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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 Maths Lessons
September 1, 2022, problem solving is at the heart of engaging and inspiring mathematics lessons. .
In the past couple of years, my faculty have gone through deep-dive OFSTED inspections—a trial inspection with three HMIs and an actual inspection . The trial inspection showed all students have a love of maths. Later, in the words of my headteacher, the real inspection simply blew the lead inspector away. In each review, we showed how we teach mathematics through problem-solving. mathematics through problem-solving.
Shortly after blogging about the inspections, I received hundreds of messages from teachers and Heads of Maths asking for advice about embedding such an approach. My answer is simple, make problem-solving questions a feature of every lesson for students of all abilities.
To help with this, I would like to share four problem-solving lessons—these range from applying the rules of arithmetic to solving real-life problems with compound interest. In addition, every resource comes with a worksheet and tutorial video that models the solutions.
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
Students are challenged to apply their understanding of the mean, mode, median and range to solve problems involving datasets.
Written Methods
Students are challenged to apply the rules of arithmetic to a series of real-life, functional problems.
Compound Percentages
Students are challenged to apply compound percentage changes to calculate an original amount after a percentage change, a percentage rate and compare real-life investments.
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About Mr Mathematics
My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.
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Edexcel AS Further Mathematics Year 1: Further Pure 1: Vectors
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Edexcel AS Further Mathematics Year 1: Further Pure 1: Fractional Inequalities
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Grade 5 GCSE mathematics revision lessons to watch and download.
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Lesson Plan Sections
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Math Lessons
In this section you will find Math lessons from kindergarten through high school. Lessons come with options for modifications and differentiation in order to help you cater to the needs of your studs. Many of the lessons are aligned to Common Core State Standards. With that said, these lessons can easily be integrated into an existing curriculum Math curriculum for any grade. The lessons you see here were submitted by real teachers working in schools across the United States. We encourage you to contact us in order to share your lesson plans with the rest of the Teacher.org community.
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Math environmental lesson plans, angles in nature.
Students will take a walk outside with their protractor and measure the angles in nature. They will record the angles that they find in branches, trees, bushes, flowers, etc… and then determine the supplementary angle.
Math Math Lesson Plans
Big and small.
A fun lesson to help students understand the concept of big and small and how to compare the two. The lesson involved hands-on activities to make the learning fun and engaging.
Box Geometry
Students will learn about using the formulas for the area of squares, rectangles, and triangles to determine how much paint and carpet to purchase for a room. In addition, they will learn about scale measurements.
Charity Begins at School
Pairs of students will design, plan, and create an imaginary fundraiser for a charitable organization.
Comparing Decimals Game
Students will play a game in which they choose cards and choose the best place to put the number they have chosen in order to get the highest answer possible. This should not be the first introduction to the topic.
Comparing Multiplication Facts (Hey Tocayo!)
Students will be assigned a number that has various factors and they will find partners with different factors that have the same product.
Counting Backwards (20-0)
Students will learn how to count backwards from 20-0 in a very fun and exciting way. The lesson includes a hands-on/interactive component where students will be asked to hop backwards while counting. This lesson is great for kindergarten through first grade.
Even or Odd Nature Walk
Students will do a nature walk to find things in nature that are grouped in pairs that are odd or even.
Exchanging Time
The lesson is used for students to practice basic time measurement, and understanding the basic units of time.
Feed the Gator
Students will compare numbers with three or more digits using visual cues.
Fractions, Decimals, Percents, & Graphs
This lesson is designed to explore fractions, decimals, percent’s, and graphs with TRIX cereal.
Fun Fraction Pizza
Students will create a “pizza” from construction paper divided into 8 slices. They will decorate each slice and then exchange slices with classmates and then evaluate the fractions of slices that they have at the end. For example, 1/8 slices of my own pizza, 4/8 or ½ of pizza that was made by a female, 2/8 or ¼ that was made by my buddy. Note: Students should have already had some lessons about simplification of fractions.
Graphing With Insects
This lesson is designed to teach students to draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Plus, solve simple put-together, take-apart, and compare problems.
Ice Cream Cones, Baseballs, and Cans
Students will work in pairs to practice finding the volume of cones, cylinders, and spheres using everyday objects.
Interest-ing Math
Students will learn about simple interest and how to calculate the real cost of a loan, credit card, and other types of borrowing.
Measuring Length
This lesson is designed to teach students how to measure lengths indirectly and by alternating length units.
Measuring Up
This lesson will allow students to demonstrate knowledge of length as compared to other objects.
