In this guide

Math warm ups for elementary
Math warm ups for middle school
Math warm ups for high school
Resources for math warm ups
General sources and additional resources

Warm-ups are a great way to get students engaged and ready to learn, especially if they’re transitioning to math from another subject.

Warm-ups are vital in ensuring your lesson will go as planned. After all, “the teacher who begins a lesson by sparking the student’s interest kindles a fire that remains lit for the balance of the period,” David Williams said in Arithmetic Teacher.

Math warm ups for elementary

For many students, their success–or struggles–in math begin in elementary school. Math or number anxiety was coined in the 1950s, and up to 93% of Americans experience it.

Neuroscientists have shown recently that for people with math anxiety, a fear center lights up in their brain — the same as when they see snakes and spiders — and the problem-solving center of the brain shuts down.
Jo Boaler told NPR.

These quick, unconventional warm-ups are designed to get students comfortable with mathematical thinking. Warm-ups are a great way to activate prior knowledge and help students build confidence in class.

1) A number a day

This activity is a classic for a reason! This is a great warm-up for lower elementary students. Consider these variations to keep students engaged.

Pick a number: Have students pick a number out of a hat or deck of cards, roll dice, or discover the daily number by solving a simple equation for it.

Creative things to do with the number students have chosen:

Illustrate the number in a creative way or take it a step further by inspiring them with unexpected examples, such medieval letters.
Write the number in Roman Numerals or explore the number’s form in ancient numerical systems like ancient Babylonian and Egyptian hieroglyphs.
Put the numbers into an equation or word problem that totals the daily number.

Modify for upper elementary with these additional prompts.

Today’s number is divisible by _.
Is the number prime or composite? Odd or even?
What’s the next prime number?
Multiply today’s number by / subtract today’s number from.

2) Which one doesn’t belong?

Which One Doesn’t Belong, or WODB, originates in Christopher Danielson’s award-winning book Which One Doesn’t Belong? The activity encourages students to expand mathematical thinking, improve communication skills, and expand critical thinking and reasoning.

There’s a catch though–there’s no right answer!

According to the Office of Superintendent of Public Instruction, this approach encourages students to “reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, {and} attend to precision.”

There are a few ways to facilitate this exercise in class. It can activate prior knowledge, check for understanding, and be incorporated into group work. Check out these 10 Examples of Evidence-Based Instructional Strategies for ideas!

The basic rules

Present students with a set of numbers, images, shapes, data sets, equations, or graphs. A common method is presenting four images on a 2×2 grid.
Ask students to identify what doesn’t belong and explain their reasoning. This routine has no right answer–the goal is for students to communicate and defend their reasoning.
Students can work in pairs or small groups to share their reasoning. They can present their theory as a group, or join in a class discussion.

Customizing the approach:

Explore Mary Bourassa’s collection of WODB puzzles. New games are continuously uploaded by people from around the world.
The games are categorized in shapes, numbers, graphs and equations.
None of the puzzles have answers, because many have more than one. This collection can help you cater the warm-up to what students are currently studying.

3) Geometry with Simon Says

This familiar game is ideal for kinesthetic and interpersonal learners, as well as energetic students. It’s a fun way to help students sharpen their decision making and communicative skills.

Designate a student as Simon, or be Simon yourself to demonstrate how to play the game. Simon will stand up and face the rest of the players.
Simon’s commands will ask students to create angles and shapes by moving their arms. For example, “Simon says make a parallel line” or “Simon says make a ninety degree angle”.
Simon can speed up the commands to increase the difficulty and promote on-the-spot-decision-making.
Students who make the wrong shape are eliminated until only one remains: the winner!
1. Alternatively, players can have a certain number of strikes before elimination.
2. Try a charades-style spin by having Simon display or show the shape and asking students to correctly identify it.

Supporting neurodiverse learners:

Simon Says tests executive function and auditory processing, so neurodiverse students may benefit from some adaptations.

The game has been used as an evaluation measure for ADHD (Attention Deficit Hyperactivity Disorder), and learners with ADHD may struggle with following the sequences. Students with ASD (Autism Spectrum Disorder) may need more guided instruction and support due to its unpredictable nature.

