## Heuristic Problem Solving: A comprehensive guide with 5 Examples

What are heuristics, advantages of using heuristic problem solving, disadvantages of using heuristic problem solving, heuristic problem solving examples, frequently asked questions.

- Speed: Heuristics are designed to find solutions quickly, saving time in problem solving tasks. Rather than spending a lot of time analyzing every possible solution, heuristics help to narrow down the options and focus on the most promising ones.
- Flexibility: Heuristics are not rigid, step-by-step procedures. They allow for flexibility and creativity in problem solving, leading to innovative solutions. They encourage thinking outside the box and can generate unexpected and valuable ideas.
- Simplicity: Heuristics are often easy to understand and apply, making them accessible to anyone regardless of their expertise or background. They don’t require specialized knowledge or training, which means they can be used in various contexts and by different people.
- Cost-effective: Because heuristics are simple and efficient, they can save time, money, and effort in finding solutions. They also don’t require expensive software or equipment, making them a cost-effective approach to problem solving.
- Real-world applicability: Heuristics are often based on practical experience and knowledge, making them relevant to real-world situations. They can help solve complex, messy, or ill-defined problems where other problem solving methods may not be practical.
- Potential for errors: Heuristic problem solving relies on generalizations and assumptions, which may lead to errors or incorrect conclusions. This is especially true if the heuristic is not based on a solid understanding of the problem or the underlying principles.
- Limited scope: Heuristic problem solving may only consider a limited number of potential solutions and may not identify the most optimal or effective solution.
- Lack of creativity: Heuristic problem solving may rely on pre-existing solutions or approaches, limiting creativity and innovation in problem-solving.
- Over-reliance: Heuristic problem solving may lead to over-reliance on a specific approach or heuristic, which can be problematic if the heuristic is flawed or ineffective.
- Lack of transparency: Heuristic problem solving may not be transparent or explainable, as the decision-making process may not be explicitly articulated or understood.
- Trial and error: This heuristic involves trying different solutions to a problem and learning from mistakes until a successful solution is found. A software developer encountering a bug in their code may try other solutions and test each one until they find the one that solves the issue.
- Working backward: This heuristic involves starting at the goal and then figuring out what steps are needed to reach that goal. For example, a project manager may begin by setting a project deadline and then work backward to determine the necessary steps and deadlines for each team member to ensure the project is completed on time.
- Breaking a problem into smaller parts: This heuristic involves breaking down a complex problem into smaller, more manageable pieces that can be tackled individually. For example, an HR manager tasked with implementing a new employee benefits program may break the project into smaller parts, such as researching options, getting quotes from vendors, and communicating the unique benefits to employees.
- Using analogies: This heuristic involves finding similarities between a current problem and a similar problem that has been solved before and using the solution to the previous issue to help solve the current one. For example, a salesperson struggling to close a deal may use an analogy to a successful sales pitch they made to help guide their approach to the current pitch.
- Simplifying the problem: This heuristic involves simplifying a complex problem by ignoring details that are not necessary for solving it. This allows the problem solver to focus on the most critical aspects of the problem. For example, a customer service representative dealing with a complex issue may simplify it by breaking it down into smaller components and addressing them individually rather than simultaneously trying to solve the entire problem.

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What are the four stages of heuristics in problem solving.

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## Primary 6 Math Heuristics

This post is all about Primary 6 Math Heuristics. If you have kids that is studying this level, you may want to read it.

Now as parents, we understand the importance of preparing our children for success in their academic journey, particularly when it comes to a crucial examination like the Primary School Leaving Examination (PSLE). In this guide, we will delve into the realm of math heuristic questions and equip you with effective strategies and the 12 Math Heuristics techniques to help your child excel in this aspect of the PSLE math paper.

## Understanding Heuristic Questions

Primary 6 Math Heuristics questions in the PSLE math paper are designed to assess a student’s problem-solving skills and critical thinking abilities. These questions often require students to apply mathematical concepts in creative ways to solve complex problems. Unlike routine exercises, heuristic questions demand a deeper understanding of the underlying principles and the ability to approach problems from multiple angles.

