problem solving activities for middle school math

• Grades 6-12
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30 Thought-Provoking Math Puzzles for Middle Schoolers

Critical thinking, trial and error, and pure logic abound.

Tired of your tried-and-true math routine? Chances are if you’re feeling the itch to incorporate new activities into your math time, your students are as well. Mixing it up in math class can bring fresh perspectives to stale concepts or standards, and your students will enjoy stretching their brains in different ways with these middle school math puzzles. Critical thinking, trial and error, and pure logic abound in these 30 though-provoking puzzles. Get ready to reignite your middle schoolers’ excitement for math!

(Just a heads up, WeAreTeachers may collect a share of sales from the links on this page. We only recommend items our team loves!)

Sudoku is way more than just an activity to pass the time on long-haul flights. This math puzzle is actually a fantastic problem-solving activity for middle schoolers. Kick-starting your typical math class with a Sudoku puzzle will have your students thinking critically, practicing trial and error, and looking at math in a totally different way. Plus, you can differentiate by providing Easy, Medium, and Difficult puzzles.

Learn more: Sodoku Puzzles To Print

2. 5 Pirates Puzzle

Ahoy and shiver me timbers! This logic puzzle is perfect for a small-group activity to get your middle schoolers working together to solve the conundrum of how pirates plan to share treasure among themselves. Multiple scenarios will play out in this puzzle, so scaffolding with problem-solving strategies is a must.

Learn more:  5 Pirates Puzzles/Math Is Fun

3. Fives Challenge Puzzle

This puzzle is perfect for reviewing addition, multiplication, division, and subtraction and would be a great activity to do when gearing up to teach order of operations. Students could work in pairs or small groups to riddle out each target number.

Learn more:  Fives Challenge Puzzle/Math = Love

4. Beehive Puzzle

Perfect for a station during math rotation or for a rainy-day recess activity, this logic puzzle involves creating a beehive shape without having any squares of the same color touching each other. Students can practice trial and error as well as problem-solving.

Learn more:  Beehive Puzzle/Math = Love

5. Guess My Number

Guess My Number is just as much a riddle as it is a math puzzle. Students use their number sense to determine the number in question. As an extension activity, students can come up with their own clues and trade them with a classmate to solve.

Learn more:  Guess My Number/Education.com

6. Math Riddles

Perfect for a morning warmup, these middle school math puzzles activate all kinds of math knowledge. You can poll the class and have them show their work before clicking to reveal the correct answer. This site even has more challenging puzzles if your middle schoolers fly through the easier ones.

Learn more:  Math Riddles/Get Riddles

My seventh graders loved playing this puzzle as an early-finisher activity. Though the idea is simple (move the tiles until two of the same numbers touch), it’s actually great for recognizing exponents and also for thinking strategically.

Learn more:  2048/Prodigy

8. Magic Squares

Magic Squares have been around for thousands of years, and they come in all shapes and sizes. The 3×3 grid is a great size to introduce to your students and then work up to larger and more complex grids. You can even bring this puzzle off the paper and have your students write the grid out in sidewalk chalk, or write the numbers on water bottle caps to make a fun tactile activity.

Learn more:  Magic Squares/Prodigy

9. Impossible Domino Bridge

Using dominoes to build a seemingly impossible bridge is a perfect activity for the first day or week of a new school year. Your students can work together in small groups and get to know one another as they attempt to construct the bridge that looks like it could turn into a game of Jenga at any moment.

Learn more:  Impossible Domino Bridge/Math = Love

10. Math Picture Puzzles

Your students communicate through emojis anyway, so why not get math involved? This self-checking site allows them to work independently (on the honor system) and also choose between three levels of difficulty. Students can take this idea to the next level, create their own emojis, and arrange them in number sentences for their classmates to solve.

Learn more: Picture Puzzles/MathEasily.com

11. What Is the Weight?

Sometimes you just need a quick resource to get your students working on solving a math puzzle. This puzzle comes from an app, so you can have it downloaded on your students’ iPads or tablets. Middle schoolers will focus on determining the weights of different animals, which is good practice for estimating and working with customary/metric units of measurement.

Learn more: Brain Teasers/Mental Up

12. Colorku

Math doesn’t always have to be just about numbers. This board game uses colors and patterns to focus on analyzing sequences, and would be great to have on hand for those rainy-day recesses as well as for inclusion in a math station. Further, Colorku can be used as a calm-down tool or even a fidget tool.

Buy it: Colorku at Amazon

13. Rubik’s Cube

Rubik’s Cubes made a major comeback in popularity when I taught fifth grade. My students would happily sit together at recess to race each other to see who could solve the cube faster. Though entertaining, Rubik’s Cubes are also suited to teach students about growth mindset, spacial awareness, and 3D space.

Buy it: Rubik’s Cube at Amazon

14. SafeCracker

Though this puzzle looks like something out of an Indiana Jones quest, it’s actually a tactilely engaging tool that will delight even your most resistant math learners. The goal is to align the wheel into columns where the sum adds up to 40. You might need to get more than one of these middle school math puzzles for your classroom.

Buy it: SafeCracker at Amazon

15. “T” Brain Teaser Puzzle

In addition to sparking structural design creativity, this boxed wooden puzzle challenges middle schoolers to engage in trial and error as they work at fitting 50+ pieces into a cube. Much of math is learning how to persevere through tricky problems or procedures, and this puzzle definitely fosters that.

Buy it: T Brain Teaser at Amazon

16. Multistep Equation Puzzle

Solve-and-sort puzzles add flair to repeatedly solving different variations of a math problem for practice. In this free puzzle, students will need to not only solve the equations with variables on both sides, they will also need to sort the problem based on if their solution is positive or negative in order to uncover the secret word.

Get it: Solve-and-Sort Puzzle/Teachers Pay Teachers

In this variation of a classic Sudoku puzzle, students practice critical thinking and exercise their knowledge of how the four math operations work. The best thing about these types of puzzles is that the differentiation potential is endless. Students can solve smaller puzzles with addition, or use only prime numbers in a more complex multiplication problem.

Learn more: Yohaku

18. Jigmaze

One of the Standards for Mathematical Practices is perseverance, and all teachers know that this is a tough one to instill in students, even more so if students are struggling in foundational skills. This type of puzzle can be used to strengthen perseverance as students physically arrange and rearrange pieces of a broken maze.

Learn more: Jigmaze/Math = Love

19. Flexagons

Flexagons, octaflexagons, and dodecaflexagons (say that one 10 times fast!) are a mathematical take on traditional origami. Through constructing these paper creations, your students will get exposure to geometrical terms such as faces ,  equilateral triangles , and all manner of types of 3D shapes.

Get it: Flexagons/Medium

20. Möbius Strip

Though the high-level mathematical equation may be well above your students’ heads (and mine too, if I’m being honest), the STEAM-centered concept of a Möbius strip can be a fun one to explore and create (no need to go into cosines and conversational belts). Middle school math puzzles for the win!

Get it for free: Make a Möbius/STEAMsational

In this complex-looking puzzle, the goal is for the sum of each vertical or horizontal line to match the number given at the beginning of the row or column. This site comes with a great explanation on exactly what that means and how to achieve it. A Kakuro puzzle would be a great “learn as you go” activity for students where they really must pay close attention to the instructions to be able to understand the goal.

Learn more: Kakuro/Braingle

22. Number Searches

This school district’s site has tons of grade-specific number puzzles that would be perfect for when you need to be out of the classroom and have a substitute teacher. They are ready to be printed and contain easy explanations for your students. Check out the number searches, patterns, and 3D riddles.

Learn more: Number Searches/Cranbury School District

23. Two Truths and One Lie

The tried-and-true icebreaker used at many a staff meeting and the first week of school, Two Truths and One Lie can also be used to review and practice tons of mathematical concepts. These middle school math puzzles cover concepts such as negative numbers, fractions, and a ton more.

Buy it: Two Truths & One Lie Math Edition at Amazon

24. Adding Integers Puzzle

The objective of this cuttable resource is for students to solve the integer problem and match up expressions that end up having the same sum. The multiple size options are great for differentiation or to make this independent activity into a small-group collaborative activity.