Natural Disaster Planning and Equations
For a natural disaster there are many variables to be accounted for when planning help for an area. This lesson will give students the opportunity to create a natural disaster plan for a part of their country.
Ocean Animals
This lesson is designed to help students identify and sort common words in basic categories.
Odd or Even
This engaging lesson will help students determine whether a group of objects (up to 20) has an odd or even number of members.
Order of Operations
This lesson is designed to help students solve problems involving the four operations, and identify and explain patterns in arithmetic.
Prices and Percentages
Using a current list of prices for food and clothing, the students will practice math skills related to percentages.
Representing Addition and Subtraction
This lesson is designed to help students represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
Roll the Dice - Probability & Statistics
Students will learn about probability and statistics while rolling dice and flipping a coin carefully recording their results.
Scale It Up
This lesson will allow students to demonstrate knowledge use of scale.
This lesson will allow students to demonstrate knowledge of various grade appropriate shapes.
Silent Geometry
The students will practice using geometry formulas measuring items in the classroom to find area and volume, radius and circumference, and identify the types of angles.
Skittles Graph
Students will learn to create a small bar graph using candy for information.
Sort It Out
Students will learn to categorize in various ways.
Symmetry Search
The students will locate manmade objects or things in nature that are symmetrical.
Take a Vacation
The students will plan a vacation for themselves, group of friends, or family, considering the costs involved.
The Ideal Town
Based on research the students will design a small town with a pre-determined population, assuring there is enough living space, parking spaces, and a sufficient water supply.
The Value of a Number
The students will work in groups of 4-6 physically learning and reviewing place value.
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Four step problem solving process lesson plan
Students are to solve word problems by using the four steps of problem solving. We will solve word problems as a class with visual representations to the
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The Four Steps for Problem Solving
His four step process can be summarized by. Understand the Problem Devise a Plan Carry out the Play Look Back
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Solving the Math Curse : Reading and Writing Math Word Problems
- Resources & Preparation
- Instructional Plan
- Related Resources
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. As they reread the word problems, fluency and comprehension increase. Finally, students use the skills they've learned creating word problems to complete a crossword puzzle. As students read the math concept words presented in the puzzle and write the correct answers, their reading and writing math vocabulary skills increase.
Featured Resources
Crossword Puzzles : Students will use what they learn about solving word problems in this fun and interactive online tool.
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
This resource has been aligned to the Common Core State Standards for states in which they have been adopted. If a state does not appear in the drop-down, CCSS alignments are forthcoming.
State Standards
This lesson has been aligned to standards in the following states. If a state does not appear in the drop-down, standard alignments are not currently available for that state.
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
Student objectives.
Students will
- 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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Four step problem solving process lesson plan
We discuss how Four step problem solving process lesson plan can help students learn Algebra in this blog post.
The Four Steps for Problem Solving
This problem-solving plan consists of four steps: details, main idea, strategy, and how. As students work through each step, they may use graphic
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4 Step Problem Solving Teaching Resources
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
Tool for the Field: Polya's Problem
Students are to solve word problems by using the four steps of problem solving. We will solve word problems as a class with visual representations to the
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Lesson Plan: Word Problems
"everyone’s got (word) problems".
Word problems are a great opportunity to bring math and literacy skills together in a format that is concrete and fun. 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.
Standards This lesson is appropriate for Upper Elementary, Middle School & High School CCSS.MATH.CONTENT.4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. CCSS.MATH.CONTENT.3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Materials — Flocabulary Math videos —Exercise sheet from video page
Time Allotted 1 class period
Sequence 1. Watch a math video relevant to what you’re teaching. This lesson is most easily used within the Operations strand (addition, subtraction, multiplication and division) but could also work for Geometry (finding the circumference of circle, the volume of a sphere), Statistics (Mean/median/mode), and other areas of math. 2. After the video, have students answer the Challenge Questions and complete any associated printable exercises. 3. Create a sample word problem that utilizes the type of math operation you’re focusing on. Walk through the problem with the class, pointing out the importance of reading it carefully (and aloud if helpful), understanding what you’re solving for, and underlining the most relevant information to help guide the problem solving process. 4. Break students up into pairs and explain that they are going to create word problems for each other to solve. Tell them that they can be as silly or creative as they want them to be, but lay down any parameters you feel are necessary (how long they have to be, how many steps they have to include, minimum/maximum value of numbers used). 5. Students should be given a certain amount of time to complete their problem (and have the answer themselves) and then they can swap with their partner.
