In my last blog What’s your favourite maths game? I shared a few of my favourites and put the call out to my fellow educators to find out what some of your favourite maths games were. A huge thank you to all of those people who shared the games they love and games they have made to engage students in the thinking and doing of mathematics. So in this blog, I share some of your ideas and link these wonderful games to some big ideas in mathematics.
James Russo (@surfmaths) was one of the first to share a favourite game – Multiple Mysteries, by Toby Russo (@tobyrusso). I love a game that starts with the goal of “score as many points as you can”! The focus is multiplication and James gives a nice explanation of what multiples are: “the trail a number leaves when you are counting by it” which creates a visual for students about the patterning structure of multiples. I also really like that the game involves choice of which multiple to focus on – great support of ‘point-of-need’ repetitive consolidation without it being ‘rote’ practice.
Multiple mysteries – the big idea
The big mathematical idea that underpins this game is in relation to divisibility. Charles (2005) has a set of 21 big ideas, one of which is about operating with rational numbers. Students need to understand that “multiplication facts can be found by breaking apart the unknown fact into known facts” (p. 16). Toby’s game Multiple Mysteries focuses on developing students’ abilities to use known facts to think of other numbers that might also be divisible by the same number – in the case of their example, the number 4. Rules of divisibility aren’t introduced until Grade 7 in the Australian Curriculum as we delve further into investigating prime and composite numbers. However, discussions relating to what students know about numbers to work out if they are divisible by say 2, 5 or 10 should be happening from about Year 2 when odd and even numbers are introduced. This game provides students with time to explore what numbers might be divisible by say 4. Through playing multiple times, students may start to ‘notice’, or we as teachers can ask them to ‘notice’, what the numbers have in common. The idea is not to tell them the rule (i.e. that if the last two digits are divisible by 4 then the whole number is divisible by 4) but to let them find it on their own, or at least come close! You can always ask ‘why’ too, if students already know the rules! I really love the ‘challenge’ aspect of Toby’s game – it stops students just randomly making numbers in the hope that they are correct.
Another favourite game came from Michael Minas (@mminus8) called Target Os and Xs a game share with Michael by Ann Downton. I really enjoy games that utilise other game boards or rules as it provides students with some familiarity to start/ engage with the game. Using the classic noughts and crosses 3 x 3 board, this game follows the same winning structure as noughts and crosses but has a focus on making equations using any of the four operations (other versions are shared). I also really like that Michael provides the types of questions to use throughout the game to assist teachers and parents to ‘bring out’ the mathematical thinking.
Target Xs and Os – the big idea
This version of Os and Xs actually addresses two big ideas – place value and partitioning. In my Stage 1 content clusters, Cluster 6 “Numbers can be partitioned in multiple ways” and Cluster 7 “A number can be regrouped or renamed to aid in operating with the number” both link to this game. Partitioning can be the focus as the players work from the numbers on the board to find equations, and place value can be used when working from the cards in your hand to find a solution. An example of using partitioning was when Nash wanted to make 15 and said “do I have any tens?”. The beauty of this game is that it allows for students at differing places along their developmental path to play together. In the example game between Michael and his daughter Nash, Michael used more complex number sentences involving more than one operation whereas Nash used addition of two numbers or subtraction of two numbers. However, there was no real advantage is being able to ‘do harder maths’ therefore the game is a perfect entry point for all students.
Lee Englefield (@EnglefieldLee) shared a great game that Marilyn Burns loves called Oh No! 99! (Not to be confused with the awesome, and still mathematical, game of the same name made by Uno! creators Mattel in the 80s). The game comes from the resource Developing Number Sense written by Rusty Bresser and Caren Holtzman. The instructions, and some helpful hints, are shared by Marilyn Burns. She provides some sage advice about playing the game that should be applied for all games, and to teaching in general for that matter:
“When introducing any new game or activity, it’s important to try it first.”
“We didn’t want to tell the students our ideas, but we wanted them to share and listen to each other’s thoughts about useful strategies”.
Oh no! 99! – The big idea
The big idea that Oh No! 99! deals with is pattern and number structure. It also has links with understanding place value but in particular it focuses on understanding that any number can be a countable unit. The game builds mental strategies for both addition and subtraction such as: bridging to ten, counting on and back, using doubles or near doubles. There is also consolidation of estimation skills – determining how close to 99 you are and what game strategy you may need to employ to win. Also reasoning – take time to check-in with pairs as they play and ask questions about how they are making their decisions, what cards they want to keep, which ones are ‘better’ and why. On Marilyn’s blogpost she also provides some follow-up lesson ideas in the form of number talks and suggests scaffolding the game for some students by providing a hundred chart to assist with working with some of the strategies, for example, counting forwards and backwards by ten.
I enjoyed reading everyone’s suggestions of their favourite games, and as most of you pointed out, it’s too hard to chose just one favourite! I also really liked the Battleship-esque game that David Butler (@DavidKButlerUoA) shared, Which Number Where? so I recommend you also check that one out. It is a great game that is perfect for playing online and has a good focus on communication and positional language. Thank you to all who shared, and I hope that some of these games get a workout in classrooms (both virtually and physically) soon!
Charles, R. I., & Carmel, C. A. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Mathematics Education, 7(3), 9-24.