middle school math problem solving

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Maneuvering the Middle

Student-Centered Math Lessons

Math Problem Solving Strategies

How many times have you been teaching a concept that students are feeling confident in, only for them to completely shut down when faced with a word problem?  For me, the answer is too many to count.  Word problems require problem solving strategies. And more than anything, word problems require decoding, eliminating extra information, and opportunities for students to solve for something that the question is not asking for .  There are so many places for students to make errors! Let’s talk about some problem solving strategies that can help guide and encourage students!

1. C.U.B.E.S.

C.U.B.E.S stands for circle the important numbers, underline the question, box the words that are keywords, eliminate extra information, and solve by showing work.  

• Why I like it: Gives students a very specific ‘what to do.’
• Why I don’t like it: With all of the annotating of the problem, I’m not sure that students are actually reading the problem.  None of the steps emphasize reading the problem but maybe that is a given.

2. R.U.N.S.

R.U.N.S. stands for read the problem, underline the question, name the problem type, and write a strategy sentence. 

• Why I like it: Students are forced to think about what type of problem it is (factoring, division, etc) and then come up with a plan to solve it using a strategy sentence.  This is a great strategy to teach when you are tackling various types of problems.
• Why I don’t like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time.

3. U.P.S. CHECK

U.P.S. Check stands for understand, plan, solve, and check.

• Why I like it: I love that there is a check step in this problem solving strategy.  Students having to defend the reasonableness of their answer is essential for students’ number sense.
• Why I don’t like it: It can be a little vague and doesn’t give concrete ‘what to dos.’ Checking that students completed the ‘understand’ step can be hard to see.

4. Maneuvering the Middle Strategy AKA K.N.O.W.S.

Here is the strategy that I adopted a few years ago.  It doesn’t have a name yet nor an acronym, (so can it even be considered a strategy…?)

UPDATE: IT DOES HAVE A NAME! Thanks to our lovely readers, Wendi and Natalie!

• Know: This will help students find the important information.
• Need to Know: This will force students to reread the question and write down what they are trying to solve for.
• Organize:   I think this would be a great place for teachers to emphasize drawing a model or picture.
• Work: Students show their calculations here.
• Solution: This is where students will ask themselves if the answer is reasonable and whether it answered the question.

Ideas for Promoting Showing Your Work

• White boards are a helpful resource that make (extra) writing engaging!
• Celebrating when students show their work. Create a bulletin board that says ***I showed my work*** with student exemplars.
• Take a picture that shows your expectation for how work should look and post it on the board like Marissa did here.

Show Work Digitally

Many teachers are facing how to have students show their work or their problem solving strategy when tasked with submitting work online. Platforms like Kami make this possible. Go Formative has a feature where students can use their mouse to “draw” their work. 

If you want to spend your energy teaching student problem solving instead of writing and finding math problems, look no further than our All Access membership . Click the button to learn more. 

Students who plan succeed at a higher rate than students who do not plan.   Do you have a go to problem solving strategy that you teach your students? 

Editor’s Note: Maneuvering the Middle has been publishing blog posts for nearly 8 years! This post was originally published in September of 2017. It has been revamped for relevancy and accuracy.

Problem Solving Posters (Represent It! Bulletin Board)

Check out these related products from my shop.

Reader Interactions

18 comments.

October 4, 2017 at 7:55 pm

As a reading specialist, I love your strategy. It’s flexible, “portable” for any problem, and DOES get kids to read and understand the problem by 1) summarizing what they know and 2) asking a question for what they don’t yet know — two key comprehension strategies! How about: “Make a Plan for the Problem”? That’s the core of your rationale for using it, and I bet you’re already saying this all the time in class. Kids will get it even more because it’s a statement, not an acronym to remember. This is coming to my reading class tomorrow with word problems — thank you!

October 4, 2017 at 8:59 pm

Hi Nora! I have never thought about this as a reading strategy, genius! Please let me know how it goes. I would love to hear more!

December 15, 2017 at 7:57 am

Hi! I am a middle school teacher in New York state and my district is “gung ho” on CUBES. I completely agree with you that kids are not really reading the problem when using CUBES and only circling and boxing stuff then “doing something” with it without regard for whether or not they are doing the right thing (just a shot in the dark!). I have adopted what I call a “no fear word problems” procedure because several of my students told me they are scared of word problems and I thought, “let’s take the scary out of it then by figuring out how to dissect it and attack it! Our class strategy is nearly identical to your strategy:

1. Pre-Read the problem (do so at your normal reading speed just so you basically know what it says) 2. Active Read: Make a short list of: DK (what I Definitely Know), TK (what I Think I Know and should do), and WK (what I Want to Know– what is the question?) 3. Draw and Solve 4. State the answer in a complete sentence.

This procedure keep kids for “surfacely” reading and just trying something that doesn’t make sense with the context and implications of the word problem. I adapted some of it from Harvey Silver strategies (from Strategic Teacher) and incorporated the “Read-Draw-Write” component of the Eureka Math program. One thing that Harvey Silver says is, “Unlike other problems in math, word problems combine quantitative problem solving with inferential reading, and this combination can bring out the impulsive side in students.” (The Strategic Teacher, page 90, Silver, et al.; 2007). I found that CUBES perpetuates the impulsive side of middle school students, especially when the math seems particularly difficult. Math word problems are packed full of words and every word means something to about the intent and the mathematics in the problem, especially in middle school and high school. Reading has to be done both at the literal and inferential levels to actually correctly determine what needs to be done and execute the proper mathematics. So far this method is going really well with my students and they are experiencing higher levels of confidence and greater success in solving.

October 5, 2017 at 6:27 am

Hi! Another teacher and I came up with a strategy we call RUBY a few years ago. We modeled this very closely after close reading strategies that are language arts department was using, but tailored it to math. R-Read the problem (I tell kids to do this without a pencil in hand otherwise they are tempted to start underlining and circling before they read) U-Underline key words and circle important numbers B-Box the questions (I always have student’s box their answer so we figured this was a way for them to relate the question and answer) Y-You ask yourself: Did you answer the question? Does your answer make sense (mathematically)

I have anchor charts that we have made for classrooms and interactive notebooks if you would like them let me me know….

October 5, 2017 at 9:46 am

Great idea! Thanks so much for sharing with our readers!

October 8, 2017 at 6:51 pm

LOVE this idea! Will definitely use it this year! Thank you!

December 18, 2019 at 7:48 am

I would love an anchor chart for RUBY

October 15, 2017 at 11:05 am

I will definitely use this concept in my Pre-Algebra classes this year; I especially like the graphic organizer to help students organize their thought process in solving the problems too.

April 20, 2018 at 7:36 am

I love the process you’ve come up with, and think it definitely balances the benefits of simplicity and thoroughness. At the risk of sounding nitpicky, I want to point out that the examples you provide are all ‘processes’ rather than strategies. For the most part, they are all based on the Polya’s, the Hungarian mathematician, 4-step approach to problem solving (Understand/Plan/Solve/Reflect). It’s a process because it defines the steps we take to approach any word problem without getting into the specific mathematical ‘strategy’ we will use to solve it. Step 2 of the process is where they choose the best strategy (guess and check, draw a picture, make a table, etc) for the given problem. We should start by teaching the strategies one at a time by choosing problems that fit that strategy. Eventually, once they have added multiple strategies to their toolkit, we can present them with problems and let them choose the right strategy.

June 22, 2018 at 12:19 pm

That’s brilliant! Thank you for sharing!

May 31, 2018 at 12:15 pm

Mrs. Brack is setting up her second Christmas tree. Her tree consists of 30% red and 70% gold ornaments. If there are 40 red ornaments, then how many ornaments are on the tree? What is the answer to this question?

June 22, 2018 at 10:46 am

Whoops! I guess the answer would not result in a whole number (133.333…) Thanks for catching that error.

July 28, 2018 at 6:53 pm

I used to teach elementary math and now I run my own learning center, and we teach a lot of middle school math. The strategy you outlined sounds a little like the strategy I use, called KFCS (like the fast-food restaurant). K stands for “What do I know,” F stands for “What do I need to Find,” C stands for “Come up with a plan” [which includes 2 parts: the operation (+, -, x, and /) and the problem-solving strategy], and lastly, the S stands for “solve the problem” (which includes all the work that is involved in solving the problem and the answer statement). I find the same struggles with being consistent with modeling clearly all of the parts of the strategy as well, but I’ve found that the more the student practices the strategy, the more intrinsic it becomes for them; of course, it takes a lot more for those students who struggle with understanding word problems. I did create a worksheet to make it easier for the students to follow the steps as well. If you’d like a copy, please let me know, and I will be glad to send it.

February 3, 2019 at 3:56 pm

This is a supportive and encouraging site. Several of the comments and post are spot on! Especially, the “What I like/don’t like” comparisons.

March 7, 2019 at 6:59 am

Have you named your unnamed strategy yet? I’ve been using this strategy for years. I think you should call it K.N.O.W.S. K – Know N – Need OW – (Organise) Plan and Work S – Solution

September 2, 2019 at 11:18 am

Going off of your idea, Natalie, how about the following?

K now N eed to find out O rganize (a plan – may involve a picture, a graphic organizer…) W ork S ee if you’re right (does it make sense, is the math done correctly…)

I love the K & N steps…so much more tangible than just “Read” or even “Understand,” as I’ve been seeing is most common in the processes I’ve been researching. I like separating the “Work” and “See” steps. I feel like just “Solve” May lead to forgetting the checking step.

March 16, 2020 at 4:44 pm

I’m doing this one. Love it. Thank you!!

September 17, 2019 at 7:14 am

Hi, I wanted to tell you how amazing and kind you are to share with all of us. I especially like your word problem graphic organizer that you created yourself! I am adopting it this week. We have a meeting with all administrators to discuss algebra. I am going to share with all the people at the meeting.

I had filled out the paperwork for the number line. Is it supposed to go to my email address? Thank you again. I am going to read everything you ahve given to us. Have a wonderful Tuesday!

Open Middle®

Free Resources for Any Middle School Math Concept

MATHCOUNTS provides many free problem sets, videos, lesson plans and activities that can complement in-person and online learning. We've categorized some of the best resources for several middle school math topics:

• Arithmetic Skills
• Introduction to Counting
• Basic Number Sense
• Exploring Equations
• Properties of Right Triangles
• Multiple Approaches to Problems
• Using Similar Figures
• Area and Perimeter
• Sequences, Series and Patterns (Part 1)
• Sequences, Series and Patterns (Part 2)
• Probability

Use these resources to help you plan your next online learning session!

Faster Arithmetic Models

Practice plan.

Using the commutative, associative and distributive properties, Mathletes will arrange arithmetic problems in a different order that allows them to be solved more readily.

Order of Operations and Defining New Rules

After refreshing Mathletes on the order of operations, the video will then focus on how to solve problems where an unfamiliar symbol is defined to be a new type of operations that follows given rules.