## Build a Strong Foundation

Before diving into heuristic questions, it’s crucial for your child to have a solid understanding of fundamental mathematical concepts. Make sure your child is well-versed in topics such as fractions, decimals, percentages, geometry, and algebra. Without a strong foundation, tackling Primary 6 Math heuristics questions can become overwhelming.

## Emphasize Problem Interpretation

Primary 6 Math Heuristics questions are notorious for their wordiness and intricate scenarios. Encourage your child to read each question carefully and identify the key information provided. Highlight or underline important details and numbers. This practice will prevent your child from overlooking vital clues while attempting to solve the problem.

## Encourage Visualization

Visualization is a powerful tool in solving heuristic questions. Help your child visualize complex problems by drawing diagrams, graphs, or charts. For geometry problems, a well-labelled diagram can provide valuable insights. Visualization not only aids comprehension but also helps your child approach problems in a systematic manner.

## Foster Creative Problem Solving

Heuristic questions demand creative thinking. Encourage your child to explore different problem- solving approaches. Discuss alternative methods and solutions together. By nurturing this creativity, you empower your child to think outside the box, an essential skill for mastering heuristic questions.

## Practice, Practice, Practice

Regular practice is key to success in heuristic questions. Provide your child with a variety of heuristic questions from different sources. Gradually increase the complexity of the problems as your child gains confidence. Remember, practice not only enhances problem solving skills but also builds stamina for tackling longer and more intricate questions during the actual exam.

## Break Down the Process

Next in the Primary 6 Math Heuristics is “break down the process”. Teach your child to break down complex problems into smaller, manageable parts. Discuss how to approach each part individually before integrating the solutions to arrive at the final answer. This step-by-step approach prevents your child from feeling overwhelmed and promotes systematic thinking.

## Develop Logical Reasoning

Logical reasoning plays a significant role in solving heuristic questions. Encourage your child to explain out loud his thought processes when solving problems. Ask questions like “Why do you think this approach is valid?” or “How does this step contribute to the solution?” This practice not only hones his logical thinking but also enhances his ability to articulate the method he has decided to choose in order to tackle the math sum.

## Time Management

In the PSLE exam, time management is crucial. Set time limits for solving heuristic questions during practice sessions. This helps your child get accustomed to the time pressure and learn how to allocate time effectively for each question. Remind him to move on if he’s stuck on a particular question and return to it later if time permits.

## Review and Learn

After practicing heuristic questions, allocate time for reviewing both correct and incorrect answers. Celebrate successes and discuss alternative methods for questions that posed challenges. Learning from mistakes is an essential aspect of improvement.

## Stay Positive and Manage Stress

Maintain a positive and supportive attitude throughout your child’s preparation journey. Exam stress can be counterproductive. Encourage breaks, physical activity, and hobbies to keep stress at bay. A calm and focused mind is more adept at tackling challenging heuristic questions.

Now let’s jump into remembering the 12 Primary 5 Math Heuristics Techniques that is in line with the MOE Syllabus

## 12 Primary 6 Math Heuristics Math Techniques (Revision)

Children act out the problem using role-playing or objects. This helps them understand the context and apply math to real-life situations.

For the sample question of ‘Act it Out’ Strategy: LINK: P1 Math Heuristics (Blog 9)

## Draw a Diagram

Encourage your child to draw visual representations of problems. This helps them grasp the problem’s context and visualize the steps needed for a solution. For the sample question of “Picture Drawing’ Strategy, learn more at P1 Math Heuristics

## Look for Patterns

Encourage students to identify patterns or relationships in numbers and operations, as it can lead to shortcuts in problem-solving. For the sample question of ‘Look for Patterns’ Strategy: P4 Math Heuristics

## Guess and Check

Have your child make educated guesses and then verify the results. This technique promotes trial and error, improving problem-solving skills. For the sample question of ‘Guess and Check’ Strategy: P5 Math Heuristics

## Make a List

Children can create lists or tables to organize information and identify patterns or trends. For the sample question of ‘Make a List’ Strategy: P2 Math Heuristics