Wrap Up/Extensions -Students can work together to create a third word problem and then pairs can swap as well. -Optional: Give the students the answer to the problem and they then have to create the word problem that will lead there. -Optional: Students can create whole stories/narratives that have a word problem at the center. They can write these with a younger audience in mind and then share them with the younger classes at school.
Guided Reflection -"I used to think ______ and now I think ______" -"One thing I learned is ________________ and one question I still have is _________"
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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. After sharing their own ideas, students illustrate a problem and solution and share it with the class.
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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
Perimeter and Area of Polygons
Perimeter of Polygons, Area of Rectangles, Parallelograms, Triangles and Trapezoids. Both metric and English units are used in these math lessons.
Circumference and Area of Circles
Geometry, parts of a circle, radius, diameter, Pi, Circumference of Circles, and Area of Circles. Both metric and English units are used in these lessons.
Elementary Math Lessons
These lessons on number theory include the following topics: Factors, Multiples, Prime and Composite Numbers, Divisibility, Exponents, and Patterns with Exponents. Connections to geometry and the real world.
Introduction to Fractions
Introduction, Classify Fractions, Equivalent Fractions, Simplify, Compare and Order. Convert Fractions to Mixed Numbers. Convert Mixed Numbers to Fractions. Math instruction is visual and conceptual.
Add and Subtract Fractions and Mixed Numbers
Add and subtract fractions with like and unlike denominators, LCD, add and subtract mixed numbers, solve real-world problems. These lessons use both visual and conceptual approaches.
Multiply and Divide Fractions and Mixed Numbers
Multiply fractions with and without cancelling, multiply mixed numbers, reciprocals, divide fractions, divide mixed numbers, solving real-world problems. Instruction is visual and conceptual.
Adding and Subtracting Decimals
Introduction, Read and Write, Compare and Order Decimals. Estimate Decimal Sums and Differences. Add and Subtract, Solve Decimal Word Problems.
Multiplying and Dividing Decimals
Estimate Decimal Products and Quotients. Multiply and Divide Decimals by Whole Numbers and by Decimals. Round Decimal Quotients, Solve Word Problems.
Understanding Percent
Meaning of Percent, Writing Fractions and Decimals as Percents, Writing Percents as Decimals and Fractions, Percents Less Than 1 or Greater Than 100.
Consumer Math with Percent Applications
Percent applications are presented, including Percentages and Proportions (IS over OF), Discount, Sale Price, Interest, Commission, Sales Tax, and Percent Change. Many connections to money in these lessons.
Integer Properties and Arithmetic
Integer properties and the number line. Absolute Value, Compare, Order, Add, Subtract, Multiply and Divide. Mixed Review of Arithmetic Operations.
Understanding Probability
Experiments, Outcomes, Certain and Impossible Events, Sample Spaces, Complement, Mutually Exclusive Events, Addition Rules, Independent and Dependent Events, Conditional Probabilities.
Pre-Algebra
Order of Operations with Whole Numbers, Integers and Exponents. PEMDAS, Writing Algebraic Expressions and Writing Algebraic Equations.
Data and Graphs
Step-by-step instruction on how to read, interpret and construct Line, Bar and Circle Graphs. Determine which graph is appropriate for a given set of data.
Mean Median Mode
Data, Range, Mean, Non-Routine Mean Problems, Median, and Mode. Strategies presented for Working Backwards, Bimodal Data, and No Mode.
Mathematical Logic
Negation, Conjunction and Disjunction. Conditional, Compound, and Biconditional Statements. Tautologies and Equivalence. Truth tables used in all lessons.
Sets and Set Theory
Basic definitions and notation, types of sets, equality, Venn diagrams, subsets, Universal set, set-builder notation, complement, intersection and union. Many visuals in these lessons.
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Solving Word Problems (Grades 1-2)
Our Solving Word Problems lesson plan provides students with strategies to help them solve word problems, such as using illustrations or drawings. Students practice solving example word problems using the given strategies.
Description
Additional information.
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 incorporate pictures or diagrams and exchange problems with other groups to solve. Students are also asked to individually complete practice problems in order to demonstrate their understanding of the lesson.
At the end of the lesson, students will be able to identify and define keywords and use pictures or diagrams for math problem solving (addition and subtraction).
State Educational Standards: LB.Math.Content.1.OA.A.2, LB.Math.Content.2.OA.A.1
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Solving Word Problems
This concept is hard for students. Thanks for explicit lesson on solving word problems.
