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This activity has endless possibilities and can be quite challenging for certain numbers. It also is accessible for almost any grade span.

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This activity has students express their thinking based off of reading a graph that shows someone's personal preferences around fruit, then has them build their own graph to communicate their preferences. Just make your own copy to edit and adjust for your classes.

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This activity has Ss create patterns with color of their own choosing. The conversation leads to generalizations of multiples of numbers, prime numbers, etc.

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These activities push students out of the standard algorithm to be more flexible with numbers and symbols.

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In this activity, students sort 10 types of fruit by tastiness and ease of eating in order to learn how those attributes can be represented on a coordinate plane, and to determine which fruit truly is "best." With gratitude and apologies to Randall Munroe. https://xkcd.com/ ###CPM COLLABORATION###

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In these tasks, students make a choice about which item doesn't belong and explain their thinking.

I love to use these sentence frames because they practice using the language of SMP 3:

I argue that _________ does not belong.

My mathematical proof that my conjecture is correct is _______________.

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

Which One Doesn't Belong?

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

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Add anything you use to help explain the SMPs or have your students reflect on being a mathematician.

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Alternate student-friendly language.

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FREE! Common Core Mathematical Practices Classroom Posters

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8 Common Core Standards for Mathematical Practices Classroom Posters Remind students of these valuable Math Practices with these colorful and simple legal-size posters. Each practice has a specially designed icon to help students not only remember the 8 Math Practices, but use them as well.

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Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It’s an ideal routine to foster mathematical practice #7 - look for and make use of structure.

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This can help you figure out if a task is aligning to a specific SMP. Would you ask this type of question to help your students move through the task? Credit to Audrey Mendevil and the SDCOE

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This is a form to have students reflect on how they were being a mathematician post activity/learning. There is an element of student choice involved.

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"MΣΣT a Mathematician!" is a collection of video interviews with mathematicians. The mission of MΣΣT a Mathematician is to share stories of mathematicians from different backgrounds, especially from historically excluded groups, with the aim of introducing students to role models and fostering a

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A survey I give at the beginning of the year to gather information about Ss, how they see themselves as learners/mathematicians, and what they are hoping to gain from the year.

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Inside Mathematics illuminates the mathematical practice standards with video excerpts of mathematics lessons. Although the practices are presented here individually, it’s important to keep in mind that the practices can, and should, be evident together in a lesson.

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Inside Mathematics illuminates the mathematical practice standards with video excerpts of mathematics lessons. Click the individual standards below to see instances of the practice standards in classroom lessons. Although the practices are presented here individually, it's important to keep in mind that the practices can, and should, be evident together in a lesson. See the Mentors of Mathematical Practice for a holistic view of the practices together.

See also our new resources incorporating social and emotional learning competencies in the mathematics classroom and how they support the mathematical practices.

Practice Standards

1. Make sense of problems & persevere in solving them

2. Reason abstractly & quantitatively

3. Construct viable arguments & critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for & make use of structure

8. Look for & express regularity in repeated reasoning

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Mathematical Practice Standards | Inside Mathematics

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Inside Mathematics illuminates the mathematical practice standards with video excerpts of mathematics lessons. Click the individual standards below to see instances of the practice standards in classroom lessons. Although the practices are presented here individually, it’s important to keep in mind…

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The Broken calculator is a good digital version of the Four 4s activity.

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Use the keys on this broken calculator to make the totals from 1 to 20. Five has already been done as an example, see below.

1 =

2 =

3 =

4 =

5 =

6 =

7 =

8 =

9 =

10 =

11 =

12 =

13 =

14 =

15 =

16 =

17 =

18 =

19 =

20 =

Recently Updated

Calendar Maths Investigation

Investigate the connection between the numbers in a T shape drawn on this month's calendar. So far this activity has been accessed 16347 times and it is ready for you to enjoy!

Broken Calculator 4

A challenge to produce the numbers from one to twenty on a calculator with some missing keys.

Click the keys on the calculator above to make the numbers 1 - 20. As you make each total your calculation will appear in the table on the right.

Make all twenty totals the earn a Transum Trophy.

Unlike a normal calculator, for this activity, you cannot use one total you have found to help make another. Each calculation starts from scratch (zero).

Try to make each total using the smallest number of calculator key presses.

Other broken calculators;
1 and 5 2 and 3 3 and 4 4 and 5 5 and 2 6 keys

There are solutions to this activity but they are only available to teachers who have subscribed to Class Admin.

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A challenge to produce the numbers from one to twenty on a calculator with some missing keys.

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Taking pieces of a cube to make one solid cube. There are 240 essentially distinct ways of doing so.

