Five fun and engaging games for building number sense
When we think of play, games come readily to mind. In the maths learning realm, games can be great teaching tools for teachers. Games provide meaningful and motivating contexts for practising foundational maths skills while building problem-solving skills like logical reasoning.
But not all maths games are created equal. And we've seen and "played" our fair share of 'roll your way to 100' variations that lack invitations to think or be strategic.
When a maths game is playful enough to relax players and spark curiosity, it gives us (the educators) a window into students' mathematical fluency. For instance, learning about which go-to arithmetic strategies they turn to can help us celebrate their existing strengths and help us teach students what they're ready for.
This article spotlights five games that bring rich opportunities for building number sense while having opportunities to play with and enjoy maths for its own sake.
These games situate the practice of retrieving number facts and using mental computation strategies within a bigger, meaningful context that requires strategic thinking and playful experimentation.
When a game has winning strategies to uncover, students can become very motivated to play multiple rounds. It's these features of play and problem-solving (decision-making and experimentation, trial and error, making discoveries and social play) which makes certain games fun and engaging, and wonderful assets for maths class.
1. The Elevens Games — Written version
2 player game
Elevens is a versatile counting game with roots in the ancient game of Nim. In it's verbal format, it requires no materials, just players.
We're not quite sure where this more well-known, verbal version of the Elevens game originated from. But we've enjoyed playing 2-player verbal and written variations in junior primary classrooms. We've also seen senior primary students in the playground playing larger group variations on Elevens šŖš¼
This written version provides a playful context for practising numeral formation.
NB: You can play as a larger group but we recommend starting with 2 players to give players a good chance of noticing play patterns and uncovering a way to win.
Image: Introductory play in a Year 1/2 classroom at Thornbury Primary School
Get ready to play: Grab a writing implement and something to write on. Decide who will go first.
How to play: Players take turns writing the next 1, 2 or 3 numbers in the number sequence from 1 to 11.
How to win: Don't be the one to write 11! See if you can find a winning strategy that forces your opponent to write 11.
Example play:
Player 1 writes 1, 2.
Player 2 writes 3, 4, 5.
Player 1 writes 6, 7.
Player 2 writes 8, 9.
Player 1 writes 10
Player 2 writes 11.
Player 1 forced Player 2 to write 11... so Player 1 wins!
Variations:
Once you've figured out how to win, or are ready for a variation, the possibilities are endless. Try asking What if...? to come up with a fun variation.
For example:
- Extra players: What if...you add a third player? How does this change how you play Elevens?
- Count down: What if...you start at 11 and try to avoid being be the person who lands on 1?
- Special numbers: What if... you choose a number that is special to you (favourite number, birth date) and make that the number to land on?
- Multiples: What if... you played with a multiple of a number? For example, for a 'multiples of 10' variation choose like 110 or 200. This time, players take turns writing the next 1, 2 or 3 multiples of 10 until someone is forced to land on the end number.
- Fractions: What if... you play to a smaller number like 7 but this time count by a given fraction? For example, for a 'multiple of 1/4' players take turns writing the next 1, 2 or 3 fractions in the sequence until someone is forced to land on 7.
2. Nim on a 120 Chart
This is a variation on Hundred Chart Nim which was created and shared by Denise Gaskin via her blog here.
2 or 3 player game
Variations of Nim on a number chart bring playful opportunities to apply the practice of addition in ways that also support key understandings about place value and the structure of number. 
Image: Some 120 Chart Nim play in Steven Taylor's class Year 3/4 at Port Elliot Primary School.
Get ready to play: Get a 120 chart and a bunch of counters. We prefer having one colour for Player 1 and a different colour for Player 2 to help us uncover play patterns. Although you can also play with a set of like counters. Don't have manufactured counters? Enjoy the opportunity to be resourceful — play with kidney beans and/or uncooked pasta shells!
