Primary Maths: Explain a Bar Model When You Prefer Algebra

Understanding a solution is different from explaining it

A Singapore discussion asked why some Primary 6 maths problems feel difficult even to people studying more advanced mathematics. A parent in the discussion described preferring algebra when helping a child. If that sounds familiar, the useful task is to express the relationship in a form the child understands, rather than insist that a familiar adult method must be the easiest teaching method.

Read for quantities and relationships

Before drawing, identify what each quantity represents, what is known and what must be found. Ask the child to explain phrases such as three times as many in their own words. A model cannot repair a misunderstanding of the story if the bars have already been labelled using the wrong relationship.

Keep quantities of the same kind comparable. If a question changes from a number of items to their total cost, label that distinction. Do not expect an unlabeled rectangle to communicate which amount it represents. It is fine to begin with a very simple problem to check the representation before tackling a more demanding one.

Try this invented equal-units example

Suppose Mei and Arun have 48 stickers altogether, and Arun has three times as many as Mei. Represent Mei’s amount with one unit and Arun’s with three equal units. Together there are four units. Each unit is 48 divided by 4, which is 12 stickers. Mei has 12 and Arun has 36.

Check both conditions: 12 plus 36 is 48, and 36 is three times 12. The bars show the same relationship that an adult might express with an unknown in an equation, but the child can reason with equal parts. This is our own practice example, not a reproduced examination question or a universal model for every problem.

Explain the choice of each operation

Ask why the total is divided by four, not three, and what one unit means. Let the child point to the part being found. If they can repeat the calculation but cannot explain the unit, change the numbers or use a small set of objects to revisit the relationship. Copying the diagram neatly is not the same as understanding it.

Some problems require a different representation or strategy. Do not force a basic part-whole model onto every before-and-after or changing-quantity question. Ask the teacher how the current class method works and where an alternative approach is useful. This article does not claim that algebra is banned or that any particular working automatically earns marks.

Use papers to practise explanation, not only speed

Select a suitable question from our Primary paper collections or Primary 6 papers. Begin with the relationship, then draw and label, calculate and check. Keep the original question visible so the final answer addresses the quantity actually requested.

If you can solve a question but cannot explain it at the child’s current level, write down your route and ask the teacher for a bridge between methods. Avoid turning the session into a contest over who learned the harder syllabus. The goal is a child who can explain a valid solution and recognise when it fits, with an adult who helps uncover the reasoning.

Sources and further reading

Checked on 30 October 2026. The question below is real; the practical planning suggestions in this article are our editorial guidance.

• Is it just me? — 31 January 2026.
• Northshore Primary: mathematics and model drawing