lesson plan problem solving strategies

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Problem solving

Problem solving lesson plan

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Problem Solving: Lesson plan

Problem solving: Presentation slides

Demonstrating your skills quick fire activity

Problem solving in practice: Interactive worksheet

Our problem solving content focuses on one of these skills and develops understanding of the six stages of problem solving, as well as identifying different types of situations in which young people might already be using these skills. Furthermore, it encourages them to use an adaptive approach, explaining that different types of problems can be approached in different ways.

The activities on this page support your teaching of these skills through an independent activity, quick activities or a full length, curriculum-linked lesson plan. 

Teaching resources:

• Problem solving: Lesson plan and presentation slides – full lesson plan including icebreaker for use with a group of students in the classroom
• Demonstrating your skills: Quick-fire activity  – 10 minute activity for a group of students in the classroom, can be used as an icebreaker for the lesson plan
• Problem solving in practice: Interactive worksheet – activity for independent learning whether remote or in class

Lesson plan

(60 -75 minutes)

This lesson is designed to equip young people with an adaptable approach to solving problems, large or small. It includes a short film and scenarios that encourage development of practical problem solving skills which can be useful for learning, day to day life, and when in employment.

By the end of the lesson, students will be able to:

• Identify problems of different scales and what is needed to solve them
• Illustrate the use of an adaptable approach to solving problems
• Understand that problem solving is a core transferable skill and identify its usefulness in a work setting
• Work on a problem solving activity in a team

The lesson aims to reinforce students’ understanding of the potential future applications of this skill as they move into the world of work, particularly in an activity differentiated for an older or more able group on creating new opportunities.

Quick-fire activity

(5 - 10 minutes)

The demonstrating your skills quick-fire activity focuses on helping young people understand the key skills that are needed in the workplace, including the importance of problem solving.

Students will be asked to name the skills being demonstrated in a variety of scenarios, and identify ways they’re already using those skills in this short activity.

You might find it useful as a starter or icebreaker activity to begin a lesson, or at the end to allow students to put what they have just learnt in the Problem solving lesson into practice.

Interactive worksheet

(20 - 25 minutes)

Please note that students below the age of 14 cannot sign up for their own LifeSkills account. Any independent tasks must be printed or downloaded and provided digitally for them to complete as they are currently hosted on educator pages.

The Problem solving in practice interactive worksheet introduces some of the themes from the full lesson plan and gives students some practical strategies for problem solving, including introducing the six stages of problem solving. The worksheet can be printed or completed digitally, so can be used flexibly to give students practise putting their problem solving skills into action. You might choose to assign it:

• As homework following the Problem solving lesson
• For independent study
• For remote learning

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Other lessons that may prove useful for students to build on these activities include the  Adaptability  and  Innovation and idea generation  lessons. Alternatively, consider encouraging them to apply their skills through  Steps to starting a business  or the  Social action toolkit .

Why not build problem solving in as a focus in your students’ wider curriculum? Refer to our  Content guide to find out how this resources can be used as part of your teaching.

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Staying positive and learning through experience are key to succeeding in challenging situations. Try this lesson and help your students succeed at work.

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Social action toolkit

Build a comprehensive social action programme and support young people to access enriching experiences that build transferable skills for work.

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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

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:

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

Looking back: How would you find the nth term?

Find the 10 th term of the above sequence.

Let L = the tenth term

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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20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

• Draw a model
• Use different approaches
• Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

• The context
• What the key information is
• How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Similarly, you could draw a model to represent the objects in the problem:

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

• Understand the problem
• Devise a plan
• Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

How Third Space Learning improves problem-solving 

Resources .

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking. 

Explore the range of problem solving resources for 2nd to 8th grade students. 

One-on-one tutoring 

Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE : 8 Common Core math examples

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies of problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

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Problem-Solving

Jabberwocky

Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically.

Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.

Problem-solving involves three basic functions:

Seeking information

Generating new knowledge

Making decisions

Problem-solving is, and should be, a very real part of the curriculum. It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum. It provides students with opportunities to use their newly acquired knowledge in meaningful, real-life activities and assists them in working at higher levels of thinking (see Levels of Questions ).

Here is a five-stage model that most students can easily memorize and put into action and which has direct applications to many areas of the curriculum as well as everyday life:

Expert Opinion

Here are some techniques that will help students understand the nature of a problem and the conditions that surround it:

• List all related relevant facts.
• Make a list of all the given information.
• Restate the problem in their own words.
• List the conditions that surround a problem.
• Describe related known problems.

