Primary School Math Problem Sums Singapore: Model Drawing and Heuristics

What Is Model Drawing?

Model drawing (also called the bar model method) is a visual strategy used in Singapore Primary Maths to solve word problems. Instead of jumping straight to a calculation, you draw rectangular bars to represent the quantities in the problem.

This method helps students see the relationship between the numbers — what is known, what is unknown, and what operation to use.

Three Steps to Solve Any Problem Sum

1. Read — read the problem carefully and identify what is given and what is asked.
2. Draw — draw a bar model to represent the quantities and their relationships.
3. Solve — use the model to write the number sentence and calculate the answer.

Always write a complete statement for your final answer. In PSLE and school exams, the statement earns marks even if your calculation has a small error.

The Part-Whole Model

The part-whole model shows how parts make up a whole. Use this when the problem talks about combining two or more groups, or when one group is taken away from a total.

When to use it:

• Finding the total when you know the parts
• Finding a missing part when you know the total and one part

Example — Finding the total:

Ali has 45 stickers. Bala has 28 stickers. How many stickers do they have altogether?

Draw one long bar divided into two parts: [45] [28]. The whole bar = 45 + 28 = 73 stickers.

Example — Finding a missing part:

There are 80 pupils in a hall. 47 are boys. How many are girls?

Draw one long bar divided into two parts: [47] [?]. The total bar = 80. Girls = 80 − 47 = 33 girls.

The Comparison Model

The comparison model shows how two quantities relate to each other — which one is more, which is less, and by how much.

When to use it:

• Problems that say "more than" or "less than"
• Finding the difference between two amounts
• Finding an unknown when you know one amount and the difference

Example — Finding the difference:

Cindy has 96 cards. David has 58 cards. How many more cards does Cindy have than David?

Draw two bars side by side. Cindy's bar is longer. The extra portion = 96 − 58 = 38 more cards.

Example — Finding an unknown:

Emma has 34 more marbles than Faiz. Faiz has 67 marbles. How many marbles does Emma have?

Draw Faiz's bar [67]. Draw Emma's bar [67][34]. Emma = 67 + 34 = 101 marbles.

Primary 5 Math Model Drawing Tuition

When a problem gives you a fraction of a quantity, divide the bar into equal units matching the denominator, then shade the correct number of units.

Example:

Grace had some cookies. She gave away ⅗ of them and had 24 left. How many cookies did she have at first?

1. Draw a bar divided into 5 equal units (because the denominator is 5).
2. She gave away 3 units, so 2 units are left.
3. 2 units = 24, so 1 unit = 12.
4. Total (5 units) = 5 × 12 = 60 cookies.

Problem Sums with Ratio

When a problem gives you a ratio, draw bars with the same unit length — one bar for each part of the ratio.

Example:

Henry and Ivan share $120 in the ratio 3 : 5. How much does each person get?

1. Draw Henry's bar with 3 units. Draw Ivan's bar with 5 units.
2. Total units = 3 + 5 = 8 units.
3. 8 units = $120, so 1 unit = $15.
4. Henry = 3 × $15 = $45. Ivan = 5 × $15 = $75.

Primary 6 Math Heuristic Problem Sums

Some problem sums show a situation before an action and ask you to find something after. Draw two sets of bars — one for before and one for after.

Example:

Jas had 3 times as many stamps as Ken. After Jas gave Ken 30 stamps, they had the same number. How many stamps did Jas have at first?

1. Before: Jas has 3 units, Ken has 1 unit.
2. After giving 30 stamps, both are equal.
3. The 30 stamps moved from Jas to Ken. Each bar changed by 30.
4. Jas before − 30 = Ken before + 30 → 3u − 30 = 1u + 30 → 2u = 60 → u = 30.
5. Jas at first = 3 × 30 = 90 stamps.

Common Mistakes in Problem Sums

• Not reading the question carefully — underline key numbers and the question being asked before drawing.
• Drawing unequal units — each unit in a bar must be the same length. This makes the model accurate and easy to read.
• Forgetting the answer statement — always end with "Therefore, _____ is/are _____."
• Mixing up "more than" and "less than" — "A has 20 more than B" means A is bigger. "A has 20 less than B" means B is bigger.
• Using the wrong total in fraction problems — the fraction applies to the total before the action, not after.

Building on Problem Sums

Model drawing is not just for Primary school. The unit value method and ratio reasoning you learn here are the same ideas used in Secondary Maths for ratio, proportion, and percentage problems.

Students who master model drawing in Primary school find the transition to algebra much easier, because both methods are about finding unknown values using relationships.

If your child needs more support with Primary Maths problem sums, StrongWill Tuition provides structured lessons that teach the model drawing method clearly, step by step, with plenty of guided practice. View our tuition fees for Primary Maths tuition rates.