I believe that games are a fantastic way of teaching young students number concepts. Games can offer an excellent balance between repetition, which is necessary for skill building and consolidation, and opportunities for new discoveries. Moreover, games can obviously make learning a lot more engaging and enjoyable for many students. Finally, on an emotional level, games teach students how to lose, and win, graciously.
It is my feeling that good mathematical games tend to share similar underlying design principles. Click on the button below for an article that introduces and unpacks five principles of educationally-rich mathematical games.
An additional advantage of teaching with games is the power to transform them into rich investigations; something that Maths300 has done with great effect. The article below outlines some ideas for how teachers might do this themselves.
I have also included many examples of the games I have developed or adapted below. Note that all of these activities below have been published in teacher journals and magazines. These games are equally relevant whether or not you have any interest in implementing the SURF framework in your classroom.
‘Over Under On’ is a fun and simply structured game that is suitable to play with a large group of students. It is an engaging way to explore probability and introduce game theory to students.
This activity has now been published in the journal Australian Primary Mathematics Classroom.
This flexible whole-class or small group game allows students to explore order of operations and algebraic thinking.
This activity has now been published in the journal Australian Primary Mathematics Classroom.
This hybrid of Guess My Number and Hangman is a challenging whole-class or small group game that supports mathematical reasoning and both thinking creatively and systematically.
This activity has now been published in the journal Australian Primary Mathematics Classroom.
This bingo game is similar in structure to Multo or Addo, however allows learners to focus on exploring equivalent fractions.
This activity has now been published in the journal Australian Primary Mathematics Classroom.
This whole-class game focuses on place value understanding, allowing for connecting representations and developing mathematical reasoning.
This activity has now been published in the journal Prime Number.
This game is focussed on addition strategies and exploring independent probability. The mouse, the cheese and the cat mimics the mechanics of greedy pig, however allows students to play individually or in small groups using a number chart to support their thinking. Follow-up investigations that complement the game are outlined.
This activity has now been published in the journal Australian Primary Mathematics Classroom.
This game-style investigation allows students to explore important ideas in probability, including:
1. As the size of the data set increases, the experimental probability of an event will approach (get closer to) the theoretical probability of an event.
2. Probability is concerned with measuring how likely some event is to occur based on long-term consistent behaviour.
3. Variability is concerned with the short-term unpredictability of outcomes (Chick, 2006).
This activity has now been published in the journal Prime Number.
Support students flexibility with multiplication through this strategic, counter-based game. The array representation is central to game play.
This activity has now been published in the journal Australian Primary Mathematics Classroom.
These two games focus on different mathematical ideas - place value (Biggest Difference) and multiplication (Choc-Chip Cookies). However, what they have in common is that they both use a Roll and Allocate game mechanic. Roll and Allocate is very useful for creating whole-class games, where all students can play with a personal stake.
This activity has now been published in the journal Prime Number.
Support students to develop a relational understanding of the equals sign through playing the card game: The Same As. The description of the card game includes a preliminary activity designed to challenge the notion that the equals sign means ‘do something’, in part through introducing students to the mathematical symbol we use when two sides of a number sentence are not equal.
This activity has now been published in the journal Prime Number.
A great game can often serve as the inspiration for another great game. If you have played Landgrab (also known as multiplication toss and multiplication paddocks) you might want to check out Reverse Landgrab. The focus of the game is building a preliminary understanding of products and factors (as well as prime and composite numbers) whilst introducing the area model of multiplication.
This activity has now been published in the journal Prime Number.
Using children’s literature can provide inspiration and drama for mathematical games. These two games are based on the text We’re Going on a Bear Hunt. One game focuses on chance and data, whilst the other involves chance and addition strategies.
This activity has now been published in the journal Prime Number.
This game and investigation provides students with an opportunity to explore place value patterns on a number chart using a ‘Pop-it’ as a gameboard.
This activity has now been published in the journal Prime Number.
Develop fluency with addition and subtraction and explore the relationship between these two operations with through simple game. Consider how a Concept Cartoon could be used to transform the game into an investigation.
This activity has now been published in the journal Prime Number.
Build fluency with addition whilst introducing students to the notion of conditional probability in this adaption of Greedy Pig. The linked article also contains two other games with an explicit probability focus (Colour, Suit, Number and Middle or Match)
Links to SURF:
Rainbow Facts (Fast Facts)
Super Rainbow Facts (Fast Facts)
Bridging through 10 (Strategies)
Number Splitting (Strategies)
Compensation - pay it back (Strategies)
Compensation - change both numbers (Strategies)
Estimation (Understanding)
This activity has now been accepted for publication in the journal Australian Primary Mathematics Classroom.
Develop students understanding of the part-whole concept through this simple yet deceptively strategic and tactically demanding game.