The Multiplication Game

National math club game.

In The Multiplication Game players take turns chosing factors to obtain a product on the game board. The first player to four squares in a row wins. The game can be used to practice multiplication tables and factor pairs as well as to discuss prime and composite numbers.

In a heads up style game, students use inverse operations to guess the card on their forehead. They may or may not realize they are doing algebra! Register for the free National Math Club to access this game and dozens of others!

A-maze-ing Fractions

National math club exploration.

Operations with fractions are often hard for students to conceptualize. With this exploration's dry erase maze boards and four basic arithmetic operations, Mathletes can begin to uncover the secrets of fractions by finding a path that results in the least value or the greatest value. Register for the free National Math Club to access this activity and dozens of others!

Counting Bee

Help students improve their basic arithmetic skills by competing in a club counting bee. Given a starting number and counting number, see how far students can count in 15 seconds! Register for the free National Math Club to access this game and dozens of others!

Counting Shapes in a Complex Figure

This plan will help Mathletes to develop a strategic approach to counting the occurrences of a certain shape in a more complex figure made of multiple intersecting lines.

Counting Paths Along a Grid

Explore combinatorics by looking at a common type of MATHCOUNTS counting problem – counting paths between two points. End with an extension that connects counting paths to another type of combinatoric problem.

The Fundamental Counting Principle

This plan will introduce students to The Fundamental Counting Principle – a faster method to determining the total number of possible outcomes of an event without listing them all out!

Counting Possibilities

Mathcounts mini.

This video focuses on using diagrams and organized lists to ensure that each possible outcome is counted once, and only once.

Constructive Counting

Moving beyond the fundamental counting principle, students will be introduced to the difference between combinations and permutations, and presented with multiple methods for solving these types of problems.

Counting & Combinatorics Stretch

Problem set.

Two sets of ten practice problems from the 2002-2003 and 2015-2016 MATHCOUNTS School Handbook that cover basic counting including some number sense, shapes and paths.

Divisibility Rules

Students will apply divisibility rules of various integers to simplify computation, better understand number composition and aid in problem solving. In the extension, Mathletes can prove why each of these rules work!

Least Common Multiple

Calculating the least common multiple is something many students are asked to do, but in this plan they will use their understanding of the least common multiple to stretch themselves to solve more complex problems.

Marble Challenge

In the Marble Challenge students will take turns removing marbles with the goal of not taking the last marble. This game encourages students to notice patterns in the numbers and can even be used to introduce modular arithmetic. Register for the free National Math Club to access this game and dozens of others!

Using increasingly popular KenKen® puzzles, Mathletes will use teamwork, number sense and logic skills to solve challenges. Register for the free National Math Club to access this activity and dozens of others!

Strategic Guessing Using Divisibility Rules

Often in MATHCOUNTS you find yourself with a unique problem you don't already have a prescribed method for solving. This mini gives examples of such problems that can be solved with a little logic, number sense and understanding of divisibility rules.

Number Sense Stretches

Problem sets.

In these number sense stretches, there are three problem sets (10 problems each) from old MATHCOUNTS School Handbooks that covers number sense topics such as factoring and divisibility. These are great additional practice in after trying the Practice Plans and MATHCOUNTS Minis.

You Don't Have to Solve for x!

Often the immediate reaction when Mathletes see an algebraic equation is to solve for the unknown but depending on what you are looking for it might be easier to manipulate the equation without solving it.

Mathemagicians

This exploration is a great way to practice translating word problems into algebraic equations and to develop understanding of the concept of inverse operations. Mathletes will be amazed at first by what appears to be magic, but they will come to understand that the tricks can be explained using algebra. Mathletes can come up with their own magic examples to impress their friends and families and become true mathemagicians! Register for the free National Math Club to access this activity and dozens of others!

Function Battleship

This exploration lets Mathletes manipulate functions in order to explore and better understand translating, stretching, compressing and other transformations of functions. Through the Desmos platform, with the added twist of similarity to the board game Battleship, Mathletes can graph functions and see the effects of changing coefficients and exponents and adding and subtracting integers. Register for the free National Math Club to access this activity and dozens of others!

In a heads up style game, students use inverse operations to guess the card on their forehead. They may or may not realize they are doing algebra! Register for the free National Math Club to access this game and dozens of others!

Algebraic Equations from Word Problems

These problems and video focus on translanting the information in word problems into representative algebraic equations.

Seeing Symmetry in Systems of Equations

When dealing with systems of equations, if you are able to recognize symmetry between the equations, you can simplify the steps to a solution. This Mini will look at some problems and demonstrate how to find and use the symmetry to your advantage.

Special Right Triangles

Mathletes will become familiar with properties of 45-45-90 and 30-60-90 triangles. In this plan, the relationships between the sides of these two special right triangles will be derived. Then, Mathletes will apply these to solve for unknown lengths in geometric figures.

Right Triangles

From special right triangles to Pythagorean Triples, this video shows how to use properties of right triangles to solve problems.

This exploration gives Mathletes a brief introduction of the Pythagorean Theorem, then guides them through what we call Proofigami. This fun exploration will feel a lot like origami, but will provide Mathletes with a better understanding of the Pythagorean Theorem and gives club leaders a visual and tactile tool that makes explaining this proof easier. Register for the free National Math Club to access this activity and dozens of others!

30-60-90 Right Triangles

This MATHCOUNTS Mini will look at ways to use known ratios of 30-60-90 triangles to help solve more complex geometric problems.

Right Triangles Stretch

Practice solving problems by using the Pythagorean Theorem, recognizing Pythagorean triples and applying properties of special right triangles.

Trapezoids and Triangles

This video explores how we can decompose a figure into trapezoids and triangles to determine its area. The problems associated with this mini will help students determine when and how to apply their right triangle knowledge to solve more complex geometry problems.

More Than One Way to Solve a Problem

This video demonstrates multiple problem-solving strategies and emphasizes the importance of solving problems in more than one way to verify that you've solved a problem correctly.

Even More Than One Way to Solve a Problem

This video reinforces the concept of solving a problem multiple ways to validate your answer.

Fun Problem-Solving Techniques

National math club problem set.

Being able to take multiple different approaches to solve problems is an invaluable skill. In this problem set, students will look at four techniques - creating a model, acting out a situation, drawing a picture and making a list.

Three Tic-Tac-Toes

Chances are students are familiar with tic-tac-toe, but these rule variants on the traditional version will challenge students to rethink their strategy. Use this game to talk about symmetry, logic and proof writing.

Draw a Picture

This video explores how to solve problems by drawing a picture to organize the given information.

Make a Sketch

This video demonstrates how making a sketch of a given scenario can be a useful strategy when solving problems.

Recognizing Squares and Solving a Simpler Problem

This video focuses on recognizing squares and using them to solve a simpler problem.

Using the Difference of Squares to Solve Problems

This video explores how to use the difference of squares to solve problems and why this method works.

Systems of Equations Stretch

Apply the difference of squares formula in order to solve problems involving systems of equations.

Difference of Squares

An important formula to know, the difference of squares identity is derived geometrically in the video for this problem set. Mathletes will then try to recognize the difference of squares structure in various expressions and use the identity to find the value.

Perfect Squares/Using a Simpler Case to Solve a Problem

This video demonstrates how to use perfect squares to find a simpler case to help solve a problem. 

This video demonstrates how to solve problems using the difference of squares.

Similar Triangles and Proportional Reasoning

This video shows how to identify and use similar triangles to solve geometry problems

Using Similarity to Solve Geometry Problems

This video explores how to apply properties of similar triangles in solving problems about two-dimensional and three-dimensional figures. 

Similarity and Proportional Reasoning Stretches

Practice with the concept of similarity by answering questions about similar figures, and see how similarity relates to proportional reasoning and geometric transformations.

This video demonstrates how to use similarity and proportional reasoning to solve difficult geometry problems.

Similarity and Proportional Reasoning

Sometimes it is necessary to create the similar triangles you'll need in order to solve a problem. This video shows how to look at and build on given diagrams to create similar figures.

Similar Triangles

This video explores how to use parallel lines and angles to identify similar triangles and solve problems.

Fence Me In

After rolling dice to determine the size, in part, of a rectangle, players then use perimeter and area formulas to determine dimensions. The goal is to try to fill up the board first.

Areas of Irregular Convex Polygons

This video demonstrates two strategies for how to find the area of an irregular convex polygon.

Geometry Stretches

Find the areas and perimeters of various figures, and see how area and perimeter measurements can be used to solve other types of geometry problems.

Area of Irregular Polygons Reboot

This video demonstrates how to find the area of an irregular polygon by dividing the figure into smaller regions for which the area is more easily determined.

This video explores how we can decompose a figure into trapezoids and triangles to determine its area.

Problem of the Week

Practice calculating area and perimeter measurements using the image of a shamrock.

Number Sense: Looking for Patterns

This video focuses on techniques for solving problems by looking for patterns that emerge among the digits in large numbers.

Patterns All Around

Recognizing patterns in objects in order to express them mathematically is an important skill for students to learn. In this game students will attempt to recognize visual and numeric patterns in a group of cards.

Sequences, Series and Patterns

This video shows how to find patterns in both visual and numerical sequences and how to use patterns to identify an unknown value in a sequence.

More Sequences, Series and Patterns

This video demonstrates how to find a pattern in a sequence or series, and prove that it works, to solve problems.

Representing Patterns Numerically

In this practice plan, Mathletes will recognize visual patterns and practice defining them numerically in order to find the number of elements in the pattern after a large number of repetitions.

Patterns Stretches

Practice with patterns through problems about visual and numerical sequences and series, the digits of large numbers and other real-world and math topics.

Arithmetic and Geometric Sequences

This video explores how to solve problems about arithmetic and geometric sequences.

Relationships Between Arithmetic Sequences, Mean and Median

This video demonstrates how to use mean and median in solving problems about arithmetic sequences.

Arithmetic Sequences

This video focuses on techniques for solving problems involving arithmetic sequences, including finding the nth term.

Sequences Stretches

Practice with standard arithmetic and geometric sequences and series, as well as with other special types of sequences and series, like the Fibonacci sequence.

Patterns, Sequences and Series

This video shows a few techniques for solving problems using patterns in sequences and series.

Sequences and Central Tendency

This video demonstrates how the relationship between measures of central tendency and sequences can be used to solve problems.

High Impact Tutoring Built By Math Experts

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9 Algebra Questions And Practice Problems To Do With Your Middle Schoolers

Beki Christian

Algebra questions involve using letters or symbols to represent unknown values or values that can change. Here you will find \bf{9} algebra questions to test your knowledge and show you the different ways that algebra can be used to solve a problem to find an unknown value or to make generalizations.

Algebra in elementary school

Students as early as kindergarten begin to solve problems with algebraic thinking. Algebraic thinking starts with students understanding the properties of the operations, the relationships between them, and the composition of numbers.