## Restate the Problem in Another Way

By restating a problem in another way, young pupils can view the problem in another perspective to help them figure out creative solutions. For the sample question – Strategies: ‘Restating a Problem’ and ‘Drawing a Diagram’: P2 Math Heuristics

## Simplify the Problem

If the problem seems too complex, encourage students to simplify it by breaking it down into smaller, more manageable parts. For the sample question of ‘Simplify the problem’ Strategy: P5 Math Heuristics

## Solve Part of the Problem

Solving part of a problem at time helps break up the job. More accuracy can come from this strategy and less confusion too. At the end, putting the parts together can help one solve the problem more easily that way. For the sample question of ‘Simplify Part of the Problem’ Strategy: P3 Math Heuristics

## Work Backwards

In some cases, it’s easier to work backward from the solution to find the starting point of a problem. For the sample question of ‘Work Backwards’ Strategy: P3 Math Heuristics

## Draw a Table

For problems that involve organizing data or comparing values, creating a table or chart can be extremely helpful. This approach allows your child to visualize the information and identify relationships between different elements. For the sample question of ‘Draw a Table’ Strategy: P4 Math Heuristics

## Make Suppositions

This math heuristic method is very useful for problems where one needs to solve for two unknown quantities. One starts by making an assumption about the problem. Most of the time, we are given two types of items and we want to make sure that we assume all the items to be one of the types first.

For the sample question of ‘Make Supposition’: P5 Math Heuristics

## Use Before-After Concept

This math heuristic method is applied where the questions show there is a change resulting in a ‘before’ situation and an ‘after’ situation. One will need compare the two situations in order to understand the question fully and find a way to solve it. For the sample question of ‘Use Before-After Concept’: P5 Math Heuristics

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## Working Backwards: Heuristic for Problem Solving

Working Backwards is a non-routine heuristic that all pupils learn in primary schools . Many pupils learn this heuristic as early as when they were in primary two. You can easily find this heuristic being included in one of the topics in assessment books .

Though common, this heuristic is in fact one of the toughest in primary Mathematics syllabus . Problem sums that can be solved using Working Backwards are usually wordy with a sequence of events taking place which make them complex. You need endurance and clarity of mind to follow through a series of events that are unfolding in sequence, not to mention in a backward manner.

Without further ado, let’s delve into one typical upper primary problem sum to find out how we can tackle this category of problem sums using the heuristic of Working Backwards .

Xiaoming and Ali were playing a card game using 96 pokemon cards. In the first game, Ali lost 1 5 of his cards to Xiaoming. In the second game, Xiaoming lost 1 3 of his cards to Ali. After the second game, both boys had the same number of pokemon cards. How many pokemon cards did Xiaoming have at first?

## Study and Understand the Problem

In this problem sum, there are only two variables – Xiaoming and Ali.

Cards are transferred between Xiaoming and Ali in a series of games, but the total number of cards between them is still the same – internal transfer.

## Think of a Plan

There are contextual clues of a typical “Working Backwards” problem sum:

- Final information is given on how a situation ends and you need to find the answer in the beginning.
- There is a focus on sequence of events.

## Act on the Plan

Reverse the solution steps by working backwards in a systematic manner using a table. A table will help to organise your working in a more orderly manner and track the steps in sequence.

Final number of cards each person had = 96 ÷ 2 = 48

## Second game

After Xiaoming lost 1 3 of his cards to Ali, he was left with 2 units as 1 unit was won by Ali (Refer to the numerator and denominator). Thus, 2 units = 48

After Ali lost 1 5 of his cards to Xiaoming, he was left with 4 units as 1 unit was won by Xiaoming (Refer to the numerator and denominator). Thus, 4 units = 24

## Reflect on my Answer

Work forward with the answer you have.

XM → 66 A → 30

A → of 30 = 6 30 – 6 = 24 XM → 66 + 6 = 72

XM → of 72 = 24 72 - 24 = 48 (correct!) A → 24 + 24 = 48 (correct!)

## More Examples of Problems Sums Involving Working Backwards

Try to pick out the contextual clues that tell you that Working Backwards can be used.