Links to SURF:
Part-Whole Concept (Understanding
This activity has now been published in the journal Australian Primary Mathematics Classroom.
This highly accessible game is an engaging way of supporting students to strengthen their sense of quantity in the early years. It makes a great follow-up to the handfuls task (Gervasoni, 2015). It can be extended into the middle years and upper years of primary school, with a focus on multiplicative thinking.
Links to SURF:
Subitising (Fast Facts)
Estimation (Understanding)
Multiplication (Understanding)
This activity has now been published in the journal Prime Number.
This activity is similar to Nearest to the Gnarly Number, however is focussed on fractions instead of whole numbers. It supports the development of conceptual strategies for comparing fractions, including benchmarking and residual thinking. It also provides opportunities to convert fraction sums to decimal numbers.
Links to SURF:
Fractions (Understanding)
Decimals (Understanding)
This activity has now been published in the journal Australian Primary Mathematics Classroom.
Looking for a maths game that plays more like a board game? You might want to check out evolution. At lower levels, students focus on skip-counting sequences; at higher levels, on factors and multiples.
Links to SURF:
Targeted skip-counting sequences (Fast Facts)
Factors and Multiples (Understanding)
This activity has now been published in the journal Primary Mathematics.
This activity was designed by my brother, Toby. He has come up with a highly engaging game to build familiarity with representing negative numbers on a hundreds chart. If you want to use this game in your classroom, you might want to check out my article which introduces the Extended Hundreds Chart as a teaching tool through presenting it as a rich, novel assessment task.
Links to SURF:
Negative numbers (Understanding)
This activity has now been published in the journal Australian Primary Mathematics Classroom.
Take on the role of Dingo. Select your ingredients and avoid rolling a poison number. The learning focus is on number patterns and probability.
Links to SURF:
Factors and Multiples (Understanding)
Skip-counting patterns; various (Fact Facts)
This activity has now been published in the journal Prime Number.
Help students build fluency with non-standard partitioning with these two enjoyable place value games.
Links to SURF:
Place Value (Understanding)
This activity has now been published in the journal Australian Primary Mathematics Classroom.
Think ‘rock, paper, scissors’, and then think The Gruffalo characters. The learning focus is on strategy, data collection/ representation and probability.
Links to SURF:
Planning and thinking ahead (Understanding)
This activity has now been published in the journal Prime Number.
Support children to explore the part-whole concept, equivalence and sequential number sentences through this enjoyable, card-based game.
Links to SURF:
Part-Whole (Understanding)
Compensation - pay it back (Strategies)
Compensation - change both numbers (Strategies)
This activity has now been published in the journal Prime Number.
This article describes four games for improving young children’s (4-6 y/o) understanding of number and magnitude using a number-line representation. The games are: String of Cards, Hat Trick, My Secret Number, and Place That Number.
Links to SURF:
Place Value (Understanding)
This activity has now been published in the journal Prime Number.
The focus of this activity is on developing students’ spatial reasoning and visualisation skills.
Links to SURF:
Planning and thinking ahead (Understanding)
This activity has now been published in the journal Prime Number.
This article presents five games, three of which are not previously linked to on this website: Skip-Counting Bingo, Probability Football and How Close Can You Get?
Links to SURF:
Skip-counting Bingo: Skip-counting by 2s, 3s, 4s, 5s and 6s (Fast Facts)
Probability Football: Planning and thinking ahead (Understanding)
How Close Can You Get: Count Up and Hop Up (Difference Method) (Strategies)
These activities has now been published in the MAV conference proceedings.
Enhance students’ multiplication skills and informally expose them to the notion of prime factors through this engaging dice- based game, inspired by the board-game Ludo.
Links to SURF:
Multiplication (Understanding)
This activity has now been published in the journal Prime Number.
Improve student estimation skills and place value understanding through this engaging, dice-based game. The goal is for students to place four of their numbers in a row on a number-line without their opponent interrupting their sequence.
Links to SURF:
Place Value/ What lives inside that number? (Understanding)
Estimation (Understanding)
This activity has now been published in the journal Prime Number.
Enhance students' number sense and develop their fluency with place value through this engaging dice-based game based on principles derived from the classic computer game Pac-Man.
Links to SURF:
Place Value/ What lives inside that number? (Understanding)
2-digit Numbers (Reading)
Count-on (Strategies)
Count-back (Strategies)
Add 10/ Take 10 (Fast Fact)
This activity has now been published in the journal Australian Primary Mathematics Classroom.
This game-based activity prompts students to explore the structure of multiplication, experiment with the distributive property, and begin investigating prime numbers.
Links to SURF:
Multiplication (Understanding)
This activity has now been published in the journal Teaching Children Mathematics.
