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## Problem Solving: Guess and Check

## Teach students the same technique research mathematicians use! (Seriously.)

Need more tips and tricks for teaching math? You can find them in our math resources center .

## What Is It?

"Guess and Check" is a problem-solving strategy that students can use to solve mathematical problems by guessing the answer and then checking that the guess fits the conditions of the problem. For example, the following problem would be best solved using guess and check:

Of 25 rounds at the regional spelling contest, the Mighty Brains tied 3 rounds and won 2 more than they lost. How many rounds did the Mighty Brains win?

## Why Is It Important?

All research mathematicians use guess and check, and it is one of the most powerful methods of solving differential equations, which are equations involving an unknown function and its derivatives. A mathematician's guess is called a "conjecture" and looking back to check the answer and prove that it is valid, is called a "proof." The main difference between problem solving in the classroom and mathematical research is that in school, there is usually a known solution to the problem. In research the solution is often unknown, so checking solutions is a critical part of the process.

## How Can You Make It Happen?

Introduce a problem to students that will require them to make and then check their guess to solve the problem. For example, the problem:

Ben knows 100 baseball players by name. Ten are Red Sox. The rest are Blue Jays and Diamondbacks. He knows the names of twice as many Diamondbacks as Blue Jays. How many Blue Jays does he know by name?

When students use the strategy of guess and check, they should keep a record of what they have done. It might be helpful to have them use a chart or table.

## Understand the Problem

Demonstrate that the first step is understanding the problem. This involves finding the key pieces of information needed to find the answer. This may require reading the problem several times, and/or students putting the problem into their own words.

For example, "I know there are twice as many Diamondbacks as Blue Jays. There are 10 Red Sox. The number of Blue Jays and Diamondbacks should equal 90."

Choose a Strategy

Use the "Guess and Check" strategy. Guess and check is often one of the first strategies that students learn when solving problems. This is a flexible strategy that is often used as a starting point when solving a problem, and can be used as a safety net, when no other strategy is immediately obvious.

## In This Article:

Featured high school resources.

## Related Resources

## About the author

## TeacherVision Editorial Staff

The TeacherVision editorial team is comprised of teachers, experts, and content professionals dedicated to bringing you the most accurate and relevant information in the teaching space.

## Fun teaching resources & tips to help you teach math with confidence

## Math Strategies: Solving Problems Using Guess and Check

Welcome to the last post in my series on problem solving strategies ! There are so many different ways to approach math word problems, but it’s important that we share these various methods with kids so that they can be equipped to tackle them. This week I’m explaining a strategy that doesn’t sound overly mathematical , but can be extremely useful when done properly: solving problems using guess and check ! As with the other strategies I’ve discussed, it’s important to help kids understand how to use this method so that they are not randomly pulling answers out of their head and wasting time .

–>Pssst! Do your kids need help making sense of and solving word problems? You might like this set of editable word problem solving templates ! Use these with any grade level, for any type of word problem :

## Guess & Check Math Strategy:

You may hear the name of this strategy and think, “Guess? Isn’t the whole point of math instruction to teach kids to solve problems so that they’re no longer merely guessing ??”

While it is certainly true that we don’t want kids to simply guess random answers for every math problem they ever encounter, there are instances when educated guesses are important, valid and useful.

For instance, learning and understanding how to accurately estimate is an important mathematical skill. A good estimate, however, is not just a random guess. It takes effort and logic to formulate an estimate that makes sense and is (hopefully) close to the correct answer. (For fun and easy estimation practice, try this Mummy Math activity ! )

Similarly, solving problems using guess and check is a process that requires logic and an understanding of the question so that it can be done in a way that is organized and time saving.

So what does guess and check mean? To be more specific, this strategy should be called, “Guess, Check and Revise.”

## The basic structure of the strategy looks like this:

- Form an educated guess
- Check your solution to see if it works and solves the problem
- If not, revise your guess based on whether it is too high or too low

This is a useful strategy when you’re given the total and you’re asked to find the kinds or number of things making up the total.

Or when the question asks for the value of two or more different kinds of things .

For instance, you might be asked how many girls and how many boys are in the class, or how many cats and how many dogs a pet owner has.

When guess and check seems like an appropriate strategy for a word problem, it will be helpful and necessary to then organize the information in a table or list to keep track of the different guesses.

This provides a visual of the important information, and will also help ensure that subsequent guesses are logical and not random .

## Using the Guess and Check Strategy:

To begin, students should make a guess using what they know from the problem. This first guess can be anything at all, so long as it follows the criteria given. Then, once a guess is made, students can begin to make more educated guesses based on how close they are to the correct answer.

For example, if their initial guess gives a total that is too high, they need to choose smaller numbers for their next guess.

Likewise, if their guess gives a total that is too low, they need to choose larger numbers.

The most important thing for students to understand when using this method is that after their initial guess, they should work towards getting closer to the correct answer by making logical changes to their guess. They should not be choosing random numbers anymore!

## Here’s an example to consider:

In Ms. Brown’s class, there are 24 students. There are 6 more girls than boys. How many boys and girls are there?

Because we know the class total (24), and we’re asked to find more than one value (number of boys and number of girls), we can solve this using the guess and check method .

To organize the question, we can form a table with boys, girls and the total. Because we know there are 6 more girls than boys, we can guess a number for the boys, and then calculate the girls and the total from there.

With an initial guess of 12 boys, we see that there would be 18 girls, giving a total class size of 30. The total, however, should only be 24, which means our guess was too high . Knowing this, the number of boys is revised and the total recalculated .

Lowering the number of boys to 10 would mean there are 16 girls, which gives a class total of 26. This is still just a little bit too high, so we can once again revise the guess to 9 boys. If there are 9 boys, that would mean there are 15 girls, which gives a class total of 24.

Therefore, the solution is 9 boys and 15 girls.

This is a fairly simple example, and likely you will have students who can solve this problem without writing out a table and forming multiple guesses. But for students who struggle with math , this problem may seem overwhelming and complicated.

By giving them a starting point and helping them learn to make more educated guesses , you can equip them to not only solve word problems, but feel more confident in tackling them.

This is also a good strategy because it helps kids see that it’s ok to make mistakes and that we shouldn’t expect to get the right answer on the first try, but rather, we should expect to make mistakes and use our mistake to learn and find the right answer.

What do you think? Do you use or teach this strategy to students? Do you find it helpful?