We recently began homeschooling my son, after learning that he has not been being taught many subjects due to being in self-contained unit at school because of his behavioral issues. After explaining a few things to him, the material really helped to guide him on to the next part in our efforts to get him caught up. Thank you.
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Problem Solving in Mathematics
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The main reason for learning about math is to become a better problem solver in all aspects of life. Many problems are multistep and require some type of systematic approach. There are a couple of things you need to do when solving problems. Ask yourself exactly what type of information is being asked for: Is it one of addition, subtraction, multiplication , or division? Then determine all the information that is being given to you in the question.
Mathematician George Pólya’s book, “ How to Solve It: A New Aspect of Mathematical Method ,” written in 1957, is a great guide to have on hand. The ideas below, which provide you with general steps or strategies to solve math problems, are similar to those expressed in Pólya’s book and should help you untangle even the most complicated math problem.
Use Established Procedures
Learning how to solve problems in mathematics is knowing what to look for. Math problems often require established procedures and knowing what procedure to apply. To create procedures, you have to be familiar with the problem situation and be able to collect the appropriate information, identify a strategy or strategies, and use the strategy appropriately.
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.
Look for Clue Words
Think of yourself as a math detective. The first thing to do when you encounter a math problem is to look for clue words. This is one of the most important skills you can develop. If you begin to solve problems by looking for clue words, you will find that those words often indicate an operation.
Common clue words for addition problems:
Common clue words for subtraction problems:
- How much more
Common clue words for multiplication problems:
Common clue words for division problems:
Although clue words will vary a bit from problem to problem, you'll soon learn to recognize which words mean what in order to perform the correct operation.
Read the Problem Carefully
This, of course, means looking for clue words as outlined in the previous section. Once you’ve identified your clue words, highlight or underline them. This will let you know what kind of problem you’re dealing with. Then do the following:
- 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
Based on what you discovered by reading the problem carefully and identifying similar problems you’ve encountered before, you can then:
- 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?
Read the problem carefully, and decide on a method to solve the problem. Once you've finished working the problem, check your work and ensure that your answer makes sense and that you've used the same terms and or units in your answer.
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Year 3 / 4 Problem Solving Maths Lesson Plan
Subject: Mathematics
Age range: 7-11
Resource type: Worksheet/Activity
A range of outstanding resources for across the primary age range. All the resources have been tried and tested and are in line with the new national curriculum. Enjoy!
Last updated
5 June 2016
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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
KEY STAGE 3
1 | Explore Proportions By Mixing Paints
In this lesson, students work on a task about pink paint, which is made from a mixture of red paint and white paint.
How much red paint do you need to add to pink paint which is 60% red to turn it into pink paint which is 80% red?
Click here to get this free lesson plan.
2 | Explore Probability by Experimenting with the Rolls of Dice
People frequently vastly overestimate or underestimate many everyday risks, which can lead to poor decision making. One way to estimate the probability of something happening is to carry out an experiment and obtain some data on how many times it occurs out of a certain number of trials. The proportion of occurrences (relative frequency) gives an estimate of the probability, and this estimate generally improves the more trials that you do.
In this lesson plan by Colin Foster, students will carry out an experiment to estimate the probability that when three ordinary dice are thrown, they will show consecutive numbers. Students will explore how their estimates change as more and more throws are included, leading to an appreciation of the law of large numbers.
3 | Use Puzzles to Show Students what Changes in Percentages Really Mean
Percentages are commonplace in everyday life, but can be sometimes be confusing and difficult to interpret. In this lesson plan by Colin Foster, students get to grips with a series of puzzles aimed at showing what changes in percentage actually mean…
4 | Can Students Carry Out A Probability Experiment And Explain The Results?
If you choose which student will answer a question by drawing lolly sticks bearing their names from a cup, how many questions would need to be asked before everyone has a chance to answer? That’s the subject of this KS3 maths lesson that sets up a problem solving activity on probability.
5 | Improve Mathematical Reasoning with a Real-Life Problem: How Many Sweets Can I Buy?
Working out how many large and small bags of doughnuts to buy so as to get your treats as cheaply as possible involves students in some careful mathematical reasoning.
6 | Help Learners Understand Adding And Subtracting Directed Numbers By Linking To The Topic Of Electricity
Lots of learners have heard that ‘two minuses make a plus’ but may not apply this rule correctly or have much sense of when or why it is the case. In this lesson, links are made to the science topic of electricity to help learners understand adding and subtracting directed (positive and negative) numbers.
