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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.

## 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.

## 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.

## 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.

## 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.

## 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.

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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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!

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.

## 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.

## 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

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.

## 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.

## 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.

## 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 .

Plus, get all the latest teaching tips and tricks when you sign up for our free newsletters .

## 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.

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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## 13 Fun and Educational Math Activities for Middle School

When students start middle school, they leap into a brand new math realm. For many children, the size of the newly acquired math schoolbook, along with the increased workload will seem intimidating.

As a middle school math teacher or educator, you’d naturally want to facilitate this tricky transition to ‘tweenhood’ math and help your students. Adding fun to your math lessons is perhaps the most effective way to do so. That’s why we’ve created a list of 13 fun and educational math activities for middle school that you can use to achieve this. Read on to learn more.

## 13 Math Activities for Middle School

1. exponent battle.

As the first activity on our math activities for middle school list, we have exponent battle. As the name suggests, you can use this game for learning and practicing exponentiation. The game is bundles of fun and its competitive aspect really sharpens the fast thinking of students. The best part of it? You don’t need anything but a deck of cards and willing players!

The steps for playing this game are as follows:

• Divide students into pairs of two and ask one player to be the dealer. They deal the cards, one by one, to the other player and themselves. The cards should be dealt face down.
• After the dealer has dealt all cards, both players simultaneously turn the top card face-up. The number on this card will serve as the base for the given player. The players then take the next card, which will be the exponent.
• For example, if the first card a player takes has the number 9 on it, and then the next card is the number 3, then 9 will represent the base and 3 the exponent for this player, i.e.93. If the other player takes a 6 and a 4, then they’ll have 64.
• Now both players should calculate the product without using a calculator and compare whose product is higher. For instance, if player one has 93 (or 9x9x9 = 729) and player two has 64 (or 6x6x6x6 = 1296), then player two is the one with the higher product in this round and wins it.
• The winner takes all cards that have been picked in the given round and gathers them in their pile. Continue playing the game until players have turned over all cards. In the end, players count how many cards each person has collected. The one who has collected the most cards is declared a winner.

## 2. ’Round the Block

To do this activity, you’ll need to bring a ball to class and prepare a list of math challenges. You can adjust the activity to practice almost any math concept in middle school.

The way you organize the activity is simple:

• Ask students to stand in a square and give the ball to a random person from the square and a math challenge.
• The student then passes the ball to the child standing next to them in the square, they pass it to the next one, and so on, until the ball goes ‘round the block and comes back to the student to whom it was initially given.
• By this time, the student should have had enough time to do the mental math and come up with an answer.
• The math challenge shouldn’t be too wordy so that the student has time to answer it before the ball comes back to them.
• For example, let’s say you want to practice rational and irrational numbers. You could prepare a list of challenges with rational and irrational numbers, such as: “Which of these is not an irrational number, a square root of 64, a square root of 5, or a square root of 3?”
• The student that answers then passes the ball to a person they randomly select from the square and the whole process is repeated.

## 3. Pairing Decimals Game

Next on our math activities for middle school list, we have the pairing decimals game. This is an easy game that will help children practice decimals. The aim of the activity is to pair decimals in order to reach the number 10. To play the Pairing Decimals Game, simply follow these guidelines:

• Prepare a set of cards with decimals on them beforehand. Make sure that each decimal that you put on a given card has a corresponding pair to reach the number 10. For example, 0.7 and 9.3, 5.5 and 4.5, etc.
• You can prepare as many cards as you wish, depending on the number of students in your class.
• Cut each of the cards and mix them. Then give one card to every student in the classroom and tell them that they should find the person that has the ‘matching card’. For example, a student that got a card with 0.7 on it will search for a student with 9.3 on their card.
• Instruct students not to reveal the decimal that’s on their cards to the whole group.
• Each student goes around the classroom, from person to person, asking students if they have a matching decimal number.
• They aren’t allowed to ask questions like “what’s your decimal?”; they can only ask “do you have xx decimal” (e.g.: “do you have 9.3?”). This way, they’ll have to calculate in advance how much they need to make 10.
• When a student finds their match, they’re declared winners. In the meantime, the game continues until everyone has found their match.
• If you want to make the game more exciting, you can add small awards for the ones that come 1st, 2nd, and 3rd.

## 4. Fractions Lottery

Use Fraction Lottery to practice fractions in your class. You’ll need to prepare chips with different numbers on them (1 through 20). Make sure you include each number twice, i.e. you should have 40 chips in total. Also, bring a large vessel where you’ll put the chips.

• Divide the class into several groups of 3, 4 students
• Then choose a person who’ll randomly draw two chips from the vessel, without looking while drawing the chips.
• The two chips will form a fraction, that is the first chip that’s drawn will represent the numerator, and the second one the denominator.
• Tell the teams that they should try to simplify the fraction, for example, 20/8 should be simplified as 5/2. The first team that manages to do this is the winner in that round.
• Continue playing until children get tired. The team that wins the most rounds wins the game.
• A variation of the game is to divide students into two groups and ask a player from each group to draw two chips in order to form a fraction.
• The teams then state their fractions in front of the whole class and race to determine which fraction is bigger.
• The team that is quicker scores a point if their answer is correct. The same procedure is then repeated and the game ends after an agreed number of rounds.
• The team that has the most points in the end is the one that wins the game.

## 5. Matching Fractions and Decimals Game

Play the Matching Fractions and Decimals Game after your students have been familiarized with the process of converting fractions into decimals since the aim of the game is to pair the fractions with corresponding decimal numbers.