## And of course, don’t miss the rest of the problem solving strategy series:

- Problem Solve by Solving an Easier Problem
- Problem Solve by Drawing a Picture
- Problem Solve by Working Backwards
- Problem Solve by Making a List
- Problem Solve by Finding a Pattern

My strategy was usually more “guess and hope for the best”. Yours sounds much wiser, lol! Thanks for sharing at the Thoughtful Spot!

Haha!! Yes, I think that’s what most people think of when they hear, “Guess and Check!” Hope this was helpful, 🙂

How exactly do you do this?

Sorry, your way was amazing…but I’m still confused:(

I’m so sorry you’re confused. Can you explain what part you don’t understand so I can try and make it clearer? The object is to make a reasonable guess, and then adjust your guess based on if your answer is too high or too low (try to be logical rather than random).

Nicely explained post and a different logic for solving problems “Guess and check”, I don’t know that how much helpful it is but I’m sure that your idea will help to change the thinking of readers. Thanks for sharing a different kind of idea for problem solving.

Comments are closed.

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## 2.5.3: Guess and Check, Work Backward

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## Guess and Check, Work Backward

Suppose that you and your brother both play baseball. Last season, you had 12 more hits than 3 times the number of hits that your brother had. If you had 159 hits, could you figure out how many hits your brother had?

## More Problem Solving Strategies

This lesson will expand your toolbox of problem-solving strategies to include guess and check and working backward . Let’s begin by reviewing the four-step problem-solving plan:

Step 1: Understand the problem.

Step 2: Devise a plan – Translate.

Step 3: Carry out the plan – Solve.

Step 4: Look – Check and Interpret.

## Develop and Use the Strategy: Guess and Check

The strategy for the “guess and check” method is to guess a solution and use that guess in the problem to see if you get the correct answer. If the answer is too big or too small, then make another guess that will get you closer to the goal. You continue guessing until you arrive at the correct solution. The process might sound like a long one; however, the guessing process will often lead you to patterns that you can use to make better guesses along the way.

## Let's use the guess and check method to solve the following problem:

Nadia takes a ribbon that is 48 inches long and cuts it in two pieces. One piece is three times as long as the other. How long is each piece?

We need to find two numbers that add to 48. One number is three times the other number.

Guess 5 and 15. The sum is 5+15=20, which is too small.

Guess bigger numbers 6 and 18. The sum is 6+18=24, which is too small.

However, you can see that the previous answer is exactly half of 48.

Multiply 6 and 18 by two.

Our next guess is 12 and 36. The sum is 12+36=48. This is correct.

## Develop and Use the Strategy: Work Backward

The “work backward” method works well for problems in which a series of operations is applied to an unknown quantity and you are given the resulting value. The strategy in these problems is to start with the result and apply the operations in reverse order until you find the unknown. Let’s see how this method works by solving the following problem.

## Let's solve the following problem by working backwards :

Anne has a certain amount of money in her bank account on Friday morning. During the day she writes a check for $24.50, makes an ATM withdrawal of $80, and deposits a check for $235. At the end of the day, she sees that her balance is $451.25. How much money did she have in the bank at the beginning of the day?

We need to find the money in Anne’s bank account at the beginning of the day on Friday. From the unknown amount, we subtract $24.50 and $80 and we add $235. We end up with $451.25. We need to start with the result and apply the operations in reverse.

Start with $451.25. Subtract $235, add $80, and then add $24.50.

451.25−235+80+24.50=320.75

Anne had $320.75 in her account at the beginning of the day on Friday.

## Plan and Compare Alternative Approaches to Solving Problems

Most word problems can be solved in more than one way. Often one method is more straightforward than others. In this section, you will see how different problem-solving approaches compare when solving different kinds of problems.

## Now, let's solve the following problem by using the both the guess and check method and the working backward method:

Nadia’s father is 36. He is 16 years older than four times Nadia’s age. How old is Nadia?

This problem can be solved with either of the strategies you learned in this section. Let’s solve the problem using both strategies.

Guess and Check Method:

We need to find Nadia’s age.

We know that her father is 16 years older than four times her age, or 4× (Nadia’s age) + 16.

We know her father is 36 years old.

Work Backward Method:

Nadia’s father is 36 years old.

To get from Nadia’s age to her father’s age, we multiply Nadia’s age by four and add 16.

Working backward means we start with the father’s age, subtract 16, and divide by 4.

Example 2.5.3.1

Earlier, you were told that you had 12 more hits than 3 times the number of hits that your brother had. If you had 159 hits, how many hits did your brother have?

Since we know how many hits you had, we can work backward to determine the number of hits that your brother had.

Because you had 12 more hits than 3 times the number of hits that your brother had, we do the opposite: subtract 12 and divide by 3.

159−12=147

147÷3=49

Your brother had 49 hits.

Example 2.5.3.2

Hana rents a car for a day. Her car rental company charges $50 per day and $0.40 per mile. Peter rents a car from a different company that charges $70 per day and $0.30 per mile. How many miles do they have to drive before Hana and Peter pay the same price for the rental for the same number of miles?

Hana’s total cost is $50 plus $0.40 times the number of miles.

Peter’s total cost is $70 plus $0.30 times the number of miles.

Guess the number of miles and use this guess to calculate Hana’s and Peter’s total cost.

Keep guessing until their total cost is the same.

Guess 50 miles.

Check $50+$0.40(50)=$70 $70+$0.30(50)=$85

Guess 60 miles.

Check $50+$0.40(60)=$74 $70+$0.30(60)=$88

Notice that for an increase of 10 miles, the difference between total costs fell from $15 to $14. To get the difference to zero, we should try increasing the mileage by 140 miles.

