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In this lesson, students will learn about apologizing as a way of showing kindness and as a tool for problem-solving in a variety of scenarios. Lesson Plan (PDF) Lesson Presentation

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In this lesson, students will learn which clues tell them when others might be frustrated, and a new way to feel calm when they’re feeling frustrated themselves. Lesson Plan (PDF) Lesson Presentation

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In this lesson, students will start learning to be better problem-solvers by managing strong feelings and stating problems without blame. Lesson Plan (PDF) Lesson Presentation Lesson Handout (PDF)

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Problem Solving Activities: 7 Strategies

• Critical Thinking

Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

Shametria Routt Banks

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2 Responses

This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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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.

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Problem solving: Using all four operations

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Lesson details

Key learning points.

• In this lesson, we will solve a multi-step problem using all four operations; addition, subtraction, multiplication and division.

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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

Looking for more ways to boost self confidence with LifeSkills?

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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Why not try one of these next?

Staying positive (resilience)

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

Good leadership styles and effective teamwork can help students excel in their future workplace. Read more about team leader skills in this lesson.

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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Lesson Plan

Problem-solving steps, view aligned standards, learning objectives.

Students will be able to identify a problem and engage in problem-solving steps to come up with a solution to strengthen their responsible decision-making competency.

Introduction

• Bring students together in a circle, either seated or standing.
• Bring blocks with you to the circle.
• Show the student the blocks and ask them to watch you build a tall castle.
• After you build it, bring out two figurines that you would like to play with in the castle.
• Say out loud, "Hmm....there seems to be a problem. This castle is too small for my toys. How can I make this bigger?"
• Take a few big breaths into your belly and ask the class to breathe with you.
• Explain that deep breathing can help you stay calm and focused when solving a problem.
• Ask the class, "How can I make this castle bigger?"
• Ask, "Would someone like to come up and think of a new way to solve this problem?"
• Invite one student to come up to solve the problem (i.e., make a larger castle).
• Ask your student volunteer, "What would you do here? How would you test a solution?"
• Give the student time to come up with a solution to make a larger castle.
• Identify the problem.
• Look at what solutions have already been tried.
• Think of new ways to solve the problem.
• Try it out!
• Thank your student volunteer for showing you how to solve the problem and send them back to their seats.
• Say, "All of us sometimes come across problems we have to solve, and sometimes friends can help us, too!"

Two-Step Equations Exercises

Two-step equations practice problems with answers.

Hone your skills in solving two-step equations because it will serve as your foundation when solving multi-step equations. I prepared eight (8) two-step equations problems with complete solutions to get you rolling.

My advice is for you to solve them by hand using a pencil or pen and paper. Believe me, you get the most benefit from this exercise by doing it yourself first before looking at the solution set.

If by any chance you get stuck or don’t know what to do next, please feel free to review my other lesson about two-step equations. Click the link below to get there. Enjoy!

Solving Two-Step Equations

1) Solve the two-step equation for [latex]g[/latex].

[latex]2g – 4 = 6[/latex]

Add both sides by [latex]4[/latex] then divide both sides by [latex]2[/latex].

2) Solve the two-step equation for [latex]x[/latex].

[latex]2x + 15 = – 3x[/latex]

Subtract both sides by [latex]2x[/latex]. Finally, divide both sides of the equation by [latex]-5[/latex].

3) Solve the two-step equation for [latex]k[/latex].

[latex]{\Large{{k \over 4}}} – 7 = – 5[/latex]

Add both sides by [latex]7[/latex]; followed by multiplying both sides by [latex]4[/latex].

4) Solve the two-step equation for [latex]m[/latex].

[latex]{\Large{{{m + 9} \over 5}}} = {\large{2}}[/latex]

Multiply [latex]5[/latex] on both sides then subtract by [latex]9[/latex] on both sides of the equation as well.

5) Solve the equation for [latex]y[/latex].

[latex]0 = – 1 – y[/latex]

Add [latex]1[/latex] to both sides of the equation. Notice that the coefficient of [latex]-y[/latex] is [latex]-1[/latex]. That means, we should divide both sides by [latex]-1[/latex] to isolate and therefore solve for [latex]y[/latex].

6) Solve the equation for [latex]r[/latex].

[latex] – 3\left( {r – 7} \right) = – 24[/latex]

First, divide both sides of the equation by [latex]-3[/latex] then add by [latex]7[/latex].

7) Solve the equation for [latex]z[/latex].

[latex]{\Large{5 \over 4}}z + {\Large{3 \over 4}}z = 1[/latex]

8) Solve the equation for [latex]x[/latex].

[latex]4.25 – 0.25x = 3.75[/latex]

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IB Applications & Interpretations SL: Teacher Guide for Guided Notes - Lesson 13.2, part 4

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Number Problems and reasoning Full lesson including MCQs, Exam questions and Problem Solving

Subject: Mathematics

Age range: 14-16

Resource type: Lesson (complete)

Last updated

27 August 2024

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A whole lesson on Number Problems and Reasoning. First topic in the Numbers chapter of the GCSE Higher Mathematics curriculum! This comprehensive PowerPoint presentation is designed to engage students in exploring the foundational concepts of number problems and reasoning. This resource offers a variety of interactive and thought-provoking activities to help students develop a deep understanding of numerical operations and problem-solving techniques. The presentation includes:

*** Multiple Choice Questions (MCQs): A set of carefully crafted MCQs to test students’ understanding and reinforce key concepts. These questions are designed to challenge students and encourage them to think critically about different number-related scenarios.

*** Exam-Style Questions: Realistic exam questions that align with the GCSE Higher syllabus. These questions provide students with the opportunity to practice their skills in a format that mirrors what they will encounter in their exams, building their confidence and familiarity with exam conditions.

*** Problem-Solving Tasks: Engaging and challenging problems that require students to apply their mathematical knowledge and reasoning skills. These tasks are designed to push students to think creatively and approach problems from different angles.

This lesson serves as a strong foundation for the rest of the Numbers chapter, equipping students with the essential skills they need to succeed in their GCSE exams. Whether used in the classroom or for independent study, this resource will help students master the complexities of number problems and reasoning.

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