There is a bit of prep work that you need to do before class. This includes gathering a large number of plastic bottle caps (24 caps per student) and writing fractions and corresponding decimals on them. You can ask your students to help you with the cap collection, but make sure that they’re brightly-colored so that it’s easier to write on them.

After you’re done with the fraction and decimal writing, follow these instructions:

• Divide students into pairs of two and place a timer next to each player.
• Give each player in the pairs 24 bottle caps, or two sets of 12 caps. One set has fractions on the caps, whereas the other one has corresponding decimals.
• Try to use fractions and decimals for which the students rely on their mental math, as they should be using calculators to find the matching pairs. For instance, you can use ¼ and its corresponding decimal 0.25, or 3/6 and 0.5.
• Explain to students that they should race against each other to match the fraction with the right decimal number. The first one that manages to match all 12 caps stops their timer and wins the game.
• Remind students to check their answers before stopping the timer, as incorrect answers will negatively impact their final score by adding five seconds to their time for every incorrect match.
• If you want to make the game even more challenging, feel free to add a third set of bottle caps with percentages on them that students have to match with the corresponding fraction and decimal. Again, you’d want to make sure you’re only using examples students can calculate by simply relying on mental math (ex: ⅕ and 0.2 and 20%).

## 6. Life-Sized Number Line

The benefits of visual number lines in classrooms have already been pointed out in  studies . Using such visual representation can work wonders for children’s understanding of the magnitude and order of numbers. And even if you’re a homeschooling parent, number lines are also great for you, as they don’t require group activities.

Number lines on the whiteboard or in individual worksheets are fine, but creating a life-sized number line on the floor is even more beneficial, as students can actually move along it, which makes the whole learning experience more exciting. This is why we had to include this one on our math activities for middle school list.

You can easily create a number line by cutting out paper squares with numbers on them or using numbered paper plates, or you can simply buy foam numbers. Then arrange the numbers in a line of the floor and use tape so that moving along them is safe and easy.

Once the number line is done, you’re ready to practice some integer operations!

• Give an integer equation to each student, and ask them ‘to solve it’ on the number line.
• Number lines are especially useful for adding and subtracting positive and negative numbers, so examples of the kinds of equations you could use are: -6 + 3; + 5 – 13 et
• Once they’re comfortable with simpler equations, move on to more complicated ones, such as 14 – (-6) + 7 -13

## 7. Percentage War

This is a group game that will boost percentage calculation skills in your students. Children should already be familiarized with expressing one amount as a percentage of another to play the game. You’ll have to prepare percentage-related math problems beforehand and adjust their number to the number of students in your class.

• Divide the class into groups of 4, 5 students. Each group sits in a different corner of the classroom.
• Explain to the groups that they have to race against each other to answer the math challenge correctly.
• Assign the first math percentage problem by reading it out loud from the card or presenting it visually on PowerPoint or an interactive whiteboard.
• This could be something like: “There are 30 sweets in Sally’s bag. 5 of the sweets are strawberry flavored. What percentage of sweets are strawberry flavored?”
• The first group to solve the given math challenge wins that round. You’ll then give the groups another challenge and repeat the process.
• In the end, the group with the biggest number of correct answers wins the game.

## 8. Pythagorean Theorem Proof

Next on our math activities for middle school list is the Pythagorean theorem proof activity. This is an excellent activity for deep learning. The objective of the Pythagorean theorem proof activity is to demonstrate the Pythagorean theorem visually. Most children will easily remember the formula of a2 + b2 = c2, but why is it so and how do you prove this?

An easy way to do this is by drawing! To do this, you’ll need large grid paper, scissors, a ruler, and a marker (if you have an interactive board, it will work even better).

• Place the grid paper on the floor and gather children in a circle around it. They can assist you in all of the following steps.
• Draw a right triangle on the grid paper and then cut it out.
• Now, cut out three squares from the grid paper with sides that are equal to each triangle side.
• Start with side  a . Measure its length and draw a square whose sides are the same length as side  a . Cut out the square and write a2 inside of it (in reference to the calculation of a square’s area, something that students are already familiar with from lower grades).
• Now repeat the same procedure to make squares based on the length of side  b  and side  c . Write b2 and c2 inside the squares respectively.
• Now place each square right next to the adequate side of the triangle: for instance, the square a2 is placed next to side  a  of the triangle, the square b2 is placed next to side  b  of the triangle and the square c2 is placed next to side  c .
• Now it’s time to show in practice the formula  a 2 +  b 2 =  c 2. Put square a2 and square b2 on top of square c2, in a way that they are covering it. To get a perfect fit, you’ll have to cut either square a2 or square b2 and then add the cut parts of the grid paper so that square c2. is entirely covered.
• Congrats! You’ve done it! And your students probably loved the visualization of this process! Now, not only do they know that a2 + b2 = c2,, but they actually know  why  a2 + b2 = c2.

## 9. Oreo Math

If you’re wondering how to introduce the concepts of median, mean, and average, here’s a fun (not to mention tasty!) activity that you could use in your classroom! You can also adjust this activity for your homeschooling lessons if you’re homeschooling your kids.

The aim of the activity is to gather data that you could later use for median, mean, and average calculations. You don’t need a lot of preparation beforehand, just make sure you have plenty of Oreo cookies (7 or 8 packs should be sufficient).

• Divide students into groups of 4 to 5 people and assign one person in each group to do data collection.
• Now give a few packs of Oreo cookies to each group.
• Tell the students that they should try to stack as many cookies as possible before the tower falls.
• All students in all groups take turns and give it a try.
• The person who is writing down the data should write down the number of cookies that each person stacked before the pile collapsed. This could look something like 10, 13, 9, 10, etc.
• Explain to students that this is not a competition, so they should be honest about the numbers.
• After each group had gathered around 5, 6 different numbers, ask them to calculate the median, mean and average! (and eat those towers of delicious Oreo!)

