lesson 6 problem solving guess check and revise

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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 .

–>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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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.

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Using the Guess, Check & Revise Method for Problem Solving

Explanation, introduction.

In algebra, problem-solving plays a crucial role in understanding and applying mathematical concepts. While there are various problem-solving strategies, one effective method is the Guess, Check & Revise method. This strategy allows you to systematically approach and solve problems by making educated guesses, checking whether those guesses are correct, and revising your guess if necessary. This method is particularly useful when dealing with equations and equalities. In this lesson, we will explore the step-by-step process of using the Guess, Check & Revise method for problem solving in algebra, along with relevant formulas and examples.

Understanding the Guess, Check & Revise Method

The Guess, Check & Revise method involves several steps to properly approach and solve algebraic problems. Let's break down each step:

Step 1: Understand the Problem

The first step in any problem-solving approach, including the Guess, Check & Revise method, is to understand the problem statement. Read the problem carefully and identify the unknown values or variables that need to be determined. It is essential to comprehend what the problem is asking you to solve before proceeding further.

Step 2: Make an Initial Guess

Based on your understanding of the problem, make an initial guess or estimate for the unknown value. This guess should be reasonable and informed by the information provided in the problem.

Step 3: Check the Guess

Take the initial guess and substitute it into the given equation or equality. Perform the necessary operations to evaluate whether the guess satisfies the condition of the equation. If the guess yields a true statement, it is the solution. However, if the guess does not satisfy the equation, move on to the next step.

Step 4: Revise the Guess

If the initial guess does not satisfy the equation, revise it. Consider possible adjustments or modifications to your guess and make a revised guess. This step requires critical thinking and analysis of the problem, taking into account any additional information provided.

Step 5: Check the Revised Guess

Similar to Step 3, substitute the revised guess into the equation or equality and check if it satisfies the condition. Repeat this step until you find a guess that satisfies the equation or until you have exhausted all possibilities.

Step 6: Verify the Solution

Once you have found a guess that satisfies the equation, it is important to verify the solution. Substitute the solution back into the original problem and verify that it meets all the conditions stated in the problem. This step ensures that the solution is valid and reliable.

Example Problem: Application of the Guess, Check & Revise Method

Problem statement:.

Solve the following equation using the Guess, Check & Revise method: 2x + 5 = 13.

The problem asks us to find the value of "x" that satisfies the equation 2x + 5 = 13.

Based on the problem, we can estimate an initial guess. Let's assume that x = 4.

Substituting the guess x = 4 into the equation, we have 2(4) + 5 = 13.

Evaluating the left-hand side of the equation, we get 8 + 5 = 13. Since this is equal to the right-hand side of the equation, our initial guess is correct.

To ensure our solution is valid, we substitute the value of x back into the original problem. Substituting x = 4 into 2x + 5 = 13, we have 2(4) + 5 = 13.

Evaluating the left-hand side, we get 8 + 5 = 13, which is equal to the right-hand side. Thus, our solution x = 4 is verified to be correct.

Common Mistakes and Tips

Mistake #1: incorrect guess.

Making an incorrect initial guess can lead to an incorrect solution. It is crucial to base your guess on the information provided in the problem and use logical reasoning to estimate a value for the unknown.

Mistake #2: Skipping Steps

Skipping any of the steps in the Guess, Check & Revise method may lead to an incomplete or incorrect solution. It is essential to follow each step systematically to ensure accurate results.

Tip #1: Use Multiple Guesses

Sometimes, a problem may have multiple possible solutions. In such cases, you can use the Guess, Check & Revise method to try different guesses until you find all the valid solutions.

Tip #2: Simplify Equations

If the equation is complex, simplify it before applying the Guess, Check & Revise method. Simplifying the equation can make it easier to work with and facilitate the guessing process.

Tip #3: Practice, Practice, Practice

To become proficient in using the Guess, Check & Revise method, practice solving various algebraic problems that involve equations and equalities. The more you practice, the more comfortable and confident you will become with this problem-solving approach.

