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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 .

Although this doesn't sound like math, using guess and check to solve problems can be a really useful strategy for kids! Learn how to use this problem solving strategy and set kids up for success!

–>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.

Guess and Check Table1

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 .

Guess and Check Table2

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.

Guess and Check Table3

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?

Great tips and helpful strategies for teaching kids to be problem solvers!

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

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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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Problem Solving: Guess and Check

TeacherVision Staff

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.

Black History Month reading comprehension packet

Related Resources

problem solving worksheet

About the author

TeacherVision Staff

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.

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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

problem solving using guess and check

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?

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?

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?

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?

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.

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Module 1: Problem Solving Strategies

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Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1

1. Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY

Screen Shot 2018-08-30 at 4.43.05 PM.png

In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

First, you have to understand the problem.

After understanding, then make a plan.

Carry out the plan.

Look back on your work. How could it be better?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

Problem Solving Strategy 1 (Guess and Test)

Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution.

Mr. Jones has a total of 25 chickens and cows on his farm. How many of each does he have if all together there are 76 feet?

Step 1: Understanding the problem

We are given in the problem that there are 25 chickens and cows.

All together there are 76 feet.

Chickens have 2 feet and cows have 4 feet.

We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.

Step 2: Devise a plan

Going to use Guess and test along with making a tab

Many times the strategy below is used with guess and test.

Make a table and look for a pattern:

Procedure: Make a table reflecting the data in the problem. If done in an orderly way, such a table will often reveal patterns and relationships that suggest how the problem can be solved.

Step 3: Carry out the plan:

Notice we are going in the wrong direction! The total number of feet is decreasing!

Better! The total number of feet are increasing!

Step 4: Looking back:

Check: 12 + 13 = 25 heads

24 + 52 = 76 feet.

We have found the solution to this problem. I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.

Videos to watch:

1. Click on this link to see an example of “Guess and Test”

http://www.mathstories.com/strategies.htm

2. Click on this link to see another example of Guess and Test.

http://www.mathinaction.org/problem-solving-strategies.html

Check in question 1:

clipboard_e6298bbd7c7f66d9eb9affcd33892ef0d.png

Place the digits 8, 10, 11, 12, and 13 in the circles to make the sums across and vertically equal 31. (5 points)

Check in question 2:

Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet . How many of each animal does he have? Make sure you use Polya’s 4 problem solving steps. (12 points)

Problem Solving Strategy 2 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric thinking visually can help!

Videos to watch demonstrating how to use "Draw a Picture".

1. Click on this link to see an example of “Draw a Picture”

2. Click on this link to see another example of Draw a Picture.

Problem Solving Strategy 3 ( Using a variable to find the sum of a sequence.)

Gauss's strategy for sequences.

last term = fixed number ( n -1) + first term

The fix number is the the amount each term is increasing or decreasing by. "n" is the number of terms you have. You can use this formula to find the last term in the sequence or the number of terms you have in a sequence.

Ex: 2, 5, 8, ... Find the 200th term.

Last term = 3(200-1) +2

Last term is 599.

To find the sum of a sequence: sum = [(first term + last term) (number of terms)]/ 2

Sum = (2 + 599) (200) then divide by 2

Sum = 60,100

Check in question 3: (10 points)

Find the 320 th term of 7, 10, 13, 16 …

Then find the sum of the first 320 terms.

Problem Solving Strategy 4 (Working Backwards)

This is considered a strategy in many schools. If you are given an answer, and the steps that were taken to arrive at that answer, you should be able to determine the starting point.

Videos to watch demonstrating of “Working Backwards”

https://www.youtube.com/watch?v=5FFWTsMEeJw

Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number?

1. We start with 11 and work backwards.

2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.

3. The opposite of doubling something is dividing by 2. 18/2 = 9

4. This should be our answer. Looking back:

9 x 2 = 18 -7 = 11

5. We have the right answer.

Check in question 4:

Christina is thinking of a number.

If you multiply her number by 93, add 6, and divide by 3, you obtain 436. What is her number? Solve this problem by working backwards. (5 points)

Problem Solving Strategy 5 (Looking for a Pattern)

Definition: A sequence is a pattern involving an ordered arrangement of numbers.