## 10. Volume Victory

This is a board game that you can use to practice calculating the volume of cones, prisms, pyramids, and cylinders. The game should be played after you’ve introduced students to the formulas for finding volumes of the mentioned geometric shapes. It can also be fun to play, so no wonder it made it on our math activities for middle school list.

For starters, you need to create a game board consisting of a line in the shape of a snake. You can draw this on colorful cardboard to make it more interesting. Then, divide the body of the snake into several spots (ex: around 20), and draw a specific geometric shape (prism, cone, etc.) on each spot.

Keep in mind that you’ll need to create 3, 4 game boards depending on the size of your class, as they’ll be split into groups and each group should have their own game board. Also, as students should move from one spot to another until they reach the end of the snake, make sure to bring plenty of chips that indicate the position of each student.

Prepare some 40 volume cards (including cones, prisms, pyramid, and cylinder cards) for each game board. On its outer side, each card should have a drawing of the shape it represents (ex: a prism), and on the inside, it should contain a math problem related to the specific geometric shape (in this case, a prism math problem).

After you’re done with the hard work, it’s time to start playing!

• Divide students into groups of 4 or 5, and place a game board and a set of Volume cards in each group. Divide the set of Volume cards into four card piles: cones, prisms, pyramids, and cylinders.
• Make sure the Volume cards are facing downwards, i.e. children are only able to see the geometric shape on each pile of cards, but not the volume challenge on the inside of the card.
• Place the appropriate number of chips in each group, depending on how many players the group has.
• Now explain the rules of the game to the students. Tell them that players in each group are competing against each other and not against other groups.
• Explain that the aim of the game is to move around the game board with the chips and reach the end of the board as fast as possible. To be able to move from spot to spot, students must find the volume of the specific figure that they landed on.
• For example, each student starts from the same spot, for example, a Cylinder spot can be the starting spot. Each student then draws a random card from the cylinder pile and reads the volume challenge on the inside of the card.
• If they’re able to find the volume of the cylinder, they can move a few spots. How many spots they move is correlated with the difficulty of the volume challenge. For instance, for very difficult challenges, they can move 3 spots and for easier challenges, they move only one spot. It will be written on each card how many spots they can move.
• The first person to reach the end of the board game wins first place, the second one comes in second, etc.

For more resources on teaching children about volumes of prisms and cylinders, check out  our blog post .

## 11. Classroom Village

Our math activities for middle school list would be incomplete without the fun classroom village game. Create a village with your students in the classroom to practice calculating a cone area. This activity is mainly given as a homework assignment, which children bring to class and present.

The aim of the activity is to create a village with different houses, each consisting of a rectangle (the main body of the house) and a cone (the roof of the house).

To implement this activity, students will need to be familiar with the formula for finding a cone’s surface area, i.e. πrs + πr2. In other words, they’re simply consolidating already acquired knowledge.

Prepare a space for a math bulletin board where the village project will be displayed at the end. Create several cards with a math challenge on finding a cone area. Then simply follow these instructions to create an awesome village project:

• Place the pile of cards with cone area challenges on your desk and ask each student to draw a random card.
• The cards should be facing downwards so that children can’t see what the challenge is.
• After each student has drawn a card, they read their math challenge and try to figure out the answer. Children do this activity as homework.
• An example of a challenge could be something like: “You have to create your house in the village. Your roof is shaped like a right circular cone, with a radius of 5 cm and a height of 12 cm. Find the total surface area of your roof. Draw the roof on paper, decorate it any way you please, and cut it out. Afterward, write the roof area on it. The body of your house is a rectangle, which you can create with any dimensions you please and glue it to the roof.”
• Next class, each student brings their house and places it on the math bulletin board, next to the houses of the other students.
• And there you have it, you’ve managed to create a coy, little village with your students!

Children are bound to enjoy the visual representation of their efforts in a joint way. Thus, the activity not only helps practice cone area but helps build a sense of community in your class.

## 12. Area and Circumference Bingo

Bingo is always an exciting game to introduce math concepts. Use this bingo game to practice calculating the area and circumference of circles. Children should be familiar with the corresponding formulas for finding the area and circumference in advance, i.e. A = πr2 and C= 2πr.

Create a set of question cards and a set of unique bingo cards (adjust the exact number according to the number of students in your class). The question cards contain circle area and circumference questions, whereas the unique bingo cards are cards with answers. Bring a number of markers, as well.

The steps for playing this activity are as follows:

• Hand out markers and a unique bingo card to each student. Keep the question cards for yourself.
• Explain the rules of the game to your students. Most of them are probably already familiar with bingo, so you can tell them that this game is played like regular bingo, but it differs in that instead of the teacher calling out numbers, they give a math question on area and circumference.
• The students then need to calculate this math problem. If they have the answer on their unique bingo card, they need to mark it with a marker.
• The student that has managed to create a straight line by marking answers on their card, shouts ‘Bingo!’
• Provide prizes for the winner, such as sweets or less homework for the next class.

## 13. Escape Room

And lastly, on our math activities for middle school list we have the escape room game. Digital escape rooms are a big hit with children, but if you don’t have the means to provide a tablet or such like each student so that they play in a digital escape room – you might as well create an escape room in your own classroom! And no, we’re not thinking literally locking children up in the classroom!

Instead, you simply bring a large lockbox in the classroom and create a captivating narrative around it. If you need ideas for what to put inside the box, you can include different types of prizes, such as chocolate, candy, etc.