They begin to relate concrete models to abstract expressions and equations, and continue this work throughout elementary school. They also look at patterns and the order of operations that will contribute to their understanding of algebra in later years.

This flexible understanding with the composition and representation of numbers, as well as the operations sets them up for more complex and abstract equations once they get to middle school. 

Summer Math Activities

Looking for math games and activities for the final weeks before summer or something to share with your students over the break? Keep math a focus and transition into the next grade with 4 separate worksheets for each grade including relevant topic-based games!

Algebra in middle school

Algebra encompasses many skills and concepts to help us make sense of the world and solve problems. In middle school, we learn to write basic algebraic expressions, write and solve linear equations, write and solve a system of linear equations, and graph linear equations on the coordinate plane. Later, we further develop these skills which allow us to work with more complex equations such as quadratic equations, polynomial equations, and exponential equations.

How to solve algebraic equations

When you are presented with an algebraic problem, it is important to make sense of the problem. Here are some of the key terms along with what they mean:

• Solve the equation – find out the value of the unknown.
• Substitute – put the values you have been given into the algebraic expression.
• Coefficients – the amount a term has been multiplied by. For example, in the expression 4c+2, \; 4 is the coefficient.
• Constants – values which are not variable and stay the same. For example, for 4c+2, \; 2 is the constant.
• Binomial – a binomial or binomial expression is one which has two parts, like our example 4c+2.
• Simplify – collect together like terms to make the expression or equation look simpler.
• Expand – multiply out the expressions inside parentheses.
• Factorize – put into parentheses.
• In terms of x – rewrite the equation in the form x = …

Remember, when working with algebra, we must still apply the order of operations, PEMDAS. i.e. Parenthesis, Exponents (powers, square roots), Multiplication, Division, Addition, Subtraction.

When working with algebraic expressions and equations we must consider carefully which operations to deal with first.

Algebra practice questions for middle school

1. A chocolate bar costs c cents and a drink costs d cents. Write down an expression for the cost of 2 chocolate bars and 2 drinks.

2 chocolate bars would cost 2 lots of c, or 2c, and 2 drinks would cost 2 lots of d, or 2d.

2. Simplify the expression 4m+5+2m-1.

We need to collect together like terms here so 4m + 2m = 6m and 5-1 = 4 (watch out for the negative).

In middle school, we learn a variety of different algebra techniques to answer algebra questions and to practice problem solving with algebra. These include:

• Simplifying algebraic expressions
• Expanding brackets and factoring
• Forming algebraic equations from word problems
• Solving algebraic equations and inequalities
• Substituting into expressions
• Changing the subject of an equation
• Working with real life graphs and straight line graphs

Algebra questions for middle school: basic algebra

3. In this pyramid, you add two adjacent blocks to find the value of the block above.

What expression will be in the top box?

4. Brian is a window cleaner. He uses the following formula to calculate the amount to charge his customers:

Charge = \$20 + 4n

Where n is the number of windows a house has.

If a house has 7 windows, how much would Brian charge?

In this question, n is 7 so we can substitute 7 into the formula.

Charge = \$20 + 4 × 7

Charge = \$48

5. The area of a rectangle is 4x-6.

Which of the following pairs could be the length and width of the rectangle?

2x and 2x-3

There are two ways of attempting this question. We know that \text{area of a rectangle } = \text{ length} \times \text{width} so we could multiply each pair together to see which pair makes 4x-6.

Alternatively, if we factorise 4x-6 we get 2(2x-3) meaning the sides could be 2 and 2x-3.

6. The formula for changing degrees Celsius to degrees Fahrenheit is:

Rearrange this formula to make C the subject.

Algebra questions for middle school: forming and solving equations

7. Work out the size of the smallest angle.

The angles in a triangle add up to 180^{\circ} therefore we can write

Now we have an equation we can solve.

The angles are :

The smallest angle is 34^{\circ} .

8. Jamie’s dad is 4 times older than Jamie. In 14 years time, Jamie’s dad will be twice the age of Jamie.

What is the sum of Jamie’s age now and Jamie’s dad’s age now?

To solve this we need to write an equation.

Let Jamie’s age now be x . Then Jamie’s dad’s age is 4x .

In 14 years time Jamie’s age will be x + 14 and Jamie’s dad’s age will be 4x + 14 .

Since we know Jamie’s dad’s age will be two times Jamie’s age, we can write

4x+14=2(x+14)

Jamie is currently 7 years old meaning his dad is 28 years old. The sum of their ages is 35 .

Note: when algebraic equations contain denominators on either side, we can use the cross multiplication method to help us work out the answer. For example with the following expressions:

This can then become, ad = bc and so on.

Algebra questions for middle school: graphs

9. Which of the following lines passes through the point (2, 5)?

At the point (2, 5), \; x is 2 and y is 5. We can check which equation works when we substitute in these values:

Looking for more algebra math questions?

• Ratio questions
• Probability questions
• Trigonometry questions
• Venn diagram questions
• Long division questions
• Pythagorean theorem questions

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by secondary teacher Beki Christian and has since been revised and adapted for US schools by elementary math teacher Jaclyn Wassell.

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Strategies for Teaching Problem Solving in Middle School Math

Problem solving is a vital skill in our middle school Math classes. It can also be really difficult for students to grasp.  By incorporating these strategies into your teaching, you can help your students become confident and successful problem solvers. So, let’s break it down and dive right in!  

Introduce the Importance of Problem Solving

Before we delve into the strategies, let’s talk about why problem solving is essential in math. Problem solving promotes critical thinking, logical reasoning, and the application of mathematical concepts in real-world situations. It encourages students to think creatively and develop problem-solving strategies that can be used across various contexts. If there’s not buy-in from students, it makes it 100% more difficult for students to care

Break Down the Problem Solving Process

To effectively teach problem solving, it’s crucial to break down the process into manageable steps. Here are four steps that can guide your students through the problem-solving journey:

Step 1 : Understand the Problem:

Encourage your students to read the problem carefully, identify the important information, and determine what the problem is asking. This step helps students gain a clear understanding of the problem before attempting to solve it. Encourage your students to talk to each other, and ask clarifying questions. Using the Notice and Wonder strategy is perfect here.

Step 2: Devise a Plan

Guide your students in developing a plan to solve the problem. This can involve strategies such as using visual representations, making a table or diagram, working backward, or using trial and error. Provide them with different problem-solving techniques to choose from.

Step 3: Implement the Plan

Once students have a plan, they can apply their mathematical knowledge and skills to solve the problem. Encourage them to show their work, explain their reasoning, and use appropriate mathematical language.

Step 4: Reflect and Evaluate

After finding a solution, it’s crucial for students to reflect on their process. Have them evaluate their work, check for reasonableness, and consider alternative approaches. This step promotes metacognition and helps students improve their problem-solving skills.

Use Real-World Contexts

Engaging students in real-world problem-solving scenarios not only makes math relevant but also enhances their motivation. Incorporate real-life contexts into your lessons, such as budgeting, measurements, or analyzing data. This will help students see the practical applications of math and develop a deeper understanding.

Provide Scaffolded Support

Differentiate your instruction by providing scaffolded support to meet the diverse needs of your students. Offer various levels of difficulty or different versions of the same problem to cater to different ability levels. Use manipulatives, graphic organizers, or step-by-step guides to support struggling students and gradually release responsibility as they become more confident.

Foster Collaboration and Discussion

Encourage collaboration and discussion among your students during problem-solving activities. Group work allows students to share strategies, learn from one another, and develop their communication skills. It also fosters a positive and supportive learning environment.

Assess and Provide Feedback

Effective assessment and feedback are crucial to help students grow as problem solvers. Use a variety of assessment methods, such as rubrics, observations, or student self-assessments, to evaluate their problem-solving skills. Use informal and formal assessments. Provide constructive feedback that highlights both strengths and areas for improvement, guiding them towards deeper understanding.

Teaching our students effective problem solving skills takes time and lots of practice. Please know this is not something that we teach once and our students will instantly “get it.” Take the time to really dive into each step and revisit.

Wanna close those learning gaps and experience more AHA moments in your middle school Math classroom? 

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100+ Brain-Teasing Math Riddles for Middle School to Unleash the Fun in Learning Math

Imagine the anticipation and curiosity that will fill the room as you present one of these captivating riddles to your eager learners at the start of a math session. It’s more than just having fun; it’s a chance to seamlessly blend enjoyment with education. As students grapple with these intellectually stimulating puzzles, they’ll naturally enhance their problem-solving abilities and hone their mathematical skills.

#TLDEUNO I love the idea of using educational riddles as bell work. This video is a great math riddle that upper-elementary students or middle school students would enjoy! For more videos like this, check out the 4 TED-Ed Riddle Playlists on YouTube. https://t.co/WN8QOJgQQ6 — Olivia Straub-Wurtele (@straub_olivia) October 19, 2020

The Cognitive Benefits of Solving Math Riddles

Engaging middle school students in the world of math riddles goes beyond mere entertainment – it offers a wealth of cognitive advantages. As students grapple with these intriguing challenges, they cultivate critical thinking skills that are essential for navigating complex problems. The process of deciphering riddles encourages them to analyze information, draw connections, and evaluate different possibilities. This analytical approach not only enhances their logical reasoning but also nurtures their ability to think critically and make informed decisions.

Furthermore, solving math riddles nurtures a growth mindset among students. When presented with a riddle that initially seems perplexing, they learn to embrace challenges and view them as opportunities for growth. Through perseverance and trial-and-error, students develop the confidence to tackle problems head-on, reinforcing the idea that intelligence and skill are developed through effort and dedication.

Incorporating Math Riddles into the Classroom

Moreover, math riddles facilitate collaborative learning experiences. When students work together to unravel the mysteries of a riddle, they engage in discussions, share insights, and collectively brainstorm strategies. This collaborative approach not only deepens their understanding but also reinforces the importance of teamwork and communication – skills that are invaluable in both academic and real-life settings.

100 Math Riddles For Middle School

Feel free to use these riddles to challenge and entertain middle school students!

More Math Riddles

Dive into the video and engage in a self-training session. While these riddles might appear deceptively simple at the outset, they often catch many off-guard. Ready to put your logic skills to the test?

Demonstrate your prowess in solving these riddles and seize the opportunity to challenge your math teacher! Prepare to be confounded as these 18 math riddles are designed to test your mettle and may even leave your math teacher stumped.

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20 Problem-Solving Activities For Middle School: Discussions, Games, Strategies, And Resources

November 20, 2023 //  by  Lesa M.K. Bullins, EdS

Problem-solving skills are important to the building of critical thinking, which in turn strengthens student executive function. Good problem solvers can build stronger cognitive flexibility, a critical component of executive functioning.

The teenage years are a crucial time for neuroplasticity, so it is a prime time for learning and developing important cognitive skills along with critical information. Bring problem-solving to life in your middle school classroom with these 20 activities.