Buy it: Adding Integers at Teachers Pay Teachers

25. Perfect Square Roots

For upper middle school students, this square-roots puzzle helps with the recognition of perfect square roots. Rather than simply memorizing the perfect square roots, students work to identify and spell out the specific square root and ensure that it fits within the crossword. In this way, the puzzle is self-checking as well.

Buy it: Square Roots Crossword at Teachers Pay Teachers

26. Factor Tree Challenge

Factor trees are an effective way to visually show students the factors of numbers. Trees allow a chain of multiple factors, so you can start with a large number and end up with “branches” that show all of the factors. Once your middle schoolers are familiar with this concept, have them explore this self-checking challenge (and many others as well) that will test their knowledge of abstract factors.

Learn more: Prime Challenges/Transum

27. Ludicross

Another take on Sudoku, Ludicross is interactive in that students can drag and drop the number into position with the goal of making the sum of the numbers in both diagonals the same. Like several of the other puzzles mentioned in this list, students can take this number puzzle to the next level by creating their own and swapping with a classmate to solve.

Learn more: Ludicross/Transum

28. Interactive Mobiles

These colorfully shaped mobiles are a unique way for students to make pattern associations. Because these puzzles are self-paced, students can begin with a simple puzzle and work their way up to complex mobiles with three or more shapes.

Try it: Mobiles/SolveMe Puzzles

29. Deleting Sheep

This logic puzzle is a doozy! The objective is to remove only two numbers in each row with the result being that each horizontal and vertical line equals 30. Trial and error and problem-solving skills abound in this puzzle, and it will keep your middle schoolers engaged for quite some time.

Get it: Deleting Sheep/Dover Publications

30. Pips Puzzle

Have any spare decks of cards lying around your classroom? This inexpensive item provides a different take on a Magic Square. Students can work in small groups, and maybe you can ignite a little class competition to see which groups can complete the challenge the fastest.

Buy it: Pips Puzzle/Math = Love

Looking for more engaging math resources? Try these Magical Math Puzzles and Number Tricks To Wow Your Students .

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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

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.

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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)

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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!

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20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

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

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

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

What are problem-solving strategies?

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

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

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

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

The ultimate guide to problem solving techniques

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

20 Math Strategies For Problem-Solving

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

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

Strategies to understand the problem

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

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

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

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

1. Read the problem aloud

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

2. Highlight keywords 

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

3. Summarize the information

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

4. Determine the unknown

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

5. Make a plan

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

Strategies for solving the problem 

1. draw a model or diagram.

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

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

2. Act it out

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

3. Work backwards

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

For example,

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

4. Write a number sentence

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

5. Use a formula

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

Strategies for checking the solution 

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

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

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

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

2. Estimate to check for reasonableness

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

3. Plug-In Method

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

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

4. Peer Review

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

5. Use a Calculator

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

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

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

Polya’s 4 steps include:

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

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

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

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

How Third Space Learning improves problem-solving 

Resources .

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

One-on-one tutoring 

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

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

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

Problem-solving

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

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

READ MORE : 8 Common Core math examples

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

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

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

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

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Differentiated Instruction: 9 Differentiated Curriculum And Instruction Strategies For Teachers 

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20 Best Math Puzzles to Engage and Challenge Your Students

Written by Maria Kampen

Reviewed by Joshua Prieur, Ed.D.

Solve the hardest puzzle

Use Prodigy Math to boost engagement, offer differentiated instruction and help students enjoy math.

• Teacher Resources

1. Math crossword puzzles

2. math problem search, 3. math riddles.

It’s time for math class, and your students are bored.

It might sound harsh, but it’s true -- less than half of 8th grade students report being engaged at school according to this Gallup survey , and engagement levels only drop as students get older.

Math puzzles are one of the best -- and oldest -- ways to encourage student engagement. Brain teasers, logic puzzles and math riddles give students challenges that encourage problem-solving and logical thinking. They can be used in classroom gamification , and to inspire students to tackle problems they might have previously seen as too difficult.

Math puzzles for kids

Puzzles to Print

Take a crossword, and make it math: that’s the basic concept behind this highly adaptable math challenge. Instead of words, students use numbers to complete the vertical and horizontal strips. Math crossword puzzles can be adapted to teach concepts like money, addition, or rounding numbers. Solutions can be the products of equations or numbers given by clues.

Have students practice their addition, subtraction, multiplication and division skills by searching for hidden math equations in a word search-style puzzle . It can be adapted to any skill you want students to practice, and promotes a solid understanding of basic math facts.

My PreCalc students love riddles... can you figure out where the other dollar went?? #MathRiddles pic.twitter.com/BclqW9nq98 — Rachel Frasier (@MsFrasierMHS) January 8, 2019

Do your students love word problems ? Try giving them some math riddles that combine critical thinking with basic math skills. Put one up on the board for students to think about before class begins, or hand them out as extra practice after they’ve finished their work.

Prodigy is an engaging, game-based platform that turns math into an adventure! While it’s not a math puzzle in the traditional sense, Prodigy uses many of the same principles to develop critical thinking skills and mathematical fluency.

Students complete standards-aligned math questions to earn coins, collect pets and go on quests. Teachers can deliver differentiated math content to each student, prep for standardized tests and easily analyze student achievement data with a free account.

See how it works below!

KenKenKenKen

is a “grid-based numerical puzzle” that looks like a combined number cross and sudoku grid. Invented in 2004 by a famous Japanese math instructor named Tetsuya Miyamoto, it is featured daily in The New York Times and other newspapers. It challenges students to practice their basic math skills while they apply logic and critical thinking skills to the problem.

6. Pre-algebraic puzzles

Pre-algebraic puzzles use fun substitutions to get students ready to perform basic functions and encourage them to build problem-solving skills. They promote abstract reasoning and challenge students to think critically about the problems in front of them. As an added bonus, students who suffer from math anxiety might find the lack of complicated equations reassuring, and be more willing to attempt a solution.

7. Domino puzzle board

Games 4 Gains

There are hundreds of ways to use dominoes in your math classroom, but this puzzle gives students a chance to practice addition and multiplication in a fun, hands-on way. You can have students work alone or in pairs to complete the puzzle.

This online game and app challenges players to slide numbered tiles around a grid until they reach 2048. It’s super fun and not as easy as it sounds, so consider sending it home with students or assigning it after the rest of the lesson is over. It encourages students to think strategically about their next move, and it’s a great tool for learning about exponents.

Math in English

Kakuro , also called “Cross Sums,” is another mathematical crossword puzzle. Players must use the numbers one through nine to reach “clues” on the outside of the row. Decrease the size of the grid to make it easier for younger players, or keep it as is for students who need a challenge. Students can combine addition and critical thinking and develop multiple skills with one fun challenge.

10. Magic square

Magic squares have been around for thousands of years, and were introduced to Western civilization by translated Arabic texts during the Renaissance. While magic squares can be a variety of sizes, the three by three grid is the smallest possible version and is the most accessible for young students.

This is also a great math puzzle to try if your students are tactile learners. Using recycled bottle caps, label each with a number from one to nine. Have your students arrange them in a three by three square so that the sum of any three caps in a line (horizontally, vertically and diagonally) equals 15.

11. Perimeter magic triangle

This activity uses the same materials and concept as the magic square, but asks students to arrange the numbers one to six in a triangle where all three sides equal the same number. There are a few different solutions to this puzzle, so encourage students to see how many they can find.

Sudoku is an excellent after-lesson activity that encourages logical thinking and problem solving. You’ve probably already played this classic puzzle, and it’s a great choice for your students. Sudoku puzzles appear in newspapers around the world every day, and there are hundreds of online resources that generate puzzles based on difficulty.

13. Flexagon

There’s a pretty good chance that by now, fidget spinners have infiltrated your classroom. If you want to counter that invasion, consider challenging your students to create flexagons. Flexagons are paper-folded objects that can be transformed into different shapes through pinching and folding, and will keep wandering fingers busy and focused on the wonders of geometry.