Afterwards, create cards with different math problems, such as multiplying and dividing negative numbers. Make sure to also create a narrative around the escape room in advance.

Now that you have your box and math resources ready, dive into the escape room!

• Divide students into groups of 4 or 5.
• Explain that you’re playing an escape room game and they need to solve a few math challenges in order to unlock the room (that is, the box).
• Place the box in the middle of the classroom. If you want to add more sensory stimulation to the whole experience, you can also have some eerie music in the background.
• Read the pre-prepared narrative to the students. An example of such a narrative could be the following:

“A horrible tragedy has struck a medieval town. The town has fallen prey to a wicked witch that has cast a curse on all the town’s residents, due to which they fell into eternal slumber. The only ones that can reverse the spell are you, the last remaining wizards on earth. However, the witch has locked all of your potions in a box! In order to unlock the box, you’ll need to solve several math riddles. The residents’ lives are in your hands!”

• Give the first card with an integer challenge to each group. You can either place the other cards in strategic locations, or you can simply hand them over to students one by one if the classroom is too small.
• After solving each integer challenge, the group writes down their answer. The answer to each integer challenge forms the lock combination.
• Thus, the first group that manages to solve the integer challenges is the group that will find out the lock combination and win the game.

This article outlined 13 math activities for middle school incorporating a broad range of math concepts. From teaching about decimals, fractions, and percentages through competitive games and movement to proving the Pythagorean theorem by drawing, these math activities for middle school are guaranteed to make your math lessons a stimulating and enjoyable experience for your students.

Are you interested in more math resources for kids? Take a look at our  blog , or head over to our site at  MathTeacherCoach , where you’ll find math curricula for kids of all ages. If you want a preview, simply sign up for these  free samples of our 4th grade curriculum .

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## 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

## 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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## Math Activities for Middle School Enrichment: Critical Thinking at a Critical Age

Gifted Free Activities for Middle School Students

May 1, 2018, by The Critical Thinking Co. Staff

Good Mathematical Habits for Young Adolescents

Mathematics content is best learned in a way that fosters good habits of mathematical thinking. The Common Core State Standards in Mathematics ( www.corestandards.org ) supplement their K-12 standards for content with eight standards for mathematical practice:

• 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. These mathematical practices, and how they relate to content, mean very different things depending upon student age.

## Middle School as a Critical Transition Period

The middle school years mark a critical transition in a child’s cognitive development – how a child thinks and learns. Generally at age 11 or 12 children enter the fourth and final stage in Piaget’s four stages of cognitive development , called the formal operational stage. During this time children show significant growth in their ability to think abstractly, use advanced reasoning skills, make hypotheses and inferences, and draw logical conclusions. Ideally, the middle school years provide educators with new opportunities to foster good thinking habits and mathematical practices.

## The Balance Between Mathematical Content and Practice

Students begin middle school exposed to mathematics as a very broad subject covering a wide array of topics: 2D geometry, probability, percentages, number theory, logic, patterns, statistics, graphing, number operations, proportions, elementary algebra, 3D geometry, and so on. They finish middle school and begin high school usually embarking on year-long studies of content-intensive mathematical subject areas: a year of Algebra 1, then a year of Geometry, then a year of Algebra 2, and so on. Though young adolescents begin middle school ready to think with more power, creativity, and independence, the accompanying increase in content expectations means that a balance between mathematical content and practice can be difficult to achieve. Developing good thinking and learning habits requires investment of time and patience, and well-intended educators can be drawn away from quality mathematical practices when the drive to learn content becomes too formidable.

## Committing to Critical Thinking at the Middle School Level

Content can be learned in ways that ask young adolescents to harness and develop their new cognitive abilities. For example, a traditional 2D geometry question might ask:

Calculate the perimeter and area of a rectangle with a 15-inch length and a 9-inch width.

This question can be answered by performing a routine calculation using formulas for the perimeter and area of a rectangle. Similar content can be studied with a question that asks for critical thinking:

For what whole number values of length and width will the rectangle have an area of 60 square yards and a perimeter of 38 yards?

This second question (from Mathematical Reasoning™ Middle School Supplement ) requires students to develop a strategy to construct a solution. Indeed, a common approach involves making a mental or physical list of pairs of whole numbers that multiply to 60 and then searching for the pair of numbers that add up to 19 (since a rectangle’s perimeter is twice the sum of the length and width). The correct answer is a length of 15 inches and a width of 4 inches (assigning the larger number to length). Note the depth and value of a critical thinking opportunity: the solution strategy connects 2D geometry with the number theory technique of factoring and is a precursor to a more sophisticated factoring procedure used in Algebra 1. The second question requires greater time investment than the first question, but is worth the extra time if one is committed to young adolescents learning content in a way that fully engages their reasoning skills.

## Fostering Perseverance

The first Common Core mathematical practice standard emphasizes the need to have students make sense of problems and persevere in solving them. The most important ingredient in Polya’s classic four-step problem solving strategy is the act of making decisions, as opposed to simply applying an algorithm that has been instructed. Young adolescent reaction to problem solving and decision making can be decidedly mixed. On the one hand, playing an active role in the solution process – figuring something out and being creative – can be fun, exciting, sometimes even addicting for young minds that are ready to be engaged. However, overcoming obstacles and persevering with a task that requires multiple steps and authentic reasoning can also sometimes be discouraging for early adolescent brains just learning how to tap into their emerging powers. The frustration level can depend on the difficulty level of the problem-solving situation, and a common, safe path is to keep decision making and creative expectations down to a minimum. However, if mathematics education in the United States is to reach a higher standard against a worldwide benchmark , children must be encouraged to persevere with critical thinking and decision making, to embrace both the excitement and occasional frustration of authentic reasoning and creativity.