1. Feelings Expression Scenarios

A huge part of problem-solving is properly expressing your own feelings. Students often struggle to state how they feel without combative, aggressive, or accusatory language; therefore opportunities to practice with realistic situations is a key problem-solving component. You can create scenario task cards to support students in realistic applications for relatable situations, or use pre-made cards.

Learn More:  Pinterest

2. Empathy Empowered Discussions

In addition to being able to calmly and kindly express one's feelings, empathy is a key problem-solving component. Teens can often struggle to express empathy as they have difficulty recognizing and interpreting due to the teenage brain functioning.

Teenage brains are still developing, so different areas of the brain are controlling different functions than we see in adult brains; furthermore, since teens are still figuring out what they think and feel about a variety of things, it can be difficult for them to recognize and consider the feelings and thoughts of others. You can instigate empathy discussions through relatable content like this short video.

Learn More:  Austin Wideman

3. Model, Model, Model...and then Model Some More!

Students learn more from what they see you do than what they hear you say! This means you have to be an active and purposeful model of what you expect. So make sure you are aware of your actions and words in front of your students!

Learn More:  Education World

4. Get Out of the Way

We need to allow students the time and space to solve problems. We cannot intervene every time they struggle to find the answer right away. Constant intervention hinders critical thinking and decision-making skills.

Make sure to leave some room for students to figure out solutions. Keep safe proximity so students have the comfort to know you are there if they cannot find a solution, but resist the urge to jump in as soon as you see them struggling.

Learn More:  Brookings

5. Plan a Road Trip

Engage problem-solving skills within context while reinforcing math, research, geography, and communication skills, too! Students can plan a road trip from start to finish in small groups. As an added bonus, you can let students travel virtually to the places they planned for their trip using Google Earth.

If time allows, they can even take screenshots and stage selfies for a presentation to share their trip with the class! This is a really great cross-curricular activity for the digital classroom, too!

6. Escape the Room

Escape rooms were made for problem-solving, so what better way to build these skills for students in an exciting way! Create different challenge activities surrounding a variety of subjects and skills to reinforce while lettings students put problem-solving to use finding practical solutions to escape the room!

Divide kids into teams and get on this engaging problem-solving activity!

7. Teach Explicit Strategies for Reflection

Students can build analytical skills by reflecting on their problem-solving process. Teach explicit skills to help students recognize and reflect on how they solve problems to reinforce future use and strengthen overall critical thinking abilities. Check out how Ellie from Cognitive Cardio made it work even in the time constraints of middle school schedules!

Learn More:  Cognitive Cardio With MSMM

8. Daily Practice

Give students short, interesting, and challenging problems to solve during the morning and afternoon transition times. Daily practice solving challenges is important for cognitive development and reinforces academic skills! You can find tons of daily challenges online or create your own.

9. Build Something

Let students work together in teams to build something from simple building materials. Increase the challenge by limiting resources or requiring students to pick their own resources for building blocks from a variety of random items. You can check out the marshmallow toothpick tower-building activity!

Learn more: Wow Sci

10. Blind Drawing Partners

Students can work in partner pairs or small groups to develop a vast array of abilities through this problem-solving activity. Blind team-building activities are excellent, low-prep ways to engage students' critical thinking and communication!

There are different ways you can implement this, but check out this video for an example of one application of the blind drawing game.

Learn more: Philip Barry

11. Laser Maze

Create a laser maze for students to get active in problem-solving. Create and implement different time durations to increase the challenge. Do not have lasers? No budget for lasers? Don't worry, red painter's tape will do the job!

Learn More:  That Phillips Family

12. Shared Story Puzzles

Creating story puzzles that force students to work in groups together to put together, add on, and create a cohesive story that is meaningful is another challenging task to engage in collaborative problem-solving.

Learn More:  Secondary English Coffee Shop

13. Yarn Webs

This social-skill-building collaborative problem-solving activity is fun for any age. Organize students into teams then let them choose a color of yarn, build a team web, and see who can navigate. There are so many ways this activity can be adapted, but you can watch a video of one interpretation here .

Learn More:  KEYSAmeriCorps

14. Scavenger Hunt

Create a series of clues that students must solve to progress through the game. Working in groups can help build conflict resolution and social skills as well. Check out how to create scavenger hunts for the classroom in this video by Learning Life.

Learn more: Learning Life

15. Boom! Math!

An excellent way to build advanced problem-solving skills, as well as mathematical analysis, is to create math Boom Cards with word problems like these from Math in the Middle. Boom cards are a great activity for students to practice and build skills!

Learn more: Boom Learning

16. Wheel of Solutions

Give students practice in exercising a number of different kinds of problem-solving skills by spinning and communicating a solution using the skills on which they land. You can make one in the classroom with a posterboard or create a digital wheel. Such a fun interactive resource! Use this great pre-made digital activity from Resource Haven on Boom Learning or create your own!

Learn More:  Boom Learning

17. Collaborative Math

Another activity for team building that supports mathematical concept reinforcement is students working together to collaboratively solve math problems. Check out how Runde's Room made sure everyone is engaged in working on solving parts of the problem through the sticky-note collaborative math activity.

18. Get Mysterious

Math Mysteries are a fun activity that builds out-of-the-box thinking and creates an inquisitive environment. Problem-solving develops through the process of inquisition! You can create your own or use Lee and Miller's 40 Fabulous Math Mysteries Kid's Can't Resist Scholastic book found here.

19. Logic Puzzles and Games

In addition to logic-building games like Chess, you can provide logic puzzles for morning and afternoon transitions, during downtime, or for early finishers. Logic puzzles help students think critically. You can make your own or get some prefabricated resources like the ones found in this book by Chris King .

Learn More:  Brainzilla

20. Lead Number Talks

Number talks are important to building problem-solving. Number talks allow students to build on one another in a collaborative way, discuss how they have solved problems before, consider how those solutions may be applicable to new skills they are about to learn, and build depth in math concepts.

So instead of getting quiet, get them talking!

Learn More:  North Dakota Teaching Kayla Durkin

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14 Powerful Math Websites for Middle School Students

Written by Jordan Nisbet

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As a school leader in the digital age, one of your greatest responsibilities is to ensure teachers are using quality math websites that can engage students, monitor their progress, close learning gaps, and address individual needs. But because they vary so much in quality, finding the best ones poses a real challenge.

Middle school, in particular, can be a trying time for students as their adolescent brains transition from tangible, foundational math concepts to more complex and abstract ones. So, here’s a list of 14 math websites for middle school that will greatly enrich your students’ learning experience.

1.  Prodigy Math

Prodigy Math is a free, adaptive math platform used by more than 1.5 million teachers, and 90 million students around the world. With 1,500+ math skills, it offers curriculum-aligned content from every math strand from 1st to 8th grade.

Teachers can use Prodigy Math as a Response to Intervention tool , to differentiate math content , to reinforce and supplement lesson plans and more!

Plus, teachers and admins can access comprehensive data reports illustrating growth, performance, and student engagement — at home or at school.

One of the biggest results I've seen is that Prodigy is able to take students who struggle with and dislike Math, and get them to love Math again! The students ask often when they are going to get to play Prodigy. They see it as fun, but as their teacher, I know they are practicing and mastering math standards.   Laney Park , K-5 Administrator, Hall County School District

Make curriculum-aligned math learning more engaging than ever this year!

2. Khan Academy

In 2008, Salman Khan created Khan Academy, a non-profit educational organization whose mission is to provide free world-class education for everyone.

Most people visit this website for one-off videos. However, teachers can also join Khan Academy using a Teacher account if they want to utilize personalized, standards-aligned math content into their daily instruction.

Just filter the available math content by grade and assign practice exercises, videos, and articles -- all while tracking student progress.

3.  CueThink

Created for students in 2nd to 12th grade, this innovative peer-to-peer application seeks to improve critical thinking skills by making math social.

Focusing on the social aspect of math, according to CueThink, will help foster a growth mindset and enable students to perceive challenges as opportunities.

Using this online program, students apply mathematician George Pólya’s four phases when tackling math problems: understand, plan, solve, and review. They’ll ask questions like:

• What does this make you wonder about?
• What do you notice?
• What’s your estimate?
• What other questions can I ask?

Once they settle on a strategy and devise a plan, students will answer the question and review their answer.

4.  SuperTeacherTools

Teachers can access a wide variety of free tools and resources for their middle school students. From the popular Jeopardy game to the upbeat Rocketship game, these are perfect for end-of-unit or end-of-chapter reviews!

SuperTeacherTools’ games are also designed to be as simple as possible for teachers. That means they’re easy to set up and easy to run. And if teachers experience difficulties, the Help Desk contains visual instructions.

Plus, everything on this website is free for both teachers and students to use.

Endless engagement. Adaptive content. Standards-aligned.

Join millions of teachers using Prodigy to make math fun, differentiate instruction and help students love learning!

5.  Illuminations

The National Council of Teachers of Mathematics started Illuminations in an effort to increase educators’ access to quality standards-based resources for teaching and learning math.

Students in middle school will find over 100 activities (e.g., virtual manipulatives, applets, and games). There are also Calculation Nation games wherein students can challenge themselves as well as opponents from anywhere in the world.

Simply search for resources by grade, topic, or standard! Teachers can easily incorporate these interactive activities into their lesson plans to help keep students engaged.

One user described MathTV as the Netflix of online learning. This website is home to 10 thousand free math videos covering topics such as algebra, geometry, trigonometry, and calculus. However, their “Basic Math” topic will be most relevant for middle school students.

Behind the videos are 34 great tutors. They have so many because their varied approaches to the same math topics and problems help students see how to solve problems differently.

MathTV has been optimized for all mobile devices so students can watch them on the go or teachers can incorporate them into daily mathematics instruction.

7.  Illustrative Mathematics

In 2017, Illustrative Mathematics 6-8 was the first open educational resource and core curriculum they released. Within a couple of years, EdReports gave it the highest rating among middle school math programs. As reported by PR Newswire :

The problem-based curriculum sparks discussion and enjoyment of mathematics. Students learn by doing, solving problems in mathematical and real-world contexts, and constructing arguments using precise language.

Illustrative Mathematics designs lessons teachers can use for independent, group, and whole-class work. After selecting a grade, they can choose the relevant unit, chapter, and lesson. It will bring you to a page with preparation instructions, a lesson plan, and practice problems.

8.  PBS Math Club

This collection of videos is aligned to the Common Core Standard for 6th to 9th grade, covering topics from integers and equations to negative numbers and statistics.

Helping students with homework -- and making them laugh -- PBS Math Club also uses pop culture references to explain math concepts.

And if the one to six-minute videos are too long, check out their 15-second InstaCram versions!

This innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge seeks to develop confident, resilient problem-solvers.