Level 1 — Learn to play: Once it's decided who will go first, Player 1 chooses a starting number of 5, 10 or 15. They place one of their counters on that number. Players then take turns adding 5,10 or 15 to the most recently marked number and placing a new counter on the sum. Play continues until no more counters can be placed. The person who places a counter on 120 wins the game.
Level 2 — Extend your play: This time, Player 1 chooses any starting number from 1 to 15. They place one of their counters on that number. Players then take turns adding 5, 10 or 15 to the most recently marked number and placing a new counter on the sum. Play continues until no more counters can be placed. The player who places the last counter (on a number in the range 116-120) wins the game.
FREE PDF DOWNLOAD: Nim on a 120 Chart
Variations:
Once you've figured out how to win, or are ready for a variation, the possibilities are endless. Try asking What if...? to come up with a fun variation. For instance:
- What if... reverse play so to start at 120 and jump backwards to get to zero?
- What if... you played on a number chart that started at 80 and ended at 200? Could you play it with the same rules? What about a chart that starts at 151 and ends at 250?
3. MathemaTic-Tac-Toe
Created by Andrew Lorimer-Derham
2 player game
MathemaTic-Tac-Toe is a rich variation on the original game of Tic-Tac-Toe involving an attacker and defender. It provides a motivating context for lots of addition practice!
Image: Play using the cards 1 to 9 or play using pencil and paper (or pen and napkin!)
Get ready to play: Decide who will be the attacker and who will be the defender. The attacker's goal is to make any row, column or diagonal of three numbers equal to 15. The defender's goal is to stop the attacker from making 15.
How to play: Using the numbers 1 to 9 (one of each) take turns placing the numbers 1-9 onto the 3 x 3 grid. Either player may start but the first turn can't go in the middle box.
Play online here using the robot that Andrew and one of his friends created for people to play against!
2 minute video - Meet Andrew and hear him share how and why he invented this Tic-Tac-Toe variation.
4. Box the Numbers
2 or 3 player game
Box the Numbers is a nifty variation on the classic game Paddocks (aka Dots and Boxes) and provides a great space for Number Play.
Get ready to play: Print or copy the game boards from here. Grab a different coloured marker for each player.
How to play: Once it's decided who will go first, players take turns adding a vertical or horizontal edge between dots. When a player closes a square, they add the number inside it to their running score AND they go again. Each player's score is the sum of all the numbers they collect by closing boxes.
How to win: In this variation, whoever collects the most points wins. This differs from the classic game where the goal is to collect the most boxes.
5. Skip-counting Bingo
Created by James Russo and Toby Russo
3-5 player game
Skip-Counting Bingo is a collaborative learning game that applies additive and multiplicative thinking in a context where players naturally begin to consider the 'richness' of different numbers based on their properties...
Image: Introductory play using a 60-chart in a Year 1/2 classroom at Thornbury Primary School
Getting ready to play: Each player needs 3 counters of one colour. On a 120-chart, each player takes turns placing 1 of their 3 counters on a Bingo number; any number higher than 20.
Tips for a positive experience:
- We've found it valuable to learn to play on a 60 chart before moving to a 120 chart, particularly with younger children like those in Year 1/2.
- In case any games have only 2 players, have each student choose 5 bingo numbers (instead of 3) to stop the game feeling too short.
How to play: Anyone can roll on a turn. On each roll, the group skip-counts by the number rolled starting at zero.
Counting stops when they land on one of the Bingo numbers. That counter (or Bingo number) is removed from the 120-chart and returned to its owner.
How to win: The winner is the first to claim back all three of their counters.
For more about how to play, how we adjusted play to a Year 1/2 class, and to access game boards, head here.
Share your maths play with us — #PlayItForward!
Are you and your class or family enjoying any of these games? Feel free to share a photo of two of your #mathsplay in action together with a caption about how you’re enjoying it, what you discovered and/or what you’re wondering. Send your caption and photo/s to [email protected]
Here's an intriguing photo from Skip-counting Bingo from Steven Taylor's class at Port Elliot Primary School. We're enjoying pondering which colour was most likely to win!