14. Turn the fish

This puzzle seems simple, but it just might stump your students. After setting up sticks in the required order, challenge them to make the fish swim in the other direction -- by moving just three matchsticks.

15. Join the dots

Cool Math 4 Kids

This puzzle challenges students to connect all the dots in a three by three grid using only four straight lines. While it may sound easy, chances are that it will take your class a while to come up with the solution. (Hint: it requires some “out of the box” thinking.)

16. Brain teasers

While they don’t always deal directly with math skills, brain teasers can be important tools in the development of a child’s critical thinking skills. Incorporate brain teasers into a classroom discussion, or use them as math journal prompts and challenge students to explain their thinking.

Bonus: For a discussion on probability introduce an older class to the Monty Hall Problem, one of the most controversial math logic problems of all time.

17. Tower of Hanoi

This interactive logic puzzle was invented by a French mathematician named Edouard Lucas in 1883. It even comes with an origin story: According to legend, there is a temple with three posts and 64 golden disks.

Priests move these disks in accordance with the rules of the game, in order to fulfill a prophecy that claims the world will end with the last move of the puzzle. But not to worry -- it’s going to take the priests about 585 billion years to finish, so you’ll be able to fit in the rest of your math class.

Starting with three disks stacked on top of each other, students must move all of the disks from the first to the third pole without stacking a larger disk on top of a smaller one. Older students can even learn about the functions behind the solution: the minimum number of moves can be expressed by the equation 2n-1, where n is the number of disks.

18. Tangram

Tangram puzzles -- which originated in China and were brought to Europe during the early 19th century through trade routes -- use seven flat, geometric shapes to make silhouettes. While Tangrams are usually made out of wood, you can make sets for your class out of colored construction paper or felt.

Tangrams are an excellent tool for learners who enjoy being able to manipulate their work, and there are thousands of published problems to keep your students busy.

Similar to Sudoku, Str8ts challenges players to use their logic skills to place numbers in blank squares. The numbers might be consecutive, but can appear in any order. For example, a row could be filled with 5, 7, 4, 6 and 8 . This puzzle is better suited to older students, and can be used as a before-class or after-lesson activity to reinforce essential logic skills.

20. Mobius band

Is it magic? Is it geometry? Your students will be so amazed they might have a hard time figuring it out. Have them model the problem with strips of paper and see for themselves how it works in real life. With older students, use mobius bands to talk about geometry and surface area.

Why use math puzzles to teach?

Math puzzles encourage critical thinking.

Critical thinking and logic skills are important for all careers, not just STEM-related ones. Puzzles challenge students to understand structure and apply logical thinking skills to new problems.

A study from the Eurasia Journal of Mathematics, Science and Technology Education found that puzzles “develop logical thinking, combinatorial abilities, strengthen the capacity of abstract thinking and operating with spatial images, instill critical thinking and develop mathematical memory.”

All these skills allow young students to build a foundation of skills they’ll draw on for the rest of their lives, no matter what kind of post-secondary route they pursue.

They help build math fluency

Math games can help students build a basic understanding of essential math concepts, and as another study shows, can also help them retain concepts longer .

In the study, early elementary students gradually moved from using the “counting” part of their brains to complete math problems to the “remembering” part that adults use, suggesting math puzzles and repeated problems can help build the essential skill of math fluency .

Many of the math puzzles above allow students to practice essential addition, subtraction, multiplication and division skills, while advanced or modified problems can be used to introduce pre-algebraic concepts and advanced logic skills.

Math puzzles connect to existing curricula

No matter what curriculum you’re using, there’s a good chance it emphasizes problem-solving, critique and abstract thinking. This is especially true of Common Core math and similar curricula.

How Math Skills Impact Student Development

Math puzzles allow students to develop foundational skills in a number of key areas, and can influence how students approach math practically and abstractly. You can also tie them into strategies like active learning and differentiated instruction.

Instead of just teaching facts and formulas, math puzzles allow you to connect directly with core standards in the curriculum. You can also use them to provide a valuable starting point for measuring how well students are developing their critical thinking and abstract reasoning skills.

Tips for using math puzzles in the classroom

View this post on Instagram A post shared by Sarah Werstuik (@teach.plan.love)

Now that you’ve got some great math puzzles, it might be tricky to figure out how to best incorporate them into your classroom. Here are some suggestions for making the most of your lesson time:

Make sure the puzzles are the right level for your class

If the problems are too easy, students will get bored and disengage from the lesson. However, if the problems are too difficult to solve, there’s a good chance they’ll get frustrated and give up early.

There’s a time and a place

While fun math puzzles are a great way to engage your students in developing critical thinking skills, they’re not a tool for teaching important math concepts. Instead, use them to reinforce the concepts they’ve already learned.

Kitty Rutherford , a Mathematics Consultant in North Carolina, emphasizes that math puzzles and games shouldn’t be based solely on mental math skills , but on “conceptual understanding” that builds fluency over time. Math puzzles help build the essential balance between thinking and remembering.

Give them space to figure it out

Rachel Keen , from the Department of Psychology at the University of Virginia, conducted a study about problem-solving skills in preschoolers. She found that “playful, exploratory learning leads to more creative and flexible use of materials than does explicit training from an adult.”

Give your students space to struggle with a problem and apply their own solutions before jumping in to help them. If the problem is grade-appropriate and solvable, students will learn more from applying their own reasoning to it than just watching you solve it for them.

Model puzzles for your students

Use problems like the mobius strip to awe and amaze your students before drawing them into a larger discussion about the mathematical concept that it represents. If possible, make math puzzles physical using recycled craft supplies or modular tools.

Afterward, have a class discussion or put up math journal prompts. What methods did your students try? What tools did they use? What worked and what didn’t? Having students explicitly state how they got to their solution (or even where they got stuck) challenges them to examine their process and draw conclusions from their experience.

Final thoughts on math puzzles

Be aware that it might take a while to get all your students on board -- they could be hesitant about approaching unfamiliar problems or stuck in the unenthusiasm that math class often brings. Consider creating a weekly leaderboard in your classroom for the students that complete the most puzzles, or work through a few as a class before sending students off on their own.

Instead of yawns and bored stares , get ready to see eager participants and thoughtful concentration. Whether you choose to use them as an after-class bonus, a first day of school activity or as part of a targeted lesson plan, math puzzles will delight your students while also allowing them to develop critical skills that they’ll use for the rest of their lives.

What are you waiting for? Get puzzling!

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Middle School Math Worksheets: FREE & Printable

Our Math Worksheets stand as an essential resource for middle school students aiming to bolster their mathematical skills. Designed to cater to the unique educational needs of grades 6 through 8, these worksheets are a fusion of comprehensive coverage and innovative teaching methods. They encompass a broad spectrum of question types, ensuring that every core math concept is thoroughly addressed.

What sets these worksheets apart is their engaging and creative exercises. They are crafted not just to educate but to intrigue and stimulate the young minds of middle schoolers. This approach to learning ensures that concepts are not only understood but also retained.

Moreover, these invaluable educational tools are offered completely free of charge. We understand the importance of accessible education, and thus, have made these worksheets available to all without any financial barriers. Each worksheet is meticulously linked to specific math topics, allowing students and educators to easily find and download materials relevant to their current study focus.

A Perfect Book to Acing 6th Grade Math

Mastering Grade 6 Math The Ultimate Step by Step Guide to Acing 6th Grade Math

By incorporating these worksheets into their study regimen, middle school students are placed on a trajectory towards academic excellence in mathematics. The worksheets are more than just practice materials; they are a stepping stone to mastering the skills essential for high school and beyond.

IMPORTANT: COPYRIGHT TERMS: These worksheets are for personal use. Worksheets may not be uploaded to the internet in any form, including classroom/personal websites or network drives.

You can download the worksheets and print as many as you need. You have permission to distribute the printed copies to your students, teachers, tutors, and friends. 