Make sure students have clear expectations of the game: what it’ll be like, what the objectives are, how long it will be, and why the game will be played. Let students ask additional questions beforehand.
Have Simon select from a list of actions, or give students a list of choices for Simon’s actions. Additionally, the class can brainstorm choices and actions beforehand.
Reduce or remove the penalties for doing the action wrong. This can alleviate anxiety and pressure.
Practice the actions beforehand by demonstrating them to the class or having students try them out.

Classroom games like Simon Says can be accessible for all students with the right adjustments.

Math warm ups for middle school

Middle school gives students a foundation for advanced math in higher grades. The following warm-ups are designed to hone students’ computational skills and inspire confidence.

4) Visual patterns

Sharpen your student’s algebraic thinking and pattern recognition with Fawn Nyguyen’s collection of Visual Patterns. Students must determine each pattern’s 43rd iteration.

Aside from being engaging, puzzle-solving fun, children with “strong pattern understanding are found also to have strong executive function skills, including cognitive flexibility (the ability to switch focus), and working memory,” says Dr Vicki Hargaves.

For example, how many stormtroopers would be present in Pattern 208’s 43rd iteration?

Math Warm Ups For Students Stormtroopers

Students need to identify the pattern of growth and calculate the number of stormtroopers in its 43rd iteration.
- The answer is 88 stormtroopers!

Some patterns are more advanced than others, so make sure to evaluate the right ones for your students. These can be great for high school students as well!

5) Card games

There’s so many ways to explore math with a simple deck of playing cards. There’s endless variations to try! These warm-ups can relax students with math anxiety and introduce a more positive spin on math.

Supplies needed:

A deck of playing cards.
Pencils or pens.

Fraction war

This spin on the classic game War will help students practice division.

Math Warm Ups For Students Card Games — Photo credit: kaylabernardez.com

Shuffle and deal the cards. A student can do this, or the teacher.
Each student will take 2 cards for their pile at the same time and turn them over. One card goes above a pencil and the other below to form a fraction.
The player with the largest fraction wins the round and collects all four cards.
The game ends once all of the cards are played. The winner has the most cards at the end.
Tips: If two fractions have the same common denominator, the fraction with the largest numerator wins. If they have the same common numerator, the fraction with the smaller denominator wins.

Flip three

This game may look simple, but it utilizes multiple arithmetic skills: addition, division, subtraction, and multiplication.

Variation 1: Equations (suitable for two to three players).
- Place all of the cards face down on a table in multiple rows.
- Each player will spend their turn flipping over three cards. They have to make an equation out of these three numbers by using any type of arithmetic.
- If they can make an equation, they keep the cards. If they can’t, they turn them back over.
- The winner with the most cards by the time only seven cards remain is the winner.

Variation 2: Prime numbers (suitable for two to four players).
- In this variation, students take turns flipping over two cards.
- The player finds the total of both cards. If the total is a prime number, they can keep the cards. If not, they flip the cards back down.
- The game ends when no cards remain or the few remaining can’t make a prime number. The player with the most cards wins.

6) Hit the target

This zero-prep warm-up is a quick and easy way to help students get ready for mathematical thinking.

How it works

Pick a number and present it to the class. This will be your “target number.”
Set a timer for a short period of time, such as three to five minutes, and ask students to come up with equations that total the target number. They can use any kind of arithmetic.

Raising the target for upper elementary

There’s several ways to modify this warm-up for more advanced students.

Increase the target number to multiple digits or make it a fraction or decimal value instead.
Add rules and requirements such as:
1. Each equation has to include two or more operations.
2. Students must include exponents in their equations.
3. Require equations to have a certain number of terms.
Don’t forget to adjust the timer!

Math warm ups for high school

Math courses in high school have been correlated with college success. In addition, better math education can give both high school graduates and drop-outs better outcomes in the labor market.

These warm-ups are designed to encourage abstract mathematical thinking, and maybe even inspire students to pursue math after graduation.

7) Famous women in mathematics

According to the AAUW, “women make up only 34% of the workforce in science, technology, engineering and math (STEM)”. Many young girls lack relatable role models in math and science.

