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Get hold of Heuristics

With the strong emphasis on the need for problem-solving skills in the current PSLE Maths syllabus, many schools have been teaching the use of problem-solving strategies known as heuristics to solve different types of Mathematical problems. Being able to apply heuristics is key to doing well in the examination. Students must familiarize themselves with how to use different heuristics such as Model Drawing, Look for Pattern, Work Backwards, Guess & Check and Simplify the Problem.

However, how and when to apply each type of heuristic is a major challenge not just for students, but their parents too! The 'mum and dad' generation which is more accustomed to using algebra and other techniques to solve most word problems, often find themselves in a fix when it comes to applying specific heuristics methods to word problems. Unfortunately, the issue of whether schools are able to accept alternative methods to attain the correct answer is a controversial one. However, most schools would agree that getting PSLE-bound students to be able to apply Maths heuristic is a key learning priority. Furthermore, being able to apply a heuristic method, even if the final answer is not correct, may help a student to get method-marks.

In the first part of this series on Heuristics, we share some tips on how to use Model Drawing.

For 'Get hold of Heuristics Part II - Guess and Check', click here.

What is Model Drawing?

In this method, we draw 
a diagram  or model to describe the problem. This helps to better visualise and understand the problem. A model also helps us to identify information we already have, and what we need to know in order to solve the problem.

When do we use Model Drawing?

Read through the question carefully. If it appears easy to describe the problem by drawing models or diagrams, try to apply the Model Drawing Method to solve the problem.

How can we use Model Drawing to solve word problems?

Some tips:
- Read the sentences of the word problem one at a time.

- Represent each sentence as part of the model.

- Underline important information or numbers in the word problem.

- Fill in the answer to each missing part as you solve the word problem.

e.g. consider this Word Problem:
Douglas sold 6 ties and 5 shirts.
Each shirt cost twice as much as one tie.
If Douglas sold the ties and shirts for $384, how much was the selling price of a shirt?

To find the right model, follow these steps:

Step 1: Identify the items: ties, shirts

Step 2: Identiy the relationship between the items
- The price of 1 shirt is the SAME as the price of 2 ties.
- 6 ties and 5 shirts cost a total of $384

Step 3: Decide if a part-whole model or a comparison model is more appropriate.
- As we are comparing the prices of two items, we use a comparison model.

Step 4: Draw the bar model for the parts

Step 5: Fill in the information that you know on the model

Step 6: Use question marks and arrows to highlight the information you are looking for.

[Diagram indicating Steps 4-7]
heuristics_model_diag3

Step 7: Use the unitary method to solve the question.

16 units -> $384

1 unit -> $384 ÷16 = $24

2 units -> 2 x $24 = $48

The selling price of a shirt is $48.

Step 8: Work backwards to check your answer.

1 shirt -> $48

5 shirts -> 5 x $48 = $240

1 tie -> $24

6 ties -> 6 x $24 = $144

$240 + $180 = $384

The ties and shirts were sold for $384.

For 'Get hold of Heuristics Part II - Guess and Check', click here.

For an overview of Heuristics methods used in Mathematics, Check out these articles at www.eph.com.sg:

Heuristics methods used in Mathematics - Part 1: http://www.eph.com.sg/edutips.php?id=29

Heuristics methods used in Mathematics - Part 2: http://www.eph.com.sg/edutips.php?id=30

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The Model Drawing methodology and example shown above were adapted from EduSCOREPlus Mathematics Primary 5 Companion Pack CD. Get your FREE 
CD when you purchase a complete  EduSCORE e-Assessment Package for Pri 5 / Pri 6 (now at 30% discount for EduCommunity readers).

 

 

 

 

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