Understand the idea.
A rule can include a choice
A decision rule chooses an action using a condition. For this rule, numbers below have added; all other numbers have subtracted. Test the current number before doing any arithmetic.
Choose only one branch in each round. “Otherwise” includes every number that does not pass the first test. In particular, is equal to ten, so it is not below ten and must use subtraction.
Check again each round
After one round, test the new number again. Starting at , the below-ten branch gives . The next round uses the otherwise branch because ten is no longer below ten, giving .
Do not keep a branch merely because you used it before. Explain each round with its current starting number, whether the condition is true, and the one calculation selected. A changed number can require a changed action.
| Input | Below 10? | Action | Result |
|---|---|---|---|
| 4 | Yes | Add 2 | 6 |
| 10 | No | Subtract 3 | 7 |
| 12 | No | Subtract 3 | 9 |
See the method in action.
One branch
Use the rule above once, starting at 6.
Worked solution
- 1
Test six against the condition.
Six is below ten, so select the add-two branch.
- 2
Apply only the selected action.
This completes one use of the rule; the subtraction branch is not also applied.
8.
Changing branches
Use the rule above twice, starting at 9.
Worked solution
- 1
Test the first starting number.
Nine is below ten, so the first round adds two.
- 2
Complete the first round.
The first result is eleven and becomes the next starting number.
- 3
Test the new starting number.
Eleven is not below ten, so select the otherwise branch.
- 4
Complete the second round.
The two results, in order, are eleven and eight.
11, then 8.
Try it yourself.
Check your understanding
For “below 10 add 2; otherwise subtract 3”, what happens to 10?
Show answer & reasoning
It becomes 7.
Ten is equal to ten, not below it. It therefore uses the otherwise branch: .
Keep practising
6 worksheet questions
Read the questions online
- Use this rule once: below 10, add 2; otherwise, subtract 3. Start at 5.
- Use the same rule once. Start at 13.
- Use the same rule once. Start at 10.
- Use the same rule twice. Start at 8.
- A different rule says: above 20, subtract 5; otherwise, add 5. Apply it once to 20.
- A child starts at 12 and adds 2 using the first rule. Explain the mistake.
Read the worked solutions
- Use this rule once: below 10, add 2; otherwise, subtract 3. Start at 5.
5 is below 10, so .
7. - Use the same rule once. Start at 13.
13 is not below 10, so .
10. - Use the same rule once. Start at 10.
Equal to 10 uses the otherwise branch: .
7. - Use the same rule twice. Start at 8.
. Check again: .
10, then 7. - A different rule says: above 20, subtract 5; otherwise, add 5. Apply it once to 20.
20 is not above 20. Use .
25. - A child starts at 12 and adds 2 using the first rule. Explain the mistake.
The condition must be checked before choosing an action.
12 is not below 10. Subtract 3 to get 9.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Number sequences; step-by-step rules; decisions; explaining resulting patterns.
Official curriculum source ↗