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## Teaching Problem Solving in Math

## The Problem Solving Strategies

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.

## The Problem Solving Steps

- 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.

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

- 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!

- 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

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.

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

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September 1, 2022, problem solving is at the heart of engaging and inspiring mathematics lessons. .

## Sample Problem Solving Mathematics Lessons

## Perimeter and Area

Students are challenged to solve problems involving perimeter and area of rectangles and triangles.

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## Four step problem solving process lesson plan

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## The Four Steps for Problem Solving

I can do mathematical tasks quite easily.

Free time to spend with your friends

The best way to spend your free time is with your family and friends.

Mathematics is a way of dealing with tasks that require e#xact and precise solutions.

## Solving the Math Curse : Reading and Writing Math Word Problems

## Featured Resources

## From Theory to Practice

- Modeling is an important form of classroom support for literacy learning. When the teacher reads the story to students using questioning techniques, the teacher engages students and conveys a purpose for reading. Explicit modeling is achieved as the teacher shows students a way to approach the task of writing their own word problem.
- Integrating language arts and math incorporates reading, writing, listening, and speaking skills as students listen to the word problems during the read-aloud, share their knowledge, provide feedback to their classmates, and write their own word problems for classmates to share.
- The rereading strategy helps students improve fluency as they share their knowledge and provide feedback to their peers.
- Children's books present interesting problems and illustrate how other children solve these problems.
- Literature can provide the means to integrate math and language skills as children learn to listen, read, write, and solve the math problems.
- As children read nonfiction books, they listen to the facts about a particular subject. The information is assimilated into what the children already know. Instead of reading the book from cover to cover, students read a small portion of the story, and then they investigate the subject matter presented.
- As students listen to the story Math Curse they will use it as a springboard for writing their own word problems.
- Writing their own word problems based on the problems in Math Curse can be motivating for students as well as an excellent way for the teacher to integrate math vocabulary and reading.

## Common Core Standards

## State Standards

## NCTE/IRA National Standards for the English Language Arts

- 3. Students apply a wide range of strategies to comprehend, interpret, evaluate, and appreciate texts. They draw on their prior experience, their interactions with other readers and writers, their knowledge of word meaning and of other texts, their word identification strategies, and their understanding of textual features (e.g., sound-letter correspondence, sentence structure, context, graphics).
- 4. Students adjust their use of spoken, written, and visual language (e.g., conventions, style, vocabulary) to communicate effectively with a variety of audiences and for different purposes.
- 5. Students employ a wide range of strategies as they write and use different writing process elements appropriately to communicate with different audiences for a variety of purposes.
- 6. Students apply knowledge of language structure, language conventions (e.g., spelling and punctuation), media techniques, figurative language, and genre to create, critique, and discuss print and nonprint texts.
- 7. Students conduct research on issues and interests by generating ideas and questions, and by posing problems. They gather, evaluate, and synthesize data from a variety of sources (e.g., print and nonprint texts, artifacts, people) to communicate their discoveries in ways that suit their purpose and audience.
- 11. Students participate as knowledgeable, reflective, creative, and critical members of a variety of literacy communities.
- 12. Students use spoken, written, and visual language to accomplish their own purposes (e.g., for learning, enjoyment, persuasion, and the exchange of information).

## Materials and Technology

- Math Curse by Jon Scieszka and Lane Smith (Viking, 1995)
- Journals or loose-leaf paper
- Crayons, markers, and pencils with erasers
- 12-inch rulers
- Yardstick (optional)
- Computers with Internet access (optional)