Guess 200 miles

Check $50+$0.40(200)=$130 $70+$0.30(200)=$130correct

- Nadia is at home and Peter is at school, which is 6 miles away from home. They start traveling toward each other at the same time. Nadia is walking at 3.5 miles per hour and Peter is skateboarding at 6 miles per hour. When will they meet and how far from home is their meeting place?
- Peter bought several notebooks at Staples for $2.25 each and he bought a few more notebooks at Rite-Aid for $2 each. He spent the same amount of money in both places and he bought 17 notebooks in total. How many notebooks did Peter buy in each store?
- Andrew took a handful of change out of his pocket and noticed that he was holding only dimes and quarters in his hand. He counted that he had 22 coins that amounted to $4. How many quarters and how many dimes does Andrew have?
- Anne wants to put a fence around her rose bed that is one-and-a-half times as long as it is wide. She uses 50 feet of fencing. What are the dimensions of the garden?
- Peter is outside looking at the pigs and chickens in the yard. Nadia is indoors and cannot see the animals. Peter gives her a puzzle. He tells her that he counts 13 heads and 36 feet and asks her how many pigs and how many chickens are in the yard. Help Nadia find the answer.
- Andrew invests $8000 in two types of accounts: a savings account that pays 5.25% interest per year and a more risky account that pays 9% interest per year. At the end of the year, he has $450 in interest from the two accounts. Find the amount of money invested in each account.
- There is a bowl of candy sitting on our kitchen table. This morning Nadia takes one-sixth of the candy. Later that morning Peter takes one-fourth of the candy that’s left. This afternoon, Andrew takes one-fifth of what’s left in the bowl and finally Anne takes one-third of what is left in the bowl. If there are 16 candies left in the bowl at the end of the day, how much candy was there at the beginning of the day?
- Nadia can completely mow the lawn by herself in 30 minutes. Peter can completely mow the lawn by himself in 45 minutes. How long does it take both of them to mow the lawn together?

Mixed Review

- Rewrite √500 as a simplified square root.
- To which number categories does −2/13 belong?
- Simplify 1/2|19−65|−14.
- Which property is being applied? 16+4c+11=(16+11)+4c
- Is {(4,2),(4,−2),(9,3),(9,−3)} a function?
- Write using function notation: y=(1/12)x−5.
- Jordyn spent $36 on four cases of soda. How much was each case?

## Review (Answers)

To see the Review answers, open this PDF file and look for section 2.14.

## Additional Resources

Activity: Guess and Check, Work Backward Discussion Questions

Practice: Guess and Check, Work Backward

Real World Application: Car Loan

## Mathematics Developmental Continuum P-10

- Measurement, Chance and Data
- Working Mathematically
- Developmental Overviews

## Guess-Check-Improve Strategy: 2.5

Indicator of progress, teaching strategies, supporting materials.

- Related Progression Points
- Developmental Overview of Working Mathematically (PDF - 31Kb)
- Developmental Overview of Structure (PDF - 35Kb)

Success depends on students being confident in using the guess-check-improve strategy to find answers for appropriate problems.

Prior to achieving this level, students are unable to use the improve aspect of the strategy to refine initial guesses to work towards answers. They can make a guess and then check whether the guess correctly answers the problem, but if it doesn’t then the initial guess is not used to inform the next guess.

## Illustration 1: Guess-Check-Improve is not just Trial and Error

Students may be familiar with trial and error or guess and check , but they may not appreciate how the improve step works. The improve phase takes the results from earlier guesses to inform the next guess. The crucial step here is recognizing that each result from previous guesses can provide information for improving the next guess.

As teachers observe students using this strategy, they can talk to students to see that they are not randomly guessing, but are gathering information for improving subsequent guesses.

## Illustration 2: Working systematically is important

The importance of working systematically is reinforced when using the guess-check-improve strategy. A systematic approach enables students to work in an efficient way, rather than choose numbers randomly with the hope that they will eventually hit upon the answer to a problem. In a numerical problem, systematic working can be related to choice of numbers and the way that results are recorded. They will learn to use tables to organise results and identify useful numbers to use as the next guess .

As students use this strategy, teachers can observe whether they record their work systematically.

Teaching a strategy for problem solving is a long term endeavour, revisited with mathematics from different dimensions. Students need to be given experiences in solving problems for themselves, and key points about the strategy can be drawn out from the experience. There is also a place for students to practise strategies, such as guess-check-improve, which apply to a wide range of problems. The key points to emphasise are listed in Activity 3.

For these activities, allow students to use calculators for any challenging calculations, to enable a focus on the strategy rather than spending considerable time performing multiplication.

Activity 1 : Mystery number is an initial activity to highlight the importance of the improve step when using guess-check-improve as a strategy. Activity 2 : Ducks and horses aims to get students to recognise the usefulness of a systematic approach and the importance of careful organisation of results. Activity 3 : Additional problems provides some other suggestions.

Activity 1: Mystery number

In this activity students use the guess-check-improve strategy to find unknown numbers. The importance of the improve phase of the guess-check-improve strategy is highlighted so that students can recognise that this strategy will provide answers more quickly than random guessing. It is important to use problems where students cannot immediately see the answer otherwise there is no need to use the strategy of guess-check-improve .

Choose a problem beyond the range of students’ mental calculation skills, such as the following. There are many different possibilities (see notes at the end of this activity, and also Activity 3).

Ask a student to guess the mystery number in the following problem quickly.

"If you multiply 14 by this number you get 252. What is the number?" [Ans: 18]

Get all students to check if the number offered is the correct answer. Use calculators, so that the focus is on the strategy, rather than being distracted by by-hand calculation. Discuss whether the result is too high or too low and what this means about the answer to the problem. For example, if the number selected was 11, then the students will have used their calculators to find that 14 × 11 = 154, so 11 is too small. This information can be used to improve the next guess. They now know that the number needed is greater than 11. Focus on the use of the words guess, check and improve .

Now ask another student for a second guess : it should be a number greater than 11. If they suggest 25 (for example), they multiply 14 by 25, get 350, and note it is too big. Discuss what this means for the mystery number. The students should now recognise that the number they want to find is between 11 and 25.

Ask for another number, now between 11 and 25, gradually funneling onto the answer of 18. Focus on the word improve so that students can see that they are using their results at each stage to refine their guesses.

Provide students with some additional problems with whole number answers, such as:

"What number multiplied by 15 gives 405?" [Ans: 27]

"If you multiply 8 by this number you get 256. What is the number?" [Ans: 32]

"I have 288 eggs in boxes which each hold a dozen eggs. How many boxes?" [Ans: 24]

Discussion should focus on how students used their checking to improve their guesses. Focus on the cycle, guess-check-improve so that students recognise the importance of using results to inform them to work towards the required numbers.

To start students thinking about the importance of working systematically and organising results it would be helpful to show how guess-check-improve can be tabulated. For example, if trying to find a number that can be multiplied by 35 to give 840 the following table allows students to see how writing down the results in an organised way can help to find the answer.