We first need to find a pattern.

Ask yourself as you search for a pattern – are the numbers growing steadily larger? Steadily smaller? How is each number related?

Example 1: 1, 4, 7, 10, 13…

Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19.

Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4.

So the next number would be

25 + 11 = 36

Example 3: 10, 7, 4, 1, -2… find the next 2 numbers.

In this sequence, the numbers are decreasing by 3. So the next 2 numbers would be -2 -3 = -5

-5 – 3 = -8

Example 4: 1, 2, 4, 8 … find the next two numbers.

This example is a little bit harder. The numbers are increasing but not by a constant. Maybe a factor?

So each number is being multiplied by 2.

16 x 2 = 32

1. Click on this link to see an example of “Looking for a Pattern”

2. Click on this link to see another example of Looking for a Pattern.

Problem Solving Strategy 6 (Make a List)

Example 1 : Can perfect squares end in a 2 or a 3?

List all the squares of the numbers 1 to 20.

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400.

Now look at the number in the ones digits. Notice they are 0, 1, 4, 5, 6, or 9. Notice none of the perfect squares end in 2, 3, 7, or 8. This list suggests that perfect squares cannot end in a 2, 3, 7 or 8.

How many different amounts of money can you have in your pocket if you have only three coins including only dimes and quarters?

Quarter’s dimes

0 3 30 cents

1 2 45 cents

2 1 60 cents

3 0 75 cents

Videos demonstrating "Make a List"

Check in question 5:

How many ways can you make change for 23 cents using only pennies, nickels, and dimes? (10 points)

Problem Solving Strategy 7 (Solve a Simpler Problem)

Geometric Sequences:

How would we find the nth term?

Solve a simpler problem:

1, 3, 9, 27.

1. To get from 1 to 3 what did we do?

2. To get from 3 to 9 what did we do?

Let’s set up a table:

Term Number what did we do

problem solving using guess and check

Looking back: How would you find the nth term?

problem solving using guess and check

Find the 10 th term of the above sequence.

Let L = the tenth term

problem solving using guess and check

Problem Solving Strategy 8 (Process of Elimination)

This strategy can be used when there is only one possible solution.

I’m thinking of a number.

The number is odd.

It is more than 1 but less than 100.

It is greater than 20.

It is less than 5 times 7.

The sum of the digits is 7.

It is evenly divisible by 5.

a. We know it is an odd number between 1 and 100.

b. It is greater than 20 but less than 35

21, 23, 25, 27, 29, 31, 33, 35. These are the possibilities.

c. The sum of the digits is 7

21 (2+1=3) No 23 (2+3 = 5) No 25 (2 + 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. Also we notice 25 is divisible by 5. By using the strategy elimination, we have found our answer.

Check in question 6: (8 points)

Jose is thinking of a number.

The number is not odd.

The sum of the digits is divisible by 2.

The number is a multiple of 11.

It is greater than 5 times 4.

It is a multiple of 6

It is less than 7 times 8 +23

What is the number?

Click on this link for a quick review of the problem solving strategies.

https://garyhall.org.uk/maths-problem-solving-strategies.html

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  • Guess and Check, Work Backward

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.

problem solving using guess and check

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.

problem solving using guess and check

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

problem solving using guess and check

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:

problem solving using guess and check

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.

problem solving using guess and check

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.

problem solving using guess and check

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.

problem solving using guess and check

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!

problem solving using guess and check

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.

Like what you see? Subscribe to our Youtube channel for more Practicle Singapore Math videos!

problem solving using guess and check

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problem solving using guess and check

Problem-Solving Strategies

October 16, 2019

There are many different ways to solve a math problem, and equipping students with problem-solving strategies is just as important as teaching computation and algorithms. Problem-solving strategies help students visualize the problem or present the given information in a way that can lead them to the solution. Solving word problems using strategies works great as a number talks activity and helps to revise many skills.

Problem-solving strategies

1. create a diagram/picture, 2. guess and check., 3. make a table or a list., 4. logical reasoning., 5. find a pattern, 6. work backward, 1. create a diagram/draw a picture.