## P3 Math question

Alan bought some fish. One day, 6 of his fish died. After that, he bought the same number of fish as those which were still alive. He gave away all his fish equally among 8 friends and each friend had 4 fish. How many fish did Alan have at first?

## P6 Math question

A MRT train left Bugis station with some passengers. At Lavender station, no passengers alighted and the number of passengers who boarded the train was 1 4 of the original number of passengers in the train. At Kallang station, 2 5 of the passengers alighted and 51 passengers boarded the train. At Aljunied station, 2 3 of the passengers alighted and 24 passengers boarded the train. At Paya Lebar station, all 122 passengers alighted from the train. How many passengers were there when the train left Bugis Station?

Whenever possible, use a table or draw boxes to help you solve Working Backwards questions in an orderly and systematic manner.

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## About the Author

Teacher Zen has over a decade of experience in teaching upper primary Math and Science in local schools. He has a post-graduate diploma in education from NIE and has a wealth of experience in marking PSLE Science and Math papers. When not teaching or working on OwlSmart, he enjoys watching soccer and supports Liverpool football team.

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## Heuristics in Mathematics Education

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- Nicholas Mousoulides 2 &
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In this entry we examine Polya’s contribution to the role of heuristics in problem solving, in attempting to propose a model for enhancing students’ problem-solving skills in mathematics and its implications in the mathematics education.

## Characteristics

Research studies in the area of problem solving, a central issue in mathematics education during the past four decades, have placed a major focus on the role of heuristics and its impact on students’ abilities in problem solving. The groundwork for explorations in heuristics was established by the Hungarian Jewish mathematician George Polya in his famous book “ How to Solve It ” (1945) and was given a much more extended treatment in his Mathematical Discovery books (1962, 1965). In “ How to Solve It ,” Polya ( 1945 ) initiated the discussion on heuristics by tracing their study back to Pappus, one of the commentators of Euclid, and other great mathematicians and philosophers like Descartes and Leibniz, who attempted to build a...

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Begle EG (1979) Critical variables in mathematics education. MAA & NCTM, Washington, DC

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Burkhardt H (1988) Teaching problem solving. In: Burkhardt H, Groves S, Schoenfeld A, Stacey K (eds) Problem solving – a world view (Proceedings of the problem solving theme group, ICME 5). Shell Centre, Nottingham, pp 17–42

English L, Sriraman B (2010) Problem solving for the 21st century. In: Sriraman B, English L (eds) Theories of mathematics education: seeking new frontiers. Springer, Berlin, pp 263–290

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Goldin G (2010) Problem solving heuristics, affect, and discrete mathematics: a representational discussion. In: Sriraman B, English L (eds) Theories of mathematics education: seeking new frontiers. Springer, Berlin, pp 241–250

Polya G (1945) How to solve it. Princeton University Press, Princeton

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Polya G (1962) Mathematical discovery, vol 1. Wiley, New York

Polya G (1965) Mathematical discovery, vol 2. Wiley, New York

Schoenfeld A (1992) Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In: Grouws DA (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp 334–370

Sriraman B, English L (eds) (2010) Theories of mathematics education: seeking new frontiers (Advances in mathematics education). Springer, Berlin

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Mousoulides, N., Sriraman, B. (2020). Heuristics in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_172

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## Tackle math word problems with greater confidence: The parent’s guide to heuristics

What are math heuristics.

Heuristics are simple rules or mental shortcuts that help us understand a problem or arrive at a decision quickly.

If you’ve followed a “rule of thumb”, you’ve used a heuristic.

If I’m sending an important e-mail, I will always review it twice, at different timings during the day, to minimise the possibility of making an embarrassing mistake!

Likewise, math heuristics are proven tactics we can use to solve problems effectively — by being more strategic, systematic, and conscientious.

Let’s say you had to tighten a screw. You could go through the screwdrivers in your toolbox one by one, or you could approximate the size of the screw and narrow down your selection to the last 3 screwdrivers. Which method gets the job done faster?