It's Elementary

For younger students, illustrations are helpful in organizing data, manipulating information, and outlining the limits of a problem and its possible solution(s). Students can use drawings to help them look at a problem from many different perspectives.

Understand the problem. It's important that students understand the nature of a problem and its related goals. Encourage students to frame a problem in their own words.

Describe any barriers. Students need to be aware of any barriers or constraints that may be preventing them from achieving their goal. In short, what is creating the problem? Encouraging students to verbalize these impediments is always an important step.

Identify various solutions. After the nature and parameters of a problem are understood, students will need to select one or more appropriate strategies to help resolve the problem. Students need to understand that they have many strategies available to them and that no single strategy will work for all problems. Here are some problem-solving possibilities:

Create visual images. Many problem-solvers find it useful to create “mind pictures” of a problem and its potential solutions prior to working on the problem. Mental imaging allows the problem-solvers to map out many dimensions of a problem and “see” it clearly.

Guesstimate. Give students opportunities to engage in some trial-and-error approaches to problem-solving. It should be understood, however, that this is not a singular approach to problem-solving but rather an attempt to gather some preliminary data.

Create a table. A table is an orderly arrangement of data. When students have opportunities to design and create tables of information, they begin to understand that they can group and organize most data relative to a problem.

Use manipulatives. By moving objects around on a table or desk, students can develop patterns and organize elements of a problem into recognizable and visually satisfying components.

Work backward. It's frequently helpful for students to take the data presented at the end of a problem and use a series of computations to arrive at the data presented at the beginning of the problem.

Look for a pattern. Looking for patterns is an important problem-solving strategy because many problems are similar and fall into predictable patterns. A pattern, by definition, is a regular, systematic repetition and may be numerical, visual, or behavioral.

Create a systematic list. Recording information in list form is a process used quite frequently to map out a plan of attack for defining and solving problems. Encourage students to record their ideas in lists to determine regularities, patterns, or similarities between problem elements.

Try out a solution. When working through a strategy or combination of strategies, it will be important for students to …

Keep accurate and up-to-date records of their thoughts, proceedings, and procedures. Recording the data collected, the predictions made, and the strategies used is an important part of the problem solving process.

Try to work through a selected strategy or combination of strategies until it becomes evident that it's not working, it needs to be modified, or it is yielding inappropriate data. As students become more proficient problem-solvers, they should feel comfortable rejecting potential strategies at any time during their quest for solutions.

Monitor with great care the steps undertaken as part of a solution. Although it might be a natural tendency for students to “rush” through a strategy to arrive at a quick answer, encourage them to carefully assess and monitor their progress.

Feel comfortable putting a problem aside for a period of time and tackling it at a later time. For example, scientists rarely come up with a solution the first time they approach a problem. Students should also feel comfortable letting a problem rest for a while and returning to it later.

Evaluate the results. It's vitally important that students have multiple opportunities to assess their own problem-solving skills and the solutions they generate from using those skills. Frequently, students are overly dependent upon teachers to evaluate their performance in the classroom. The process of self-assessment is not easy, however. It involves risk-taking, self-assurance, and a certain level of independence. But it can be effectively promoted by asking students questions such as “How do you feel about your progress so far?” “Are you satisfied with the results you obtained?” and “Why do you believe this is an appropriate response to the problem?”

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The learning network | no quick fix developing problem-solving skills.

No Quick Fix? Developing Problem-Solving Skills

Academic Skills

Teaching ideas based on New York Times content.

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Overview | How can real problems be approached and analyzed in ways that lead to practical solutions? What distinguishes effective solutions from ineffective ones? In this lesson, students consider how to work through a practical problem. They identify problems in their school that need fixing, then devise viable solutions to one of those problems, using problem-solving models and drawing on strategies like the social science of behavioral change. They then test some of their proposed solutions in the field and propose them to the school.

Materials | Computers with Internet access (optional); copies of the What’s Your Problem? handout (PDF)

Warm-Up | Tell students they will now consider a problem they recently confronted and make flow charts showing all the possible solutions they considered, including the final “fix.” You might explain that this exercise allows them to examine the critical thinking skills that they already use when looking for solutions to everyday problems.

To stimulate thinking, you might start by brainstorming some typical decisions, like when to do homework (modeled partly on the handout) or how to study for a challenging exam, or even relatively “light” problems, like what Halloween costume to wear.

Give students the What’s Your Problem? graphic organizer (PDF) to help them break down the various possible solutions and why each one did or did not work. You might also share some basic problem-solving steps to lead them in thinking through their problems.