Creating a diagram helps students visualize the problem and reach the solution. A diagram can be a picture with labels, or a representation of the problem with objects that can be manipulated. Role-playing and acting out the problem like a story can help get to the solution.

Alice spent 3/4 of her babysitting money on comic books. She is left with $6. How much money did she make from babysitting?

problem solving using guess and check

2. Guess and check

Teach students the same strategy research mathematicians use.

With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly.  By repeating this process, a student can arrive at a correct answer that has been checked. It is recommended that the students keep a record of their guesses by making a chart, a table or a list. This is a flexible strategy that works for many types of problems. When students are stuck, guessing and checking helps them start and explore the problem. However, there is a trap. Exactly because it is such a simple strategy to use, some students find it difficult to consider other strategies. As problems get more complicated, other strategies become more important and more effective.

Find two numbers that have sum 11 and product 24.

Try/guess  5 and 6  the product is 30 too high

  adjust  to 4 and 7 with product 28 still high

  adjust  again 3 and 8 product 24

3. Make a table or a list

Carefully organize the information on a table or list according to the problem information. It might be a table of numbers, a table with ticks and crosses to solve a logic problem or a list of possible answers. Seeing the given information sorted out on a table or a list will help find patterns and lead to the correct solution.

To make sure you are listing all the information correctly read the problem carefully.

Find the common factors of 24, 30 and 18

problem solving using guess and check

Logical reasoning is the process of using logical, systemic steps to arrive at a conclusion based on given facts and mathematic principles. Read and understand the problem. Then find the information that helps you start solving the problem. Continue with each piece of information and write possible answers.

Thomas, Helen, Bill, and Mary have cats that are black, brown, white, or gray. The cats’ names are Buddy, Lucky, Fifi, and Moo. Buddy is brown. Thoma’s cat, Lucky, is not gray. Helen’s cat is white but is not named Moo. The gray cat belongs to Bill. Which cat belongs to each student, and what is its color?

A table or list is useful in solving logic problems.

Since Lucky is not gray it can be black or brown. However, Buddy is brown so Lucky has to be black.

Buddy is brown so it cannot be Helen’s cat. Helen’s cat cannot be Moo, Buddy or Lucky, so it is Fifi.

Therefore, Moo is Bill’s cat and Buddy is Mary’s cat.

5. Find a pattern.

Finding a pattern is a strategy in which students look for patterns in the given information in order to solve the problem. When the problem consists of data like numbers or events that are repeated then it can be solved using the “find a pattern” problem-solving strategy. Data can be organized in a table or a list to reveal the pattern and help discover the “rule” of the pattern.

 The “rule” can then be used to find the answer to the question and complete the table/list.

Shannon’s Pizzeria made 5 pizzas on Sunday, 10 pizzas on Monday, 20 pizzas on Tuesday, and 40 pizzas on Wednesday. If this pattern continues, how many pizzas will the pizzeria make on Saturday?

6. Working backward

Problems that can be solved with this strategy are the ones that  list a series of events or a sequence of steps .

In this strategy, the students must start with the solution and work back to the beginning. Each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backward they will need to subtract. And if they multiply working forwards, they must divide when working backward.

Mom bought a box of candy. Mary took 5 of them, Nick took 4 of them and 31 were given out on Halloween night. The next morning they found 8 pieces of candy in the box. How many candy pieces were in the box when mom bought it.

For this problem, we know that the final number of candy was 8, so if we work backward to “put back” the candy that was taken from the box we can reach the number of candy pieces that were in the box, to begin with.

The candy was taken away so we will normally subtract them. However, to get back to the original number of candy we need to work backward and do the opposite, which is to add them.

8 candy pieces were left + the 31 given out + plus the ones Mary took + the ones Nick took

8+31+5+4= 48   Answer: The box came with 48 pieces of candy.

Selecting the best strategy for a problem comes with practice and often problems will require the use of more than one strategies.