## How do math heuristics help my child with problem-solving?

As your child approaches upper primary (P5, P6), they’ll find that word problems become more complex — the approaches and solutions are less obvious.

Hence, knowing common math heuristics will give them the tools they need to tackle challenging problem sums that come up in their homework or exams.

Not only can it dramatically increase your chances of solving any Math problem and help you get started, it can also guide you along your thinking processes to reduce the effort and time needed when problem solving.

To prepare your child for PSLE questions, it helps to know a variety of ways to tackle any problem that comes their way. PSLE questions are complex, so mastering heuristics is like having every tool you could ever need in your toolbox!

We teach the heuristics that your child will learn in school in a way that is fun and easy to understand — just check out some of our videos below if you’re curious! We have many more of such videos in our system.

## Why do parents need to know about math heuristics too?

Practicle’s math content covers all heuristics that are tested by MOE, but we recommend that parents have foundational knowledge to supervise their children, especially when preparing for exams.

Want to know how your child is performing? We’ll send you reports about how well they’ve mastered their math concepts and heuristics.

You’ll no longer need to rely on teachers for guidance and feedback all the time, or spend exorbitant amounts of money on assessment books.

## What heuristics does MOE test for primary school mathematics?

According to the Singapore Mathematics framework developed by the Curriculum Planning and Development Division (CPDD) team at the Ministry of Education Singapore (MOE), the types of heuristics in Mathematics that can be applied to primary school math problems can be grouped as follow:

1. Visualise a problem 2. Make a calculated guess 3. Walk through the process 4. Simplify the problem 5. Consider special cases

Hence, it is crucial for your child to learn how to use them.

Here’s an example of a heuristic that your child will learn from P4-P6:

We have more of such math videos on our YouTube channel , and if you’d like to try to out our questions and receive question-specific video explanations, how about signing up for a free trial ? No minimum commitment, cancel anytime.

## How does Practicle teach math heuristics?

As a team of former teachers and game developers, we put a great deal of thought into making the learning experience in Practicle engaging for your kids using a 2-pronged approach:

1. It needs to be educationally sound and aligned with the school’s syllabus 2. It needs to stir interest and encourage kids to learn more, making it truly effective

#2 is where many math learning solutions fall short, especially traditional methods like tuition and assessment books. Students usually tune out quickly.

Practicle makes learning math heuristics fun, while ensuring your kids learn the proper skills needed to do well in their tests and exams.

## Experience Practicle free, no commitment no hidden cost no lock-in

Try our learning platform free with a 7 day trial and see if your child likes it.

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## Some Helpful Problem-Solving Heuristics

A heuristic is a thinking strategy, something that can be used to tease out further information about a problem and thus help you figure out what to do when you don’t know what to do. Here are 25 heuristics that can be useful in solving problems. They help you monitor your thought processes, to step back and watch yourself at work, and thus keep your cool in a challenging situation.