You Do NOT have permission to send these worksheets to anyone in any way (via email, text messages, or other ways). They MUST download the worksheets themselves. You can send the address of this page to your students, tutors, friends, etc.

Middle School Mathematics Topics

Whole numbers.

• Whole Number Addition and Subtraction
• Whole Number Multiplication and Division
• Rounding and Estimates

Fractions and Decimals

• Simplifying Fractions
• Adding and Subtracting Fractions
• Multiplying and Dividing Fractions
• Adding and Subtracting Mixed Numbers
• Multiplying and Dividing Mixed Numbers
• Adding and Subtracting Decimals
• Multiplying and Dividing Decimals
• Comparing Decimals
• Rounding Decimals
• Factoring Numbers
• Greatest Common Factor
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Real Numbers and Integers

• Adding and Subtracting Integers
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• Integers and Absolute Value

Proportions, Ratios, and Percent

• Simplifying Ratios
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• Ratio and Rates Word Problems
• Percentage Calculations
• Percent Problems
• Discount, Tax, and Tip
• Percent of Change
• Simple Interest

Algebraic Expressions

• Simplifying Variable Expressions
• Simplifying Polynomial Expressions
• Translate Phrases into an Algebraic Statement
• The Distributive Property
• Evaluating One Variable Expression
• Evaluating Two Variables Expressions
• Combining like Terms

Equations and Inequalities

• One-Step Equations
• Multi-Step Equations
• Graphing Single–Variable Inequalities
• One-Step Inequalities
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• Systems of Equations
• Systems of Equations Word Problems
• Quadratic Equation

Linear Functions

• Finding Slope
• Graphing Lines Using Line Equation
• Writing Linear Equations
• Graphing Linear Inequalities
• Finding Midpoint
• Finding Distance of Two Points

Exponents and Radicals

• Multiplication Property of Exponents
• Zero and Negative Exponents
• Division Property of Exponents
• Powers of Products and Quotients
• Negative Exponents and Negative Bases
• Scientific Notation
• Square Roots

Polynomials

• Writing Polynomials in Standard Form
• Simplifying Polynomials
• Adding and Subtracting Polynomials
• Multiplying Monomials
• Multiplying and Dividing Monomials
• Multiplying a Polynomial and a Monomial
• Multiplying Binomials
• Factoring Trinomials
• Operations with Polynomials

Geometry and Solid Figures

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• Rectangular Prism
• Pyramids and Cone

Statistics and Probability

• Mean and Median
• Mode and Range
• Stem–and–Leaf Plot
• Probability Problems
• Combinations and Permutations

The Absolute Best Books for Middle School Math Worksheets

Mastering grade 6 math word problems the ultimate guide to tackling 6th grade math word problems, mastering grade 7 math word problems the ultimate guide to tackling 7th grade math word problems, mastering grade 8 math word problems the ultimate guide to tackling 8th grade math word problems.

by: Effortless Math Team about 5 months ago (category: Blog , Free Math Worksheets )

Effortless Math Team

Related to this article, more math articles.

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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.

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20 Problem-Solving Activities for Middle School Students

• Middle School Education

Introduction:

As students progress through middle school, it becomes increasingly important to develop their problem-solving skills. By engaging in problem-solving activities, students can enhance their critical thinking abilities, foster creativity, and become better prepared for the challenges they may face both in and out of the classroom. Here are 20 problem-solving activities that are perfect for middle school students.

1. Brainstorming Sessions: Encourage students to share their ideas on a particular topic or issue, fostering a collaborative environment that promotes creative problem solving.

2. Riddles: Challenge students with riddles that require critical thinking and lateral thinking skills to determine the answers.

3. Sudoku: Introduce sudoku puzzles as a fun and challenging math-based activity.

4. Chess Club: Encourage students to participate in chess clubs or tournaments to practice strategic thinking.

5. Escape Rooms: Plan an age-appropriate escape room activity to develop teamwork and problem-solving skills among the students.

6. Role-Playing Exercises: Use role-playing scenarios to allow students to think critically about real-life situations and practice problem-solving strategies.

7. Science Experiments: Design science experiments that require students to troubleshoot problems and test possible solutions.

8. Word Problems: Incorporate word problems in math lessons, encouraging students to use logic and math skills to solve them.

9. Puzzle Stations: Set up different puzzle stations around the classroom where students can work on spatial reasoning, logic puzzles, and other brain teasers during free time.

10. Debates: Organize debates on controversial topics, allowing students to present and argue their views while developing their critical thinking and persuasion skills.

11. Engineering Challenges: Provide engineering-based challenges such as bridge building or packaging design activities that require teamwork and creative problem solving.

12. Storytelling Workshops: Host a storytelling workshop where students collaborate to create stories from a given prompt and gradually face more complex narrative challenges.

13. Coding Clubs: Support students in learning coding basics and encourage them to develop problem-solving skills through coding projects.

14. Treasure Hunts: Create treasure hunts with clues that require problem solving, reasoning, and collaboration among the students.

15. Cooperative Games: Facilitate games that promote cooperation and communication, such as “human knot” or “cross the lava.”

16. Geocaching: Introduce geocaching as a fun activity where students use GPS devices to locate hidden objects and work as a team to solve puzzle-like tasks.

17. Exploratory Research Projects: Assign open-ended research projects that require students to investigate topics of interest and solve problems or answer questions through their research efforts.

18. Mock Trials: Set up mock trials in which students participate as lawyers, witnesses, or jury members, allowing them to analyze cases and think through legal problem-solving strategies.

19. Creative Writing Prompts: Share creative writing prompts requiring students to think critically about characters’ actions and decisions within fictional scenarios.

20. Invention Convention: Host an invention convention where students present their unique solutions to everyday problems, fostering creativity and innovative thinking.

Conclusion:

Problem-solving activities are essential for middle school students as they help in cultivating valuable life skills necessary to tackle real-world challenges. These 20 activities provide diverse and engaging opportunities for students to develop key problem-solving skills while fostering creativity, communication, critical thinking, and collaboration. Teachers and educators can easily adapt these activities to suit the individual needs of their middle school classrooms.

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Free Math Worksheets — Over 100k free practice problems on Khan Academy

Looking for free math worksheets.

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That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!

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30 Math Club Activities For Middle School: Puzzles, Challenges, And Tricks

December 14, 2023 //  by  Nicole Muir

There are so many fantastic school clubs to take part in! Whether they run during break times, lunch times, or after school, there is usually something for everyone. Math clubs are particularly fun and engaging for students because they often learn and get to be with their friends, or students who share their interests, while they do. There are a variety of math activities that you can focus on if you are running or leading a math club at school.

1. Mind Reading Tricks

This is an addictive math game that your students will definitely want to play with their friends and family outside of the math club. They will also be very curious about how this trick works using these numbers. It's a puzzle that kids will enjoy trying to solve!

Learn More: Mei Assets

2. Who's Who?

Mathematical puzzles like this one are a crowd pleaser. This math problem presents a fun challenge for the students. They will read about a network of friends and people who are not friends. They must figure out how these people are connected.

Learn More: Wild Maths

3. Equation Math Bingo

Students love to play bingo. This activity is an all-out challenge because they must solve the equations mentally and quickly before you move on to find out if they can cover their square. You may consider making your own set of cards.

Learn More: Math Seeds

4. Tossing Snowballs

This game gives the kids some more math practice as well. Having them solve the equation and then throw the fake snowballs into the bucket is a mix of math and fun physical games as well. You can definitely switch up the equations cards too.

Learn More: We Are Teachers

5. NumberStax

If you are looking for an app for the students to spend their time on, check out this one called NumberStax. It is similar to Tetris and better than boring math worksheets for sure. It will also encourage some math club fun and competition.

Learn More: Amazon

6. ChessKid

This online game is another excellent one to include in your math club or even your local chess club. There are tons of math education ideas and math skills that can be taught through chess, like a strategy for example. Chess integrates many skills.

Learn More: Commonsense

7. Scavenger Hunt

This activity could become one of the students' favorite math club activities. Math is made even more interesting, fun, and engaging for students when it is hands-on and they can move around while they learn. Math scavenger hunts are rare!