NRICH -- as its name suggests -- aims to enrich the mathematical experiences of all learners by providing thousands of free online resources for Pre-K to 12th grade that are:

• Thought-provoking
• Challenging

Middle school students can, for example, play a collection of games called “Is there a better way?” wherein each game has multiple routes to the same solution. Hearing how students arrive at solutions differently will deepen their understanding and broaden their problem-solving skills.

10.  Get the Math

Geared toward middle and high schoolers, this website aims to reveal the real-life application of algebra through combining video and web interactivity.

Teachers can switch up their algebra lessons and show their students short videos about how young professionals use math in music, fashion, video games, restaurants, basketball, and special effects.

At the end of each video, the featured individual will pose a challenge to two teams of students. But the creators of Get the Math highly encourage classes to try and complete the challenges by applying the same algebraic concepts.

Note : This website is no longer actively maintained, so some material and features may be unavailable.

11.  Math is Fun

Despite this website’s dated appearance, the math resource that started on April 19, 2000 still gets updated today! Math is Fun is a simple yet fun resource to help engage students while learning math.

The content covers topics including data, geometry, numbers, money, algebra, calculus, physics, and measurement. In addition to exercises, teachers can also direct their students to the game, puzzle, and activity sections of the website.

For the teachers who are in need of inspiration, there is a Teacher’s Page with ideas to help get their creative juices flowing. They’ll find tools such as symmetry artist, tessellation artist, function grapher, math puzzles , and more.

12.  Moby Interactive

A branch of the award-winning online paid resource MobyMax, Moby Interactive gives teachers free access to whiteboard activities, skills review, and printable worksheets which include over half a million problems and manipulatives.

Whether teachers want to use existing problems from MobyMax’s curriculum or create their own, the Whiteboard Activities module can help engage students of all learning levels.

The Skills Review will also evaluate students using a placement test so teachers can appropriately plan their lessons to help close student learning gaps.

13.  National Library of Virtual Manipulatives

Dating back to 1999 and created by Utah State University, this is a digital library of web-based interactive tools teachers can use to help teach math concepts from Pre-K to 12th grade.

Teachers and students alike find the most success when using these tools combined with in-class lessons, homework, or traditional practice.

It’s important to note that tech-savvy students may comment on this website’s datedness. As Common Sense states: “Students who struggle with difficult math concepts may like the trial-and-error format, but the vintage design and unclear feedback may scare some away.”

14.  Math Antics

Rob and Jeremy of Math Plus Motion create all the content on this website. The goal of Math Antics is to make learning math a little easier for everyone through simple yet engaging math resources.

The math videos you’ll find are not categorized by grade but by topic. However, the majority of content they cover falls between U.S. 3rd and 8th grade.

All of their video lessons covering topics -- arithmetic, fractions, geometry, percents, and algebra -- are free! To access their print-based exercises, example videos, worksheets and answer sheets, you can subscribe for $20 per year.

Final thoughts about math websites for middle school

Every school -- every classroom -- presents incredibly diverse learning styles. Using this list, the teachers in your building or district will surely find math content that satisfies students’ many learning needs.

Some of the websites emphasize math word problems and mental math practices , whereas others focus on specific math concepts such as multiplication .

However, they all have one thing in common: helping engage students as they learn to love math.

Ready to engage your students and help them to love learning math?

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Early math review

Kindergarten, basic geometry and measurement, pre-algebra, algebra basics, high school geometry, trigonometry, statistics and probability, high school statistics, ap®︎/college statistics, college algebra, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra, 6th grade (illustrative mathematics), 7th grade (illustrative mathematics), 8th grade (illustrative mathematics), algebra 1 (illustrative mathematics), 3rd grade (eureka math/engageny), 4th grade (eureka math/engageny), 5th grade (eureka math/engageny), 6th grade (eureka math/engageny), 7th grade (eureka math/engageny), 8th grade (eureka math/engageny), algebra 1 (eureka math/engageny), geometry (eureka math/engageny), algebra 2 (eureka math/engageny), precalculus (eureka math/engageny), 3rd grade foundations (eureka math/engageny), 4th grade foundations (eureka math/engageny), 5th grade foundations (eureka math/engageny), 6th grade foundations (eureka math/engageny), 7th grade foundations (eureka math/engageny), 8th grade foundations (eureka math/engageny), integrated math 1, integrated math 2, integrated math 3, arithmetic (all content), algebra (all content), geometry (all content), get ready for 3rd grade, get ready for 4th grade, get ready for 5th grade, get ready for 6th grade, get ready for 7th grade, get ready for 8th grade, get ready for algebra 1, get ready for geometry, get ready for algebra 2, get ready for precalculus, map recommended practice, get ready for ap® calculus, get ready for ap® statistics, grade 6 math (fl b.e.s.t.), grade 7 math (fl b.e.s.t.), grade 8 math (fl b.e.s.t.), algebra 1 (fl b.e.s.t.), geometry (fl b.e.s.t.), algebra 2 (fl b.e.s.t.), grade 6 (va sol), grade 7 (va sol), grade 8 (va sol), grade 3 (fl b.e.s.t.), grade 4 math (fl b.e.s.t.), grade 5 math (fl b.e.s.t.), class 9 (od), class 10 (od).

Summer is a great time to explore cool problems and keep your skills sharp!   Schedule a class today !

Need help finding a book? Have questions about particular items?

AoPS Curriculum

A comprehensive textbook covering Algebra 2 and topics in Precalculus. This book is the follow-up to the acclaimed Introduction to Algebra textbook. In addition to offering standard Algebra 2 and Precalculus curriculum, the text includes advanced topics such as those problem solving strategies required for success on the AMC and AIME competitions. Related course: Intermediate Algebra

A comprehensive textbook covering precalculus topics. Specific topics covered include trigonometry, complex numbers, vectors, and matrices. Includes many problems from the AIME and USAMO competitions. Related course: Precalculus

A comprehensive textbook covering single-variable calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, and differential equations. Related course: Calculus

Beast Academy

• Guide materials are written in an engaging, comic-book style which provides comprehensive, rigorous instruction.
• Practice materials provide hundreds of exercises, problems, puzzles, and games to reinforce the lessons from the Guide.

In Level 1, each unit (A through D) contains both Guide and Practice materials in a single book. In Levels 2-5, the Guide and Practice materials are separated into two books per unit.

Beast Academy covers the core fundamentals and then goes well beyond these basics to present material at a deeper and more challenging level than a typical elementary-school math curriculum.

Visit BeastAcademy.com to learn more about our Beast Academy Online learning system.

Beast Academy 1A is the first part in a four-part series for students ages 6–8. Level 1A includes chapters on counting, shapes, and comparing.

Beast Academy 1B is the second part in a four-part series for students ages 6–8. Level 1B includes chapters on addition, subtraction, and categories.

Beast Academy 1C is the third part in a four-part series for students ages 6–8. Level 1C includes chapters on addition & subtraction, comparison, and patterns.

Beast Academy 1D is the fourth part in a four-part series for students ages 6–8. Level 1D includes chapters on big numbers, measurement, and problem solving.

Beast Academy Guide 2A and its companion Practice 2A are the first part in a four-part series for students ages 7–9. Level 2A includes chapters on place value, comparing numbers, and addition.

Beast Academy Guide 2B and its companion Practice 2B are the second part in a four-part series for students ages 7–9. Level 2B includes chapters on subtraction, expressions, and problem solving.

Beast Academy Guide 2C and its companion Practice 2C are the third part in a four-part series for students ages 7–9. Level 2C includes chapters on measurement, addition and subtraction strategies, and odds & evens.

Beast Academy Guide 2D and its companion Practice 2D are the fourth part in a four-part series for students ages 7–9. Level 2D includes chapters on big numbers, algorithms, and problem solving.

Beast Academy Guide 3A and its companion Practice 3A are the first part in a four-part series for students ages 8–10. Level 3A includes chapters on shape classification, skip-counting, and perimeter and area.

Beast Academy Guide 3B and its companion Practice 3B are the second part in a four-part series for students ages 8–10. Level 3B includes chapters on multiplication, perfect squares, and the distributive property.

Beast Academy Guide 3C and its companion Practice 3C are the third part in a four-part series for students ages 8–10. Level 3C includes chapters on variables, division, and units and measure.

Beast Academy Guide 3D and its companion Practice 3D are the fourth part in a four-part series for students ages 8–10. Level 3D includes chapters on fractions, estimation, and area.

Beast Academy Guide 4A and its companion Practice 4A are the first part in a four-part series for students ages 9–12. Level 4A includes chapters on shapes, multiplication, and exponents.

Beast Academy Guide 4B and its companion Practice 4B are the second part in a four-part series for students ages 9–12. Level 4B includes chapters on counting, division, and logic.

Beast Academy Guide 4C and its companion Practice 4C are the third part in a four-part series for students ages 9–12. Level 4C includes chapters on factors, fractions, and integers.

Beast Academy Guide 5A and its companion Practice 5A are the first part in a four-part series for students ages 10–13. Level 5A includes chapters on 3D solids, integers, and expressions & equations.

Beast Academy Guide 5B and its companion Practice 5B are the second part in a four-part series for students ages 10–13. Level 5B includes chapters on statistics, factors & multiples, and fractions.

Beast Academy Guide 5C and its companion Practice 5C are the third part in a four-part series for students ages 10–13. Level 5C includes chapters on sequences, ratios & rates, and decimals.

Beast Academy Guide 5D and its companion Practice 5D are the fourth part in a four-part series for students ages 10–13. Level 5D includes chapters on percents, square roots, and exponents.

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Teachers: Resources for Middle Grades (6-8)

The North Carolina Collaborative for Mathematics Learning (NC 2 ML) aims to support NC math educators in implementing the revised mathematics content standards in ways that align with what we know from research on students’ mathematical thinking, mathematics teaching, and teacher learning. To do so, we bring together mathematics educators to co-design research-based resources and professional learning opportunities.

6-8 Resources Home

First Week Problem Solving Tasks

The Instructional Frameworks at each grade level recommend spending the first week of school doing general, high cognitive demand tasks with students in order to establish strong communication practices (SMP 3). Students can be enculturated into the discourse, listening and writing practices essential for strong mathematical reasoning while working these problems.

Additional Supporting Articles

Herbel-Eisenmenn, B. & Breyfogle, M. (2005). Questioning our patterns of questioning. Mathematics Teaching in the Middle School, 10(9), 484-489.

Stephan, M. (2014). Establishing standards for mathematical practice. Mathematics Teaching in the Middle School, 19(9), 532-538.

• K-5 Resources
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In this intensive summer course, middle school students develop the critical math skills and strategies they need to succeed in prestigious middle school competitions.

Middle School Math Contests: Number Theory and Geometry is designed for students in grades 6 through 8 who want to excel at math competitions such as MATHCOUNTS and the American Mathematics Competitions 8 (AMC 8), and prepare for high school events like American Mathematics Competitions 10 (AMC 10).