- Ask somebody else how to do the problem. This strategy is probably the most used world-wide, though it is not one we encourage our students to use, at least not initially.
- Guess and try (guess, check, and revise). Your first guess might be right! But incorrect guesses can often suggest a direction toward a solution. (N.B. A spreadsheet is a powerful aid in guessing and trying. Set up the relationships and plug in a number to see if you get what you want. If you don’t, it is easy to try another number. And another.)
- Restate the problem using words that make sense to you. One way to do this is to explain the problem to someone else. Often this is all it takes for the light to dawn.
- Organize information into a table or chart. Having it laid out clearly in front of you frees up your mind for thinking. And perhaps you can use the organized data to generate more information.
- Draw a picture of the problem. Translate problem information into pictures, diagrams, sketches, glyphs, arrows, or some other kind of representation.
- Make a model of the problem. The model might be a physical or mental model, perhaps using a computer. You might vary the problem information to see whether and how the model may be affected.
- Look for patterns , any kind of patterns: number patterns, verbal patterns, spatial/visual patterns, patterns in time, patterns in sound. (Some people define mathematics as the science of patterns.)
- Act out the problem , if it is stated in a narrative form. Acting it out can have the same effect as drawing a picture. What’s more, acting out the problem might disclose incorrect assumptions you are making.
- Invent notation . Name things in the problem (known or unknown) using words or symbols, including relationships between problem components.
- Write equations . An equation is simply the same thing named two different ways.
- Check all possibilities in a systematic way. A table or chart may help you to be systematic.
- Work backwards from the end condition to the beginning condition. Working backwards is particularly helpful when letting a variable (letter) represent an unknown.
- Identify subgoals in the problem. Break up the problem into a sequence of smaller problems (“If I knew this, then I could get that”).
- Simplify the problem . Use easier or smaller numbers, or look at extreme cases (e.g., use the minimum or maximum value of one of the varying quantities).
- Restate the problem again . After working on the problem for a time, back off a bit and put it into your own words in still a different way, since now you know more about it.
- Change your point of view . Use your imagination to change the way you are looking at the problem. Turn it upside down, or pull it inside out.
- Check for hidden assumptions you may be making (you might be making the problem harder than it really is). These assumptions are often found by changing the given numbers or conditions and looking to see what happens.
- Identify needed and given information clearly . You may not need to find everything you think you need to find, for instance.
- Make up your own technique . It is your mind, after all; use mental actions that make sense to you. The key is to do something that engages you with the problem.
- Try combinations of the above heuristics .

These heuristics can be readily pointed out to students as they engage problems in the classroom. However, real-world problems are often confronted many times over or on increasingly complex levels. For those kinds of problems, George Polya, the father of modern problem-solving heuristics, identified a fifth class (E) of looking-back heuristics. We include these here for completeness, but also with the teaching caveat that solutions often improve and insights grow deeper after the initial pressure to produce a solution has been resolved. Subsequent considerations of a problem situation are invariably deeper than the first attempt.

- Check your solution . Substitute your answer or results back into the problem. Are all of the conditions satisfied?
- Find another solution . There may be more than one answer. Make sure you have them all.
- Solve the problem a different way . Your first solution will seldom be the best solution. Now that the pressure is off, you may readily find other ways to solve the problem.
- Solve a related problem . Steve Brown and Marion Walter in their book, The Art of Problem Posing , suggest the “What if not?” technique. What if the train goes at a different speed? What if there are 8 children, instead of 9? What if . . .? Fascinating discoveries can be made in this way, leading to:
- Generalize the solution . Can you glean from your solution how it can be made to fit a whole class of related situations? Can you prove your result?

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?

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

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?

Heuristic: Draw a diagram/model

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?

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

There were 158 children.

Word Problem (Grade 3) :

The smaller of two numbers is 1217. The greater number is 859 more than the smaller number. (a) What is the greater number? (b) What is the sum of the numbers?

Word Problem (Grade 5) :

Tammy has 3 boxes of apples. Box A is 550 grams heavier than Box B and 770 grams heavier than Box C. The average mass of the 3 boxes is 2150 grams. Find the average mass of Box B and Box C. Give your answer in kilograms and grams.

1. Understand: What to find: The average mass of Box B and Box C. What is known: Box A is 550 grams heavier than Box B. Box A is 770 grams heavier than Box C. The average mass of Box A, Box B and Box C is 2150 grams.

Box A is 550 grams heavier than Box B.

Heuristic: Look for pattern(s)

Word Problem (Grade 4) :

Carmen uses the letters in her name to form the pattern below. C A R M E N C A R M E N C A . . . What will be the 405 th letter in the pattern?

1. Understand: What to find: The 405 th letter in the pattern. What is known: The pattern is formed by the letters CARMEN. The pattern starts repeating itself from the 7 th letter.

2. Choose: Look for patterns

CARMEN is the repeating block of letters. There are 6 letters in each block. 405 ÷ 6 = 67 remainder 3 There are 67 such blocks. The remainder of 3 means we have to count 3 more letters to get to the 405 th letter. C A R M E N 1 2 3 The 405 th letter in the pattern is the letter R.

4. Check: How many letters are there in 67 blocks of CARMEN? 67 x 6 = 402 Did I count to the 405 th letter? 402 + 3 = 405. Yes

Draw the shape that comes next.