7 | Gain Essential Skills in Simplifying Algebraic Expressions without Repetitious Drills
‘Simplifying Expressions’ lesson plan and accompanying task sheet (originally published in volume 5, issue 2 of Teach Secondary magazine).
Exercises are not the only way to improve students’ fluency in mathematical procedures – sometimes the very same skills can be developed in a more exploratory fashion.
Expanding brackets and collecting like terms to simplify expressions are perhaps not the most exciting of mathematical topics, but fluency in these skills is needed in order to solve equations and engage with more stimulating mathematical problem solving. Unless students take the time to master these skills, they will be disadvantaged later – but how can we avoid lessons on algebraic manipulation descending into endless mindless drill and practice?
One way is to engage students in devising expressions that will simplify to produce a given result – in this lesson, the expression ‘5x + 8y’. Restricting the possible expressions that can be combined to make this to five given linear binomials forces students to engage in some careful trial and improvement.
To find all the possible solutions, they will have to engage with negative coefficients, leading to plenty of opportunities for strengthening their skills in expanding and simplifying algebraic expressions.
8 | Develop an Understanding of Numbers by Exploring What Makes Prime Numbers Special
Prime numbers are all around us, and they’re important, yet some are more important than others. Help your pupils discover how and why that is, using this lesson plan from Colin Foster.
9 | Find The Centre Of Enlargement For A Given Shape
Students can often learn to perform a procedure successfully without much understanding of what they are doing – let alone why they are doing it! A good way to help them get a deeper understanding is to present them with an inverse task, where they have to try to do the opposite process.
This is usually harder and, unless they have learned it as a standard procedure, requires some careful thinking to unpick what they know. In the topic of enlargements of 2D shapes, students are normally asked to enlarge a given shape with a given scale factor about a given centre of enlargement, or to describe in these terms an enlargement that has already been drawn.
Sometimes they are asked to find the centre of enlargement or scale factor for a given enlargement.
In this lesson, students are asked to decide where the centre of enlargement can go for a given shape with a scale factor of 3 enlargement so that no part of the image will go off the edge of the grid. Solving this problem involves students in intelligent trial and error as they experiment with various possible centres of enlargement in order to locate the locus of possible positions.
10 | Practise Estimating By Converting One Million Pounds Into Coins
A million pounds sounds like a lot of cash, but exactly how much is it really? Converting a vague notion of ‘wealth’ or ‘riches’ into actual pound coins can be an extremely useful and engaging way of encouraging learners to carry out estimations involving large numbers, mass and volume.
11 | Spend A Lesson Exploring One Arithmagon Problem
Learning mathematics is about making sense of mathematical situations. These puzzles provide an interesting context in which students can make predictions and conjectures and develop their powers of mathematical reasoning.
In this lesson students will investigate the relationship between numbers in a diagram and justify their reasoning.
12 | Use This Trial-And-Error Activity To Practise Multiplication
Multiplication is a fundamental operation in mathematics which every student needs to understand and be comfortable with. Although nowadays we have computers and calculators to do routine calculations for us, we still need to understand what multiplication does and when to use it.
It is also important to have a sense for what size an answer should be, so that we can make useful estimates when accuracy is not essential and spot errors when using technology.
In this lesson, students have to try to make the maximum product possible by making two numbers from the digits 1 to 9 and multiplying them together. This task allows students to generate lots of practice through trial and error but also focuses their thinking on place value and the optimal positions for the highest-value digits.
13 | The Power of Puzzles
Instead of treating algebra as a foreboding, abstract topic to be feared, says Colin Foster students ought to see it as a useful tool that can actually make their learning of maths a whole lot easier.
14 | A day at the C-side
‘A Day at the C-Side’ gets Pythagoras’ theorem stuck in learners’ minds by allowing them to discover it themselves.
In this lesson, pupils draw tilted squares and find their areas, then use these values to draw conclusions about the lengths of oblique lines on a square grid – leading to a statement and proof of Pythagoras’ theorem.
15 | The Simple Life
In this lesson, assistant maths professor Dr Colin Foster shows how you can start with an answer – ‘5x + 8y’ in this instance – and work back from there, getting your students to find as many solutions as they can, while picking up key knowledge of negative coefficients along the way.
16 | Change the Subject
‘Change the Subject’ develops pupils’ algebra skills so that they can rearrange equations confidently, which is an important skill both in mathematics and other subjects like science and design and technology.