This article introduces ten simple subitising-related activities that can be undertaken with a set of subitising plates. These activities are particularly suitable for Kindergarden, Foundation and Grade 1 students, and can be arranged as one-on-one educator-student (or parent-child) interactions, teacher-facilitated small group work, or as a whole-of-class number fluency warm-up.
Links to SURF:
Subitising (Fast Facts)
Rainbow Facts (Fast Facts)
Count On (Strategies)
Count Up (Strategies)
This activity has now been published in the journal Prime Number.
This game-based activity engages students in discussions around benchmarking (a form of estimation) to one-half and equivalent fractions, whilst also exposing students to the procedure for converting fractions into decimals.
Links to SURF:
Fractions (Understanding)
Decimals (Understanding)
Estimation (Understanding)
This activity has now been published in the journal Australian Primary Mathematics Classroom.
This short article introduces Dynamic Counting, a process for building fluency with counting-related strategies and place value.
Links to SURF:
Count-on (Strategies)
Count-back (Strategies)
Add 10/ Take 10 (Fast Fact)
Place Value/ What lives inside that number? (Understanding)
This activity has now been published in the journal Australian Primary Mathematics Classroom.
The major focus of these games is on building subitising skills and strengthening student understanding of the part-whole concept (e.g., 5=3+2 or 5=4+1 or 5=3+1+1 etc.). They will also be exposed potentially to a variety of counting and decomposition strategies (e.g., count-on, bridging through 10).
Links to SURF:
Subitising (Fast Facts)
Part-whole (Understanding)
This activity has now been published in the journal Prime Number.
This game is focussed around building mental computation skills and developing fluency with doubles facts in particular. It requires dice and playing cards.
Links to SURF:
Doubles (Fast Facts)
Skip-counting by 2's (Fast Facts)
Count-on (Strategies)
Bridging through 10 (Strategies)
This activity has now been published in the magazine Common Denominator.
This dice-based game is targetted towards improving number sense, estimation skills and place value understanding.
Links to SURF:
Place Value/ What lives inside that number? (Understanding)
Estimation (Understanding)
This activity has now been published in the journal Teaching Children Mathematics.
These two variants on the counting game aim to support students in the early years to make sense about place value amid the vagaries of the English language in naming numbers.
Links to SURF:
Place Value/ What lives inside that number? (Understanding)
2-digit Numbers (Reading)
This activity has now been published in the journal Australian Primary Mathematics Classroom.
Nearest to the gnarly number is a highly tactical, absorbing card game. It provides opportunities for students to practise addition strategies, whilst enhancing their estimation skills. It is suitable for primary school students of all ages.
Links to SURF:
Rainbow Facts (Fast Facts)
Super Rainbow Facts (Fast Facts)
Bridging through 10 (Strategies)
Number Splitting (Strategies)
Compensation - pay it back (Strategies)
Compensation - change both numbers (Strategies)
Estimation (Understanding)
This activity has now been published in the journal Australian Primary Mathematics Classroom.
Place that number is a whole-class game-based activity aimed at building student understanding of place-value and magnitudethrough representing numbers on a number-line. It can be easily modified for primary school students of all ages.
Links to SURF:
Place Value (Understanding)
This activity has now been published in the journal Prime Number.
Caught red-handed is a counter-based game introducing students to strategic thinking. It is suitable for primary students of all ages.
Links to SURF:
Planning and thinking ahead (Understanding)
This activity has now been published in the journal Australian Primary Mathematics Classroom.
This article considers how a simple board game, Snakes and Ladders, can be used to teach a rich variety of number concepts from Foundation to Year 4, through subtle modifications of game rules and student instructions. One modification in particular offers a powerful means of attempting to move students on from count-on to using more efficient mental computation strategies. The different variants of the game cover many of the teaching points on the SURF Board.
This activity has now been published in the journal Prime Number.
Multiple Mysteries is a challenging, thought-provoking card game which requires students to efficiently identify multiples of 6, 7, 8 and 9. It builds on the concepts explored in the Factor Fiction game.
Potentially relevant teaching points include:
Fast Facts/ Strategies: Various timestables and skip-counting patterns
Understanding: Factors, Multiples and Prime Numbers
This activity has now been published in the journal Prime Number.
These two games are further editions to the 3-in-a-row series of games. Both focus on the SURF strategies: Count On and Count Back; and both are played exclusively with dice.
These activities has now been published in the journals: Primary Mathematics and Learning and Teaching Mathematics.
These two playing-card based games are designed to encourage students to develop fluency with complements to 100 (Fast Facts), which are referred to in the second game as super rainbow facts.
This activity has now been published in the journal Prime Number.