Invite students to share their problems and solutions with the group and to reflect on the difference between solutions that seemed feasible but were not really effective in the long term. Invite students to reflect, too, on their thought process. Ask: What did you need to know about yourself and the task or problem in order to solve it successfully? What else did you need to know, about things like available resources, environment and so on? What is the difference between a quick fix and a successful solution?

Related | In the Op-Chart “Lunch Line Redesign,” Brian Wansink, David R. Just and Joe McKendry illustrate some tactics that have been used to influence children to make more healthful choices in the school cafeteria:

School cafeterias are much criticized for offering the kind of snack foods and desserts that contribute to childhood obesity. But banning junk food from cafeterias, as some schools have tried, or serving only escarole or tofu, can backfire. Students then skip lunch, bring in their own snacks or head out for fast food. We’ve even seen some pizzas delivered to a side door. Children and teenagers resist heavy-handed nutritional policies — and the food that is associated with the heavy hand. No food is nutritious, after all, until it is actually eaten. A smarter lunchroom wouldn’t be draconian. Rather, it would nudge students toward making better choices on their own by changing the way their options are presented. One school we have observed in upstate New York, for instance, tripled the number of salads students bought simply by moving the salad bar away from the wall and placing it in front of the cash registers.

Read the entire chart with your class, using the questions below.

Questions | For discussion and reading comprehension:

• How does food placement — both location and type of display — seem to affect the choices students make in the cafeteria?
• How do direct appeals,  in the form of questions from cafeteria workers and descriptive text, seem to affect choice?
• How would you describe and categorize the other strategies?
• Why do you think these strategies resulted in more students buying more healthful foods?
• Which of these tactics do you think might work in our own cafeteria? Why?

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• Invention Convention
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Activity | Explain to students that they will now brainstorm problems in the school, then choose one to try to solve.

Encourage students to think in categories. Here are some categories to get you started, along with an example of a specific topic for each one:

• Technology; cellphones as learning tools
• Design ; desks and workstations
• Resource management ; energy efficiency
• Use of classrooms and public spaces; overcrowding
• Environmentalism; recycling
• Health and hygiene; hand sanitizers
• School culture; bullying and cyberbullying

Make sure students narrow categories and topics down to specific problems. For example, for overcrowding, they might focus on the question of how to ease hallway congestion during passing times. Students might also expand beyond strictly school-based problems to include school-related problems, like chronic lack of sleep among students.

After brainstorming is over, have the class vote on one problem to tackle as a group. Then put students in working groups of pairs or trios to identify, research and propose a viable and innovative solution for the problem.

You may wish to first familiarize students with the four-step problem-solving method of the mathematician George Polya . Have students approach their problem using the following steps, which apply Polya’s method:

Step 1: Understand the Problem — Formulate a clear statement of the desired outcome of the problem by asking the questions: What do we know about the problem? What do we not know? Is there enough information to help us find a solution? If not, what information do we need?

Step 2: Collect Data — Go out into the field to make observations and collect data that will help us better understand the problem and identify its most significant factors. For example, if students are trying to solve the problem of hallway overcrowding, they might post students in various places to observe traffic and congestion spots at different times of day (analogies to car traffic jams might be useful), interview teachers, students, administrators and school employees, and collect data like hallway width, number of total students, number of students coming out of classrooms and time between classes. (Groups might collaborate on this step to avoid redundancies.)

Step 3: Devise a Plan — With data in hand, working groups discuss and brainstorm possible solutions, using the What’s Your Problem? graphic organizer (PDF).

Students might consider using one of the following innovative problem-solving methods:

• Crowdsourcing , which uses social networks and collaboration to find possible solutions to problems that include improving software and improving education .
• Behavioral change , which uses social science and various behavior change theories , along with related strategies like the use of design and tools like commitment contracts to influence behavior.
• Positive deviance , an unorthodox approach to problem solving that focuses on what some people do right rather than what most people do wrong.

For further inspiration, they might look at the annual Year in Ideas issues of The Times Magazine from 2009 , 2008 and earlier .

For each potential solution to their real-world problems , students discuss reasons that it may or may not work. In the instance of overcrowded hallways, for example, students might propose increasing passing time, encouraging students to put large bags into lockers or mandating traffic routes.

Carry Out the Plan — Each group takes on one solution to develop further and, if possible, tests it either in the field or even through role playing .