17 | Use Geometry to Define the Attributes of the Shapes Around Us, Like Parallelograms and Rhombuses
Remind your students that maths isn’t just about numbers with this detailed lesson from Colin Foster that encourages pupils to take a closer look at what we know about geometry, and polygons in particular.
What makes a parallelogram a parallelogram? Can the attributes of a shape be mathematically defined and used to decide whether, say, something that looks like a rhombus actually is one?
18 | Boost 3D Shape Understanding By Making A Children’s Toy
Can you make a shape sorter, with at least four different shapes and holes, so that each shape will go through just one of the holes?
This lesson plan looks at shape sorter toys – which will be familiar to most students, particularly if they have a younger sibling – as designing and making one can be a good challenge for those in Key Stage 3. It requires a lot of careful thought, particularly if we want to avoid any shapes fitting through the ‘wrong’ hole.
Students will have to decide which shapes to include (they can go for easy or hard options), how big to make them, and how to draw out the required nets accurately. An additional constraint can be that all of the shapes should be able to fit inside the finished box at the same time.
19 | Use Creative Approaches to Calculating Angles of Overlapping Polygons to Deepen Mathematical Understanding
The angles created by overlapping regular polygons can be easy or difficult to calculate, depending on what information you are given. So, taking a creative approach to important mathematical processes like this can deepen students’ understanding of the principles involved and develop vital skills of reasoning and deduction.
20 | Explore The Properties Of Triangles And Spot Patterns In A Sequence
In this open ended lesson, learners explore a sequence of gradually larger shapes and consider what mathematical questions they can ask about them. What is the same and what is different about a group of triangles, and how can they be drawn accurately. What measurements make an impossible triangle, and can students work out which triangles come next in a sequence? This KS4 lesson also gives students the chance to use Cosine.
21 | Use A Clock Face To Investigate Angles
Although we live in a digital age, analogue timepieces are still all around us and provide a helpful context for exploring angles.
Students often approach the topic of angles by memorising lots of vocabulary (acute, obtuse, right angle, etc) and ‘facts’ about angles around a point, on a straight line, inside and outside a triangle and other polygons and between a transversal and parallel lines.
Then they have to choose the appropriate rule to get the right answer to each calculation.
In this lesson, a clock face is used to stimulate some calculations involving angles. First, students are invited to estimate the size of the angle and then to calculate it exactly. Initially, some of the calculations are quite easy, while others are more complicated as the lesson progresses. Provided that students know that there are 360° in a whole turn, they should be able to work out everything else for themselves.
22 | Show how Line and Rotational Symmetry are Linked by Inventing and Drawing Your Own Shapes
‘Shape Up’ teaches students about line and rotational symmetry and how they are related, getting them to invent and draw their own shapes with particular symmetries.
23 | Use Leaning Ladders To Explore Triangles
Ladders leaning against walls is a classic scenario for mathematics problems and is often used to address topics such as Pythagoras’ theorem and trigonometry.
In this lesson, the situation of two crossing ladders is used as an opportunity to work on ideas relating to similar triangles.
How high will the crossing point be above the ground and how far will it be from each wall? What happens for different lengths of ladders? What happens if the walls are further apart or closer together?
Students need to identify triangles that are similar and then construct equal ratios to work out their answers. They will notice interesting properties, such as the fact that the distance between the walls does not affect the height of the crossing point. There are also connections with an average called the harmonic mean.
24 | Work Out The Topic Area By Finding The Three Angles Of A Triangle
Learners are often asked to practise finding the third angle of a triangle when the other two are given. In this lesson they get the opportunity to work on the topic area by finding all three angles according to different constraints.
KEY STAGE 4
25 | use perimeters and pythagoras’ theorem to calculate the shortest route on a map.
Applying their knowledge of scale and Pythagoras’ Theorem, students are tasked with calculating the shortest route between two destinations on a map and explaining their reasoning as clearly as possible in this detailed lesson plan devised by Colin Foster.
26 | Examine the Effects that Margins of Error Have on Time, Distance and Estimation
‘Hopping Along’ sees students examine the effect that margins of error can have on otherwise seemingly clear results. Starting with the seemingly clear result of a race, students look at how multiple inaccuracies in the measurement of distance and time can combine to produce a very different – and even counter-intuitive – outcome.
27 | Use Pythagoras’ Theorem To Find Accurate Values For Triangle Perimeters
In this lesson, students use Pythagoras’ theorem to find accurate values for the perimeters of some triangles. Although the values of the perimeters are so close that it would be very hard to distinguish them by measurement, mathematics makes it possible to be absolutely sure about the order in which they come.