- Using division: The problem above can solved immediately by using division. This activity has been suggested because it provides a simple context and at this level students are unlikely to identify the division strategy. However, if a student does suggest using division to solve the problem, show all students that this is correct and the best way, but then challenge the student to find the answer to the problem without using division.
- Variations: All the examples above involve multiplication, but addition or subtraction examples may be more appropriate for many students. The examples here also all involve only one operation, but this too can be varied (e.g. I thought of a number, added 12, then added my number again, and the answer was 50. What was my number? Ans: 19)

Activity 2: Ducks and horses

This activity is useful for showing how systematic recording of results can assist in solving problems using guess-check-improve where students have to do more than multiply one number.

Start by posing the problem for students.

"A farmer has some ducks and some horses. Altogether the ducks and horses have 40 legs and 14 heads. How many ducks and horses are there on the farm?" [Ans: 6 horses and 8 ducks]

Begin with the first step of problem solving: understanding the problem. Students need to recognise that ducks have two legs and one head and horses have four legs and one head. Some students might also say that if there are four legs then this could be for one horse or two ducks. Some students might want to guess the answer at this early stage (e.g. 3 horses and 3 ducks, as in the picture). It is always a good problem solving strategy to try an example, so work out the number of legs and heads for this first case. In this way, students will fully understand the problem requirements.

Now ask students to attempt the problem and then discuss some of the strategies used.

Many students will guess both the numbers of horses and ducks. For example, they might draw 8 horses and 10 ducks and count the legs (52) and heads (18), and then make another guess of both numbers.

A better strategy is to guess the number of horses and calculate the number of ducks (or vice versa) to get the right number of heads, and then check whether the number of legs is correct. For example, if a student guesses that there are 8 horses then there must be 6 ducks to get 14 heads. They can draw these animals, or just calculate that there are too many legs. Making a drawing or diagram is a strategy that will be used by children right through to secondary school, so it is a useful strategy to learn. Encourage students to record their results in a table. Discuss how students can improve their guess now, as they know that the number of horses must be less than 8.

A final table might look like this:

At each stage discuss how the table is being used to organise the data to systematically work towards the answer. Discuss how it is possible to improve the guess as more information is available to narrow down the possibilities. Finally students need to answer the problem and say that there are 8 ducks and 6 horses. Always encourage students to check that they have answered the actual problem.

Another systematic way is to start with one horse, then two, then three and so on. This is certainly systematic, but not often an efficient method for solving the problem. It is good to encourage students to think about what a reasonable guess might be for the first number, and then work from there.

Activity 3: Additional problems

Some additional problems to practise use of working systematically when using guess-check-improve are given below. Many variations can easily be constructed.

- I thought of a number, added 12, then added my original number again, and the answer was 50. What was my number? Ans: 19
- Some galahs were sitting in a tree. Half of them flew away, and then another 5 flew away. Then 10 more arrived, and there were 16 galahs in the tree. How many were there to start with? (Ans: 22)
- A number multiplied by 42 gives 798. What is the number? (Ans: 19)
- On a farm there are ducks and horses. Altogether the ducks and horses have 108 legs and 36 heads. How many ducks are there on the farm? (Ans: 18 horses & 18 ducks)
- A farmer has some ducks and some horses. Altogether the ducks and horses have 106 legs and 39 heads. How many ducks and horses are there on the farm? (Ans: 14 horses & 25 ducks)
- Some birds and spiders are in a shed. Altogether they have 64 legs and 17 heads. How many spiders are there? (Ans: 5 spiders & 12 birds)

## How Do You Solve a Problem Using the Guess, Check, and Revise Method?

Some problems can be solve by guessing an answer, checking it, and then revising your guess. This tutorial goes through that process step-by-step and shows you how to solve a word problem using the guess, test, revise method!

- word problem

## Background Tutorials

Operations with whole numbers.

## How Do You Add Whole Numbers?

To add numbers, you can line up the numbers vertically and then add the matching places together. This tutorial shows you how to add numbers vertically!

## A Problem-Solving Plan

## How Do You Solve a Problem by Making a Table and Finding a Pattern?

Making a table can be a very helpful way to find a pattern in numbers and solve a problem. This tutorial shows you how to take the information from and word problem to create a table and use it to find the answer!

## How Do You Make a Problem Solving Plan?

Planning is a key part of solving math problems. Follow along with this tutorial to see the steps involved to make a problem solving plan!

## Further Exploration

## How Do You Solve a Problem Using Logical Reasoning?

Using logic is a strong approach to solving math problems! This tutorial goes through an example of using logical reasoning to find the answer to a word problem.

- Terms of Use

## Learn the Guess and Check Method

What is the guess and check math strategy.

The Guess and Check Math strategy is one of the first few Math Heuristics that is introduced to Primary 3 students. Although some students may switch to more advanced techniques like the Assumption method in Primary 4, mastering this method is still going to be useful to those who don’t in their upper primary years. The main idea behind the Guess and Check method is to guess the answer to a problem and then check if the answer fits the given scenario. If it doesn’t, we’ll adjust our guess accordingly until all conditions are met.

Here’s what we’re going to cover:

- How does the Guess and check method work
- Examples of guess and check questions
- How to identify guess and check questions
- How to part 1: Building the guess and check table
- How to part 2: How to do the guess and check method

## How does the Guess and Check Method work?

The Guess and Check problem solving strategy is a fairly easy way of solving problems. Think of it as a 3-step-approach:

## 1. Guess –> 2. Check –> 3. Repeat if needed

While we are guessing the numbers, we’ll need to learn how to make smart guesses. Knowing how to do that helps us minimize the number of guessing, making the process more efficient. We’ll see how to do that in a while.

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## Examples of Guess and Check Questions

Here are some samples of how Guess and Check Math Questions can look like. Can you figure out what they have in common?

Primary 3 and 4 Math:

There are 15 cats and birds in a park. There are 42 legs altogether.

How many cats are there?

Primary 5 and 6 Math: Jay did 20 Math questions during his math practice. He received 5 marks for every correct answer and he got 2 marks deducted for every wrong answer. If Jay earned 35 experience points in total, how many questions did he answer wrongly?

## How do we identify questions that use the Guess and Check Method?

If you looked carefully, both problems that you see above has a total that’s made up of 2 kinds of items. on top of that, we also have some information about each item and we need to find the number of one of those items. Let’s use the lower primary math problem as an example and go through the Guess and Check method step by step.

## Part A: How to build the Guess and Check table the right way

Before we start guessing and checking, it’s always a good habit to build a guess and check table so that we know exactly what to look out for and keep things organised.