## Enrichment Activities to Stimulate Critical Thinking

The Critical Thinking Co.™ specializes in activities that stimulate use of reasoning skills and creativity when learning content. These enrichment activities challenge students to make decisions and construct solutions – to play an active role when learning content. Variety is favored over repetition, although care is taken to have common themes emphasized and connections reinforced. Presentation is often graphic intensive, resulting in visual appeal to young eyes. Real-world applications are easily identifiable. Problem-solving is supported with clear, comprehensive solutions and explanations. An example is provided with the activity sets Dimension Detective and Linear Patterns and accompanying solution pages from Mathematical Reasoning™ Middle School Supplement . In Dimension Detective students deduce missing dimensions for a variety of geometric shapes by using proportional reasoning, number theory ideas, and connections between 2D and 3D shapes. In Linear Patterns students determine number patterns and geometric patterns, and then deduce algebraic expressions to describe these patterns (a precursor to creating algebraic equations to describe linear graphs). Each activity set is accompanied by needed math facts, strategy tips, and comprehensive solutions that teachers and parents can use to help support student investigations. These sorts of enrichment activities provide middle school students with an opportunity to explore mathematical content, create or reinforce ideas, make connections, and use abstract reasoning. Young adolescents have emerging cognitive powers to accompany their rapid physical growth, and math enrichment can provide middle school students with appealing opportunities to use their maturing reasoning skills.

## Free Printable Math Worksheets for Grades 6-9

• Dimension Detective (Number Theory)
• Linear Patterns
• Geometry & Introduction to Trigonometry
• Uncovering All the Angles
• Algebraic Cryptograms
• The Finest Pyramid

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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!

## 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.

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!

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?

• Latest Posts

## Megan Zechman

@edupossible, latest posts by megan zechman ( see all ).

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## 20 Problem-Solving Activities for Middle School Students

June 28, 2022 //  by  Lesa M.K. Bullins, EdS

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

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

## 1. Feelings Expression Scenarios

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

## 2. Empathy Empowered Discussions

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

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

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

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

## 4. Get Out of the Way

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

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

## 5. Plan a Road Trip

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

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

## 6. Escape the Room

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

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

## 7. Teach Explicit Strategies for Reflection

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

## 8. Daily Practice

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

## 9. Build Something

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

## 10. Blind Drawing Partners

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

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

## 11. Laser Maze

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

## 12. Shared Story Puzzles

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

## 13. Yarn Webs

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

## 14. Scavenger Hunt

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

## 15. Boom! Math!

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

## 16. Wheel of Solutions

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

## 17. Collaborative Math

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

## 18. Get Mysterious

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

## 19. Logic Puzzles and Games

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

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

So instead of getting quiet, get them talking!

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## Solving Equations in Middle School Math

Solving equations is foundational for middle and high school math. Students actually have been doing this since first grade! However, students can make careless errors or struggle when it comes to following the many procedural steps required to solve an equation.

## Why the struggle?

Solving equations is very revealing. If your students struggle with integer operations , then it will show up again when solving equations. If your students struggle with rational number operations, then it will show up again when solving equations.

We asked our Facebook group what students mostly struggle with, and here are some of the responses:

• Combining like terms incorrectly
• Not distributing when they should. Example: 5 – 2(x + 2) = 10 simplifying to 3(x +2) = 10
• Students completing inverse operations on the same side of the equal sign instead of combining like terms (see below for picture)

Does this sound familiar?

## Use Algebra Tiles (No, really, use them!)

I was resistant! Manipulatives can cause undue stress (tiny items + 30 children); it is a lot! However, I think that if I had used algebra tiles in my classroom, students would have been way more engaged ! I occasionally drew a model to demonstrate solving equations, but then Noelle showed me all the ways algebra tiles could be used to combine like terms, distribute, and solve two-step equations (even quadratics). I was on board!

Before using algebra tiles to introduce students to solving equations, use algebra tiles to demonstrate combining like terms. Combining like terms can be challenging for students, but when you ask students to combine all of the long green tiles (x), the long red tiles (-x), the small yellow tiles (+1), and the small red tiles (-1), it provides excellent concrete practice. It will also assist with zero pair understanding, which will be essential to solving equations with algebra tiles.

What would you rather combine as a student?  The terms or the algebra tiles?

Let’s move on to solving equations. Look at the following example:

Before exposing your students to two-step equations with variables on both sides, let them practice with one-step equations first. Scaffolding is key. I chose this example to show you how versatile algebra tiles are (variables on both sides and negative values)

To isolate the variable, students would need to recognize that they needed to get rid of positive 2.  To do this, they would add two negative tiles to make a zero pair. Adding negative 2 to one side would mean they would add to the other side to keep the equation balanced.

After students have removed the two zero pairs on the left side of the equation, they might be a little stuck. They are exploring, after all. Remind students that we want all variables on one side, since we want to find out what one x is equal to. Students would then add a negative x to both sides to create another zero pair.

Lastly, to get the solution for one x, students would divide the remaining red tiles among the two x tiles: X = -4.

Students are actually solving for x by undoing the problem, by using inverse operations (adding -2 to both sides and dividing by 2), and by keeping the equation balanced (they are adding tiles to both sides). All the procedural steps that might mean nothing to students in a traditional problem have meaning when students have been exposed to practicing with algebra tiles.

Remember that algebra tiles (like most manipulatives) exist to make the math visual. They provide conceptual understanding. Eventually, students will move into the algorithm. When students are exploring, make sure all of the solutions are integers (you can’t break the tiles into pieces).