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A solid dissection puzzle invented by Piet Hein during a lecture on Quantum Mechanics by Werner Heisenberg. There are seven soma pieces composed of all the irregular face-joined cubes ( polycubes) with cubes. The object is to assemble the pieces into a cube. There are 240 essentially distinct ways of doing so (Beeler 1972, Berlekamp et al. 1982), as first enumerated one rainy afternoon in 1961 by J. H. Conway and Mike Guy.

A commercial version of the cube colors the pieces black, green, orange, white, red, and blue. When the 48 symmetries of the cube, three ways of assembling the black piece, and ways of assembling the green, orange, white, red, and blue pieces are counted, the total number of solutions rises to .

REFERENCES:

Albers, D. J. and Alexanderson, G. L. (Eds.). Mathematical People: Profiles and Interviews. Boston, MA: Birkhäuser, p. 43, 1985.

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 112-113, 1987.

Beeler, M. Item 112 in Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, pp. 48-50, Feb. 1972. https://www.inwap.com/pdp10/hbaker/hakmem/polyominos.html#item112.

Berlekamp, E. R.; Conway, J. H.; and Guy, R. K. Ch. 24 in Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, 1982.

Bundgaard, T. "Thorleif's SOMA Page." https://www.fam-bundgaard.dk/SOMA/SOMA.HTM.

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 203-205, 1989.

Gardner, M. "Mathematical Games: A Game in Which Standard Pieces Composed of Cubes are Assembled into Larger Forms." Sci. Amer. 199, 182-192, Sep. 1958.

Gardner, M. "The Soma Cube." Ch. 6 in The Second Scientific American Book of Mathematical Puzzles & Diversions: A New Selection. New York: Simon and Schuster, pp. 65-77, 1961.

Maas, M. and Retina GbR. "3-D Soma Cube Online." https://www.retina.de/cube/somacube.html.

Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 168-169, 1999.

Referenced on Wolfram|Alpha: Soma Cube

CITE THIS AS:

Weisstein, Eric W. "Soma Cube." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SomaCube.html

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A solid dissection puzzle invented by Piet Hein during a lecture on Quantum Mechanics by Werner Heisenberg. There are seven soma pieces composed of all the irregular face-joined cubes ( polycubes) with cubes. The object is to assemble the pieces into a cube. There are 240 essentially distinct ways of doing so (Beeler 1972, Berlekamp et al.

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If you have 27 small cubes, 3 each of nine colours, can you make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour?

A great way to get students using technology or real-life manipulatives. A great discussion on how color can help support thinking and explanation.

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If you have 27 small cubes, 3 each of nine colours, can you make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour?

In the picture, the top face and the left face have one of each colour.

Unfortunately the third face has two greens, two blacks, no reds and no browns, so this is not a valid solution.

You might like to explore this problem using cubes. If you don't have any cubes, you could record your work on squared paper by drawing and colouring each layer, or use the interactivity below.

Instructions:
Choose a colour, and click on a square on the left to colour a cube on the right.
When you complete a face correctly, a "tick" will appear.

Printable NRICH Roadshow resource.

Click here for a poster of this problem.

You may also be interested in the other problems in our What if...? Feature.

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If you have 27 small cubes, 3 each of nine colours, can you make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour? In the picture, the top face and the left face have one of each colour.

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This work is inspired by Fawn Nguyen (@fawnpnguyen on Twitter), Rio School District, and the many incredible free, online resources from which I curated these collections.

Most of these problems would touch upon many practices!

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Notice and Wonder activities get students engaged and brainstorming about the mathematics in a safe space where all answers are acceptable. A focus could definitely be placed on clear and precise explanations of what they are noticing.

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When students become active doers of mathematics, the greatest gains of their mathematical thinking can be realized. The process of sense making begins when we create classrooms full of curious students' thoughts and ideas.

By asking "What do you notice? What do you wonder?" we help our students see problems in big-picture ways.

Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to discover multiple strategies for tackling a problem.

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Notice and Wonder - National Council of Teachers of Mathematics

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What is Notice and Wonder? When students become active doers of mathematics, the greatest gains of their mathematical thinking can be realized. The process of sense making begins when we create classrooms full of curious students' thoughts and ideas. By asking " What do you notice? What do you wonder?"

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Some characteristics of a High Quality Mathematics Task.docx.pdf

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Compiled by Traci Jackson

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Many Math Games have students act like Mathematicians. Why not have a game day where they can play different games and then reflect on how they are being mathematicians?

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https://setwithfriends.com/

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Set with Friends * Free, Real-Time Multiplayer Game

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An online card game testing reaction speed and pattern matching abilities. Play by yourself, or compete with your friends in real time!