Our expert instructors use content developed by the Art of Problem Solving curriculum team to teach Middle School Math Contests: Number Theory and Geometry. As a deep exploration of challenging mathematics, AoPS curriculum prepares students for success at top universities, and competitive careers. No books are required for this class.

Middle school math contests are a launching pad for many of the best math students. In this course, we draw problems from several middle-school contests, including MATHCOUNTS and the American Mathematics Competitions 8 (AMC 8), as well as early high-school contests like the American Mathematics Competitions 10 (AMC 10). We introduce students to important topics in number theory and geometry, and work both individually and collaboratively to solve challenging problems.

During the camp, students also participate in individual and team practice competitions to develop both the mathematical skills and test-taking experience that will prepare them for the upcoming school year.

Our instructors hold classes virtually, in a small-sized (10-16 students) videoconferencing classroom.

There is no required homework for Middle School Math Contests: Number Theory and Geometry. However, we've prepared more materials than we can cover during class and many students continue working on them after class for extra practice.

If you drop a summer course before the start of your first class session, we'll issue a full refund for the course tuition. No refunds will be issued for withdrawing from a summer course after the start of your first class session.

Our summer course offerings meet five days a week, Monday through Friday. We offer this course in two timing formats. Both cover the same course material.

• The two-week course meets for 3 hours each day.
• The four-week course meets for 1.5 hours each day.

• Grades 6-12
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80+ Awesome Websites for Teaching and Learning Math in 2023

Bookmark this list STAT!

The internet is full of incredible new ways to teach and learn math, from games and videos to lessons and even complete curricula. Teachers, students, and parents can all benefit from these online learning resources. This list of the best math websites has options for every skill level, from learning to count to advanced math like calculus. You’re bound to find a new favorite!

• Comprehensive Math Programs
• Interactive Tools to Use in Instruction
• Games and Activities for Students
• Resources for Teachers

These are some of the best math websites that provide complete standards-based math curricula. Try them if you’re looking for a new way to teach math at your school. These can be good choices for homeschoolers too.

The littlest learners will benefit from ABCMouse’s complete online curriculum, including math. The progressive program builds on the math skills kids need to master. (Grades pre-K–2; monthly and annual subscriptions available)

Adventure Academy

From the same company that created ABCMouse, Adventure Academy is geared toward older elementary kids. It offers programs in math, language arts, science, and social studies. (Grades 3–8; monthly and annual subscriptions available)

Art of Problem Solving

Along with textbooks, Art of Problem Solving has a stable of robust online resources. You’ll find videos, math problems from math contests, and online classes. (Grades 5–12; pricing varies by program)

Buzzmath is one of the best math websites for middle schoolers. It helps them practice their math skills with high-quality problems, gives immediate and detailed feedback, and lets students progress at their own pace. Randomly generated values let students retry problems to obtain mastery. Teachers also receive detailed results that help them guide and monitor student progress. (Grades 1–9; free demo with subscription plans for students and families)

Make free detailed charts of all kinds, including bar graphs, pie charts, scatter plots, and more. (K–12; free)

Corbettmaths

This resource from England provides math videos with associated math practice questions and worksheets. It’s basic, but it’s a good way to get no-cost practice. (Grades K–12; free)

This National Science Foundation–funded program helps students strengthen math skills. Students will learn to solve problems and explain their thinking using mathematician George Polya’s four-step approach. (Grades K–12; priced per teacher or school, with free trial available)

Desmos Math

A blend of paper and technology puts student ideas at the center of learning. Lessons pose problems that invite a variety of approaches, engaging kids more fully. (Grades 6–8; contact them for pricing)

An adaptive learning platform designed to complement classroom instruction and deliver results. Includes resources for teachers, student data reports, and instructive insights. (Grades K–8; home users can sign up for individual or family subscriptions, schools pay per student or school)

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Take courses online from universities across the world, in math subjects ranging from statistics to calculus and many other options. (Grades 9+; audit courses are free, while courses for credit vary in cost)

Effortless Math

With dozens of online math courses, along with puzzles, worksheets, tips, and e-books, Effortless Math is a one-stop shop for math needs. (Grades K–12; cost varies by item)

eMathInstruction

This site provides e-textbooks, answer keys, video lessons, and printables. Topics include Algebra 1 and 2, geometry, and trigonometry. (Grades 6–12; free lessons plans, homework sets, and videos; paid subscriptions include answer keys, assessments, and more)

First in Math

We love the friendly competition and game-based content offered by First in Math. Kids gain skills practice and fluency as they play games targeted toward fact proficiency and logical thinking. (Grades K–8; subscriptions available for schools and parents, with 45-day free trial)

Freckle Education

This site allows kids to practice math at their own level and pace. It has more than 30,000 math questions, starting with a diagnostic that assigns material at just the right level. Freckles also features lessons, assessments, and reports for teachers. (Grades K–12; basic use is free for teachers; premium subscriptions available)

Illuminations

This site from the National Council of Teachers of Mathematics (NCTM) features complete lesson plans, mobile games for students, interactive activities, and brainteasers. (Grades pre-K–12; free)

Illustrative Mathematics

Get high-quality educational resources for teachers and students. Excellent math tasks, videos, lesson plans, and problem-based curriculum modules. (Grades K–12; free)

Imagine Learning

Formerly known as Edgenuity, Imagine Learning offers several online digital curricula for primary or supplementary instruction. Give students the support they need exactly when they need it. (Grades pre-K–12; priced per subject, per student)

Istation makes personalized learning easy with computer-adaptive instruction, assessments, personalized data profiles, and teacher resources. Includes digital lessons and face-to-face teaching strategies. (Grades pre-K–8; priced per student)

Make math about more than numbers with engaging items, real-world scenarios, and unlimited questions. Teachers choose the strand and then set up students to work independently. (Grades pre-K–12; free 30-day trial, pricing is per classroom or site)

Khan Academy

Khan Academy is on a mission to give a free, world-class education to anyone, anywhere. Their personalized learning resources make them one of the best math websites available for all ages, in a huge array of subjects. (Grades K–12; free)

Here’s an online learning space that is engaging, supportive, and designed to get kids interested in math. (Grades K–12; yearly subscription required; school and family pricing available)

MIND Research Institute

Through ongoing research, MIND Research Institute continues to investigate key questions about learning, mathematics, and how the brain works. ST Math is their pre-K–8 visual instructional program, helping teachers engage kids more deeply in math learning. (Grades pre-K–8; pricing based on total school enrollment)

This award-winning program finds and fixes learning gaps with the power of personalized learning. The three-pronged approach features personalized learning, pinpoint assessments, and an interactive classroom. (Grades K–8; pricing per student, school, and district)

Origo Education

Stepping Stones 2.0 from Origo is a unique and comprehensive curriculum that combines print and digital materials. It features problem-solving activities, strategies, and practice. (Grades pre-K–6; price varies by program)

PowerMyLearning

This organization is geared toward students, teachers, and families in low-income communities. The program features school workshops, instructional coaching, and professional learning communities. (Grades K–12; try limited Family Playlists for free, request consultation for pricing)

Prodigy Math

Join the 1 million teachers already using Prodigy Math in their classrooms at no cost. This fun and engaging curriculum-aligned game lets students engage in a fun wizarding world that motivates them to practice more math than ever. It contains 1,500+ standard-aligned skills. Plus you can track student progress with a teacher dashboard that provides instant feedback on areas of progress with no grading necessary. (Grades 1–8; free for teachers, monthly memberships available for parents)

Enter an interactive, game-based learning world that motivates kids through rewards. Features include a daily challenge, step-by-step lessons, and parent connections. (Grades K–5; 30-day free trial, then monthly subscription)

SplashLearn

Boost confidence, increase scores, and get ahead. Fun for enrichment or regular practice. (Grades K–5; free for teachers and schools, monthly subscriptions available for parents)

Math games make learning fun! Focus on specific skills, target interventions, and make assessment easy. (Grades K–8; teachers can try six games for free, subscription unlocks more games and features)

Tang Math strives to provide unparalleled math lessons for students as well as professional development for in-service teachers. Find games and puzzles, plus other resources like free downloads, worksheets/word problems, and math centers. (Grades K–5; free)

Woot Math offers adaptive practice for teaching rational numbers and related topics, such as fractions, decimals, and ratios. (Grades 3–7; free tier for teachers, additional features available for extra cost)

Personalized math curriculum that includes digital lessons and small-group instruction. Also has online modules, workbooks and answer keys, and professional development. (Grades K–5; free for individual teachers and classrooms)

These are some of the best math websites that offer engaging videos and tools to use in your daily math instruction.

Engaging animated learning videos, games, quizzes, and activities to encourage kids on their unique learning path. (Grades pre-K–8; teacher, school, and district pricing available, as well as parent or homeschool options)

Teachers prep an assignment, students work on their devices, everybody gives feedback, and the teacher sees it all! (Grades K–12; free basic plan, Pro accounts unlock more features)

A website that allows teachers to assign math practice content to their students. Students get immediate feedback as they complete the problems. (Middle school+; free, with premium school and district plans available)

Desmos Graphing Calculator

An online graphing calculator that students can use for free. Includes a teacher-centric activity builder for creating digital math activities. (Grades 9–12; free)

Save money by using virtual math manipulatives like geoboards, base-10 blocks, 10-frames, pattern blocks, and more. (Grades K–12; free)

An award-winning series of math apps that harness the power of digital tools to create a better, deeper, more fun learning experience. Blogs such as “Making Math Social” and “Saying No to Math Anxiety” are included as resources for teachers and parents. (Grades K–6; priced per app, with free trials for teachers and bulk pricing for schools)

Flocabulary

Use hip-hop to teach math! Flocabulary offers songs, activities, and videos. (Grades K–12; teacher, school, and district pricing available)

Upload your own materials or build them from scratch, find something pre-made, act on live responses, and track student growth over time. (Grades K–12; free, premium subscription unlocks additional features)

Another graphing calculator for functions, geometry, algebra, calculus, statistics, and 3D math, along with a variety of math resources. (Grades 9–12; free)

You know it. Your kids love it. Why not use it to teach math? Engage your students with this game-based classroom-response system played by the whole class in real time. Multiple-choice questions are projected on the screen, then students answer with their smartphone, tablet, or computer. (Grades K–12; free, Kahoot+ AccessPass subscription offers premium content)

Math Central

Run by the University of Regina in Canada, this site offers free resources for math teachers and their students, including a database where users can search for the answers to math questions. Their “Mathematics With a Human Face” page includes information about careers in mathematics as well as profiles of mathematicians. (Grades K–12; free)

Teachers know that one of the best ways to make sure learning sticks is through song. Numberock features ad-free music videos of songs about math topics, like fractions, money, and integers, produced by an Emmy Award–winning studio. Numberock also has anchor charts, worksheets, comics, games, and more. (Grades K–5; limited free videos, monthly subscription offers six-month free trial)

Transform presentations into classroom conversations with Pear Deck for Google Slides. Effortlessly build engaging instructional content, formative assessments, and interactive questions. (Grades K–12; basic access is free, premium subscriptions unlock more features)

Take a photo of an equation, and this site will explain how to solve it, step-by-step. It even explains different options to get to the answer. Students can use it for help with homework, and teachers can incorporate it in their own lesson plans. (Grades 6+, free with premium options available)

TeacherTube

Think of this site like YouTube but specifically for teachers and schools. Find videos created by other teachers, and upload your own to share. (Grades K–12; free)

These are some of the best interactive math websites and provide students with instruction and independent practice.