As students consider their future after high school graduation, introduce them to the amazing stories and discoveries of female mathematicians.

Introduce students to trailblazers in mathematics such as:

Maryam Mirzakhani was an Iranian mathematician who focused on geometry, dynamical systems, and topology. She became the first woman to win the Fields Medal in 2014.
Karen Uhlenbeck is the first woman to receive the Abel Prize in 2019 for achievements in mathematics. She’s impacted new mathematical models that explain the forces in our universe.
Ingrid Daubechies is a physicist and mathematician who pioneered the image-compression technology we use to watch tv and play games today, and she’s one of the world’s most cited mathematicians.
Katherine Johnson was one of the first African-American women to work for NASA, and her orbital mechanics and trajectories launched modern space exploration. She’s received several awards and honors, and NASA built the Katherine G. Johnson Computational Research Facility in honor of her legacy.

Katherine Johnson: Trailblazing NASA Mathematician

8) Word problem warm-ups

Many students struggle with word problems, and I was one of them. This can put high schoolers at a serious disadvantage in standardized testing such as the SATs.

In general, between 30 percent and 50 percent of standardized-test items in math feature these kinds of story problems.
Sarah Powell on Education Week

Change the way students confront word problems in these warm-ups:

Flip the prompt

Have students solve a word problem backwards by starting with the solution first, such as:
- The solution is _ meters. What’s the question?
- The solution is _ minutes. What’s the question?
- The solution is _ dollars. What’s the question?

Omit the question by proving the beginning of a story problem and nothing else. For example:
- The original problem: Ronald and Elisa each had $100. Ronald spent $55 on clothes and Elisa spent $42 on books. How much more did Ronald spend than Elisa?
- The new problem: Ronald and Elisa each had $100. Ronald spent $55 on clothes and Elisa spent $42 on books. What’s the question?

Numberless problems

“The conversation is the goal” of number problems according to Brain Bushart. Numberless problems are a type of scaffolding that helps students face problems conceptually.

Any word problem can be made numberless, such as this prompt from Bushart’s bank.

The florist has 24 roses. She is going to use 6 of the roses in each bouquet she makes. How many bouquets can she make using all of the roses?

The florist has some roses. She is going to use some of the roses in each bouquet she makes.

Ask students to explain what they think the story is. What numbers do they think are reasonable or unreasonable for this story/question? Why?
You can slowly reintroduce numbers back into the prompt and ask students to reassess with the new information at each stage. Once the entire prompt is revealed, ask students to state what that question is asking in their own words.
- A 2021 study found that improving math-specific vocabulary helps students with word problems.

9) Activate prior knowledge

Before students tackle a new topic, give them time to work out what they already know and how they can apply that knowledge. This gives students a chance to consider new strategies and prepare to learn something new.

Think, Pair, Share

Students will spend two to five minutes answering a question or prompt individually. The prompt can focus on a word problem or specific subjects students are studying, or you can get creative! Getting students talking about math is the goal.
1. Convince your partner that you’ll have enough money to buy a car in six weeks if you deposit $3 and double your account balance every day.
Afterwards, they’ll pair up with a partner to reflect on what ideas they had in common. The pair will choose one major idea or answer and can share it in a class discussion afterwards.
You can modify this warm-up by setting time limits on the paired discussions, having students write out their ideas or present answers on the board, or by mixing up partners.

Resources for math warm ups

Still looking for more warm-ups and inspiration? Check out our video resource collections!

For Elementary: Create-to-Learn: Moved by Math
For Middle School: BBC Bitesize: Maths
For High School: Maths Essentials
For High School and Beyond: Consumer and Workplace Math

General sources and additional resources

Williams, D.E. (1984). Warm-Ups—Keys to Effective Mathematics Lessons. The Arithmetic Teacher, [online] 32(1), pp.40–43. Available at: https://www.jstor.org/stable/41193949.
Danielson, C. (2019). Which one doesn’t belong? : playing with shapes. Watertown, Ma: Charlesbridge.
Yeager, D. and Yeager, M. (2016). Simon Says Pay Attention: Help for Children with ADHD.

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