To learn more about students making the jump from concrete to abstract, please check out our posts about the CRA Framework – Part 1 and Part 2 .

Another tip I recommend is to have students write out what is happening as they are using algebra tiles to solve an equation. If they are combining 3 green tiles with two red tiles, then they would need to write 3x-2x with evidence of only 1x remaining.

If you don’t have access to algebra tiles, students can use this website .

Be sure to grab our Getting Started with Algebra Tiles freebie to learn more about using algebra tiles to tackle simplifying expressions, the distributive property, solving linear equations, adding and subtracting polynomials, multiplying and dividing polynomials, and factoring polynomials.

• Draw a line to separate the two sides of the equation.
• Do Undo Line – this is another strategy that can help students.
• Color-coding to help with combining like terms
• Making sure to actually say (and make students say), “2 times x equals 5” as opposed to “2x = 5.”

For more resources, check out these units and bundles.

What additional tips do you have? Do you use algebra tiles in your classroom?

## Getting Started with Algebra Tiles

Check out these related products from my shop.

## Small Group Math Activities

• 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.

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.

## 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.

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.

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## Building a Thinking Classroom in Math

Over more than a decade, the author has developed a 14-point plan for encouraging students to engage deeply with math content.

One day in 2003, I was invited to help June implement problem solving in her grade 8 classroom. She had never done problem solving with her students before, but with its prominence in the recently revised British Columbia curriculum, she felt it was time.

June, as it turned out, was interested in neither co-planning nor co-teaching. What she wanted from me was simply a collection of problems she could try with her students. The first one I gave her was a Lewis Carroll problem that I’d had much success with, with students of different grade levels: If 6 cats can kill 6 rats in 6 minutes, how many will be needed to kill 100 rats in 50 minutes?

June used it the next day. It did not go well. A forest of arms immediately shot up, and June moved frantically around the room answering questions. Many students gave up quickly, so June also spent much effort trying to motivate them to keep going. In general, there was some work attempted when June was close by and encouraging the students, but as soon as she left the trying stopped. This continued for the whole period.

The following day I was back with a new problem. The results were as abysmal as they had been on the first day. The same was true the third day. Over the course of three 40-minute classes, we had seen little improvement in the students’ efforts to solve the problems, and no improvements in their abilities to do so. So June decided it was time to give up.

I wanted to understand why the results had been so poor, so I stayed to observe June and her students in their normal routines. After three full days of observation, I began to discern a pattern. That the students were lacking in effort was immediately obvious, but what took time for me to realize was that the students were not thinking. More alarming was the realization that June’s teaching was predicated on an assumption that the students either could not or would not think.

Once I realized this, I proceeded to visit 40 other mathematics classes in a number of schools. In each class, I saw the same thing—an assumption, implicit in the teaching, that the students either could not or would not think. Under such conditions it was unreasonable to expect that students were going to be able to spontaneously engage in problem solving.

This motivated me to find a way to build, within these same classrooms, a culture of thinking. I wanted to build what I now call a thinking classroom—one that’s not only conducive to thinking but also occasions thinking, a space inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion.

Over 14 years, and with the help of over 400 K–12 teachers, I’ve been engaged in a massive design-based research project to identify the variables that determine the degree to which a classroom is a thinking or non-thinking one, and to identify the pedagogies that maximize the effect of each of these variables in building thinking classrooms. From this research emerged a collection of 14 variables and corresponding optimal pedagogies that offer a prescriptive framework for teachers to build a thinking classroom.

1. The type of tasks used: Lessons should begin with good problem solving tasks. In the beginning of the school year, these tasks need to be highly engaging, non-curricular tasks. Later these are gradually replaced with curricular problem solving tasks that then permeate the entirety of the lesson.

2. How tasks are given to students: As much as possible, tasks should be given verbally. If there are data, diagrams, or long expressions in the task, these can be written or projected on a wall, but instructions should still be given verbally.

3. How groups are formed: At the beginning of every class, a visibly random method should be used to create groups of three students who will work together for the duration of the class.

4. Student work space: Groups should stand and work on vertical non-permanent surfaces such as whiteboards, blackboards, or windows. This makes the work visible to the teacher and other groups.

5. Room organization: The classroom should be de-fronted, with desks placed in a random configuration around the room—away from the walls—and the teacher addressing the class from a variety of locations within the room.

6. How questions are answered: Students ask only three types of questions: proximity questions, asked when the teacher is close; “stop thinking” questions—like “Is this right?” or “Will this be on the test?”; and “keep thinking” questions—ones that students ask in order to be able to get back to work. The teacher should answer only the third type of question.

7. How hints and extensions are used: The teacher should maintain student engagement through a judicious and timely use of hints and extensions to maintain a balance between the challenge of the task and the abilities of the students working on it.

8. Student autonomy: Students should interact with other groups frequently, for the purposes of both extending their work and getting help. As much as possible, the teacher should encourage this interaction by directing students toward other groups when they’re stuck or need an extension.

9. When and how a teacher levels their classroom: When every group has passed a minimum threshold, the teacher should pull the students together to debrief what they have been doing. This should begin at a level that every student in the room can participate in.

10. Student notes: Students should write thoughtful notes to their future selves. They should have autonomy as to what goes in the notes and how they’re formatted. The notes should be based on the work already on the boards done by their own group, another group, or a combination.

11. Practice questions: Students should be assigned four to six questions to check their understanding. They should have freedom to work on these questions in self-selected groups or on their own, and on the vertical non-permanent surfaces or at their desks. The questions should not be marked or checked for completeness—they’re for the students’ self-evaluation.