These are just a few examples to show you how Singapore Math heuristics are used to solve basic and intermediate word problems in lower grade levels and complex word problems in upper grade levels.

Look out for parts three, four and five of this series for the other 9 Singapore Math heuristics and word problems with step-by-step worked solutions.

This is part two to S.A.M Singapore Math Heuristics series. Read part one here.

Established in 2010, Seriously Addictive Mathematics (S.A.M) is the world’s largest Singapore Math enrichment program for children aged four to 12. The award-winning S.A.M program is based on the global top-ranking Singapore Math curriculum with a focus on developing problem solving and thinking skills.

The curriculum is complemented with S.A.M’s two-pillared approach of Classroom Engagement and Worksheet Reinforcement, with an individual learning plan tailored to each child at their own skill level and pace, because no two children learn alike.

## Singapore Math Heuristics: Draw a Table, Make Suppositions and Use Before-After Concept

Heuristics, in the context of problem-solving, are a set of strategies to help students solve mathematical problems. Although problem-solving is by and large the process of working towards a goal to which a solution may not be immediately present, it is important that problem solvers (or students) are not only aware of what they are […]

## Singapore Math Heuristics: Solve Part of the Problem, Simplify the Problem and Work Backwards

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 […]

## Singapore Math Heuristics: Make A Systematic List, Guess And Check, Restate The Problem In Another Way

The skills children pick up in math are indispensable; they can be applied to other academic subjects and to solve real-world problems in their daily lives and future work. The Singapore Math curriculum focuses on problem solving. Through problem solving, children develop thinking skills such as creative thinking and critical thinking. When children analyse math […]

## What are Singapore Math Heuristics?

Ever tried to help your child with primary math homework and got stumped? Today’s math questions can be challenging – even for adults. Math education is changing. While many parents spent time memorising procedures and formulas, today’s students are expected to not only understand and master the concepts, but also to have strong thinking skills […]

## COMMENTS

Many parents struggle to support their P3 to P6 children with math homework, especially in problem-solving. While they may be proficient in most math topics, heuristic problem-solving often poses a challenge. These strategies are typically encountered in university, making it difficult to simplify and convey them effectively to children.

With alternative heuristics provided whenever appropriate, pupils are able to gain exposure in selecting the right heuristic to solve any word problem. Read more Read less Report an issue with this product. Previous page. Print length. 170 pages. Language. English. Publication date. 1 January 2016. ISBN-10. 9814661317. ISBN-13.

The four stages of heuristics in problem solving are as follows: 1. Understanding the problem: Identifying and defining the problem is the first step in the problem-solving process. 2. Generating solutions: The second step is to generate as many solutions as possible.

P3 is a crucial year for mastering math problem-solving strategies. With fewer topics that are challenging compared to Primary 4 to 6, students can focus more on understanding heuristic strategies. Starting with this course is highly recommended if your child struggles with math problems.

Session 2A Problem-Solving using Heuristics at P3 and P4 - Free download as PDF File (.pdf), Text File (.txt) or view presentation slides online. 1) Originally, Adam had 789 more marbles than Zack. 2) Adam gave Zack 98 marbles. 3) To find how many more marbles Adam has than Zack now, we subtract the 98 marbles Adam gave Zack from his original 789 more marbles.

Objectives. Enhance students' conception in Mathematics through various techniques and methods of solving. Inspire students to investigate Mathematical concepts and acquire analytical thinking skills to further understand and appreciate the concepts. Topics covered are subjected to change depending on the ability of students.

Heuristics like "local search" help narrow down the array of possible locations. 20 locations and a possible solution with 5 facilities. All of these are combinatorial problems, where a computer would need to search an exponentially growing number of combinations to find the optimal answer.

Heuristics are essential problem solving skills for difficult word problems in MOE's Math paper 2. Heuristics are key in achieving AL1. Master Word Problems in Paper 2. ... Discover the 12 heuristics often tested by MOE, so you have a clear idea of what might come out in exams. And instead of waiting for tutors or teachers for help, you can ...