Addition Bingo, a simple dice-based game, can be used to help ‘build’ the framework for students in Prep (Foundation), Years 1 and 2. It covers a variety of teaching points, including:
Strategies: Count On, Near Doubles, Bridging through 10, Number Splitting
Understanding: Turnaround Facts, More than one way, Partitioning (into 10’s and 1’s) (i.e., What lives inside a number?).
Reading: Single-digit numbers, 2-digit numbers , +
Fast Facts: Subitising, Counting forwards, Rainbow facts, Doubles, Friendly numbers
This activity has now been published in the journal Prime Number.
Build on students' love for doubling by introducing exponential growth with this strategic bingo game. Potentially relevant teaching points include:
Doubles (Fast Facts)
Number Splitting (Strategies)
Odd and even numbers (Understanding)
Doubling patterns/ exponential growth (Understanding)
This activity has now been published in the journal Teaching Children Mathematics.
Factor Fiction (Fact-or-Fiction) is a strategy-based card game that encourages students to develop an intimate knowledge of how to efficiently factorise numbers between 1 and 99.
Potentially relevant teaching points include:
Fast Facts/ Strategies: Various timestables and skip-counting patterns
Understanding: Factors and Multiples
This activity has now been published in the journal Prime Number.
3 Little Pigs vs The Big Bad Wolf is a dice-based game that builds mental computation skills, whilst exposing students to the idea that the equals sign means 'the same as', rather than simply 'the answer'. At the heart of the activity is the intention to strengthen students' relational understanding of the equals sign through introducing inequalities.
Potentially relevant teaching points include:
Fast Facts: Rainbow Facts, Doubles, Friendly Numbers , Add 10/ Take 10
Strategies: Count On, Near Doubles, Bridging through 10, Compensation, Number splitting and Hop On
Reading: Greater than sign/ Less than sign (i.e., < and >) and equals sign (=).
Understanding: More than one way, Change the order
This activity has now been published in the journal Australian Primary Mathematics Classroom.
3-in-a-row is a series of games all based around the same principle; placing three of your counters in a row on a hundreds board. The games have been designed around this common theme to take advantage of the fact that students already have some familiarity with the rules and workings of the game. There is a version of three-in-a-row that covers the following teaching points:
Doubles (Fast Facts) and Near Doubles (Strategies);
Friendly Numbers (Fast Facts);
Add 10/ Take 10 (Fast Facts) and Friendly Numbers (Fast Facts);
Super Rainbow Facts (Fast Facts), also known as complements to 100;
Bridging through 10 and compensation strategies
This activity has now been published in the journal Prime Number.
Building on from the 3-in-a-row games, Target Number provides a simple and effective games-based scaffold for supporting more advanced mental computation skills and strategy-use. There is a version of target number which covers the following teaching points:
Target 120 Addition: Number splitting (Strategies), Hop On (Strategies)
Target 1 Subtraction: Hop Back (Strategies), Hop Up (Strategies)
Target 120 Multiplication: Distributive Property (Understanding), Change the order/ Associative Property (Understanding)
Target 1 Division: Factorising (Understanding); Multiplication undoes division, Division undoes multiplication (Understanding)
This activity has now been published in the journal Prime Number.
Student teams battle one another by skip counting by different numbers and switching their counts when the teacher shouts, “Switch!” This game promotes numerical fluency, numerical pattern recognition, and addition/multiplication operations, and can be linked to the learning of various skip-counting sequences (Fast Facts). This activity has now been published in the journal Teaching Children Mathematics.
Hopping to 100’ is a strategy-based game which exposes students to skip-counting from non-zero starting points. The mathematics in the activity is suitable for students in Years 2, 3 and 4, with more mathematically capable students encouraged to employ their knowledge of multiplication facts and mental strategies for adding two-digit numbers, rather than skip-counting.
Potentially relevant teaching points include:
Skip counting: 2's, 3's, 5's and 10's (Fast Facts)
Multiplication facts: 2's, 3's, 5's, 10's (Fast Facts)
Multi-digit addition: Number splitting (Strategies), Hop On (Strategies)
This activity has now been published in the journal Prime Number.
This simple activity is a simple way of simultaneously investigating and consolidating many of the key ideas, strategies and facts on the SURF board. Students really enjoy this activity, which they seem to find highly intuitive. It provides an excellent opportunity for whole-class sharing, helping to build students' mathematical language and reasoning ability as they justify their choices. Note that if dice are not available, the activity can also be undertaken with playing cards.
A good way of getting students to think about why they need to be able to use both count up and count back as subtraction strategies. When students are sharing their decisions with the whole-class, there is an opportunity for teachers to represent student thinking using an open number line. This activity has now been published in the journal: Mathematics Teaching.
Additional games and activities are available under lesson plans and Challenging Tasks.