Print and digital activities

I have created a collection of print and digital activity cards and worksheets with word problems (print and google slides) to solve using the strategies above. The collection includes 70 problems (5 challenge ones) and their solution s and explanations.

sample below

problem solving using guess and check

How to use the activity cards

Allow the students to use manipulatives to solve the problems. (counters, shapes, lego blocks, Cuisenaire blocks, base 10 blocks, clocks) They can use manipulatives to create a picture and visualize the problem. They can use counters for the guess and check strategy. Discuss which strategy/strategies are better for solving each problem. Discuss the different ways. Use the activities as warm-ups, number talks, initiate discussions, group work, challenge, escape rooms, and more.

Ask your students to write their own problems using the problems in this resource, and more, as examples. Start with a simple type. Students learn a lot when trying to compose a problem. They can share the problem with their partner or the whole class. Make a collection of problems to share with another class.

For the google slides the students can use text boxes to explain their thinking with words, add shapes and lines to create diagrams, and add (insert) tables and diagrams.

Many of the problems can be solved faster by using algebraic expressions. However, since I created this resource for grades 4 and up I chose to show simple conceptual ways of solving the problems using the strategies above. You can suggest different ways of solving the problems based on the grade level.

Find the free and premium versions of the resource below. The premium version includes 70 problems (challenge problems included) and their solutions

There are 2 versions of the resource

70 google slides with explanations + 70 printable task cards

70 google slides with explanations + 11 worksheets

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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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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 techniques, Polyas problem solving techniques, Reading comprehension practice test.

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1. Problem-Solving Strategies: Guess and Check, Work Backward

2. 7 practice using guess and check, 3. unit 1: guess and check: a decoding strategy, 5. fractions section 1: iterating and partitioning, 6. polyas problem solving techniques, 7. polyas problem solving techniques, 8. reading comprehension practice test.

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problem solving using guess and check

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Using Guess, Check and Revise

  • Differentiate

National Standards

  • Students will determine the information they need to solve a problem.
  • Students will use the guess and check method to solve their problem.
  • Students will test their answer using this method with real coins.

Subject Area

  • Total Time: 0-45 Minutes minutes
  • Web sites with math problem-solving strategies such as https://mylearningspringboard.com/problem-solving-strategies/
  • Math journals
  • Circulating coins

Lesson Steps

  • Explain to the students that there are many different strategies for solving math problems. It is important to know the strategies, and also to know when to use which strategy. Tell them that they will be using the Guess, Check and Revise method.
  • As a class, discuss how many different combinations of circulating coins (nickels, dimes and quarters) can be used to add up to 50 cents. You must use at least one of each coin. Have the students make a guess and write several guesses on the board.
  • Write out the specifics of the problem: To make 50 cents using only nickels, dimes and quarters, at least one of each coin.
  • Work with your students to develop a chart with the possible solutions. There will only be two solutions for this problem (1 quarter 2 dimes and a nickel; 1 quarter, 1 dime and 3 nickels). Students can then revise their answer based on the chart.
  • Now give the students a problem to solve on their own using the same method you did as a class. Have them record the steps in their math journal. For example: How many different combinations of nickels, dimes and quarters can make $2.25 when you must use 17 coins.

Connections to Related Material

  • U.S. Mint Coin Classroom Free Activity, Coin Combination Riddles

Common Core Standards

  • For example, know that 1ft is 12 times as long as 1in. Express the length of a 4ft snake as 48in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
  • 4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
  • 4.MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
  • develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 × 50;
  • develop fluency in adding, subtracting, multiplying, and dividing whole numbers;
  • develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results;
  • develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience;
  • use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals; and
  • select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.
  • understand various meanings of multiplication and division;
  • understand the effects of multiplying and dividing whole numbers;
  • identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems; and
  • understand and use properties of operations, such as the distributivity of multiplication over addition.
  • understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals;
  • recognize equivalent representations for the same number and generate them by decomposing and composing numbers;
  • develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;
  • use models, benchmarks, and equivalent forms to judge the size of fractions;
  • recognize and generate equivalent forms of commonly used fractions, decimals, and percents;
  • explore numbers less than 0 by extending the number line and through familiar applications; and
  • describe classes of numbers according to characteristics such as the nature of their factors.
  • Build new mathematical knowledge through problem solving
  • Solve problems that arise in mathematics and in other contexts
  • Apply and adapt a variety of appropriate strategies to solve problems
  • Monitor and reflect on the process of mathematical problem solving