The Guess, Check & Revise method is a valuable problem-solving strategy when dealing with equations and equalities in algebra. By following the systematic steps of understanding the problem, making an initial guess, checking the guess, revising the guess, and verifying the solution, you can approach and solve algebraic problems effectively. Remember to avoid common mistakes, such as making incorrect guesses or skipping steps. By practicing and applying this method, you will become more proficient in solving algebraic problems and developing your problem-solving skills.

Questions related to Using the Guess, Check & Revise Method for Problem Solving

C. write an equation

Step-by-step explanation:

The best method would be to write an equation to solve this problem. This would be the best option because you are given all of the values/measurements of the table and the distance between balloons. Therefore, you would simply need to create an equation that calculates the perimeter of the table and divides a variable number of balloons 2 feet apart along the perimeter. Guessing is not a valid solution, especially when you are given actual data. Tables, Charts, and Lists are mainly used for large sets of data.

• profile amberduff56 Question: Jan and Wayne went to the store to buy some groceries. Jan bought 2 cans of corn beef hash and 3 cans of creamed chipped beef for $4.95. Wayne bought 3 cans of corn beef hash and 2 cans of creamed chipped beef for $5.45. Let H represent the price of a can of corn beef hash, and C represent the price of a can of creamed chipped beef. solve for H and C You can solve this by using the system of equations. Jan - 4.95 = 2H + 3C Wayne - 5.45 = 3H + 2C Use elimination. -3(2H + 3C = 4.95) 2(3H + 2C = 5.45) Solve. And you'll get: -6H + (-9C) = -14.85 6H + 4C = 10.9 Cross out -6H and 6H because they cancel out. And you're left with: -9C = -14.85 4C = 10.9 Add -9C with 4C, and -14.85 with 10.9. -5C = -3.95 Divide each side with -5. C = $0.79 Now to figure out what H is, just substitute the C in one of the equations with 0.79. 5.45 = 3H + 2(0.79) 5.45 = 3H + 1.58 -1.58            -1.58 3.87 = 3H 3.87/3 = 3/3(H) 1.29 = H Finished!

Final answer:

Visual learners should use diagrams and charts to model the problem, use colors and highlights for differentiating and organization of information, and should use flashcards and visual aids while studying.

Explanation:

If you are a visual learner , there are a few strategies that could help you most in problem-solving. First, you could use diagrams and charts to model or outline the problem visually. For example, if you are trying to solve a math problem, you might draw a diagram or figure that represents the problem. Second, you could use colors and highlights to differentiate and organize information . For instance, use different colored highlighters or pens to categorize different types of information or ideas. Lastly, you could use flashcards or visual aids when studying or trying to recall information.

Learn more about Visual Learner here:

https://brainly.com/question/34705855

For a visual learner, the most beneficial strategy for problem-solving is to draw a diagram. This allows for a visual representation of the problem, aiding comprehension. It's also useful to identify the unknown and known quantities within the problem.

If you are a visual learner , the strategy that would help you most in solving a problem would be 'B. Draw a diagram'. This strategy allows you to visualize the problem and the components involved, making it easier for your brain to process. For instance, if you are dealing with a math problem, you might find it helpful to draw a diagram that represents the relations or operations between the numbers . This visual representation can give you a better understanding of what the problem is asking and how to approach the solution.

Another key step in problem-solving is to identify the unknown quantities – what exactly needs to be determined in the problem. It might also help to make a list of the known quantities – what is given or can be inferred from the problem as stated. Working through these steps systematically can help you navigate the problem more efficiently.

Learn more about Visual learning here:

https://brainly.com/question/1357584

Using the guess and check strategy for problem solving

Lesson details, key learning points.

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

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

Lesson appears in

Unit maths / numbers within 15.

Problem-Solving Strategies

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?

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

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.

Thomas	Lucky	Not gray, the cat is black
Helen	Not Moo, not Buddy, not Lucky so Fifi	White
Bill	Moo	Gray
Mary	Buddy	Brown

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?

Sunday	5
Monday	10
Tuesday	20
Wednesday	40
Thursday
Friday
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

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

>   >

Chapter 1, Lesson 6: Problem-Solving Strategy: Guess and Check

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