## Step 1: List the 2 items that is in the question

The first thing that we’ll want to do is to build our guess and check table is to think about what we want to solve for. This is the answer that we are going to guess and it goes into our first column. In our case, it’s going to be the number of cats. Next, we’ll list the number of the second item, which happens to be the number of birds as shown below:

## Step 2: List the common thing that the 2 items have

What do the cats and birds have in common? Legs. So the number of cats’ legs and the number of birds’ legs go into another 2 columns.

## Step 3: Add in what we need to check

Time to think about the relationship between the columns and how they help us check if the answer that we have guessed is correct. For our answer to be right, the total number of legs that we have has to add up to 42 and the way that we calculate this is to add the number of cats’ legs to the number of birds’ legs. Let’s add another column to include the total number of legs and because we are going to use this to check of our guess is correct, we are going to add in another special column called “Check” to help us keep track of our progress.

## Is the Guess and Check Table really necessary?

When we are busy making guesses, it is easy to lose track of the numbers that we have tried along with their calculations. That’s where a guess and check table can really come in handy. Not only does a guess and check table help us organize our guesses in a neat visual way, it also prevents us from making careless mistakes.

## How to use the Guess and Check method efficiently

As you might have guessed, guessing and checking comes with a lot of hits and misses. Here’s the trick to keep our guesses to a minimal and make the guess and check method work better!

## Step 1: Start with the middle number as your first guess

In our example, since we have 15 pets, half of 15 would be approximately 7 or 8 (not 7.5 because we can’t have half a pet). Let’s pick 7 as our guess.

## Step 2: Filling up our guess and check table from left to right

Once we have our guess, it’s time to work through the columns of our guess and check table and decide if our guess is correct. If we had 7 cats and each puppy has 4 legs, we are going to have 7 x 4 cats’ legs = 28 cats’ legs. To find the number of birds, let’s subtract 7 from the total of 15 pets. This gives us 8 birds. 8 birds are going to have 8 x 2 birds’ legs, 16 legs in all. Let’s check the total number of legs we have against what is given in the problem. When we add 28 and 16, we are going to get a total of 44 legs. However, this is more than the 42 legs that we are given in the problem. Let’s make a note of that under the “Check” column.

## Step 3: Adjust our guess accordingly and check again

The next thing that we’ll want to do is to estimate how far our guess is to our target, and make a better guess. Comparing our guess which resulted in 44 legs against the 42 legs that we want, we can tell that our guess is very close. Since we want to reduce the number of legs, should we increase or decrease our second guess? Because the cats have more legs than birds and we want fewer legs, we’ll need to lower what we’ve guessed. When we work systematically across our guess and check table, this happens to be the answer that we are looking for!

All it takes for us to get the correct answer are 2 guesses, and this definitely didn’t happen by chance. When we made the first guess, it gave us some information about how far we are from the answer. This helped us make a better guess the second time. As you can see, we are making logical guesses instead of just guessing random numbers and trying our luck.

## And that’s how you do the Guess and Check method!

Using the Guess and Check method is good when you are dealing with smaller numbers which are easier to work with. However, it does take practice to improve the accuracy of your guesses and some children may take a longer time to do the calculations in between, giving room to possible careless mistakes. If you are looking for a faster alternative that involves fewer steps, you might want to check out the Assumption Method and see if that works better for you.

## Need more examples?

Check out how this Math video on how to use the guess and check method to solve a Primary 3 question.

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## Key Questions

You should use the guess and check method when you do not know how to solve a problem.

The guess and check method includes:

- make a logical guess
- test your guess
- adjust your guess based on results of #2 until you are correct

There are 20 children in the kindergarten class. The children are a mix of 5 year olds and 6 year olds. The total age of the children equals 108 years. How many 5 year olds are there?

Guess & check method:

- Let's guess that there are 10 five year olds.
- If there are 10 five year olds, there must be 10 six year olds since there are 20 children in total. Their combined age is equal to (10 x 5) + (10 x 6), or 110 years.
- Since 110 years is greater than 108 (the correct answer), our initial guess was incorrect. To get closer to the correct answer, we need to guess a higher number of five year olds (since five years is less than six years).
- Let's now guess that there are 12 five year olds.
- If there are 12 five year olds, there must be eight six year olds since there are 20 children in total. Their combined age is equal to (12 x 5) + (8 x 6), or 108 years. Therefore, the correct answer is 12 five year olds.

The problem with the above "proof" is that, if the initial statement was false, using seemingly correct transformations, we can come up to an obviously true statement. So, the fact that from our original statement we have derived the obviously true final statement does not necessarily prove that our initial statement was true.

But, if all transformations we made are not only "correct", but invariant (or equivalent ), which, in short, means reversible , then after we have derived a true statement we can conclude: since all transformations are invariant (that is reversible), from the final true statement we can derive the initial, and that is the actual proof. This is actually the "working back" part of a proof.

For the example above the real proof is the following sequence: #(x-2)^2>=0# - add 2 to both sides - #(x-2)^2+2>=2>1# - open parenthesis - #x^2-4x+4+2>1# - simplify - #x^2-4x+6>1# - which is what we had to proof.

Research provides a striking revelation about problem solvers. The best problem solvers approach problems much differently than novices. For instance, one meta-study showed that when experts evaluate graphs , they tend to spend less time on tasks and answer choices and more time on evaluating the axes’ labels and the relationships of variables within the graphs. In other words, they spend more time up front making sense of the data before moving to addressing the task.

While slower in solving problems, experts use this additional up-front time to more efficiently and effectively solve the problem. In one study, researchers found that experts were much better at “information extraction” or pulling the information they needed to solve the problem later in the problem than novices. This was due to the fact that they started a problem-solving process by evaluating specific assumptions within problems, asking predictive questions, and then comparing and contrasting their predictions with results. For example, expert problem solvers look at the problem context and ask a number of questions:

- What do we know about the context of the problem?
- What assumptions are underlying the problem? What’s the story here?
- What qualitative and quantitative information is pertinent?
- What might the problem context be telling us? What questions arise from the information we are reading or reviewing?
- What are important trends and patterns?

As such, expert problem solvers don’t jump to the presented problem or rush to solutions. They invest the time necessary to make sense of the problem.

Now, think about your own students: Do they immediately jump to the question, or do they take time to understand the problem context? Do they identify the relevant variables, look for patterns, and then focus on the specific tasks?

