Choose a representation that exposes the relationship.
Many errors occur before arithmetic begins: a number is attached to the wrong thing, a comparison is reversed, or an important condition is ignored. Pause briefly to represent the information. Use a labelled line for change, a table for repeated groups, or a quick sketch for position and shape.
- Circle what is being found. Name it in words.
- List quantities with labels. Write “each”, “total”, “remaining” or another useful label beside a number.
- Show the relationship. Use a bar, table, diagram or equation before computing.
- Check the answer against the situation. Ask whether its size and units make sense.
Original worked example
A garden has 6 rows of 8 seedlings. Two seedlings in each row do not grow. How many seedlings grow? A quick table gives: 8 per row − 2 per row = 6 growing per row; 6 rows × 6 = 36. Writing the “per row” label prevents the common slip of subtracting only 2 from the final total of 48.
Check the model, then the maths.
If an answer is wrong, review the representation first. A correct calculation based on a reversed comparison still gives the wrong result. When practising, ask the student to show their labelled note before explaining the calculation.
Common error
Starting with an operation because a familiar number appears. Multiplication, division, addition and subtraction are tools; the relationship tells you which one to use.
Self-check
Could another person look at the labels or sketch and tell what every number represents?