Student Self-Assessment Checklist

## Preparation

- Implement the four reading modalities by reading and writing their own word problems, presenting their own word problems, and listening to their peers' word problems
- Create math word problems with smooth transitions, a conclusion, and a correct answer, using a nonfiction book as a guide, to increase fluency and enhance comprehension
- Apply math vocabulary skills by completing a crossword puzzle using correct spelling of number words
- Use the rereading strategy to increase fluency and comprehension
- On the inside back cover of the book Math Curse there is a Venn diagram that includes all the stories that Jon Scieszka and Lane Smith wrote together and separately. Students can work in groups and pick one of the stories to read to the class. To help increase fluency, students can practice reading in their groups before they read aloud to the class.
- Create a "Work Box" for students to access when they have free time. Put word problems in a box. When students are finished their work in reading or math class, they can pick a problem from the box and solve it.
- Have students access the Kidsreads.com Authors website to find the biographies of Jon Scieszka and Lane Smith. Students can then compare the lives of both authors, using the Compare & Contrast Map .
- Students can create their own word problems as homework to be bound into a three-ring binder for display in the classroom. Students' problems should include a drawing of their word problem and the correct answer.
- For more ideas for using the online Crossword Puzzles tool, see More Ideas to Try . This page is also appropriate to share with parents and afterschool educators.

## Student Assessment / Reflections

- Have students complete a Student Self-Assessment Checklist after they write their word problem. You may want to model filling out your own assessment using the word problem from page 9 of Math Curse . Look to see if the student ended the word problem with a question and included a hidden answer. If not, you might want to go back and review the requirements or check to see if the student understands the assignment.
- Use the Word Problem Rubric to assess each student’s word problem. Is the problem organized? Does the student understand the requirements of a word problem—to end with a question and include an answer to the problem? Is there a drawing? Is spelling correct? Is math computation correct?
- Observe students as they recite their word problems. Note whether students were able to speak in a clear voice using correct pronunciation of math terms. Note whether students present their information in a logical, sequential format. Plan a minilesson if presentation skills are lacking or in need of improvement.
- Collect and assess students’ “ Math Curse Word Problems” crossword puzzles from the online Crossword Puzzles tool. Were students able to complete the crossword puzzle and correctly spell the math number words?
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## Problem Solving in Mathematics

## Use Established Procedures

## Look for Clue Words

Common clue words for addition problems:

Common clue words for subtraction problems:

Common clue words for multiplication problems:

Common clue words for division problems:

## Read the Problem Carefully

- Ask yourself if you've seen a problem similar to this one. If so, what is similar about it?
- What did you need to do in that instance?
- What facts are you given about this problem?
- What facts do you still need to find out about this problem?

## Develop a Plan and Review Your Work

- Define your problem-solving strategy or strategies. This might mean identifying patterns, using known formulas, using sketches, and even guessing and checking.
- If your strategy doesn't work, it may lead you to an ah-ha moment and to a strategy that does work.

If it seems like you’ve solved the problem, ask yourself the following:

- Does your solution seem probable?
- Does it answer the initial question?
- Did you answer using the language in the question?
- Did you answer using the same units?

If you feel confident that the answer is “yes” to all questions, consider your problem solved.

## Tips and Hints

Some key questions to consider as you approach the problem may be:

- What are the keywords in the problem?
- Do I need a data visual, such as a diagram, list, table, chart, or graph?
- Is there a formula or equation that I'll need? If so, which one?
- Will I need to use a calculator? Is there a pattern I can use or follow?

## Year 3 / 4 Problem Solving Maths Lesson Plan

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## 44 free maths lesson plans for KS3 and KS4 by Colin Foster

## KEY STAGE 3

## 1 | Explore Proportions By Mixing Paints

Click here to get this free lesson plan.

## 2 | Explore Probability by Experimenting with the Rolls of Dice

## 3 | Use Puzzles to Show Students what Changes in Percentages Really Mean

## 4 | Can Students Carry Out A Probability Experiment And Explain The Results?

## 5 | Improve Mathematical Reasoning with a Real-Life Problem: How Many Sweets Can I Buy?

## 6 | Help Learners Understand Adding And Subtracting Directed Numbers By Linking To The Topic Of Electricity

## 7 | Gain Essential Skills in Simplifying Algebraic Expressions without Repetitious Drills

## 8 | Develop an Understanding of Numbers by Exploring What Makes Prime Numbers Special

## 9 | Find The Centre Of Enlargement For A Given Shape

Sometimes they are asked to find the centre of enlargement or scale factor for a given enlargement.