If your students are struggling to develop the habit of sense-making in a problem- solving context, this is a perfect time to incorporate a few short and sharp strategies to support them.

## 3 Ways to Improve Student Problem-Solving

1. Slow reveal graphs: The brilliant strategy crafted by K–8 math specialist Jenna Laib and her colleagues provides teachers with an opportunity to gradually display complex graphical information and build students’ questioning, sense-making, and evaluating predictions.

For instance, in one third-grade class, students are given a bar graph without any labels or identifying information except for bars emerging from a horizontal line on the bottom of the slide. Over time, students learn about the categories on the x -axis (types of animals) and the quantities specified on the y -axis (number of baby teeth).

The graphs and the topics range in complexity from studying the standard deviation of temperatures in Antarctica to the use of scatterplots to compare working hours across OECD (Organization for Economic Cooperation and Development) countries. The website offers a number of graphs on Google Slides and suggests questions that teachers may ask students. Furthermore, this site allows teachers to search by type of graph (e.g., scatterplot) or topic (e.g., social justice).

2. Three reads: The three-reads strategy tasks students with evaluating a word problem in three different ways . First, students encounter a problem without having access to the question—for instance, “There are 20 kangaroos on the grassland. Three hop away.” Students are expected to discuss the context of the problem without emphasizing the quantities. For instance, a student may say, “We know that there are a total amount of kangaroos, and the total shrinks because some kangaroos hop away.”

Next, students discuss the important quantities and what questions may be generated. Finally, students receive and address the actual problem. Here they can both evaluate how close their predicted questions were from the actual questions and solve the actual problem.

To get started, consider using the numberless word problems on educator Brian Bushart’s site . For those teaching high school, consider using your own textbook word problems for this activity. Simply create three slides to present to students that include context (e.g., on the first slide state, “A salesman sold twice as much pears in the afternoon as in the morning”). The second slide would include quantities (e.g., “He sold 360 kilograms of pears”), and the third slide would include the actual question (e.g., “How many kilograms did he sell in the morning and how many in the afternoon?”). One additional suggestion for teams to consider is to have students solve the questions they generated before revealing the actual question.

3. Three-Act Tasks: Originally created by Dan Meyer, three-act tasks follow the three acts of a story . The first act is typically called the “setup,” followed by the “confrontation” and then the “resolution.”

This storyline process can be used in mathematics in which students encounter a contextual problem (e.g., a pool is being filled with soda). Here students work to identify the important aspects of the problem. During the second act, students build knowledge and skill to solve the problem (e.g., they learn how to calculate the volume of particular spaces). Finally, students solve the problem and evaluate their answers (e.g., how close were their calculations to the actual specifications of the pool and the amount of liquid that filled it).

Often, teachers add a fourth act (i.e., “the sequel”), in which students encounter a similar problem but in a different context (e.g., they have to estimate the volume of a lava lamp). There are also a number of elementary examples that have been developed by math teachers including GFletchy , which offers pre-kindergarten to middle school activities including counting squares , peas in a pod , and shark bait .

Students need to learn how to slow down and think through a problem context. The aforementioned strategies are quick ways teachers can begin to support students in developing the habits needed to effectively and efficiently tackle complex problem-solving.

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## Problem solving strategies

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## What are problem solving strategies?

Strategies are things that Pólya would have us choose in his second stage of problem solving and use in his third stage ( What is Problem Solving? ). In actual fact he called them heuristics . They are a collection of general approaches that might work for a number of problems.

There are a number of common strategies that students of primary age can use to help them solve problems. We discuss below several that will be of value for problems on this website and in books on problem solving.

Common Problem Solving Strategies

- Guess (includes guess and check, guess and improve)
- Act It Out (act it out and use equipment)
- Draw (this includes drawing pictures and diagrams)
- Make a List (includes making a table)
- Think (includes using skills you know already)

We have provided a copymaster for these strategies so that you can make posters and display them in your classroom. It consists of a page per strategy with space provided to insert the name of any problem that you come across that uses that particular strategy (Act it out, Draw, Guess, Make a List). This kind of poster provides good revision for students.

## An in-depth look at strategies

We now look at each of the following strategies and discuss them in some depth. You will see that each strategy we have in our list includes two or more subcategories.