Arithmetic Four

Two users play a game in which each player tries to connect four game pieces in a row (like Connect 4). The players answer math questions to connect the pieces. The teacher chooses how much time each player has to answer, the level of difficulty, and the type of math problem. (Grades 2–8; free)

Coolmath Games

Yes, math games can be cool! Check out the hundreds of games on this site and on Coolmath4kids . (Grades K–12; free with ads, premium subscription removes ads and provides extra features)

Figure This!

Figure This is a site designed to encourage families to practice math together. It includes fun and engaging math games and high-quality challenges. It even offers challenges in Spanish. (Grades 6–8; free)

Funbrain has been helping students learn key math concepts and develop crucial skills since 1997. Students can choose from a slew of games. Why is it one of the best math websites? It’s all free! (Grades pre-K–8; free)

Get the Math

Get the Math is about algebra in the real world. Students see how professionals use math in music, fashion, video games, restaurants, basketball, and special effects. Then take on interactive challenges related to those careers. (Grades 6–12; free)

Your students will love fun math games like Speed Math Deluxe, Mystery Math, Place Value Game, and more. (Grades 3–12; free)

A popular game-based site for online math-learning resources. It covers algebra, geometry, statistics, and more. (Grades K–12; schools can contact them for a quote; parents pay per child)

Math Game Time

There are dozens of games to explore here, organized by grade and subject. (Grades pre-K–7; free)

MATHHelp.com

In-depth lessons with videos, guided practice, interactive self-tests, and more. (Grades 5–12; monthly or yearly subscription required)

Math Is Fun

Find general information along with games and practice for a variety of math subjects, including geometry, algebra, calculus, physics, and more. (Grades 6–12; free)

Math Playground

More than 425 math games, logic puzzles, and brain workouts for students to practice their math skills. (Grades 1–6; free with ads, Premium removes ads and provides extra features)

Most learners do best when they can see a problem walk-through, step-by-step. This site features multiple example problems, with walk-throughs by three separate instructors (including one in Spanish). They offer some basic math but are focused on advanced subjects from algebra on up. (Grades 6–12; free)

Thousands of original math games, workshops, and practice modules, as well as math printables. (Grades 1–6; monthly or yearly subscription required)

Multiplication.com

Need to master your multiplication facts? This is the site to try! Fun games and memory-building strategies will help students tackle this key skill. (Grades 2–6; free, with Premium membership available for extra features)

Numeracy Ninjas

This is a free intervention tool designed to fill gaps in students’ mental calculation skills and empower them with number fluency. Students can earn ninja belts of different colors for their skill level. (Grades 2–8; free)

PBS Math Club

From PBS Learning Media, this is one of the best math websites for middle schoolers. They love this entertaining video blog. Not only does each episode cover Common Core Standards, it makes math learning culturally relevant with pop-culture references. (Grades 6–9; free)

Students can create study flash cards, play educational games, practice skills, collaborate with other students, and more. (Grades 5–12; free, QuizletPlus provides additional features)

Another resource to help students build fact fluency. Each game is tailored to students’ ability levels. (Grades 2–6; school and home licenses available)

Sheppard Software

Tons of fun and educational online math games, from basic operations to algebra and geometry. (Grades K–6; free)

Simple math test activities for teachers and students, from beginning math operations to calculus. You set the skill level, number of problems, and time limit. A report, which tallies right and wrong answers, is provided after each quiz. (Grades 3–12; free)

Toy Theater

How would your students like to learn multiplication while shooting hoops? They can do that and more at Toy Theater, which teaches early math concepts through game-based learning. (Grades K–5; free)

Wolfram MathWorld

Upper-level math students will appreciate the no-frills information that’s easy to find on this site. Get overviews and see examples of advanced math subjects. (High school+; free)

XtraMath is like a daily math vitamin. An interactive online tool that helps students practice and master basic arithmetic facts, it’s quick and easy to use. Weekly emails provide progress reports for teachers and parents. (Grades K–8; free, with premium licenses that offer additional features)

These are some of the best math websites that provide lesson-planning resources and professional-development materials.

Get differentiated, standards-aligned math practice problems that you can generate, assign, and evaluate online. (Grades 6–8; limited free plan with paid plans available)

Casio has a lot more to offer math teachers besides calculators. Their Worldwide Education Site is packed with free resources like worksheets, activities, teaching videos, how-to videos, font sets, and software options.

Citizen Math

Formerly known as Mathalicious, this site provides supplemental math lessons. Experience an immersive, participatory approach that makes learning and teaching more rewarding. (Grades 6–12; monthly or yearly subscriptions available)

Common Core Sheets

Find math worksheets for just about any area of study. Use them for planning lessons, review, and independent work. (Grades K–6; free)

Education.com

Here’s a reliable site for worksheets, games, and even lessons plans. They cover a variety of subjects, with lots of math options to choose from. (Grades K–8; limited free access, monthly subscriptions unlock all content)

This platform allows teachers to create technology-enhanced online math assessments from a huge question bank. (Grades K–12; free teacher accounts)

Kuta Software

For teachers of pre-algebra through calculus. Create the math worksheets you need, exactly how you want them, in minutes. You can also create customizable homework, quizzes, and tests. (Grades 8–12; free two-week trial, then single-user and site licenses available)

Mashup Math

A creative solution that aims to revive students’ passion and interest in math. Mashup Math has a library of 100+ math video lessons as well as a YouTube channel that features new math video lessons every week. A free e-book of math challenges is also available. (Grades K–8; free)

Math-Aids.com

Dynamically created math worksheets for students, teachers, and parents. (Grades K–10; free with ads, paid membership removes ads)

MathsBot.com

Tools for math teachers, including bell ringers and drills, math tools and manipulatives, question generators, printables, and puzzles. (Grades K–12; free with ads)

National Library of Virtual Manipulatives (NLVM)

This National Science Foundation–supported project provides a large library of uniquely interactive, web-based virtual manipulatives and concept tutorials for math instruction. (Grades K–12; free)

TeacherMade

Convert all of your paper assignments, quizzes, homework, etc., into digital activities delivered online. (Grades K–12; free basic version, Pro plan adds multiple extra features)

TeacherVision

For a very affordable monthly fee, gain access to thousands of resources created by teachers like you. They cover every topic and every grade level. (Grades K–12; monthly subscription)

Topmarks is one of the best U.K.-based math websites that provides a database of resources for teachers as well as online learning games for students. (Grades pre-K–8; free)

Varsity Learning

The Varsity Learning Online Math Management System is one of the best math websites because it provides course templates, assignments, an online teacher’s assistant, and thousands of practice problems so you can get organized, save assignments and videos on the web, share resources, and incorporate technology in your classroom. (Grades: 7–12; free)

Virtual Nerd

More than 1,500 video lessons ranging from middle-grade math through Algebra 2. (Grades 6–12; free)

What’s on your list of the best math websites? Come share your ideas in our We Are Teachers HELPLINE group on Facebook.

Plus, our favorite websites for teaching kids and teens to code ..

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Problem Solving the Thinking Blocks® Way!

We updated our thinking blocks suite of learning tools with all new features. read aloud word problems - visual prompts - better models - engaging themes - mobile friendly.

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Fraction of a Set A

Fraction of a Set B

Fraction of a Set C

Add and Subtract A

Add and Subtract B

Multiply and Divide

% of a Number

Taxes, Tips, Sales

% Challenge A

% Challenge B

Three Quantities

Math Wheels for Note-taking?

Help Middle School Math Students Improve Problem Solving Skills

Tips to develop problem solving skills and math communication.

• Do they get to the end of a word problem and then guess at the operation they need to choose, maybe not realizing that there are multiple operations?

What methods have you found to help those who struggle? What methods can you use to help each student at his or her current level?

I’ve used many strategies over the years, to help students sort out how to make sense of word problems and how to approach them. These methods didn’t have a specific name at the time (like close reading or talking to the text), but some would fit into these categories.

Prompts to Help Focus One of the methods I found to be most helpful for my math students to develop both their math problem solving skills AND their math communication skills was having them write responses to specific prompts before they attempted to solve a word problem. The prompts are general and applicable to any problem:

• “What I know…because,” from the problem
• “What I know…because,” from background information and
• “What I need to know….,” or what the problem is asking

We started using this framework many years ago, when writing in math/open-ended questions was new on the standardized test scene (new in my state any way:-). Every couple of days, we did sample problems that incorporated  various strategies to solve problems  – make a simpler problem, make a table, make an organized list, write an equation, etc. And as we practiced, the students became excellent at communicating what they understood about the information provided in the problem, as well as what they needed to figure out and  how  they did so.

• We’d typically underline or highlight important information and cross out extra information.
• Instead of just highlighting/underlining, students also wrote the information, putting it into their own words as much as possible.
• Writing the information helps solidify it in their minds, and if they reword it or add detail to clarify the meaning, they understand it a bit better.

For “what I need to know,” students highlight/underline what the question is asking and then wrote it in their own words.

For example , with a problem like this: Steve runs every other day and trains with weights every 3rd day. If he does both on Monday, how many times will he do both on the same day during the next 2 weeks?

Students might write: What I know:

• Runs every 2 days. I know this because every other day means the same things as every 2 days.
• Weights every 3rd day – the problem states this information. 
• Runs and uses weights on Monday – the problem states that he does both activities on Monday.

What I need to know:

• I need to figure out how many times will Steve run and use weights on the same day, during the next 14 days – I know that 2 weeks is the same as 14 days. 

After students completed these written parts, we’d discuss what they identified as what they knew and what they needed to know,  before getting started with the solving. Then students would solve on their own and write a paragraph to explain exactly what they did to solve the problem.

Solution Explanation Example: To solve this problem, I decided to make a table to find how many days Steve will do both activities.

• Since I want to know how many times this happened in 2 weeks, I made the table 2 rows of 7, and I labeled the days of the week at the top of the table, starting with Monday.
• In the first square of the table, I wrote an R and a W, since Steve did both on Monday.
• Then I wrote an R in every other square, and I wrote a W in every 3rd square.
• When I was finished, I counted how many squares had both R and W in them. There were 3 days total (including the Monday he started), so the answer is: Steve will do both activities on the same day 3 different times in 2 weeks.