IMAGES

  1. Problem Solving: Guess and Check practice 21.5 Worksheet for 3rd

    problem solving using guess and check

  2. Guess and check problem solving

    problem solving using guess and check

  3. Solving Equations Using Guess & Check

    problem solving using guess and check

  4. Guess and Check

    problem solving using guess and check

  5. Problem Solving: Guess and Check Worksheet for 2nd

    problem solving using guess and check

  6. Problem Solving: Guess and Check Worksheet for 3rd

    problem solving using guess and check

VIDEO

  1. Lecture 18 More Examples using Guess and Verify Method

  2. MATH 1350

  3. Math 🔥 Can you solve this question ?

  4. problem solving using determinant #matrices #maths

  5. Problem Solving using Greedy approach

  6. Unitary Method Problem Solving Using Easy Method @NJClasses25

COMMENTS

  1. Math Strategies: Solving Problems Using Guess and Check

    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."

  2. Problem Solving: Guess and Check

    "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:

  3. Problem Solving (Guess and Check)

    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 ...

  4. 2.5.3: Guess and Check, Work Backward

    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.

  5. Guess & Check Method

    To solve guess and check division, guess the quotient to the division problem. Then, check it by multiplying the quotient to the divisor. If the product is the same as the dividend, the...

  6. How to solve algebraic equations using guess and check

    Guess and check is often used to solve problems. This method is sometimes called Trial and Improvement. Have a go Click to see the slideshow. YOU WILL NEED - a whiteboard, a ruler, an...

  7. Guess and Check

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

  8. PDF Problem Solving Strategy: Guess & Check

    Problem Solving Strategy: Guess & Check. Use the guess and check strategy to solve the following questions. have 25¢. If... Each of the COUNTDOWN teachers has 4 pets. They either have dogs (which have 4 legs) or birds (which have 2). Use this chart to figure out how many and what types of pets each teacher has.

  9. Using the guess and check strategy for problem solving

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

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

    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.

  11. Module 1: Problem Solving Strategies

    The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems! Problem Solving Strategy 1 (Guess and Test) Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution.

  12. Guess and Check, Work Backward

    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.

  13. Guess and Check, Work Backward

    Key Questions When do you use the guess and check method? 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.

  14. Guess and Check method, what is it?

    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.

  15. Guess and Check, Work Backward ( Read )

    The strategy for the method "Guess and Check" is to guess a solution and then plug the guess back into the problem to see if you get the correct answer. If the answer is too big or too small, make another guess that will get you closer to the goal, and continue guessing until you arrive at the correct solution.

  16. How to Guess and Check Problems

    Learn how to solve a math problem by guessing an answer, and then checking to make sure the answer makes sense in the problem.We hope you are enjoying this v...

  17. Welcome to CK-12 Foundation

    Develop and use the strategy "Guess and Check." Develop and use the strategy "Work Backward." Plan and compare alternative approaches to solving problems. Solve real-world problems using selected strategies as part of a plan. Introduction In this section, you will learn about the methods of Guess and Check and Working Backwards. These ...

  18. Solve word problems using guess-and-check

    Improve your math knowledge with free questions in "Solve word problems using guess-and-check" and thousands of other math skills.

  19. Solving Problems With the Guess, Check & Revise Method

    Solving Problems With the Guess, Check & Revise Method In this lesson, we will look at how to solve problems using the guess, check, and revise method in mathematics. Through...

  20. Problem-Solving Strategies

    Guess and check Teach students the same strategy research mathematicians use. With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly.

  21. Problem solving strategies

    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.

  22. Guess And Check Worksheets

    1. Problem-Solving Strategies: Guess and Check, Work Backward 2. 7 Practice Using Guess and Check 3. Unit 1: Guess and Check: A Decoding Strategy 4. Group Couldn't preview file You may be offline or with limited connectivity. Try downloading instead. 5. Fractions Section 1: Iterating and Partitioning 6. Polyas Problem Solving Techniques 7.

  23. Using Guess, Check and Revise

    Objectives. Students will determine the information they need to solve a problem. Students will use the guess and check method to solve their problem. Students will test their answer using this method with real coins.