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https://docs.google.com/document/d/1RDDnrg0Acja8pSetq2a7wG1Rky_EJKuh_PBGzyaWaWk/edit?usp=sharing

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https://docs.google.com/presentation/d/1drvhGyJHDf1arrc-WIVG1Mjh4zt0mnqATdj92qP0jms/edit?usp=sharing

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Object of the game is to move all the disks over to Tower 3, but you cannot place a larger disk onto a smaller disk.

This will get students talking about strategies and has a very high ceiling when talking about patterns of how you can determine the smallest number of moves required when increasing the number of disks in the problem.

There are also awesome connections to Hindi folklore: https://www.scientificamerican.com/article/the-tower-of-hanoi/

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Play Tower of Hanoi. Object of the game is to move all the disks over to Tower 3 (with your mouse).
But you cannot place a larger disk onto a smaller disk.

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https://mathequalslove.net/puzzles/

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Collection of Free Printable Puzzles for the Math Classroom (or any Classroom)

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In these tasks, students need to decide what they would rather have out of the two choices. A great opportunity to have a Debate in math class!
https://www.wouldyourathermath.com/

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Would You Rather Math – ASKING STUDENTS TO CHOOSE A PATH AND JUSTIFY IT WITH MATH

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Teachers, sign up for my mini-workshop to learn about how to implement Would You Rather Math into your classroom routines. We will explore some sentence frames, what happens when things don’t go as planned, how to use the prompts in a remote learning setting, and much more. See you there!

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These tasks get your students talking about math. And again, a great way for them to be very clear about their mathematical thinking.
https://www.samebutdifferentmath.com/

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Same But Different is a powerful routine for use in math classrooms. The images can be used for teaching a way of thinking: grayscale thinking, categorical thinking; helping students to build a network of ideas and an approach for learning and thinking about mathematics.

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Chris Luzniak has some excellent books, videos, and other learning/task resources about how to get students debating about math problems in class. Students love the competition element!
https://www.luzniak.com/debate-math.html

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Watch a 5 minute Ignite Talk introducing the idea of debate in math-- VIDEO . See my classroom debates in action in this PBS VIDEO . Hear a more thorough discussion in my Global Math Department...

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This Desmos activity is a digital way of having students access the pool border problem. Students will need to create expressions that will help them count the number of tiles needed around a pool area. This is also a great way to get students being very clear and precise!

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In this Desmos-ified treatment of a classic math problem, students will first construct expressions with numbers to determine the number of tiles that border a pool. Then they’ll use those numerical expressions to help them write an expression with VARIABLES. Then they’ll put the algebraic expressio…

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I love to have my students play math games. It gets them thinking critically and away from their computers. (Although there are great digital games out there as well!) You can see some of my favorite games on this Amazon Wishlist. Plus, the students totally agree that playing games is a real-world thing! So, it shows that there is more than just word problems.

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Sell Best Sellers Customer Service New Releases Books Pharmacy Registry Early Black Friday Deals Fashion Kindle Books Toys & Games Gift Cards Amazon Home Automotive Computers Find a Gift Shopper Toolkit Coupons Home Improvement Video Games Smart Home Beauty & Personal Care Health & Household Amazon Basics Pet Supplies TV & Video Baby Handmade Sports & Fitness Disability Customer Support

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Once you have started diving into standards aligned learning, you want to keep the idea of perserverance alive! Open middle has great problems across all grade levels that are challenging and make sure that students understand underlying concepts and don't just have skill strategies memorized. They are more challenging than your average problem and create the opportunity to re-visit the conversation about never giving up!

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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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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? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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I did an activity with my students this year that required them to not give up, but also use number sense (SMP 2). Adapted from Peter Liljedahl's Building Thinking Classrooms.

Have the class pick a target number between 1-100.

Then, write down the numbers 1-9 on the board. Ask students to choose 4 numbers from that list.

Once their four numbers are chosen, tell them that their goal is to use their 4 numbers and any operations to create their target number. An example is in the document attached.

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Depending on how you feel about calculators and math facts, this mathematical practice is a great way to have a conversation about how a calculator is a tool. It may be able to do the arithmetic but it will never be able to replace the brain that they have to use when figuring out what to type in!

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I love to have my students play math games. It gets them thinking critically and away from their computers. (Although there are great digital games out there as well!) You can see some of my favorite games on this Amazon Wishlist. Plus, the students totally agree that playing games is a real-world thing! So, it shows that there is more than just word problems.

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Sell Best Sellers Customer Service New Releases Books Pharmacy Registry Early Black Friday Deals Fashion Kindle Books Toys & Games Gift Cards Amazon Home Automotive Computers Find a Gift Shopper Toolkit Coupons Home Improvement Video Games Smart Home Beauty & Personal Care Health & Household Amazon Basics Pet Supplies TV & Video Baby Handmade Sports & Fitness Disability Customer Support

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This website has so many different images that can be used as dot or number talks!