## 10 | Practise Estimating By Converting One Million Pounds Into Coins

## 11 | Spend A Lesson Exploring One Arithmagon Problem

## 12 | Use This Trial-And-Error Activity To Practise Multiplication

## 13 | The Power of Puzzles

## 14 | A day at the C-side

## 15 | The Simple Life

## 16 | Change the Subject

## 17 | Use Geometry to Define the Attributes of the Shapes Around Us, Like Parallelograms and Rhombuses

## 18 | Boost 3D Shape Understanding By Making A Children’s Toy

## 19 | Use Creative Approaches to Calculating Angles of Overlapping Polygons to Deepen Mathematical Understanding

## 20 | Explore The Properties Of Triangles And Spot Patterns In A Sequence

## 21 | Use A Clock Face To Investigate Angles

Then they have to choose the appropriate rule to get the right answer to each calculation.

## 22 | Show how Line and Rotational Symmetry are Linked by Inventing and Drawing Your Own Shapes

## 23 | Use Leaning Ladders To Explore Triangles

## 24 | Work Out The Topic Area By Finding The Three Angles Of A Triangle

## KEY STAGE 4

25 | use perimeters and pythagoras’ theorem to calculate the shortest route on a map.

## 26 | Examine the Effects that Margins of Error Have on Time, Distance and Estimation

## 27 | Use Pythagoras’ Theorem To Find Accurate Values For Triangle Perimeters

## 28 | Develop Spatial Awareness and Problem-Solving Skills by Exploring Two Successive Geometrical Transformations

In this lesson by Colin Foster, that’s precisely what they’re tasked with doing…

## 29 | Use Spatial Reasoning in Geometry to Understand How Shapes Move when Broken Down into Points and Lines

## 30 | Teach Highest Common Factor and Lowest Common Multiple Together to Show the Connection Between Them

## 31 | Use Algebra To Find Out Why A Number Trick Works

In this lesson, algebra is used to make sense of a number trick that the teacher performs.

## 32 | Calculating Rate and Time by Exploring How Long it Takes Multiple People to Paint a Wall

This download contains one lesson plan guide and one accompanying task sheet.

## 33 | Explore Probability by Playing Dice Games

In many everyday scenarios, we cannot calculate a theoretical probability of something happening.

## 34 | Embed Adding and Subtracting Fractions into a Richer Problem to get the Technique to Stick

## 35 | Link Maths To Real Life In This Problem Solving Lesson About Money

## 36 | Quadratic Equations Bring Together A Host Of Different Mathematical Ideas And Techniques

## 37 | Help Students Understand When One Integer Will Divide Exactly Into Another

## 38 | Let Students Construct Their Own Quadratic Equations to Boost Mathematical Fluency

## 39 | Shading Graphical Linear Inequalities by Locating Mystery Pairs of Coordinates

## 40 | Show Students the Importance of Histograms by Illustrating the Limitations of Bar Charts

## 41 | Use Flowcharts To Set Up Rules About Iterative Operations

## 42 | Use A Problem-Based Approach To Recap Adding And Subtracting Fractions

## 43 | Make Sense Of The Mean And Find Efficient Ways To Calculate It

## 44 | Use Ratio to Work out How to Carry Enough Food to Stay Alive in the Desert

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## Praxis Core Math

- Algebraic properties | Lesson
- Algebraic properties | Worked example
- Solution procedures | Lesson
- Solution procedures | Worked example
- Equivalent expressions | Lesson
- Equivalent expressions | Worked example
- Creating expressions and equations | Lesson
- Creating expressions and equations | Worked example

## Algebraic word problems | Lesson

- Algebraic word problems | Worked example
- Linear equations | Lesson
- Linear equations | Worked example
- Quadratic equations | Lesson
- Quadratic equations | Worked example

## What are algebraic word problems?

- Translating sentences to equations
- Solving linear equations with one variable
- Evaluating algebraic expressions
- Solving problems using Venn diagrams

## How do we solve algebraic word problems?

- Define a variable.
- Write an equation using the variable.
- Solve the equation.
- If the variable is not the answer to the word problem, use the variable to calculate the answer.