Learn More: Taylor J's Math Materials

8. Hands-on Algebraic Equations

Many students often benefit from visual representations when working with and working through math problems. It helps them understand key math concepts and they can have more fun with math. There are kits you can purchase as well and bring to the math club or math class.

Learn More: Organized Homeschooler

Math mazes are an excellent challenge to bring into your math club. Your math club students can practice and strengthen their skills in logic, reasoning, planning, and strategy. Middle school students will love to work through complex mazes during math club.

Learn More: Cognitive Cardio Math

10. Alien Power Exponents

This online math game is so fun! Many students are intrigued by aliens. They can play this game for part of the meeting period of the math club. Incorporating topics students are already interested in will make them excited and want to attend the club!

Learn More: EZ School

11. Numbers About Me

This game is a quick get-to-know-you game that can be used on the first day of math club when you have students gather from different grades altogether who might not know each other. They can write down they have 1 sibling, 2 parents, 4 pets, etc.

Learn More: Math Equals Love

12. Math Book Report

Mixing math and literacy might be something you are interested in doing. Blending literacy and math might not be a concept students are familiar with or have done before. There are many read-aloud stories and books that incorporate math too that they could study.

Learn More: Mash Up Math

13. Dropping Eggs

This math word problem will really get your students thinking. You could even follow up this math word problem with a STEM activity either afterward if time allows or at your next math club meeting if you like. Students will love to test out their theories!

14. Find the Missing Number

Missing number problems and equations like these could be utilized as quick activities you can have the students do when they arrive at math club initially or while you are waiting for all of the students to arrive. The problems range from simple to complicated.

Learn More: Mrs. E Teaches Math

15. Star Realms

If you happen to have some money in the budget, purchasing a game like this can be beneficial. Students will have the experience where they feel like they are playing a board game in school! This game will let students practice using negative numbers.

16. Quadrilaterals Game

If you are teaching the students about the property of shapes, then this game is perfect. They will learn about which shapes have which properties. It also helps them practice quadrilateral shape identification and use their proper names as well.

Learn More: Edu Gov.

17. Math is All Around Us

Students will think about how math is involved in their everyday lives. From telling time to reading recipes to scoring sports games and more. This idea is excellent to include before jumping into a math game. They can draw and write about how they use math every day.

Learn More: On Lemon Lane

18. Mountain Climber Slope Man

Learning about slopes has never been so fun and interactive! To progress through the game, the students must answer questions about slopes and solve the equations. They will be highly encouraged and motivated to solve the equations! They will love helping the character.

Learn More: Mr. Nuss Baum

19. Initials

This game involves everyone. Each student will solve an equation on each math page that looks at different math topics. When they are done, they will sign their initials beside the equation they completed. This will take a little bit of prep on the part of the instructor.

Learn More: Number Dyslexia

20. Math About Me 

This is another introductory activity. The students can even pass around their sheets when they are finished and their friends can solve which page belongs to who based on solving the equations given and matching them with a person. Who knows you best?

Learn More: Math Geek Mama

21. Fantastic Problems

Outrageous math problems can be hilarious. The students will be very excited to work on the problem that asks them to find out how much popcorn would it take to fill up the school gym, for example. You can create your own questions as the instructor, too!

Learn More: 2 Peas And A Dog

22. Estimation 180 Tasks

Estimation is also an important skill in mathematics. This website features so many different types of estimation tasks for the students. Your math club participants will have vastly different answers, which will make the big reveal more exciting! Check out these tasks at the link below.

Learn More: Estimation180

23. Pumpkin STEM

If you are looking for a festive task to introduce to your students and for them to work on, have them build, construct, make blueprints and work through the equations necessary to keep pillars up and holding up these pumpkins.

Learn More: Stress Free Math For Kids

24. Two Truths and A Lie Math Edition

You can create two truths and lie equations for your students to solve. Which one is the incorrect equation? This idea will get them to solve at least 3 equations per question you pose to them. Purchasing this book is one option, but it is not necessary.

25. 3D View of You

A fun math craft like this is perfect. Your math club students will construct a 3D shape- a cube! They will write different pieces of important information about them that they want to share with their other fellow math club participants. Make your own to share with them.

Learn More: Rise Over Run Teacher

26. Number Talks

Computation practice is fundamentally important. Working on a number talk with your students each math club session can have them solving cool problems while strengthening their computation skills as well. Number talks can take up a long time or be quick and simple.

Learn More: Google Docs

27. Which One Doesn't Belong?

Which one doesn't belong activities are great because there is more than one right answer. This website features so many different puzzles for students. They can look at numbers, shapes, or more. You will never run out of choices!

Learn More: WODB

28. Blue Whales

Your math club students can work with interactive data to learn about blue whales. Many students are fascinated by animals and love to learn more information about them. Non-fiction information like this will hook them and they will manipulate data.

Learn More: You Cubed

29. Taxi Cab

This task is very open-ended and you can do a lot with it. You could discuss different possible paths, patterns, or more. You could replace this taxicab on a different sheet and you can plot Santa's path, a bunny or tiger, for example.

30. Guess the Weight

Have your math club students gather up 100 of certain items and have them guess the weight.

Learn More: Education

Small Group Math Activities

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• Math Stations

Discover small group math activities that promote student engagement and foster a love for math. This blog post explores 10 activities, including math games, hands-on manipulatives, real-world investigations, technology tools, problem solving activities, and more to help you transform your math stations into a dynamic learning environment.

I have a secret confession to make. 

Teaching reading has never been my cup of tea. 

Don’t get me wrong, I adore immersing my students in captivating books and opening their minds to new worlds. 

But when it comes to reading workshop, let’s just say it didn’t exactly light a fire in my soul. 

The never-ending cycle of reading from the textbook series and completing author’s purpose, inference, and comprehension worksheets felt mundane and, dare I say it, a bit dull. #yawn 🥱 

Despite my best efforts, I struggled to make it truly exciting. 

So, when the opportunity to introduce math workshop came knocking, I must admit, I wasn’t exactly jumping for joy.

It’s All About Engagement

Math stations are a powerful tool for promoting student engagement and deepening our students’ mathematical understanding. 

By incorporating engaging activities into your math station rotations, you can create a dynamic learning environment that sparks excitement and curiosity in your students. 

In this blog post, we will explore 10 engaging small group math activities that will captivate your students and inspire them to develop a love for math.

10 Small Group Math Activities for Any Math Station Rotation

Activity 1: Math Games Galore

Math games are a fantastic way to make learning fun and interactive. These small group math activities provide opportunities for students to practice math skills while communicating mathematically with their peers. Here are a few examples of card and dice games that can be incorporated into your math station rotations:

• War Games: This classic math game requires only a deck of cards. Partners each turn over a card and use their math skills to compare the numbers, such as whole numbers, fractions, decimals, or even simple expressions. The player with the higher value wins the round. Players continue playing until no cards are remaining. 
• Cover-Up Games: This simple board game requires two dice. In turn, each student rolls the dice and completes the problem associated with the dice sum. Then, they cover the solution with a marker in a grid trying to get four in a row, column, or diagonal. 
• Traditional Board Games: Pair a set of task cards with a traditional board game to create this math station activity. After correctly answering a question, students can roll a die or toss a coin to move along the path.

Activity 2: Hands-On Manipulatives

Hands-on manipulatives bring abstract math concepts to life, making them more concrete and tangible. These activities provide students with a visual and kinesthetic experience, enhancing their understanding of mathematical concepts. Consider incorporating the following manipulative-based activities into your math stations:

• Pattern Block Puzzles: Provide students with pattern blocks and challenge them to create different shapes and designs, exploring concepts like symmetry, fractions, and geometry.
• Base Ten Blocks: Use base ten blocks to reinforce place value concepts. Students can build and represent numbers and explore operations with whole numbers and decimals.
• Data Analysis with Spinners: Use spinners with different sections labeled with numbers or categories. Students spin the spinner multiple times, record the results, and represent the data they collected by creating a frequency table, bar graph, or dot plot.