- Guess and check is one of the simplest strategies. Anyone can guess an answer. If they can also check that the guess fits the conditions of the problem, then they have mastered guess and check. This is a strategy that would certainly work on the Farmyard problem described below but it could take a lot of time and a lot of computation. Because it is so simple, you may have difficulty weaning some students away from guess and check. As problems get more difficult, other strategies become more important and more effective. However, sometimes when students are completely stuck, guessing and checking will provide a useful way to start to explore a problem. Hopefully that exploration will lead to a more efficient strategy and then to a solution.
- Guess and improve is slightly more sophisticated than guess and check. The idea is that you use your first incorrect guess to make an improved next guess. You can see it in action in the Farmyard problem. In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess. In some problems though, where there are more variables, it may not be clear at first which way to change the guessing.
- Young students especially, enjoy using Act it Out . Students themselves take the role of things in the problem. In the Farmyard problem, the students might take the role of the animals though it is unlikely that you would have 87 students in your class! But if there are not enough students you might be able to include a teddy or two. This is an effective strategy for demonstration purposes in front of the whole class. On the other hand, it can also be cumbersome when used by groups, especially if a largish number of students is involved. Sometimes the students acting out the problem may get less out of the exercise than the students watching. This is because the participants are so engrossed in the mechanics of what they are doing that they don’t see the underlying mathematics.
- Use Equipment is a strategy related to Act it Out. Generally speaking, any object that can be used in some way to represent the situation the students are trying to solve, is equipment. One of the difficulties with using equipment is keeping track of the solution. The students need to be encouraged to keep track of their working as they manipulate the equipment. Some students need to be encouraged and helped to use equipment. Many students seem to prefer to draw. This may be because it gives them a better representation of the problem in hand. Since there are problems where using equipment is a better strategy than drawing, you should encourage students' use of equipment by modelling its use yourself from time to time.
- It is fairly clear that a picture has to be used in the strategy Draw a Picture . But the picture need not be too elaborate. It should only contain enough detail to help solve the problem. Hence a rough circle with two marks is quite sufficient for chickens and a blob plus four marks will do a pig. All students should be encouraged to use this strategy at some point because it helps them ‘see’ the problem and it can develop into quite a sophisticated strategy later.
- It’s hard to know where Drawing a Picture ends and Drawing a Diagram begins. You might think of a diagram as anything that you can draw which isn’t a picture. But where do you draw the line between a picture and a diagram? As you can see with the chickens and pigs, discussed above, regular picture drawing develops into drawing a diagram. Venn diagrams and tree diagrams are particular types of diagrams that we use so often they have been given names in their own right.
- There are a number of ways of using Make a Table . These range from tables of numbers to help solve problems like the Farmyard, to the sort of tables with ticks and crosses that are often used in logic problems. Tables can also be an efficient way of finding number patterns.
- When an Organised List is being used, it should be arranged in such a way that there is some natural order implicit in its construction. For example, shopping lists are generally not organised. They usually grow haphazardly as you think of each item. A little thought might make them organised. Putting all the meat together, all the vegetables together, and all the drinks together, could do this for you. Even more organisation could be forced by putting all the meat items in alphabetical order, and so on. Someone we know lists the items on her list in the order that they appear on her route through the supermarket.
- Being systematic may mean making a table or an organised list but it can also mean keeping your working in some order so that it is easy to follow when you have to go back over it. It means that you should work logically as you go along and make sure you don’t miss any steps in an argument. And it also means following an idea for a while to see where it leads, rather than jumping about all over the place chasing lots of possible ideas.
- It is very important to keep track of your work. We have seen several groups of students acting out a problem and having trouble at the end simply because they had not kept track of what they were doing. So keeping track is particularly important with Act it Out and Using Equipment. But it is important in many other situations too. Students have to know where they have been and where they are going or they will get hopelessly muddled. This begins to be more significant as the problems get more difficult and involve more and more steps.
- In many ways looking for patterns is what mathematics is all about. We want to know how things are connected and how things work and this is made easier if we can find patterns. Patterns make things easier because they tell us how a group of objects acts in the same way. Once we see a pattern we have much more control over what we are doing.
- Using symmetry helps us to reduce the difficulty level of a problem. Playing Noughts and crosses, for instance, you will have realised that there are three and not nine ways to put the first symbol down. This immediately reduces the number of possibilities for the game and makes it easier to analyse. This sort of argument comes up all the time and should be grabbed with glee when you see it.
- Finally working backwards is a standard strategy that only seems to have restricted use. However, it’s a powerful tool when it can be used. In the kind of problems we will be using in this web-site, it will be most often of value when we are looking at games. It frequently turns out to be worth looking at what happens at the end of a game and then work backward to the beginning, in order to see what moves are best.
- Then we come to use known skills . This isn't usually listed in most lists of problem solving strategies but as we have gone through the problems in this web site, we have found it to be quite common. The trick here is to see which skills that you know can be applied to the problem in hand. One example of this type is Fertiliser (Measurement, level 4). In this problem, the problem solver has to know the formula for the area of a rectangle to be able to use the data of the problem. This strategy is related to the first step of problem solving when the problem solver thinks 'have I seen a problem like this before?' Being able to relate a word problem to some previously acquired skill is not easy but it is extremely important.

## Uses of strategies

Different strategies have different uses. We’ll illustrate this by means of a problem.

The Farmyard Problem : In the farmyard there are some pigs and some chickens. In fact there are 87 animals and 266 legs. How many pigs are there in the farmyard?

Some strategies help you to understand a problem. Let’s kick off with one of those. Guess and check . Let’s guess that there are 80 pigs. If there are they will account for 320 legs. Clearly we’ve over-guessed the number of pigs. So maybe there are only 60 pigs. Now 60 pigs would have 240 legs. That would leave us with 16 legs to be found from the chickens. It takes 8 chickens to produce 16 legs. But 60 pigs plus 8 chickens is only 68 animals so we have landed nearly 20 animals short.

Obviously we haven’t solved the problem yet but we have now come to grips with some of the important aspects of the problem. We know that there are 87 animals and so the number of pigs plus the number of chickens must add up to 87. We also know that we have to use the fact that pigs have four legs and chickens two, and that there have to be 266 legs altogether.

Some strategies are methods of solution in themselves. For instance, take Guess and improve . Supposed we guessed 60 pigs for a total of 240 legs. Now 60 pigs imply 27 chickens, and that gives another 54 legs. Altogether then we’d have 294 legs at this point.

Unfortunately we know that there are only 266 legs. So we’ve guessed too high. As pigs have more legs than hens, we need to reduce the guess of 60 pigs. How about reducing the number of pigs to 50? That means 37 chickens and so 200 + 74 = 274 legs.

We’re still too high. Now 40 pigs and 47 hens gives 160 + 94 = 254 legs. We’ve now got too few legs so we need to guess more pigs.

You should be able to see now how to oscillate backwards and forwards until you hit on the right number of pigs. So guess and improve is a method of solution that you can use on a number of problems.

Some strategies can give you an idea of how you might tackle a problem. Making a table illustrates this point. We’ll put a few values in and see what happens.

From the table we can see that every time we change the number of pigs by one, we change the number of legs by two. This means that in our last guess in the table, we are five pigs away from the right answer. Then there have to be 46 pigs.

Some strategies help us to see general patterns so that we can make conjectures. Some strategies help us to see how to justify conjectures. And some strategies do other jobs. We’ll develop these ideas on the uses of strategies as this web-site grows.

What strategies can be used at what levels?

In the work we have done over the last few years, it seems that students are able to tackle and use more strategies as they continue with problem solving. They are also able to use them to a deeper level. We have observed the following strategies being used in the stated Levels.

Levels 1 and 2

- Draw a picture
- Use equipment
- Guess and check

Levels 3 and 4

- Draw a diagram
- Guess and improve
- Make a table
- Make an organised list

It is important to say here that the research has not been exhaustive. Possibly younger students can effectively use other strategies. However, we feel confident that most students at a given Curriculum Level can use the strategies listed at that Level above. As problem solving becomes more common in primary schools, we would expect some of the more difficult strategies to come into use at lower Levels.

Strategies can develop in at least two ways. First students' ability to use strategies develops with experience and practice. We mentioned that above. Second, strategies themselves can become more abstract and complex. It’s this development that we want to discuss here with a few examples.

Not all students may follow this development precisely. Some students may skip various stages. Further, when a completely novel problem presents itself, students may revert to an earlier stage of a strategy during the solution of the problem.