## What's a Venn diagram?

- Your answer should be
- an integer, like 6 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text
- (Choice A) $ 4 \$4 $ 4 dollar sign, 4 A $ 4 \$4 $ 4 dollar sign, 4
- (Choice B) $ 5 \$5 $ 5 dollar sign, 5 B $ 5 \$5 $ 5 dollar sign, 5
- (Choice C) $ 9 \$9 $ 9 dollar sign, 9 C $ 9 \$9 $ 9 dollar sign, 9
- (Choice D) $ 14 \$14 $ 1 4 dollar sign, 14 D $ 14 \$14 $ 1 4 dollar sign, 14
- (Choice E) $ 20 \$20 $ 2 0 dollar sign, 20 E $ 20 \$20 $ 2 0 dollar sign, 20
- (Choice A) 10 10 1 0 10 A 10 10 1 0 10
- (Choice B) 12 12 1 2 12 B 12 12 1 2 12
- (Choice C) 24 24 2 4 24 C 24 24 2 4 24
- (Choice D) 30 30 3 0 30 D 30 30 3 0 30
- (Choice E) 32 32 3 2 32 E 32 32 3 2 32
- (Choice A) 4 4 4 4 A 4 4 4 4
- (Choice B) 10 10 1 0 10 B 10 10 1 0 10
- (Choice C) 14 14 1 4 14 C 14 14 1 4 14
- (Choice D) 18 18 1 8 18 D 18 18 1 8 18
- (Choice E) 22 22 2 2 22 E 22 22 2 2 22

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## Problem-Based Tasks in Math

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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 (10 minutes) Bring students together in a circle, either seated or standing. Bring blocks with you to the circle.

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).

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Promote problem solving skills with challenging math problems that encourage gifted math students to go beyond the standard math curriculum. Distance to the Hurricane A short geometry and trigonometry lesson involving a hurricane and a house Fun Christmas Math Problems A set of Christmas themed math problems for high school students

Math Lesson Plans for Teachers. Filter. Sort by: Most-Popular Relevance; Most Popular; Most Recent; Most Popular. x Mathematics. x Lesson Plans (85) results found ... Using a Formula is a problem-solving strategy that students can use to find answers to math problems involving geometry,… Subjects: Mathematics. Formulas and Functions. Download ...

Sample Problem Solving Mathematics Lessons Perimeter and Area Students are challenged to solve problems involving perimeter and area of rectangles and triangles. Go teach it Averages Students are challenged to apply their understanding of the mean, mode, median and range to solve problems involving datasets. Go teach it Written Methods

File previews. doc, 66 KB. notebook, 822.5 KB. Problem Solving, patterns and sequences, algebra. This lesson achieved outstanding by Ofsted today. SMartboard file is based on a resource I found on Primary Resource called 'Magic Carpet'. Please e-mail me with any questions: [email protected] Tes classic free licence.

Problem Solving Lesson Plan Instructor: Sharon Linde Sharon has an Masters of Science in Mathematics and a Masters in Education Problems come in all shapes and sizes, and so do solutions....

This lesson is designed to help students solve problems involving the four operations, and identify and explain patterns in arithmetic. Prices and Percentages Length of Time: About 1 - 2 Class Periods Using a current list of prices for food and clothing, the students will practice math skills related to percentages.

Four step problem solving process lesson plan - Apps can be a great way to help learners with their math. Let's try the best Four step problem solving process. ... SMARTboard lesson with four steps to solving a math word problem suing UPSA: understand, pick a strategy, solve, and answer and check. 26 ...