Want to use math manipulatives but need more resources? Try virtual manipulatives !

Activity 3: Puzzle Power

Puzzles are not only engaging but also promote critical thinking and problem solving skills. They challenge students to think creatively and persevere through complex tasks. Here are a few puzzle-based activities to include in your math stations:

• Number Crossword: Create a crossword puzzle where students respond to math-related clues and fill in the corresponding numbers in the grid.
• Logic Grids: Challenge students with logic puzzles that require them to use deductive reasoning and critical thinking skills to solve.
• Sudoku: Provide students with Sudoku puzzles focusing on numbers, shapes, or mathematical operations, encouraging them to apply logical reasoning to complete the puzzles.

Activity 4: Real-World Math Investigations

Real-world math investigations allow students to apply their mathematical knowledge and skills to authentic situations. These activities promote problem-solving, critical thinking, and the ability to connect math and the real world. Consider the following examples for your math station rotations:

• Recipe Conversions: Provide students with recipes that need to be converted to serve a different number of people. Students must adjust ingredient quantities using proportional reasoning and fractions.
• Budgeting and Shopping: Give students a budget and a list of items with prices, such as a local grocery ad or restaurant menu. They must plan a shopping trip, choose items based on their budget, and calculate the total cost.
• Measurement Scavenger Hunt: Create a list of objects in the classroom or nearby hallway students need to measure using various units of measurement. Students will use rulers, measuring tapes, or scales to gather the data and record their measurements.

Activity 5: Technology Tools

Incorporating technology into math stations can engage students and provide interactive learning experiences. Consider utilizing the following online resources and educational apps:

• Online Math Games and Activities: Websites such as IXL Learning, Prodigy, and Math Playground provide opportunities to gamify the learning experience. Students can earn points and virtual rewards while building math skills. 
• Digital Activities: Activities designed for Google Classroom and Seesaw provide engaging opportunities for students to use digital tools to review math concepts and skills .
• Digital Task Cards: Take task cards to the next level with digital task cards . Task cards created for use at Boom Learning or even with Google Forms can increase student engagement while students practice essential math skills.

Activity 6: Ready-Made Math Activities

In addition to creating your small group math activities, incorporating ready-made resources can provide a valuable and time-saving option for engaging your students. These pre-made activities offer an interactive and hands-on way to reinforce math skills and concepts. 

• Electronic Flashcard Games: Electronic flashcard games provide an exciting and interactive way for students to practice and reinforce math facts. These games often offer various difficulty levels and customizable options to cater to students’ needs. Math Whiz and Math Shark are two of my favorites!
• VersaTiles: VersaTiles is a hands-on, puzzle-inspired activity with an interactive workbook system designed to reinforce math skills. Students use a unique answer case and answer tiles to complete activities and self-check their answers. It’s a favorite of my elementary and middle school students alike!
• Marcy Cook Tiling Tasks: Marcy Cook Tiling Tasks are critical thinking activities that require students to use a set of tiles labeled 0-9 to complete math puzzles. These tasks promote problem-solving skills, logical reasoning, and mathematical thinking. Students arrange the tiles to fill in the blanks and create equations and solutions that satisfy the given conditions. 

Activity 7: Math Task Cards

Math task cards offer various practice opportunities and allow students to work independently. They are also easy to make and readily available on teacher marketplaces across the web. Here are some examples of task card activities: 

• Showdown: Partners select one card and complete it individually. Then, students “showdown” and share their responses using math talk and supporting each other as necessary. 
• Math Game: Pair a set of task cards with a game board to gamify the learning experience! Students place their game markers at the start line. To move down the path, students must correctly respond to a task card, toss a die (or flip a coin), and move the number of spaces indicated on the die or based on the side of the coin visible after the coin toss (heads = 2 spaces, tails = one space).
• Cover Up: To create a Cover Up game, program a 4 x 4 grid with the solutions to a set of task cards. Then, when students respond correctly, they can cover the answer with a board marker, such as centimeter cubes, color tiles, Bingo chips, or beans. The goal is to get four markers in a row, column, or diagonal. Note: This activity works best with multiple-choice questions, true or false questions, or questions with numerical answers.  

Activity 8: Math Picture Books

Integrating math and literature activities enhances students’ mathematical understanding and develops their reading comprehension, critical thinking, and analytical skills. Consider incorporating the following math and literacy activities into your math stations:

• Math Investigations: Use the storyline in a book to practice a skill. For example, use the Pigs Will Be Pigs book by Amy Axelrod to practice adding and subtracting decimals as the pigs find money hidden around their home and then spend it at a restaurant. 
• Story-based Problems: Use the book as a springboard to reinforce a specific skill. Either re-create scenarios from the book or create new problems based on the problems the characters faced in the story such as comparing the amounts in two different groups after reading Amanda Bean’s Amazing Dream by Cindy Neuschwander.
• Famous Mathematicians Book Study: Create a set of questions to help students learn more about famous mathematicians, such as Katherine Johnson , and provide students with access to a physical or digital biography to read and use to respond to the questions.

Activity 9: Calculator Challenges

Incorporating calculator challenges into your math stations can allow upper elementary students to deepen their understanding of math concepts while developing their computational skills. Calculator activities engage students in hands-on exploration, problem-solving, and critical thinking while building their technology proficiency skillset. 

These activities encourage students to use calculators to investigate, solve problems, and make connections. Consider incorporating the following calculator challenges into your math stations:

• The Broken Calculator Challenge: In this challenge, students are shown an image of a calculator with only three or four working buttons. Students then determine how to use the remaining keys on the broken calculator to create specific values, such as using +, x, 2, and 3 to achieve a value of 8.
• Calculator Corrections: This task requires students to determine how to correct a calculator mistake without clearing the calculator. Using the calculator, students determine how to fix a mistake, check the answer, and make adjustments as necessary. After completing the task, students can justify the changes they made. For example, Brandi wanted to enter the number 4265 into her calculator. By mistake, she typed 4165. Without clearing her calculator, how can she fix her mistake? 
• Target Number: For this task, students represent place value in numbers, determine what number to add or subtract to reach the target number, and use the calculator to check their process. For example, students are given the following directions: Start with 7,254. Find a number to subtract that will result in a 0 in the hundreds column.

Activity 10: Problem Solving and Critical Thinking

Problem-solving and critical thinking are essential life skills for students to develop. Engage your students in meaningful and challenging math experiences by incorporating problem solving and critical thinking activities into your small group math activities. Click here for a list of problem solving activities ; that encourage students to think critically, analyze situations, and apply their mathematical knowledge to real-world scenarios.

A Shift in Thinking

While I never found a way to make reading workshop exciting, math workshop was my students’ favorite part of the day. 

Integrating various small group math activities into the rotation was the key to keeping students engaged in learning and wanting more. 

If you’re new to math stations, the best way to get started is to choose 1-2 new activities to implement. Consider adding another activity after students are comfortable with the previous activities and staying engaged with minimal support.

Adding new small group math activities gradually will help maintain order during the rotation and save your sanity! If you’d like more tips and tools for managing math stations, download the Math Station Management Toolbox using the form at the bottom of this post. 

Math station rotation boards are an excellent organizational tool for implementing the small group math activities above. This visual display helps students understand the structure of the math station rotation and enhances their independence and accountability. 

The small group math activities shared above can be assigned to specific stations on the rotation board. Then, teachers can use the math station rotation board to effectively monitor student progress as they rotate through various math stations. 

Experiment with these small group math activities and adapt them to meet the needs and interests of your students, ensuring math station time is an exciting and transformative experience for all.

What are your favorite small group math activities? Respond in the comments below. 

Shametria Routt Banks

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Fun Math Activities for Middle School

Engage tweens with fun math activities for middle school . Math is an essential subject, and it’s important for tweens and teens to master the concepts in middle school math .

But math lessons can also be boring, especially when working on mastery review. Kids need to do more than work on math problems. So, it’s a good idea to make learning as interactive as possible.

