Singapore Math Heuristics: Act It Out, Draw A Diagram, Look For Patterns

In part one of our Singapore Math Heuristics series, we gave an overview of the 12 heuristics in Singapore Primary Math syllabus, with tips from the curriculum team at Seriously Addictive Mathematics (S.A.M) on how to solve various math word problems using them.

To recap, heuristics are methods or strategies students can use to solve complex math word problems. They are general guidelines of what students can do to tackle a word problem when the solution is not obvious.

Besides using heuristics to solve a word problem, Singapore Math also adopts Polya’s 4-step problem-solving process:

1. Understand the problem: What to find? What is known and unknown?
2. Devise a plan: Choose the most suitable heuristic
3. Carry out the plan: Solve the problem
4. Look back: Check the answer

To solve word problems efficiently, students must be familiar with both the problem solving methods (heuristics) and the problem solving process (Polya’s 4-step).

In this article, we will focus on 3 heuristics – Act it out, Draw a diagram/model, and Look for pattern(s).

Sample word problems are solved using these 3 heuristics and Poly’s 4-step process in the step-by-step worked solutions provided by the curriculum team at S.A.M.

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Heuristic: Act it out

Word Problem (Grade 2):

Ben cuts a cake into 5 equal pieces. He wants to eat some of the pieces of cake so that the fraction of cake he eats is smaller than the fraction of the cake left. What is the greatest possible fraction of the cake that Ben can eat?

Solution:

1. Understand:
What to find: The greatest possible fraction of the cake that Ben can eat.
What is known: The cake is cut into 5 equal pieces. The fraction of cake he eats is smaller than the fraction of the cake left.

2. Choose: Act it out

3. Solve:

If Ben eats 1 piece, 4 pieces are left. 1/5 is smaller than 4/5
If Ben eats 2 pieces, 3 pieces are left. 2/5 is smaller than 3/5

 

If Ben eats 3 pieces, 2 pieces are left. 3/5 is greater than 2/5. This does not match the word problem.

The greatest possible fraction of the cake that Ben can eat is 2/5.

4. Check:
Did I give the answer as a fraction? Yes
Is the fraction he ate smaller than the fraction left? Yes
Is it the greatest possible fraction of cake he can eat? Yes

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

Word Problem (Grade 1):

Alan, Ben and Carol are in the school’s Art Club. Their teacher, Mr Tan, wants two of them to join a contest. How many ways can Mr Tan choose two pupils?

Answer: Mr Tan can choose two pupils in 3 ways.
See the solution in part one of our Singapore Math Heuristics series.

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Heuristic: Draw a diagram/model

Word Problem (Grade 2):

There were 158 children in a movie theatre. There were 267 more adults than children in the theatre. 236 of the adults were men. How many women were there in the theatre?

 

Solution:

1. Understand:
What to find: The number of women in the theatre.
What is known: There were 158 children. There were 267 more adults than children. There were 236 men.

2. Choose: Draw a diagram/model

3. Solve:

There were 158 children.