This lesson uses the four modalities of reading (reading, writing, listening, and speaking) on a math word problem to bridge the gap between reading and math. After a read-aloud from the book Math Curse by Jon Scieszka and Lane Smith, students create their own word problems with answers. Students solve each other's problems.

Let's try the best Four step problem solving process lesson plan. Get Homework Help Now Tutorial 8: An Introduction to Problem Solving. Identify the problem. Look at what solutions have already been tried. ... SMARTboard lesson with four steps to solving a math word problem suing UPSA: understand, pick a strategy, solve, and answer and check. 26

This lesson asks students to use the math skills they are learning and applying them by creating word problems for their peers to solve. Objectives Students will: —Select one more more math operations to use in a word problem; —Produce multi-step word problems that their classmates can solve; —Solve word problems created by their classmates.

The Lesson Plan Diva. 3.2k. $12.00. PDF. This interactive notebook includes interactive math activities to use in the students math journal. Included are problem solving activities with graphic organizers and math journal prompts. There are picture manipulatives included with each word problem for the students to cut and glue down.

This Problem Solving lesson plan also includes: Project. Vocabulary. Join to access all included materials. First graders explore problems and solutions. In this math lesson, 1st graders brainstorm problems they have encountered and how they solved them. Then students watch a video about how professionals solve problems.

FREE Step by Step Math Lessons. Our math lessons are designed to make math meaningful to the student. Each math lesson provides in-depth instruction ideal for learners of all ages and abilities. Read the terms and conditions for using our sample lessons below. Get our ad-free, complete math curriculum on our Math Goodies CD.

Our Solving Word Problems lesson plan develops math problem-solving strategies for young students. This interactive lesson equips students to identify and define keywords and use pictures or diagrams for math problem solving (addition and subtraction). Students are asked to work collaboratively, in pairs, to compose word problems that ...

TED-Ed lessons on the subject Problem Solving. TED-Ed celebrates the ideas of teachers and students around the world. ... Want a daily email of lesson plans that span all subjects and age groups? Learn more. Subjects All Subjects. All Subjects; ... The simplest math problem no one can solve. lesson duration 22:09 33,331,203 views. 05:55 ...

Problem-solving requires practice. When deciding on methods or procedures to use to solve problems, the first thing you will do is look for clues, which is one of the most important skills in solving problems in mathematics. If you begin to solve problems by looking for clue words, you will find that these words often indicate an operation.

An ideal resource to teach problem solving involving money. Deals with misconceptions and supports teaching of problem solving. ... Year 3 / 4 Problem Solving Maths Lesson Plan. Subject: Mathematics. Age range: 7-11. Resource type: Worksheet/Activity (no rating) 0 reviews. Sparkle1978's Shop. 2.2155172413793105 66 reviews.

44 free maths lesson plans for KS3 and KS4 by Colin Foster We've got everything you need for your secondary maths classroom from algebra and geometry to improving number sense and mathematical fluency by Colin Foster DOWNLOAD A FREE RESOURCE! Bumper KS3 maths worksheets pack Download Now Download Now Secondary Maths KEY STAGE 3

lesson design provided by the math department which begins daily with a calendar math lesson, a problem-solving lesson, and computation. Math facts are also part of this lesson ... their own effectiveness, and plan with one another to ensure consistency and high expectations. Teachers analyze the data available to them and make adjustments as

Solving algebraic word problems requires us to combine our ability to create equations and solve them. To solve an algebraic word problem: Define a variable. Write an equation using the variable. Solve the equation. If the variable is not the answer to the word problem, use the variable to calculate the answer.

Problem-Based Tasks Require Studentsto Apply Their Knowledge in New Contexts. Problem-based tasks are math lessons built around a single, compelling problem. The problems are truly "problematic" for students — that is, they do not offer an immediate solution. The problems provide an opportunity for students to build conceptual understanding.