Fortunately, there are plenty of engaging activities to help tweens learn math in creative ways. No matter the specific topic you’re studying, there’s an easy way to make lessons engaging.

From games and puzzles to hands-on projects, these activities will make it easier for middle schoolers to practice math in a unique, creative way.

Table of Contents

What are fun math activities? They are fun, creative, and interactive ways of learning math. These fun ways to teach order of operations are a good example.

They can range from games, scavenger hunts, art projects, competitions, and exploratory projects. The possibilities are almost endless!

No matter the form, math activities get students off of the page and bring math to life in a real-world setting.

Ultimately, they can enhance the learning experience for all middle school kids!

What are the benefits of using math activities?

Math activities offer a valuable opportunity for middle school students to strengthen their math skills in a fun and engaging way.

Not only do they keep the topic interesting, they also offer some important educational benefits. 

By taking math from the pages of textbooks to engaging hands-on experiences, math-related activities help students explore concepts through experimentations, projects, and collaborative problem solving.

Activities like online math games for middle school offer kids a fun way to take the process from book-learning to real world application. Students of all grade levels not only gain a deeper understanding of math concepts but also learn to think critically.

Hands-on activities make math learning far less intimidating for kids and way more exciting!

How to Add Fun Math Activities to your Lesson Plan

Math activities can be a great way to engage and motivate middle school students, but you have to make time for them. It works best when you use them with a solid math curriculum, like CTCMath .

The truth of the matter is, most activities end up collecting dust on the shelf. To keep this from happening in your homeschool, use these practical tips for adding them to your lesson plans.

• Before starting the math lesson, take a few minutes to do a quick activity as a warm-up.
• If your tweens are getting overwhelmed or lose focus, take a brain break and play a fun game.
• Find an activity that goes along with the subject and use it along with the main lesson. These order of operations math task cards work well.
• Put aside the textbook for a day and let your tweens work on one of the many math projects for middle school instead.
• Play a math board game as a part of a family game night.

When choosing math activities for your lesson plans, make sure that the task is relevant and engaging.

Keep in mind that these don’t have to have fancy bells and whistles. Just use things that have open-ended questions that get kids thinking creatively.

And start small. There isn’t a need to pull out every math activity you own. Instead, choose one or two to begin with and set aside a few days and times per week dedicated to doing them.

With a few simple steps, math classes can be fun or even exciting!

Any links in this post may be affiliate links. See my disclosure statement .

Math Activities for Middle School

The fun activities below provide invaluable learning experiences that are sure to make math exciting and enjoyable.

Middle School Math Games

Math-related games are amazing teaching tools.

With game-based learning, kids feel less pressure because they’re just focused on the fun. That makes it easier for kids to practice basic operations.

Choose from math board games , dice games , online games, printable games, and more.

Math Scavenger Hunts

Scavenger hunts are an awesome way to problem solve, practice math facts, and get kids thinking outside the box.

Make up math problems for your tweens to solve in order to find the clues that will lead them to their final destination.

Active Math Games

Get your tweens up and moving with some physical games.

Middle schoolers will love playing trashketball , math tag, and even musical chairs.

When you create your own sets of questions, games like these are a great addition to your review of important concepts.

Create a Kahoot that covers the topics you are studying. Kahoot is an interactive online game where students answer questions in real time on an electronic device.

Because you design the multiple-choice questions, it’s easy to tailor it to your child’s needs. It’s a great activity for math review, whether you use it in your math classroom or homeschool.

Logic Puzzles

Math is more than simply learning formulas. It’s also an opportunity to think critically and problem solve. That’s why I love logic games. They get kids thinking creatively.

Math crossword puzzles , minesweeper , Sudoku, elimination grids, and Kanoodle are a few for older students. You can also give them some word problems to work through.

Use cool math books (not textbooks) to engage your middle schooler. There are a wide variety of choices.

Things like math mysteries , This Book Thinks You’re a Math Genius , and Math for Every Kid are fun to read and get kids thinking about math in a new way.

Comparison Shopping

Take a trip to the grocery store to work on math with your middle schooler. While shopping, have tweens use math to figure out unit rates to decide which item is the best buy.

Don’t want to take the time to go to the store? You can also do this at home by choosing a bunch of items to compare and giving your tween their sizes and prices.

It’s a fun activity that builds essential skills.

Measuring Volume

Have your kids use household items to measure volume.

Decide on what you want to measure (boxes, spheres, liquid, cylinders, etc.) and send them on a hunt around the house to find objects to use.

It’s a great way to show tweens how math is used in real life.

Kitchen Math

There are a number of math topics you can work on in the kitchen with your tweens.

Bake some bread or double up a cookie recipe to work on ratios.

Or use the smallest measuring tool when baking so kids have to convert the measurements. For example, let’s say a recipe calls for 1 cup of flour and 1/4 cup of sugar. Give your tweens a 1/8 measuring cup and have them do the conversions.

Paper Airplane Math

Paper airplanes are the perfect activity for kids to practice graphing.

Pull out a bunch of paper and have your tweens build a variety of airplanes. Then, as they throw them, collect the data and use it to create a graph.

Aside from graphing, it’s also a fun way to work on measurement, spatial reasoning, and averages.

These middle school math activities are a wonderful way to get tweens engaged in the subject and will definitely build your students’ understanding of various math topics.

It’s time to make math fun!

Do you use fun math activities with your middle schooler?

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10 Fun Math Problem Solving Activities

I love using fun games and activities to get my kids excited about math. That’s why I was so excited to discover Beast Academy Playground! The site includes a wide variety of math problem solving activities, games, puzzles, and ideas that can be used with your current homeschool curriculum. If you’re looking for some fun ways to get your child interested in math again or some new ideas for teaching math at home, this is a great place to start.

I received compensation in exchange for my honest review, but all the opinions in this post are my own.

What is Beast Academy Playground?

As a homeschool parent, I know that fun math problem solving activities are hard to come by. Practicing math can be frustrating and boring for kids. And, it’s not enough to just teach math facts – children need to learn how to solve complex problems too!

Beast Academy Playground is the perfect solution. This site was created by Beast Academy, a homeschool curriculum for kids ages 8-13 that’s written as a comic book. Beast Academy Playground is a website that includes a growing library of fun activity ideas for kids ages 4-11.

The site includes both tabletop games that can be played with paper and pencil and more active games that can be played outside. Parents can sort the activities by concept, age, number of players, and more to find the perfect activity to complement any math lesson. New activities, games, and crafts are added to the site weekly.

Key Features of Beast Academy Playground

I love that every game on the site includes variations. These are different ways to adapt the game to fit the number of kids in your family or the age and grade level of your child.

In addition, most of the games can be played alone or in small groups. This makes Beast Academy Playground so easy for the whole family to use together!

Beast Academy Playground was developed by the experts at Art of Problem Solving, who are global leaders in K-12 math education. Each activity is intentionally designed to help kids learn new math concepts.

I was excited to see that each game also includes learning notes. This section helps parents understand what their kids will be learning when they play the game. I felt like I was prepared to be a better math teacher after I read the tips in this section!

Check out Beast Academy Playground and learn more now!

How to use Math Problem Solving Activities in Your Homeschool

Introduce a new concept.

One way to use problem-solving activities in your math lessons is to help introduce a new concept. For example, when we were learning about even and odd numbers, we started our math lesson by playing the Odds vs. Evens game from Beast Academy Playground. This simple math problem solving activity is a variation on the game Rock Paper Scissors. This was a fun way to help us review addition facts while introducing the concept of odd and even numbers.

Practice Problem-Solving Skills

Another great way to use Beast Academy Playground is to help kids practice their problem-solving skills. One fun problem solving game that my kids love is the Fox and Hare game. In this outdoor game, the fox needs to use strategy to try to catch the hare on a grid, while the hare tries to avoid capture. You can change the size of the grid to create a variety of problems for kids to solve.

Practice Math Facts

If your kids need extra practice with their math facts, games and math puzzles can be a fun way to practice these important skills. Beast Academy Playground has games for addition and subtraction, as well as concepts like skip counting that will help kids learn their multiplication facts.