Once students finished solving and writing their paragraphs, several of them would read their paragraphs to the class, giving students the opportunity to see if they could follow their peers’ explanations, compare the explanations to their own to see how similar they were, and learn/consider a new method if a student had solved a different way.

While this process did take a while, it was SO worth it. It really helped students break down the problems, become more in tune with how they were solving, and resulted in less “random” use of operations/solving methods. It also greatly improved their math communication abilities.

These days, with shorter math classes:-(, and therefore less time to write, I’ve consolidated the “what I know” and “what I need to know” into ‘Find out,’ so it encompasses both the important info the question that needs to be answered. Where I used to have several students read their examples with the class, I now have students do a quick “pair-share” after the first stages, and then share a couple of the final explanations with the entire class. It still takes a good chunk of time, but I believe that time is made up with fewer struggles as we move through the year.

Tips When Reading Word Problems

A few tips  to help students as they read the problem:

• Underline important information
• Cross out information that isn’t needed
• Read carefully to find numbers written as words and write the # above the word
• Underline or highlight words that indicate operations and add the operation symbol nearby
• When writing, write the information with fewer words, so key info doesn’t get “lost”

I created some handy bookmarks that I give my students, to help them remember some of these ideas:-)

Another Example of Solving a Word Problem

Manny spent 64 minutes on 3 different subway trains. The first train ride was twice as long as the second. The third train ride was 10 minutes longer than the other two combined. He arrived at his destination at 4:00 in the afternoon. How long was each train ride?

What I know:

• 3 different trains
• Train 1 = 2 x as long as train 2 (change words into numbers – sub words with symbols – x instead of times)
• Train 3  = 10 min longer than train 1 + train 2

I need to find the length of each train ride.

Solution Explanation: I decided to write an equation and use  x  as the variable to represent the shortest ride.

I know that all 3 rides add up to 64, so 64 is one side of the equation.

• I think Train 2 is the shortest time, because Train One is 2 times as long, so Train Two is  x  and Train One is  2x .
• Train Three is 10 more than the other trains combined, so Train Three is  x + 2x + 10 .

This gives me the equation   x + 2x + (x + 2x + 10) = 64 .

1) I solve by combining all the like terms, which gives me 6x + 10 = 64. 

2) Then I subtract 10 from both sides to isolate the variable and that gives me 6x = 54 .

3) Next I divide both sides by 6 and get x = 9 .

I have to  figure out the other 2 trains based on Train Two = 9. If T rain Two = 9 , then T rain One  (2 (9)) =  18  and T rain Three  (9 + 2(9) + 10 ) =  37 .

• 9 + 18 + 37 = 64, which is the total number of minutes Manny spend on the trains

I hope this is helpful!!

What methods are most helpful for your students to continually develop their math problem solving skills?

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10 Math Problem Solving Activities for Middle School

Published on june 26, 2017 at 7:25 am by ethan jacobs in lists , news.

Looking for some math problem-solving activities for middle school ? Good, you’re at the right page then.

Right before children enter Middle School (around the age of 11 or 12), they enter a critical developmental stage known as Piaget’s fourth and final stage of cognitive development.  It’s at this stage that children demonstrate marked growth in a number of areas, ranging from making hypotheses and inferences to thinking abstractly and using advanced reasoning skills.  In line with this crucial phase of a child’s development, Middle School Math curricula are designed to stretch the bounds of adolescent thinking while also helping them to establish new skills and sound mathematical habits.

One way that educators try to ensure this is through common core standards that can be applied to Middle School-aged students.  These standards seek to achieve eight distinct objectives, which help foster the developmental transition addressed by Piaget.  The objectives:

• Make sense of problems and persevere in solving them;
• Reason abstractly and quantitatively;
• Construct viable arguments and critique the reasoning of others;
• Model with mathematics;
• Use appropriate tools strategically;
• Attend to precision;
• Look for and make use of structure;
• Look for and express regularity in repeated reasoning

allow for a lot of leeways as well as creativity in the way that problems are both presented to and solved by students.

Marijus Auruskevicius/Shutterstock.com

The first objective, for example, emphasizes a student’s ability to not simply apply an algorithm to a problem, but more pointedly, make a decision and implement it.  This process can draw out drastically different reactions in different students.  For some, the prospect of being creative and innovative in thinking of ways to solve brain-bending problems is exciting, and often even addicting.  On the other hand, getting past the roadblocks that come along with solving a tough problem can be frustrating and, at times, discouraging for students.  It is in these moments that establishing math skills that promote perseverance are most critical.

A quick and easy way of avoiding that anticipated frustration that students might encounter in the face of challenging math problems is equipping them with an arsenal of tools and approaches through which they can tackle such problems.  

If, for example, you told me that I was a bird with a short, stubby beak that had to find a way to drink water from a glass that was only half-full with only a pile of stones at hand, I might get frustrated pretty quickly upon realizing that my beak did not reach far enough down to allow me to drink.  I might peck a few times in vain but would remain parched.  

With the right set of dynamic problem-solving skills at my disposal, however, I might think of the problem in a different light, and realize that by dropping enough stones into the glass, I could make the water level rise enough that my beak could easily extract all the water I desired.

Applying these kinds of problem-solving skills to questions that are appropriate for Middle School students can fortify grit, the quality of not giving up easily, and help students to solve problems they may face in their own lives.

Taking all of this into consideration, there are a few basic skills and approaches that students can use to help them crack just about any age-appropriate problem that you, the teacher, throw at them.  In the interest of time, we’ll introduce just four here, though plenty of others can certainly be applied where appropriate. The most common methods for solving problems that students may encounter are:

• Guess and Check;
• Draw a picture;
• Work Backward; and
• Use an Equation with a variable.

The first method on our list of math problem-solving activities for middle school is fairly self-explanatory. In a sense, it involves a bit of reverse-engineering, as the student starts with a proposed solution and works his or her way back to the beginning of the problem to see if that solution is effective.  

Drawing a picture may be more effective for visual learners, as it enables students to lay eyes on the problem and conceive of a solution in ways that they may not have otherwise.

Working backward is like a more scientific version of guessing and checking.  Students can use the information provided to step backward one piece at a time, like Guy Pearce in Memento, until they reach the solution that is in accordance with all of the details provided in the problem.

Finally, an equation that uses a variable can be effective when information is missing, or when an approach unlike the first three is required.

Again–these approaches are mere suggestions that students can apply to solving problems that they may encounter.  Ultimately, a healthy combination of different tactics can serve a student well in handling any problem thrown their way.  Skills such as these, though tough to develop at first, can go a long way toward helping US students stand up to their peers around the world in global math benchmarks , while also making day-to-day problems that they face easier to solve.  

Without further ado, here are ten math problem-solving activities for middle school students that can help them develop a number of crucial skills.  If you find these interesting, you may also like our article on the Best Problem Solving Activities For Middle School . Beyond just math, there are other areas where problem-solving can be extremely useful for that age group.  And now, the problems.

Slideshow List XFinance Piaget's Stages of Cognitive Development Work Backward Math Problem Solution Method Guess and Check Math Problem Solution Method Missing Mangoes math problem solving activity Drawing a picture math problem solution method math problem-solving activities for middle school 10 Math Problem Solving Activities for Middle School 10 Best Problem Solving Activities For Middle School Use an Equation with a variable math problem solution method Common Core Educational Standards for Middle School Students Full HD Math Problem solving activity for middle school students Wild Dog Math Problem solving activity for middle school students Supersize Me Math Problem solving activity for middle school students Domino Effect Math Problem solving activity for middle school students Family Matters Math Problem solving activity for middle school students Mystery Weight Math Problem solving activity for middle school students Show Me the Money Math Problem solving activity for middle school students Cookie Decorations Math Problem solving activity for middle school students Castaways and Coconuts Math Problem solving activity for middle school students Show more... Show less

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The Best Math Apps for Middle School Students

What are the best math apps for middle school students .

Not all educational apps are created equal. Some are more fun than others. Some are more pedagogically sound than others. And some are better for certain age groups than others.

In the App Store, it is difficult to find out which apps are best for a particular age group, like, say, middle school students. Below is a collection of apps for middle school students to learn and practice math, or used as math assessment tools.

1. Khan Academy

The most obvious place to start when looking for the best math apps for middle school students is Khan Academy. The long-running and popular online learning platform offers a wide range of free math lessons, quizzes, and exercises for middle school students with video explanations. It covers topics such as arithmetic, algebra, geometry, and non-mathematical content areas.

2. Socratic by Google

3. Photomath

Photomath is a free math-solving app that uses the camera on your device to scan and solve math problems. It helps middle school students with everything from basic arithmetic to advanced calculus.

4. DragonBox 

DragonBox is a collection of math games that make learning math fun and engaging. It covers topics such as algebra, geometry, and logic.

5. Mathway 

Mathway is a free app that provides step-by-step solutions to a wide range of math problems. It covers topics such as algebra, geometry, calculus, and more.

6. Prodigy 

Prodigy is a free math game that helps students practice their math skills using a game-based learning approach.

7. MathPapa

8. Mathletics

Mathletics is an online learning platform that offers a wide range of math lessons, quizzes, and games for middle school students. It covers topics such as arithmetic, algebra, geometry, and more.

9. Math Bingo

Math Bingo is a fun and interactive math game that helps students practice basic math skills, such as addition, subtraction, multiplication, and division. The app includes multiple levels of difficulty and provides instant feedback on each answer.

10. Brilliant

11. Quizlet

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The relationship between problem-solving skills and environmental literacy of class X students

• Muhdhar, Mimien Henie Irawati AL
• Delinda, Ardelia
• Abdillah, Racy Rizky
• Ramadhana, Nurhikma
• Mardiyanti, Lely
• Purwanti, Wiedia Carullina

Environmental literacy is an individual's ability to build an understanding of the main concepts based on phenomena and apply knowledge to improve environmental problems. Environmental literacy focuses on real behaviour, not just knowledge about the environment. Problem-solving skills are one of the skills in the world of education that include the process of identifying problems, considering options, and making informed choices. This study aims to determine the relationship between problem-solving skills and environmental literacy of class X students at SMAN 8 Malang. The population in this study includes all students of class X at SMAN 8 Malang. The research sample was taken randomly from as many as 112 students of class X majoring in Mathematics and Natural Sciences at SMAN 8 Malang. The instrument used is a test of problem-solving skills based on Greenstein and an environmental literacy test based on the Middle School Environmental Literacy Survey. The results showed that the average problem-solving skills score of students was 1.9 in the medium category, and the average environmental literacy score was 279.3 in the medium category. Data analysis using Pearson Correlation obtained a significance value of 0.112 > 0.05. The correlation test shows that there is no relationship between the problem-solving skills and environmental literacy of class X students at SMAN 8 Malang. The results of the correlation test, which are not significant, indicate that further research is needed to determine the relationship between problem-solving skills indicators and environmental literacy indicators.

• BIOLOGY EDUCATION