Use four parts to make reasoning visible.
- State the target. Say what must be found, including the unit or response type.
- Name the clue. Identify the relationship or information that suggests a method.
- Show the steps. Write enough calculation, table entries or diagram labels for another person to follow.
- Check the result. Test it against the original condition or estimate whether it is sensible.
This structure does not require a long speech. A few accurate sentences can reveal more than an answer alone, especially when a student is learning to notice why a strategy works.
Original worked example: explain a comparison.
A box holds 6 rows of 8 pencils. Another box holds 35 pencils. How many more pencils does the first box hold?
Target: find the difference between the two totals. Clue: equal rows mean multiplication gives the first total. Steps: 6 × 8 = 48; 48 − 35 = 13. Check: 35 + 13 = 48, so the first box holds 13 more pencils.
Notice that “multiply because there are rows” is stronger than simply writing 6 × 8. It gives a reason another problem can reuse.
Self-check: can another person follow the method?
Try this fresh example: a 72-page book is read at 9 pages each day. How many days does it take to finish the book?
Write a four-part explanation. Include why division is appropriate and a check that links your result back to 72 pages.
Check your reasoning
The target is the number of days. The clue is that the same number of pages is read each day, so divide the total by pages per day: 72 ÷ 9 = 8. Check: 8 × 9 = 72, so 8 days is consistent.
Use explanation to improve review, not to demand a perfect performance.
After a practice question, ask “What did you notice first?” and “How did you check it?” If the student cannot explain every step yet, model one sentence and ask them to complete the next. The aim is to make the next choice clearer.
Use the pattern method when a regular change is the important clue, or working backwards when the final value is known. The wider AMC Upper Primary preparation guide places both methods in a practical routine.
This article uses original examples. It is independent preparation advice, not official Australian Mathematics Competition material.