Solve Part of the Problem. Solving part of a problem at time helps break up the job. More accuracy can come from this strategy and less confusion too. At the end, putting the parts together can help one solve the problem more easily that way. For the sample question of 'Simplify Part of the Problem' Strategy: P3 Math Heuristics. Work Backwards

Problem Solving. In contrast to a routine task, a problem is a situation in which a person is trying to attain a goal but does not dispose of a ready-made solution or solution method. Problem solving involves then "cognitive processing directed at transforming the given situation into a goal situation when no obvious method of solution is ...

It delivers the foundation for learning Unit Transfer Method at Primary 5 where mathematical problems are expanded to involve ratios and percentages. Ultimately, Unit Transfer Method is a simple, logical yet powerful problem-solving technique that complements the model approach and the algebraic approach.

Working Backwards is a non-routine heuristic that all pupils learn in primary schools. Many pupils learn this heuristic as early as when they were in primary two. You can easily find this heuristic being included in one of the topics in assessment books. Though common, this heuristic is in fact one of the toughest in primary Mathematics syllabus.

The term "Heuristic" comes from the Greek word "Evriskein," which means "Discover.". According to the definition originally coined by Polya in 1945, heuristics is the "study of means and methods of problem solving" (Polya 1962, p. x) and refers to experience-based techniques for problem solving, learning, and discovery that ...

There are roughly six different kinds of heuristics tested at the primary school level, but this list is non-exhaustive as teachers continue finding new ways to solve problem sums effectively. Keep on reading to see the different types of heuristics, including examples and solutions! 6. Types of Heuristics . 1. Draw a Diagram

Heuristics, in the context of problem-solving, are a set of strategies to help students solve mathematical problems. Although problem-solving is by and large the process of working towards a goal to which a solution may not be immediately present, it is important that problem solvers (or students) are not only aware of what they are doing and why they are doing it, but also have the ability to ...

1. It needs to be educationally sound and aligned with the school's syllabus. 2. It needs to stir interest and encourage kids to learn more, making it truly effective. #2 is where many math learning solutions fall short, especially traditional methods like tuition and assessment books. Students usually tune out quickly.

A heuristic is a thinking strategy, something that can be used to tease out further information about a problem and thus help you figure out what to do when you don't know what to do. Here are 25 heuristics that can be useful in solving problems. They help you monitor your thought processes, to step back and watch yourself at work, and thus ...

In part 4 of this series, we will zoom in on these 3 heuristics: Solve Part of the Problem, Simplify the Problem and Work Backwards. Heuristic: Solve Part of the Problem. Word Problem (Primary 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 ...

In Singapore Math, there are 12 heuristics in the primary math syllabus that can be grouped into four main categories: To give a representation: Draw a diagram/model, draw a table, make a systematic list. To make a calculated guess: Look for pattern (s), guess and check, make suppositions. To go through the process: Act it out, work backwards ...

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) .

The scenario occurs when the quantity data is insufficient to work from the beginning.Working Backwards is a problem-solving strategy in which you start with the end goal and work backward to figure out the steps needed to get there. In other words, instead of starting from the beginning and moving forward, you start from the end and move backward.

Part 4: Math Heuristics: Solve Part of the Problem, Simplify the Problem and Work Backwards Part 5: Math Heuristics: Draw a Table, Make Suppositions and Use Before-After Concept. Established in 2010, Seriously Addictive Mathematics (S.A.M) is the world's largest Singapore Math enrichment program for children aged four to 12. The award-winning ...

The quantum alternating operator ansatz (QAOA) is a generalized approach for solving challenging optimization problems that builds on the alternating structure of the quantum approximate optimization algorithm. Finding high-quality parameters efficiently for QAOA remains a major challenge in practice. In this work, we introduce a classical strategy for parameter setting, suitable for cases in ...

The Guess-and-Check method is a problem-solving strategy used in math to find a solution by making an initial guess and checking whether it is correct or not.If the guess is incorrect, a new guess is made and checked until the correct answer is found.This method can be used when there is no obvious formula or method to solve the problem, and is particularly useful when dealing with word problems.