12. Formative assessment: Formative assessment should be focused primarily on informing students about where they are and where they’re going in their learning. This will require a number of different activities, from observation to check-your-understanding questions to unmarked quizzes where the teacher helps students decode their demonstrated understandings.

13. Summative assessment: Summative assessment should focus more on the processes of learning than on the products, and should include the evaluation of both group and individual work. Summative assessment should not in any way have a focus on ranking students.

14. Reporting out: Reporting out of students’ performance should be based not on the counting of points but on the analysis of the data collected for each student within a reporting cycle. The data need to be analyzed on a differentiated basis and focused on discerning the learning a student has demonstrated.

My research also shows that the variables and accompanying pedagogical tools are not all equally impactful in building thinking classrooms. And there is an optimal sequence for both teachers and students when first introducing these pedagogies. This sequence is presented as a set of four distinct toolkits that are meant to be enacted in sequence from top to bottom, as shown in the chart. When these toolkits are enacted in their entirety, an optimal transformation of the learning environment has been achieved in the vast majority of classrooms.

## 10 Math Problem Solving Activities for Middle School

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

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

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

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

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

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

Marijus Auruskevicius/Shutterstock.com

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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## 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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Career Readiness | Middle School | Critical Thinking

## Problem Solving Lesson Plans Your Middle School Students Will Love

July 11th, 2022 | 8 min. read

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Need resources for teaching problem solving in your middle school career readiness classes?

As a career readiness curriculum developer, middle school teachers often ask if we have resource to help teach problem solving.

While our digital curriculum includes content on critical thinking, decision making, and other 21st Century skills , our solution may not be the best fit for everyone.

Our Business&ITCenter21 curriculum is designed to teach dozens of skills such as professionalism, communication, public speaking, digital citizenship, and more.

However some teachers are only looking for supplemental problem solving lessons and activities to add to their existing curriculum.

To help you teach these skills, we've found four popular providers of problems soling lessons and activities for middle school:

• TeacherVision
• Ed Creative

All of these resources have both pros and cons, so looking at each one individually is key when planning your problem solving lessons!

## 1. TeacherVision's Problem Solving Lesson

TeacherVision is a digital resource that offers free online lesson plans, including a problem solving lesson.

This problem solving lesson has two key objectives:

• Students will be introduced to a problem-solving procedure
• Students will participate in a structured practice of resolving conflict

Along with the lesson objectives, you'll find the materials list and the procedure for completing the lesson.

That makes TeacherVision a robust resource with an easy to follow lesson plan for introducing students to problem solving.

On the downside, the lesson is listed as being appropriate for students between first and eighth grade.

That means you may want to bulk it up a bit in order to really be relevant and engaging to your middle school students.

## 2. Ed Creative's Problem Solving and Critical Thinking Lesson Plans

Ed Creative   is a subdivision of Education.com that collects lesson plans from other online resources.

That makes Ed Creative one of the best lesson plan databases online.

It includes a variety of lesson plans and activities to teach creativity , problem solving, and critical thinking skills .

Many of these lessons are intended for children up to   eighth grade. That means you'll likely find some resources that fit perfectly in your middle school classes.

In addition, some lessons overlap with other subjects you may need to teach in your career readiness classes. For example, one resource is entitled   Thinking Critically About Advertising and would tie in well with lessons on media literacy .

The lesson encourages students to consider behind the scenes angles when presented with ads, encouraging them to think critically and logically about   why   the ad is what it is.

Still, these resources are a little disorganized which means it will take you time to review each option and decide if it's a good fit.

## 3. BrainPOP's Critical Thinking and Problem Solving Activities

BrainPOP   is an educational resource provider with many teaching resources for every grade level.

In this case, their critical thinking and problem solving lesson plan is intended for any student from   sixth to 12th grade.

In this lesson, students will:

• Apply critical thinking, problem solving, and decision-making skills to online game play and writing tasks
• Analyze situations from multiple perspectives and viewpoints
• Distinguish between facts, opinions, and solutions
• Demonstrate 21st Century skills such as global awareness, information literacy , communication , and collaboration

BrainPOP lays out the procedure, materials, and everything else you’ll need for the lesson — even time approximations!

That thorough approach to detail makes it easier for you to plan different tasks you’ll carry out throughout the lesson each day.

Even if the lesson takes you a full week, you can still plan appropriately and stay on task.

Unfortunately, BrainPOP doesn’t have a lot of downloadable resources that you can print and use in the classroom.

## 4. TEDEd's Resources for Teaching Problem Solving Skills

TEDEd   is an active advocate of education and learning materials. That’s why they have an enormous section of their website dedicated to problem solving skills .

In this section, you’ll find videos and interactive tasks that walk students through riddles, problems, and complications to find desirable results.

Every riddle and problem comes with an answer, so you don’t have to worry about figuring it out yourself. Even better, you can be sure that there’s a practical solution to every issue.

Best of all, you leave students with the freedom to innovate their own solutions, potentially creating a   new solution   that a riddle maker hadn’t considered.

The varying complexity and length of these lessons makes them ideal for a variety of grade levels, however you can choose to filter specifically for middle school.

On the downside, these aren’t literal “lesson plans.” TEDEd provides a whole host of resources, but they’re not contextualized for a classroom.

This makes TEDEd an excellent catchall for any time you need problem solving materials.

You’ll just have to do a little extra work to make it classroom ready.

## Which Problem Solving Lessons Are Best?

Overall, there isn't a simple "best" option for teaching problem solving in middle school. It all depends on the needs of you, your course, and your students.

However, if you need a curriculum that includes problem solving skills among other career readiness topics, consider looking into Business&ITCenter21.

