Must-Know Maths Problem Sums & Model Methods

Problem sums are often the trickiest part of math exams for students in Singapore. They require more than just knowing formulas. They test your child’s comprehension, logic, and application skills. One proven way to tackle these complex word problems is by using model methods, a signature technique in Singapore Math.

At Mavis Tutorial Centre, we help students master essential problem sums through visual, step-by-step learning. This blog shares the must-know problem types and the model methods that will make solving them easier and more effective.

Why Are Problem Sums So Important?

Problem sums, especially in the PSLE Math Paper 2, account for a large portion of the marks. They test higher-order thinking skills such as:

• Interpretation of information
• Logical reasoning
• Application of math concepts in real-world situations

Mastering these questions early builds a strong math foundation and prepares your child for more advanced topics in secondary school and beyond.

What Is the Model Method?

The model method is a powerful visual strategy that helps students break down word problems using bar diagrams. It is especially useful for:

• Whole numbers
• Fractions
• Ratios
• Percentages
• Algebra-like reasoning

Instead of jumping straight into equations, students draw rectangles or “bars” to represent parts of the problem, making it easier to see relationships and find solutions.

Must-Know Problem Sums (With Model Methods)

Here are the most common types of math problem sums your child must know along with how model methods make them easier to solve:

1. Part-Whole Problems

These are common in lower primary and involve understanding how different quantities make up a whole.

Example:

Ali has 80 marbles. He gave 35 marbles to Ben. How many marbles does he have left?

Model Method:

• Draw one bar for 80 marbles
• Show a cut-off of 35 marbles
• The remainder is the answer: 80 - 35 = 45 marbles

2. Comparison Problems

These problems involve comparing two quantities and finding the difference or total.

Example:

Tom has 60 stickers. Jerry has 25 fewer stickers than Tom. How many stickers does Jerry have?

Model Method:

• Draw equal bars, then shorten Jerry’s bar by 25
• Use subtraction to find the answer: 60 - 25 = 35 stickers

3. Before-and-After Problems

These involve changes in quantity, either increasing or decreasing and require comparing situations.

Example:

A box had 120 apples. After giving away 45, how many are left?

Model Method:

• One bar for before (120 apples)
• Subtract the smaller bar (45 apples) to find the remaining: 75 apples

4. Fraction of a Whole

Students must calculate parts of a whole using fractions.

Example:

1/4 of the class are girls. There are 8 girls. How many students are there in total?

Model Method:

Represent 1 part out of 4 as 8

Multiply: 8 × 4 = 32 students

5. Ratio Problems

These are essential in upper primary and PSLE Maths.

Example:

The ratio of boys to girls is 3:5. If there are 24 boys, how many girls are there?

Model Method:

Total ratio parts = 3 + 5 = 8 parts

Each part = 24 ÷ 3 = 8

Girls = 5 parts = 8 × 5 = 40 girls

6. Remainder Concept Problems

These are often seen in challenging PSLE questions.

Example:

A number when divided by 4 leaves a remainder of 3. What could be the number?

Model Method:

• Use bar models to show equal groups of 4
• Add 3 units as the remainder
• Try multiples of 4 and add 3: 4×1+3 = 7, 4×2+3 = 11, etc.

This develops logical thinking and number pattern recognition.

7. Working Backwards

This strategy is useful for multi-step questions.

Example:

After spending $50, John had $130 left. How much did he have at first?

Model Method:

Final amount = $130

Add back the spent amount: 130 + 50 = $180

How Mavis Teaches Model Methods

At Mavis Tutorial Centre, we break down each math concept and guide students to:

• Visualise the problem using models
• Interpret questions correctly
• Solve step-by-step with confidence
• Practice a wide variety of sums with increasing difficulty

We use worksheets, in-class exercises, and exam-style problems to ensure every student builds solid math fundamentals.

Benefits of Using Model Methods

• Makes abstract problems easier to understand
• Encourages logical thinking
• Reduces careless mistakes
• Builds confidence for PSLE and school exams
• Works across all types of math topics

Final Thoughts

Problem sums do not have to be intimidating. With the right strategies, especially model drawing, students can tackle even the most challenging questions with confidence and clarity. At Mavis Tutorial Centre, our experienced math tutors guide students through every step, helping them master the must-know math problems and model methods that matter most.

Help Your Child Master Math Problem Sums Today!

Ready to boost your child’s math skills and exam performance? Join Mavis Tutorial Centre, where we turn confusion into clarity and help students succeed in math one problem at a time.

Visit a Mavis Tutorial Centre near you or call us now to schedule a free trial lesson.

Let us master math together starting today!