28 | Develop Spatial Awareness and Problem-Solving Skills by Exploring Two Successive Geometrical Transformations
Traditionally, pupils are taught geometrical transformations by learning a set of skills they can apply to reflecting, rotating and enlarging shapes without giving the process too much thought. But what if they were to called upon to use those skills to solve a mathematical problem?
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
In geometry students need to use their spatial reasoning and visualisation skills to understand the shapes and how they will move when broken down into points and lines. This lesson allows pupils to look at two fixed points and how they relate to other points.
30 | Teach Highest Common Factor and Lowest Common Multiple Together to Show the Connection Between Them
‘The What Factor?’ takes the ideas of highest common factor and lowest common multiple, which are often taught separately, and deals with them together to help learners to appreciate the connections 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.
Students are asked to explore the mechanics, experiment with some numbers, and then use algebra to try to probe exactly how and why the trick works.
It’s easy to check the rule on a few numerical examples by working them out, but a short piece of algebra helps students to see what is going on under the surface.
This lesson provides an opportunity to work on expanding brackets and simplifying algebraic expressions, as well as making sense of the final answer in terms of the place value of the original numbers.
32 | Calculating Rate and Time by Exploring How Long it Takes Multiple People to Paint a Wall
This lesson is about calculating how long it will take to paint a wall if several people work at it at the same time. Will it take less time with more people helping? And if so then how much less?
Students need to make assumptions that are realistic to the real-world situation, but they also have to make assumptions that will make the calculations easy to do and give an answer that is close enough for practical purposes. Pupils often find calculations involving rates difficult. They may be tempted to add up the times rather than the rates, and this provides an opportunity for discussion and for deciding whether or not different possible answers obtained are reasonable.
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.
Even some simple-sounding games involving dice are complicated to analyse and the easiest way to estimate the probability of a win is often to run a simulation on a computer.
In this lesson , students are asked to estimate the probability of winning a game in which they throw an ordinary dice and move a counter that many spaces forwards.
To win, they must ‘hit ten’ by landing on the tenth square from the start. This game is too complicated for students to work out the probability of winning theoretically, so they must estimate it by playing the game several times and seeing how often they win. This enables them to calculate how much money they might be willing to pay to play the game, if the prize for winning is £1.
34 | Embed Adding and Subtracting Fractions into a Richer Problem to get the Technique to Stick
They’ve been taught the technique a dozen times or more…but through embedding it within a richer problem, ‘adding and subtracting fractions’ might finally make sense to students.
35 | Link Maths To Real Life In This Problem Solving Lesson About Money
Mathematical questions about a photo in a carpark gives a real-life context to this maths lesson. Students will devise their own investigations about the photo that will involve money, algebra, and finding patterns. Logical thinking and careful arithmetic are also required in this KS4 lesson.
36 | Quadratic Equations Bring Together A Host Of Different Mathematical Ideas And Techniques
Quadratic expressions are considerably more complicated to work with than linear expressions, and students often find them hard to handle.
Students may carry out factorising of quadratics by applying poorly-understood procedures that make little mathematical sense to them, and this can be especially so when it comes to non-monic quadratics (those where the coefficient of x2 is not 1).
In this lesson, students approach factorising non-monic quadratics by trying to find factorisations which will expand and simplify to produce a quadratic expression of a specified form.
This entails lots of useful practice at expanding pairs of brackets and collecting like terms, and also gives opportunity for students to unpick what is going on, so as to gain insight into how the inverse process of factorising works.
By working backwards in this way to obtain the necessary factors, students build a deeper understanding of factorising quadratics.
37 | Help Students Understand When One Integer Will Divide Exactly Into Another
Understanding when one integer will divide exactly into another helps students to ‘make friends’ with the integers and feel more secure when carrying out calculations.
Even when students are using calculators, this sort of familiarity with factors enables students to estimate the sizes of answers (and such things as whether an integer should be obtained or not).
All of this provides valuable checks on the work that they are doing and can be more intellectually stimulating than merely following standard algorithms to get an answer.
In this lesson, students have the opportunity to experiment with producing ‘nice’ answers like 123 456 from multiplying integers.