Thousands of teachers like you use the curriculum to teach  career exploration ,  personal financial literacy ,  communication skills ,  professionalism , and more.

Overall, it helps you save time with planning, assessing, and grading student work all while maximizing student understanding and information retention.

## 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

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

## Conquering the Fraction Division Challenge

Welcome to Cognitive Cardio Math! I’m Ellie, a wife, mom, grandma, and dog ‘mom,’ and I’ve spent just about my whole life in school! With nearly 30 years in education, I’ve taught:

• All subject areas in 4 th  and 5 th  grades
• Math, ELA, and science in 6th grade (middle school)

I’ve been creating resources for teachers since 2012 and have worked in the elearning industry for about five years as well!

Let's connect.

## 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 .

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6. Math Problem Solving Through Strategies and Models

1. 50 Challenging Math Puzzles For Middle School Students

1. Numbers in a Triangle Working with the numbers 1 to 9 only, your kiddies will need to manipulate these numbers to ensure that the sum of numbers on every side of the triangle is the same. Your learners might need to give this puzzle a couple of tries! Learn More: Homeschool Math 2. Minesweeper

2. Problem Solving Activities: 7 Strategies

Problem Solving Activities: 7 Strategies 2 Comments Critical Thinking Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

3. 30 Thought-Provoking Math Puzzles for Middle Schoolers

1. Sudoku 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.

4. 55 Math Activities For Middle School: Algebra, Fractions, Exponents

1. M & Maths Use M&Ms to teach math! Provide students with a pile of M&Ms to count and convert into fractions, decimals, and percentages. You can also extend this activity by getting the students to graph their findings. Materials needed: M&Ms Topic: Fractions, decimals, percentages, and graphs Learn more: Our Journey Westward 2.

5. 6-8 First Week Problem Solving Tasks

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).

6. 13 Fun and Educational Math Activities for Middle School

1. Exponent Battle As the first activity on our math activities for middle school list, we have exponent battle. As the name suggests, you can use this game for learning and practicing exponentiation. The game is bundles of fun and its competitive aspect really sharpens the fast thinking of students. The best part of it?

7. Free Resources for Any Middle School Math Concept

Sequences, Series and Patterns (Part 1) Sequences, Series and Patterns (Part 2) Probability Circles Use these resources to help you plan your next online learning session! Arithmetic Skills Faster Arithmetic Models Practice Plan

8. Math Problem Solving Strategies

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.'

9. Math Activities for Middle School Enrichment: Critical Thinking at a

Problem-solving is supported with clear, comprehensive solutions and explanations. ... These sorts of enrichment activities provide middle school students with an opportunity to explore mathematical content, create or reinforce ideas, make connections, and use abstract reasoning. ... Award-Winning Math Books for Middle School Students.

10. Problem Solving Strategies & Activities for Middle School Math

Are you a student or a teacher? As a middle school math teacher, you want to give your students plenty of opportunities to solve problems, as well as strategies for doing so. This...

11. 20 Best Math Puzzles to Engage and Challenge Your Students

1. Math crossword puzzles 3. Math riddles 4. Prodigy 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.

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Make Sense of Math. 4.8. (30) \$4.00. PDF. After a long break, wake-up your student's problem-solving skills with these middle school math activities that are just right for back to school. These are tasks that require problem-solving skills to complete. These are approachable for various skill levels.

13. Fun Math Activities for Middle School

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 ...

14. Free Math Worksheets

Algebra 1 High school geometry Algebra 2 Trigonometry Statistics and probability High school statistics AP®︎/College Statistics Precalculus Differential Calculus Integral Calculus AP®︎/College Calculus AB AP®︎/College Calculus BC Calculus 1 Calculus 2 Multivariable calculus Differential equations Linear algebra Early math Counting

15. 20 Problem-Solving Activities for Middle School Students

15. Boom! Math! An excellent way to build advanced problem-solving skills, as well as mathematical analysis, is to create math Boom Cards with word problems like these from Math in the Middle. Boom cards are a great activity for students to practice and build skills! Learn more: Boom Learning. 16.

16. Solving Equations in Middle School Math

These teacher tips from our Math Teacher VIP Facebook Group might help your students. Draw a line to separate the two sides of the equation. Do Undo Line - this is another strategy that can help students. Making sure to actually say (and make students say), "2 times x equals 5" as opposed to "2x = 5.".

17. Small Group Math Activities

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:

18. Open Middle

WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version Secondary Version CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

19. Building a Thinking Classroom in Math

1. The type of tasks used: Lessons should begin with good problem solving tasks. In the beginning of the school year, these tasks need to be highly engaging, non-curricular tasks. Later these are gradually replaced with curricular problem solving tasks that then permeate the entirety of the lesson. 2.

20. 10 Math Problem Solving Activities for Middle School

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...

21. 20 Problem-Solving Activities for Middle School Students

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.

22. Problem Solving Lesson Plans Your Middle School Students Will Love

1. TeacherVision's Problem Solving Lesson TeacherVision is a digital resource that offers free online lesson plans, including a problem solving lesson. This problem solving lesson has two key objectives: Students will be introduced to a problem-solving procedure Students will participate in a structured practice of resolving conflict

23. Help Middle School Math Students Improve Problem Solving Skills

Solving: 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 Train Two = 9, then Train One (2 (9)) = 18 and Train Three (9 + 2 (9) + 10 ) = 37.

24. 10 Helpful Worksheet Ideas for Primary School Math Lessons

The post 10 Helpful Worksheet Ideas for Primary School Math Lessons appeared first on Mom and More. Mathematics is a fundamental subject that shapes the way children think and analyze the world.