One favorite that we enjoyed was Troll Hole . In this game, we took turns writing numbers on a special game board. In the end, we had to add up all the numbers to see who was the winner. My kids had so much fun with the theme of this game and loved getting to draw the troll in the hole!

Independent learning

As homeschool parents, we always need ideas for independent learning activities. Beast Academy Playground includes some great math problem solving games that are perfect for self-directed math learning. The many different activities on the site include several fun activities for one player that kids can work through independently to reinforce their math skills.

For extra review

Hands-on activities are also helpful when kids need a little extra review on a topic. For example, we played Kanga Ruler to help review skip counting. The kids loved this game because it was active and fun!

Top 10 Math Problem Solving Activities from Beast Academy Playground

Here are 10 of our favorite games that help kids develop a deeper understanding of mathematical concepts, all while having fun at the same time.

Trashketball

In this game, kids aim and try to score a basket into a trash can. Then, they add up the points they score. You can modify this game to add extra intellectual challenges for older kids or adapt the math so that younger kids can play too!

Trashketball was my kids’ favorite Beast Academy game, hands down. They loved trying to score as many baskets as they could. They had so much fun that they decided to keep playing even after our math lesson was finished!

Learn how to play Trashketball here.

In this math game for young children, kids race to stack towers of number cards. This is a great way to review numbers and counting. My kids really enjoyed trying to build the tallest tower that they could!

Learn how to play Towers here.

Bumper Cars

Although it took us a few tries to understand the strategy behind this game, my kids loved the concept of trying to figure out new ways to move the cars on the road. This was another great mathematical practice for strategy and solving difficult math problems.

Learn how to play Bumper Cars here.

Hungry Monster

This was a great way to practice inequalities and comparing numbers, and my kids loved feeding the correct answer in each inequality to the hungry monster!

Learn how to play Hungry Monster here.

Fruit Flies

In this math game for older problem solvers, kids try to claim as many grapes as they can for themselves, while blocking their opponent from getting any. This game is like an interactive logic puzzle, and it’s a good way for kids to learn critical thinking skills.

Learn how to play Fruit Flies here.

Blind Heist

In this game, Battleship meets addition as kids try to build the highest towers on their own secret side of the board. There are many different solutions and strategies to be successful, and my kids loved trying different solutions to this open-ended problem.

Learn how to play Blind Heist here.

Möbius Madness

This is a classic brain teaser for a reason- my kids were fascinated by the magic of a piece of paper with only one side. My kids were able to follow the directions easily and afterwards, they were excited to show their magical piece of paper to everyone who would watch.

Learn how to play Möbius Madness here.

This fast-paced card game was the perfect way to help my kids practice their addition facts.

Learn how to play Fifteen here.

Cookie Cutter

This game helps kids practice both spatial reasoning skills and fine motor skills at the same time. And, the result is a fun picture that they can color!

Learn how to play Cookie Cutter here.

Odd Knights

This was a fun way to practice even and odd (and it even led to a history lesson about the Knights of the Round Table!)

Learn how to play Odd Knights here.

What math problem solving activities will you use?

Whether it’s for extra practice or math review , Beast Academy Playground has something for every math learner. This site is a great resource to find exciting games that help kids develop number sense, problem solving, and logical thinking skills. If you want fun and engaging math activities that don’t require a textbook, this is the place to go. For more math problem solving activities and fun math games, check out Beast Academy Playground !

Find hands on activities to teach spelling and reading here!

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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 Helpful Worksheet Ideas for Primary School Math Lessons

M athematics is a fundamental subject that shapes the way children think and analyze the world. At the primary school level, laying a strong foundation is crucial. While hands-on activities, digital tools, and interactive discussions play significant roles in learning, worksheets remain an essential tool for reinforcing concepts, practicing skills, and assessing understanding. Here’s a look at some helpful worksheets for primary school math lessons.

Comparison Chart Worksheets

Comparison charts provide a visual means for primary school students to grasp relationships between numbers or concepts. They are easy to make at www.storyboardthat.com/create/comparison-chart-template , and here is how they can be used:

• Quantity Comparison: Charts might display two sets, like apples vs. bananas, prompting students to determine which set is larger.
• Attribute Comparison: These compare attributes, such as different shapes detailing their number of sides and characteristics.
• Number Line Comparisons: These help students understand number magnitude by placing numbers on a line to visualize their relative sizes.
• Venn Diagrams: Introduced in later primary grades, these diagrams help students compare and contrast two sets of items or concepts.
• Weather Charts: By comparing weather on different days, students can learn about temperature fluctuations and patterns.

Number Recognition and Counting Worksheets

For young learners, recognizing numbers and counting is the first step into the world of mathematics. Worksheets can offer:

• Number Tracing: Allows students to familiarize themselves with how each number is formed.
• Count and Circle: Images are presented, and students have to count and circle the correct number.
• Missing Numbers: Sequences with missing numbers that students must fill in to practice counting forward and backward.

Basic Arithmetic Worksheets

Once students are familiar with numbers, they can start simple arithmetic. 

• Addition and Subtraction within 10 or 20: Using visual aids like number lines, counters, or pictures can be beneficial.
• Word Problems: Simple real-life scenarios can help students relate math to their daily lives.
• Skip Counting: Worksheets focused on counting by 2s, 5s, or 10s.

Geometry and Shape Worksheets

Geometry offers a wonderful opportunity to relate math to the tangible world.

• Shape Identification: Recognizing and naming basic shapes such as squares, circles, triangles, etc.
• Comparing Shapes: Worksheets that help students identify differences and similarities between shapes.
• Pattern Recognition: Repeating shapes in patterns and asking students to determine the next shape in the sequence.

Measurement Worksheets

Measurement is another area where real-life application and math converge.

• Length and Height: Comparing two or more objects and determining which is longer or shorter.
• Weight: Lighter vs. heavier worksheets using balancing scales as visuals.
• Time: Reading clocks, days of the week, and understanding the calendar.

Data Handling Worksheets

Even at a primary level, students can start to understand basic data representation.

• Tally Marks: Using tally marks to represent data and counting them.
• Simple Bar Graphs: Interpreting and drawing bar graphs based on given data.
• Pictographs: Using pictures to represent data, which can be both fun and informative.

Place Value Worksheets

Understanding the value of each digit in a number is fundamental in primary math.

• Identifying Place Values: Recognizing units, tens, hundreds, etc., in a given number.
• Expanding Numbers: Breaking down numbers into their place value components, such as understanding 243 as 200 + 40 + 3.
• Comparing Numbers: Using greater than, less than, or equal to symbols to compare two numbers based on their place values.

Fraction Worksheets

Simple fraction concepts can be introduced at the primary level.

• Identifying Fractions: Recognizing half, quarter, third, etc., of shapes or sets.
• Comparing Fractions: Using visual aids like pie charts or shaded drawings to compare fractions.
• Simple Fraction Addition: Adding fractions with the same denominator using visual aids.

Money and Real-Life Application Worksheets

Understanding money is both practical and a great way to apply arithmetic.

• Identifying Coins and Notes: Recognizing different denominations.
• Simple Transactions: Calculating change, adding up costs, or determining if there’s enough money to buy certain items.
• Word Problems with Money: Real-life scenarios involving buying, selling, and saving.

Logic and Problem-Solving Worksheets

Even young students can hone their problem-solving skills with appropriate challenges.

• Sequences and Patterns: Predicting the next item in a sequence or recognizing a pattern.
• Logical Reasoning: Simple puzzles or riddles that require students to think critically.
• Story Problems: Reading a short story and solving a math-related problem based on the context.

Worksheets allow students to practice at their own pace, offer teachers a tool for assessment, and provide parents with a glimpse into their child’s learning progression. While digital tools and interactive activities are gaining prominence in education, the significance of worksheets remains undiminished. They are versatile and accessible and, when designed creatively, can make math engaging and fun for young learners.

The post 10 Helpful Worksheet Ideas for Primary School Math Lessons appeared first on Mom and More .