Going Further | Students share their ideas, then discuss and vote on the solutions. Which is most innovative? Which is most practical? Which do they expect to be most effective, and why? Which one deserves to be tried first?

They pitch their solution, or a grab bag of solutions, by starting a public service announcement campaign , writing letters to the editor of the school paper or giving a presentation to the school administration or PTA.

Alternatively or additionally, to have students undertake a larger issue, they might read up on social entrepreneurship , including Nicholas Kristof’s Times Magazine article “D.I.Y. Foreign-Aid Revolution” and his related blog post, “How to Change the World.” They can also follow the new Fixes blog, which “explores solutions to major social problems” and “examines creative initiatives that can tell us about the difference between success and failure.”

Standards | This lesson is correlated to McREL’s national standards (it can also be aligned to the new Common Core State Standards ):

Life Skills: Thinking and Reasoning 1. Understands and applies the basic principles of presenting an argument 2. Understands and applies basic principles of logic and reasoning 3. Effectively uses mental processes that are based on identifying similarities and differences 4. Understands and applies basic principles of hypothesis testing and scientific inquiry 5. Applies basic troubleshooting and problem-solving techniques 6. Applies decision-making techniques

Life Skills: Life Work 6. Makes effective use of basic life skills

Life Skills: Working With Others 1. Contributes to the overall effort of a group 4. Displays effective interpersonal communication skills

Behavioral Studies 1. Understands that group and cultural influences contribute to human development, identity and behavior 2. Understands various meanings of social group, general implications of group membership, and different ways that groups function 3. Understands that interactions among learning, inheritance and physical development affect human behavior 4. Understands conflict, cooperation and interdependence among individuals, groups and institutions

Family/Consumer Sciences 4. Understand how knowledge and skills related to consumer and resources management affect the well-being of individuals, families and society

Economics 1. Understands that scarcity of productive resources requires choices that generate opportunity costs

Language Arts 4. Gathers and uses information for research purposes 8. Uses listening and speaking strategies for different purposes

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Educational

Before finding solutions of a problem, the reason for the existence of the problem should be examined and understood. When searching for the “reason of reasons” of a problem (using a fishbone diagram for example) the result is a solution that not only takes care of the problem, but may improve the whole process that was the origin of the problem.

This is a great resource for problem-solving lesson material. The cafeteria Op-chart is a perfect example of strategic thinking in action and the school setting makes it very transferable to students. With that as an example – students can go on to solve other real-world problems.

I’ve been a long-time proponent of rigor, relevance and project based learning. Two good places for readers to start are these problem solving lessons:

“First Day of School? Don’t Pass Out Books – Problem Solve.” //bit.ly/9eS0l

“Why Don’t We Teach Sequencing Skills? It’s an Essential Higher-Order Thinking Strategy” //bit.ly/142djQ

Teachers will find a variety of teaching plans under my “strategy” category //peterpappas.blogs.com/copy_paste/strategies/

Very good work. In fact I am now using this content as my base for training my student teachers (I am a teacher educator) the steps and pedagogy of Action Research, and this topic shall form as an example. Good job… and thanks

Planning is very important in each step of career development. Students will do well in education and career in which they are interested; hence choosing the right education is very important. It is not possible to achieve “Excellence in education” if you are in a education towards which you are not seriously inclined. Hence people advocate choosing a education and profession based on your passion.

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Teaching Problem Solving in Math

• Freebies , Math , Planning

Every year my students can be fantastic at math…until they start to see math with words. For some reason, once math gets translated into reading, even my best readers start to panic. There is just something about word problems, or problem-solving, that causes children to think they don’t know how to complete them.

Every year in math, I start off by teaching my students problem-solving skills and strategies. Every year they moan and groan that they know them. Every year – paragraph one above. It was a vicious cycle. I needed something new.

I put together a problem-solving unit that would focus a bit more on strategies and steps in hopes that that would create problem-solving stars.

The Problem Solving Strategies

First, I wanted to make sure my students all learned the different strategies to solve problems, such as guess-and-check, using visuals (draw a picture, act it out, and modeling it), working backward, and organizational methods (tables, charts, and lists). In the past, I had used worksheet pages that would introduce one and provide the students with plenty of problems practicing that one strategy. I did like that because students could focus more on practicing the strategy itself, but I also wanted students to know when to use it, too, so I made sure they had both to practice.

I provided students with plenty of practice of the strategies, such as in this guess-and-check game.

There’s also this visuals strategy wheel practice.

I also provided them with paper dolls and a variety of clothing to create an organized list to determine just how many outfits their “friend” would have.