38 | Let Students Construct Their Own Quadratic Equations to Boost Mathematical Fluency
‘Connected Quadratics’ helps students become confident and fluent with techniques such as factorising quadratics by offering a scenario in which they need to construct their own quadratic equations in order to solve a bigger problem…
39 | Shading Graphical Linear Inequalities by Locating Mystery Pairs of Coordinates
‘What’s the Point?’ teaches shading graphical inequalities, but not as a sequence of instructions to follow, as it is often done. Instead, asking learners to find a ‘mystery point’ can bring the process to life…
40 | Show Students the Importance of Histograms by Illustrating the Limitations of Bar Charts
If your maths students are struggling to see the point of why we have histograms, this lesson devised by Colin Foster will quickly highlight the limitations of the bar charts they learnt about in primary school.
Students here are tasked with devising bar charts in a deliberately misleading way, by splitting data concerning visitor numbers at a sports centre into different categories. However, when they use the same data to plot histograms, it will soon become clear that their ability to show frequency density helps to communicate an accurate sense of what the data distribution really is.
41 | Use Flowcharts To Set Up Rules About Iterative Operations
Flowcharts are a highly visual way of communicating information and are used in this lesson to set up rules about operations that will be performed iteratively. Students are invited to explore what happens when they put different numbers into a given flowchart, and later to experiment with varying the features of the flowchart themselves. They will encounter some converging sequences and use algebra to predict and explain the outcomes.
42 | Use A Problem-Based Approach To Recap Adding And Subtracting Fractions
Developing fluency with a particular mathematical technique to the point where students no longer need to think about the details can give them a powerful sense of mastery. This enables them to tackle more demanding mathematical problems that rely on that process and contributes to a wider confidence in the subject.
Adding and subtracting fractions is a procedure which students often find it very difficult to master, despite sometimes having been taught it every year from upper primary school to the sixth form. They’ll do it for a few lessons but then quickly forget it again for another year – particularly in this age of calculators and computers.
When revisiting this topic at Key Stage 4, therefore, it can bring up powerful memories of failure, so it is important to address the area without it feeling like an exact repetition of what they have done before.
One way to make the practice of a technique less tedious than a page of exercises is to embed it in a bigger problem which students are trying to solve. Having their attention on a grander purpose helps them to internalise the method to the point where they don’t have to think about it any more, which is always the goal of mathematical fluency.
A problem-based approach also means that the answers obtained have some significance for the wider problem, so students are more inclined to check their answers and notice if any of them doesn’t seem to be about the right size.
43 | Make Sense Of The Mean And Find Efficient Ways To Calculate It
The language of averages is used all the time in the world around us – and budding mathematicians need to understand exactly what such terms represent.
Many students will know how to calculate the mean: they add up all the numbers and divide by how many there are. However, it is common to find that students are less sure about exactly what the value that they have calculated actually means.
This lesson helps to make sense of the meaning of the mean as well as exploring efficient ways to calculate it.
44 | Use Ratio to Work out How to Carry Enough Food to Stay Alive in the Desert
Working out how to carry enough food to stay alive in a challenging environment poses interesting problems.
In this lesson, students use their knowledge of ratio to make sense of a real-world scenario in which enough food must be carried into the desert to allow a group of people to survive for a certain length of time.
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Praxis Core Math
Unit 1: lesson 4.
- 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?
What skills are needed.
- 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
Things to remember
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Problem-Based Tasks in Math
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Providing students with opportunities to grapple with math has led to amazing things happening in my class. Students are totally excited and are driven to figure out not just how to solve a problem but why it works.
– Jessica Proffitt, Fifth-Grade Teacher at Two Rivers
Watch two rivers’s teachers and students at work on problem-based tasks in math.
Problem-Based Tasks Require Students to 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. Problem-based tasks require students to apply their current understanding and skills to new contexts that highlight core math concepts. For example, when students solve a problem that could be solved with multiplication before they have formally been taught what multiplication is and how it works, they build an understanding that multiplication is repeated addition.
Well-designed problem-based tasks provide multiple entry points for students to engage in problem solving, ensuring that all students have access to the same concepts. When students solve the problems in different ways—including drawing pictures, acting out the problem, writing algorithms, and using manipulatives—they make connections between the variety of models that all accurately illustrate the underlying mathematics.
Problem-Based Tasks in Math Resources
IMAGES
VIDEO
COMMENTS
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).
Math Sort by Subtraction with Regrouping Lesson Plan Sub Plans for Second Grade Lesson Plan Identifying Coin Values Lesson Plan Equivalent Fractions Using Area Models Lesson Plan Show Me Equivalent Fractions! Lesson Plan Less Than or Greater Than Alligators Lesson Plan Second Grade Daily Sub Plan Day 3 Lesson Plan Adding it All Up Lesson Plan
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.