.
; .
15. - Start at 6. Add 3, then double. Compare with the previous answer.
; .
18; it is 3 more than 15. - Start at 10. Subtract 2 each round. Give the first 3 results.
; ; .
. - Start at 2. Each round, double then add 1. Find the second result.
Round 1 gives . Round 2 gives .
11. - Change 7 into 15 using add 1 and double, each once. Give the order.
; . Adding 1 first would give 16.
Double, then add 1.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Number sequences; step-by-step rules; decisions; explaining resulting patterns.
Official curriculum source ↗