Then, as I said above, we practiced in a variety of ways to make sure we knew exactly when to use them. I really wanted to make sure they had this down!

Anyway, after I knew they had down the various strategies and when to use them, then we went into the actual problem-solving steps.

The Problem Solving Steps

I wanted students to understand that when they see a story problem, it isn’t scary. Really, it’s just the equation written out in words in a real-life situation. Then, I provided them with the “keys to success.”

S tep 1 – Understand the Problem.   To help students understand the problem, I provided them with sample problems, and together we did five important things:

• read the problem carefully
• restated the problem in our own words
• crossed out unimportant information
• circled any important information
• stated the goal or question to be solved

We did this over and over with example problems.

Once I felt the students had it down, we practiced it in a game of problem-solving relay. Students raced one another to see how quickly they could get down to the nitty-gritty of the word problems. We weren’t solving the problems – yet.

Then, we were on to Step 2 – Make a Plan . We talked about how this was where we were going to choose which strategy we were going to use. We also discussed how this was where we were going to figure out what operation to use. I taught the students Sheila Melton’s operation concept map.

We talked about how if you know the total and know if it is equal or not, that will determine what operation you are doing. So, we took an example problem, such as:

Sheldon wants to make a cupcake for each of his 28 classmates. He can make 7 cupcakes with one box of cupcake mix. How many boxes will he need to buy?

We started off by asking ourselves, “Do we know the total?” We know there are a total of 28 classmates. So, yes, we are separating. Then, we ask, “Is it equal?” Yes, he wants to make a cupcake for EACH of his classmates. So, we are dividing: 28 divided by 7 = 4. He will need to buy 4 boxes. (I actually went ahead and solved it here – which is the next step, too.)

Step 3 – Solving the problem . We talked about how solving the problem involves the following:

• taking our time
• working the problem out
• showing all our work
• estimating the answer
• using thinking strategies

We talked specifically about thinking strategies. Just like in reading, there are thinking strategies in math. I wanted students to be aware that sometimes when we are working on a problem, a particular strategy may not be working, and we may need to switch strategies. We also discussed that sometimes we may need to rethink the problem, to think of related content, or to even start over. We discussed these thinking strategies:

• switch strategies or try a different one
• rethink the problem
• think of related content
• decide if you need to make changes
• check your work
• but most important…don’t give up!

To make sure they were getting in practice utilizing these thinking strategies, I gave each group chart paper with a letter from a fellow “student” (not a real student), and they had to give advice on how to help them solve their problem using the thinking strategies above.

Finally, Step 4 – Check It.   This is the step that students often miss. I wanted to emphasize just how important it is! I went over it with them, discussing that when they check their problems, they should always look for these things:

• compare your answer to your estimate
• check for reasonableness
• check your calculations
• add the units
• restate the question in the answer
• explain how you solved the problem

Then, I gave students practice cards. I provided them with example cards of “students” who had completed their assignments already, and I wanted them to be the teacher. They needed to check the work and make sure it was completed correctly. If it wasn’t, then they needed to tell what they missed and correct it.

To demonstrate their understanding of the entire unit, we completed an adorable lap book (my first time ever putting together one or even creating one – I was surprised how well it turned out, actually). It was a great way to put everything we discussed in there.

Once we were all done, students were officially Problem Solving S.T.A.R.S. I just reminded students frequently of this acronym.

Stop – Don’t rush with any solution; just take your time and look everything over.

Think – Take your time to think about the problem and solution.

Act  – Act on a strategy and try it out.

Review – Look it over and see if you got all the parts.

Wow, you are a true trooper sticking it out in this lengthy post! To sum up the majority of what I have written here, I have some problem-solving bookmarks FREE to help you remember and to help your students!

You can grab these problem-solving bookmarks for FREE by clicking here .

You can do any of these ideas without having to purchase anything. However, if you are looking to save some time and energy, then they are all found in my Math Workshop Problem Solving Unit . The unit is for grade three, but it  may work for other grade levels. The practice problems are all for the early third-grade level.

• freebie , Math Workshop , Problem Solving

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Math Interventions

Introduction.

• Subitizing Interventions
• Counting Interventions: Whole Numbers Less Than 30
• Counting Interventions: Whole Numbers Greater Than 30 (Place Value)
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• Planning and Executing a Solution Interventions
• Monitoring Progress & Reflecting on a Solution Interventions
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You can use either  Explicit Instruction  or Self-Regulated Strategy Development when you intervene to support your student's problem solving skills. The following lesson plan targets a specific problem-solving skill using explicit instruction. As you read this plan, consider: 

How does this plan support objective mastery?