Draw: Earlier on we talked about drawing a picture and drawing a diagram. Students often start out by giving a very precise representation of the problem in hand. As they see that it is not necessary to add all the detail or colour, their pictures become more symbolic and only the essential features are retained. Hence we get a blob for a pig’s body and four short lines for its legs. Then students seem to realise that relationships between objects can be demonstrated by line drawings. The objects may be reduced to dots or letters. More precise diagrams may be required in geometrical problems but diagrams are useful in a great many problems with no geometrical content.

The simple "draw a picture" eventually develops into a wide variety of drawings that enable students, and adults, to solve a vast array of problems.

Guess: Moving from guess and check to guess and improve, is an obvious development of a simple strategy. Guess and check may work well in some problems but guess and improve is a simple development of guess and check.

But guess and check can develop into a sophisticated procedure that 5-year-old students couldn’t begin to recognise. At a higher level, but still in the primary school, students are able to guess patterns from data they have been given or they produce themselves. If they are to be sure that their guess is correct, then they have to justify the pattern in some way. This is just another way of checking.

All research mathematicians use guess and check. Their guesses are called "conjectures". Their checks are "proofs". A checked guess becomes a "theorem". Problem solving is very close to mathematical research. The way that research mathematicians work is precisely the Pólya four stage method ( What is Problem Solving? ). The only difference between problem solving and research is that in school, someone (the teacher) knows the solution to the problem. In research no one knows the solution, so checking solutions becomes more important.

So you see that a very simple strategy like guess and check can develop to a very deep level.

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## VIDEO

## COMMENTS

Use the "Guess and Check" strategy. Guess and check is often one of the first strategies that students learn when solving problems. This is a flexible strategy that is often used as a starting point when solving a problem, and can be used as a safety net, when no other strategy is immediately obvious. Prev.

Form an educated guess. Check your solution to see if it works and solves the problem. If not, revise your guess based on whether it is too high or too low. This is a useful strategy when you're given the total and you're asked to find the kinds or number of things making up the total.

This lesson will expand your toolbox of problem-solving strategies to include guess and check and working backward. Let's begin by reviewing the four-step problem-solving plan: Step 1: Understand the problem. Step 2: Devise a plan - Translate. Step 3: Carry out the plan - Solve. Step 4: Look - Check and Interpret.

Doing the guess and check method is similar to finding the answer without guessing and checking the answer. Just this time, people will actually guess what the solution is. Say in the problem 5 x ...

Students need to be given experiences in solving problems for themselves, and key points about the strategy can be drawn out from the experience. There is also a place for students to practise strategies, such as guess-check-improve, which apply to a wide range of problems. The key points to emphasise are listed in Activity 3.

Elementary Math Problem Solving - Guess and CheckIn this video, we explore one of eight problem-solving strategies for the primary math student. Students are...

This foundations of math video explains an example of the four-step process of problem solving using the method of guess and check. We look at understanding ...

Using logic is a strong approach to solving math problems! This tutorial goes through an example of using logical reasoning to find the answer to a word problem. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long.

The Guess and Check problem solving strategy is a fairly easy way of solving problems. Think of it as a 3-step-approach: 1. Guess -> 2. Check -> 3. ... However, it does take practice to improve the accuracy of your guesses and some children may take a longer time to do the calculations in between, giving room to possible careless mistakes. ...

Include 3 'h' squares (representing the hats), a 5 (representing the scarf) and a 17 (the overall value). STEP 3 - Guess that h = 5; this is wrong because the total will equal 20. It is too ...

Guess and Check and Working Backwards. In this section, you will learn about the methods of Guess and Check and Working Backwards. These are very powerful strategies in problem solving and probably the most commonly used in everyday life. Let's review our problem-solving plan. Step 1. Understand the problem. Read the problem carefully.

She has 20 years of experience teaching collegiate mathematics at various institutions. In this lesson, we will look at how to solve problems using the guess, check, and revise method in ...

Worksheet (pdf) Teacher View. Clicking 'yes' will take you out of the classroom and to our Teacher Hub, a dedicated area for teachers to access our resources. No. Yes. Using the guess and check strategy for problem solving. In this lesson, we will begin to apply the guess and check strategy to a problem involving numbers within 15.

Key learning points. In this lesson, we will begin to apply the guess and check strategy to a problem involving numbers within 15.

This video teaches students to guess, check, and revise as a strategy to solve mathematical word problems.

Explore how to solve word problems using the guess, check, and revise strategy. Click Create Assignment to assign this modality to your LMS. We have a new and improved read on this topic.

This lesson will expand your toolbox of problem-solving strategies to include guess and check and working backward. Let's begin by reviewing the four-step problem-solving plan: Step 1: Understand the problem. Step 2: Devise a plan - Translate. Step 3: Carry out the plan - Solve. Step 4: Look - Check and Interpret.

You should use the guess and check method when you do not know how to solve a problem. The guess and check method includes: make a logical guess; test your guess; adjust your guess based on results of #2 until you are correct; Example: There are 20 children in the kindergarten class. The children are a mix of 5 year olds and 6 year olds.

Guess And Check. Guess And Check - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Problem solving strategies guess and check work backward, 7 practice using guess and check, Unit 1 guess and check a decoding strategy, Group, Fractions section 1 iterating and partitioning, Polyas problem solving ...

While slower in solving problems, experts use this additional up-front time to more efficiently and effectively solve the problem. In one study, researchers found that experts were much better at "information extraction" or pulling the information they needed to solve the problem later in the problem than novices. This was due to the fact that they started a problem-solving process by ...

Guess: Moving from guess and check to guess and improve, is an obvious development of a simple strategy. Guess and check may work well in some problems but guess and improve is a simple development of guess and check. But guess and check can develop into a sophisticated procedure that 5-year-old students couldn't begin to recognise.

guess and check

Explore more than 51 "Guess And Check Problem Solving" resources for teachers, parents and pupils as well as related resources on "Using The Guess And Check Strategy For Problem Solving". Check out our interactive series of lesson plans, worksheets, PowerPoints and assessment tools today! All teacher-made, aligned with the Australian Curriculum.

Many of the problem solving strategies that students learn in mathematics classes, such as 'Guess, Check and Improve' or 'Try a simpler problem' are similar to algorithm design strategies. Algorithmic thinking and 'coding' are often conflated, but the two disciplines are quite different. The focus of algorithmic thinking is the algorithm ...