Problem-solving in mathematics helps children develop reasoning and communication skills that are transferrable and important life skills.

Reasoning is required on three levels when children solve word problems. First, they use reasoning to recognise what information is provided or missing. Then, they use reasoning to figure out what information they need to find. Finally, they use reasoning to draw on relevant prior knowledge and choose the most suitable heuristic to work out the solution.

Communication is required for comprehension and expression during problem-solving. Children need to read and understand word problems and then write and express their solutions. When children are encouraged to explain their thinking verbally, visually and in written form, they gain a better understanding of math concepts and develop stronger communication skills.

When students understand and recognise how they learn and are given opportunities to monitor and regulate their thinking during problem-solving...

Singapore Math Heuristics

In part one of our Math Heuristics series, we gave an overview of the 12 heuristics in Singapore Primary Math syllabus...

In part two, we expanded on heuristics – Act It Out, Draw A Diagram and Look For Patterns...

In part three, we focused on: Make Link Systematic List, Guess and Check, and Restate the Problem...

In part four, we looked at: Solve Part of the Problem, Simplify the Problem and Work Backwards...

In the final part of the series, we will explore: Draw a Table, Make Suppositions and Use Before–After Concept.

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Heuristic: Solve part of the problem

Word Problem (Grade 3):

At a school library, each student could borrow up to 4 books. The bar graph below shows how many books students borrowed from the school library in one week. What was the total number of books borrowed from the library that week?

Solution:

1. Understand:
What to find: total number of books borrowed
What is known: 19 students borrowed 1 book. 27 students borrowed 2 books. 16 students borrowed 3 books. 11 students borrowed 4 books.

2. Choose: Solve part of the problem

3. Solve:
19 students borrowed 1 book = 19 × 1 = 19 books
27 students borrowed 2 books = 27 × 2 = 54 books
16 students borrowed 3 books = 16 × 3 = 48 books
11 students borrowed 4 books = 11 × 4 = 44 books
19 + 54 + 48 + 44 = 165 books

165 books were borrowed from the library that week.

4. Check:
Did I read the information from the bar graph correctly? Yes
Did I calculate the number of books for each bar correctly? Yes
Did I add the number of books for all bars? Yes

Try solving the following word problem using Polya’s 4-step process.

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Word Problem (Grade 3):

The diagram below shows 4 shaded triangles in Triangle ABC. All the triangles in the diagram are equilateral triangles. If the area of Triangle ABC is 64 cm2, find the total area of the shaded triangles.

Answer: The total area of the shaded triangles is 28 cm2
See the solution in part one of our Singapore Math Heuristics series.

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Problem-solving in mathematics helps children develop reasoning and communication skills that are transferrable and important life skills.

Reasoning is required on three levels when children solve word problems. First, they use reasoning to recognise what information is provided or missing. Then, they use reasoning to figure out what information they need to find. Finally, they use reasoning to draw on relevant prior knowledge and choose the most suitable heuristic to work out the solution.

Communication is required for comprehension and expression during problem-solving. Children need to read and understand word problems and then write and express their solutions. When children are encouraged to explain their thinking verbally, visually and in written form, they gain a better understanding of math concepts and develop stronger communication skills.

When students understand and recognise how they learn and are given opportunities to monitor and regulate their thinking during problem-solving...

Singapore Math Heuristics

In part one of our Math Heuristics series, we gave an overview of the 12 heuristics in Singapore Primary Math syllabus...

In part two, we expanded on heuristics – Act It Out, Draw A Diagram and Look For Patterns...

In part three, we focused on: Make Link Systematic List, Guess and Check, and Restate the Problem...

In part four, we looked at: Solve Part of the Problem, Simplify the Problem and Work Backwards...

In the final part of the series, we will explore: Draw a Table, Make Suppositions and Use Before–After Concept.

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Heuristic: Simplify the problem

Word Problem (Grade 3):

At a school library, each student could borrow up to 4 books. The bar graph below shows how many books students borrowed from the school library in one week. What was the total number of books borrowed from the library that week?

Solution:

1. Understand:
What to find: total number of books borrowed
What is known: 19 students borrowed 1 book. 27 students borrowed 2 books. 16 students borrowed 3 books. 11 students borrowed 4 books.

2. Choose: Solve part of the problem

3. Solve:
19 students borrowed 1 book = 19 × 1 = 19 books
27 students borrowed 2 books = 27 × 2 = 54 books
16 students borrowed 3 books = 16 × 3 = 48 books
11 students borrowed 4 books = 11 × 4 = 44 books
19 + 54 + 48 + 44 = 165 books

165 books were borrowed from the library that week.

4. Check:
Did I read the information from the bar graph correctly? Yes
Did I calculate the number of books for each bar correctly? Yes
Did I add the number of books for all bars? Yes

Try solving the following word problem using Polya’s 4-step process.

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Word Problem (Grade 3):

The diagram below shows 4 shaded triangles in Triangle ABC. All the triangles in the diagram are equilateral triangles. If the area of Triangle ABC is 64 cm2, find the total area of the shaded triangles.

Answer: The total area of the shaded triangles is 28 cm2
See the solution in part one of our Singapore Math Heuristics series.

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