Problem Solving Intervention Plan

Art, E. (2017). Problem solving intervention packet. New York, NY: Relay Graduate School of Education.

This lesson plan supports objective mastery because the teacher employs Principles of Specialized instruction to help the student visualize Part/Part/Whole (Part Unknown) problems to identify what she is supposed to figure out. In this lesson plan, she isolates the skill (identifying what the problem is), and uses explicit instruction to teach the student how to identify two what is happening in the story and what she is trying to figure out. After she explains the process she'll take, she uses metacognition and shows the student how she asks these two questions as she is reading. Finally, she builds in multiple at-bats so that the student has the opportunity to practice this strategy over and over so that she can reach her objective.

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Problem Solving

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Second graders practice problem solving strategies. In this problem solving lesson, 2nd graders use strategies such as guess and check, acting out, drawing pictures and looking for patterns to solve problems. Students work in groups to solve problems using buttons. Students make lists of attributes and compare with other groups.

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Math Problem Solving Strategies (Primary) - Lesson Plan & Templates

Grade Level: Primary (PK-2) | Featured Topics: Lessons and Activities | Academic Subject: Mathematics | Featured Topics: Templates for FREE download

This lesson plan is part of our partnership with two super creative educators from  The Curriculum Corner , bringing you free Common Core aligned lesson ideas, teacher resources, and templates you can easily print with your VariQuest Perfecta Poster Design System - and be sure you have the latest version of the VariQuest Software ! 

Lesson:  introduction to problem solving strategies (two-day lesson) , level:  primary, objectives & ccss alignment:  students will increase independence in using various strategies to solve different types of word problems., *note: ccss has problem solving strategies spread throughout the domains for math.  this lesson focuses on giving them a review of each of the various strategies.  it is suggested that teachers follow up this review with a more in-depth lesson in each of the strategies as they fit naturally into the curriculum or as there is student need. , materials & visuals: , anchor chart – problem solving strategies, my math notes for problem solving.

Click on each image to download the PDF and print to a poster!

Preparation:

Think through a sample problem for each of the strategies listed on the anchor chart.  these will be shown to the students as examples., prepare “problem solving” anchor chart for mini-lesson., copy the “my math notes for problem solving” page for each child in the classroom.  you may choose to three-hole-punch this page for use in a math notes binder/folder to be kept by students and referred to throughout the year. , mini-lesson: , ask students what a “strategy” is.  accept several answers and then lead the class to the conclusion that a strategy is a plan to reach a goal.  in math a strategy would be a plan to reach a final answer., display the anchor chart titled “problem solving strategies” for the students.  tell them that these are some ways that they can use to solve all kinds of different math problems., pass out “my math notes for problem solving” to each student and explain that this page is a place for them to write down some notes that will help them to remember what each strategy is and how to use it.  they will keep this in their math binder/folder and can pull it out as a reminder when needed., *note: the boxes of this resource have been left blank so that the teacher can decide the level of support needed to fill it out.  students may need to draw or write exactly what the teacher shares for each strategy or they may be allowed to draw or write whatever they feel will help them to remember the strategy., briefly explain a few of the eight strategies and guide students as to how you would like for them to take their notes (copying the teacher notes or creating their own depending on grade or skill level).  introduce however many strategies that time allows for in this first lesson, and then complete the note-taking for the final strategies the following day., have students place their math notes into an organized binder or folder that will be kept and used throughout the year..

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Multiplication Word Problems Dive - Lesson Plan

In this paper, the focus is on teaching students how to solve multiplication word problems by recognizing different problem types and using specific strategies. the paper provides a teacher guide and outlines various tasks and activities for the class..

Know more about Multiplication Word Problems Dive - Lesson Plan

To help your students solve multiplication word problems effectively, you can teach them different problem-solving strategies such as identifying keywords, breaking down the problem, and using visual representations. Encourage them to practice these strategies through hands-on activities and real-world examples.

Some common types of multiplication word problems include equal groups, arrays, and comparison problems. Equal groups involve multiplying the number of items in each group by the number of groups. Arrays involve multiplying the number of rows by the number of columns. Comparison problems involve comparing two quantities using multiplication.

You can assess your students' understanding of solving multiplication word problems through exit slips or short quizzes that require them to solve various word problems independently. You can also observe their participation and engagement during class activities and discussions to gauge their comprehension.

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