Five playful games for building number sense
When we think of play, games come readily to mind. In the maths learning realm, games can 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. Learning what their go-to arithmetic strategies are helps us to celebrate existing strengths and allow us to teach individual students what they're ready for.
As part of this year's Maths Play's Big Day of Maths Play (BDoMP!) celebrations, we are spotlighting five of our favourite games for building number sense.
Each of these games situates retrieval practice of number facts and strategies within a bigger, meaningful context that requires strategic thinking and playful experimentation.
And when a game is enticing; when the idea of playing multiple rounds is attractive, then playing further rounds (today or on another day) pairs repeated arithmetic practice with mathematical thinking.
And perhaps most of all, regular opportunities to play with and enjoy maths for its own sake 🛼 🔢 ✨
1. The Elevens Games
2 player game
Elevens is a versatile counting game that has roots in the ancient game of Nim. In it's verbal format, it requires no materials, just players.
We're not quite sure where the more 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 💪🏼
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
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 forced Player 2 to write 11... so Player 1 wins!
Variations:
Once you've both figured out how to win, or are ready for a variation, the possibilities are endless.
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. Hundred Chart Nim
2 or 3 player game
Nim on a Hundred Chart is deeply playful and applies addition practice while supporting critical understandings about place value and the structure of number.
Get ready to play: Get a 100 chart and a bunch of counters (e.g kidney beans). We prefer having one colour for Player 1 and a different colour for Player 2 to help us uncover play patterns. Although you can play with a set of like counters.
How to play: Once it's decided who will go first, Player 1 chooses any number from 1 to 15 and places a counter on that square.
Players then take turns adding 5, 10, or 15 to the most recently marked number and placing a token on the new sum. Play continues until no more counters can be placed on the 100 chart.
How to win: The player who places the last counter on the board wins.
To see an example game in action, check out this 3 minute episode of Maths Play TV.
Variations:
Explore other chart variations: What if... you played on a number chart that started at 101 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 that involves an attacker and defender. It gives 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'll be the attacker and who will be the defender. The attacker's goal is to make any row, column or diagonal equal 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 is different to 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: Players take turns choosing a ‘bingo number’ to place each of their three counters on.
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.
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.
What's your favourite maths game? #PlayItForward!
Do you have a favourite maths game that pairs practice with an underlying problem to solve (e.g. How to win)?
We'd love to know — simply share this article on social media and include your game recommendation in the post.
OR send a photo or two of your #mathsplay in action together with any information that you'd like us to play forward about how to play. Send these to [email protected]