How can chess enhance pupils’ maths skills? Find out with these chess games you can use in your maths lessons, from Hari Neocleous.

Why chess + maths? As a special educational needs (SEN) Primary Maths Teacher, my focus is to find learning gaps, figure out why they happened and close them. My lessons must instil self-belief and an enjoyment of maths. The lessons I plan always have a theme or a link to a future career so that pupils can understand why we are learning about a particular topic or skill. Chess gives us a theme, a backdrop. They’ve all seen it referenced somewhere, whether in a film, book or in real life. We build on a curious moment they have had. Chess + maths is a great way to introduce algebra.

This ancient game, these beautiful pieces, the fact that some of the most intelligent people on the planet are chess players, hooks my learners in.

We start with an introduction to the chess pieces, their names and point values. Do they notice something special about the numbers? Which piece has the lowest/greatest value? Can they order them by point value? Below are some of the ideas I am developing for a ChessPlus course for teachers and coaches.

"How the pieces move and capture - The king: 1 square in all directions; The queen: diagonally, horizontally and vertically; The bishop: diagonally; The rook: orthogonally; The knight: moves in an L shape (2 straight, 1 to the side); The pawn: moves 1/2 squares forward on its first move. After only 1 square forward cut captures diagonally." "The point values (represented with both Numicon pieces and digits) - Queen (Q): 9, Rook (R): 5, Knight (N): 3, Bishop (B): 3, Pawn (P):1, King (K): 0.

(c) Logiqboard and Hari Neocleous, 2022

5 Chess activities for developing maths skills

Activity 1: Missing totals

Our first focus is basic number sentences with missing totals. Dice are a great image to begin with as we want children to learn to subitise (instantly recognise a number without counting one by one). Children can also use Numicon to add up totals. Try to include a ‘chess piece (other than a pawn) + pawn’ at first e.g., Bishop + Pawn and then follow on with doubles. Children record their number sentences as ‘R+R+B=’ or ‘5+5+3=’ We can also show the calculations on a number line, to support their mental maths. For children who struggle, I model drawing spots underneath or even tapping on the piece as we visualise.

Each chess piece has it's value and pupils are asked to find the total of the Bishop + Bishop + Knight. There is also a 'Teaching tip' that reads, "You can also use a number line to explore addition The number line helps children move onto mental calculations.

(c) Logiqboard and Hari Neocleous, 2022

Activity 2: Empty box questions

The next type of questions are empty box questions where children need to find the missing chess piece to make the number sentence correct. Writing number sentences on large pieces of paper and moving the physical chess pieces around is fun! Counters/milk bottle tops with the first letter for each piece also works well for building number sentences.

"Empty box questions: Find the missing piece: 1. Bishop + Pawn + _ = Rook. 2. Rook + Bishop + _ = Queen. 3. Bishop + Bishop + _ = Queen."

(c) Logiqboard and Hari Neocleous, 2022

Activity 3: Game time – Piece grab

In this game, you take turns to pick four chess pieces (without looking) and find the total. The greatest total wins, but if you pick a King, your points are wiped out – it’s a zero in that round for you! When this happens, I ask the children to add up their points then draw a line through the number sentence. The key skill in this activity is what I call ‘smart addition.’ I talk about ‘friendly numbers’ where we look for doubles, pairs that make 10 and discuss step-counting with multiples of 3, 5 and 9. I’m hoping there are minimal pupils counting in ones and more of them looping doubles and pairs that make 10 and using multiples.

Quick addition - Exploring strategies: A) 27 + 1 (picture of 3 Queens + 1 pawn =_) B Making tens (pic of Queen + rook + pawn + rook = _ with loops adding the queens together). C) Making doubles 6+6 (Bishop + rook + bishop + pawn with loop joining 2 bishops together). D) Start with 9+9 or make a 10? (Queen + knight + pawn + queen = _ with pawn and queen looped together. E) 9+1 = (Knight + bishop + pawn + knight with loop joining knights and bishop). F) 10+2 or 9+3? (pawn + pawn + queen + pawn = _ with loops joining queen and pawn).

(c) Logiqboard and Hari Neocleous, 2022

Activity 4: Trial and error

Back to our number sentences. The next step would be to have a set of empty boxes that make a total. Children can use trial and error to solve and explore possible solutions. Children are encouraged to record this process systematically. If we’re exploring pieces that are equal to a Queen, then we might record, for example, B+B+B=Q, B+B+N=Q and so on. They should also be able to understand and explain why they cannot repeat the same sequences in a different order.

More than one solution. 1) _ + _ + _ = Rook. Can you find another solution? How many solutions are there? 2) Can you find 3 pieces that are equal to the queen? How many different ways can you find? 3) Can you find 4 pieces that are equal to the queen? What did you find? Explain... Moments for deeper learning: So we know that the chess pieces have odd numbers as values. The queen is an odd number. Could 2 chess pieces be added together to make an odd number? Could 4 chess pieces be added together to make an odd number? What do you think? Why?

(c) Logiqboard and Hari Neocleous, 2022

Activity 5 – Missing values

My final task is finding the missing value of a mystery piece. We use bar models to make sense of the question, work through it by breaking it down into several steps and learn to solve using different operations and higher numbers.

"Missing values 4 cones (added) = 72 The cone has an unknown value. Work out the cone's value. Can you represent this calculation as a bar model? You could also find half of 72 and half again. " Workings on bar model and as dividing by 4 etc. shown on sheet with explanation: "So the value of c = 18."

Deeper conversations

Maths debates

We want children to be brave enough to make a statement and explain why. We praise ideas and predictions, even if they’re wrong. Mistakes are where we grow and make sense of something. If you look at point values, you’ll see the King has no point value. He has value but no point value as he can’t be captured like the other pieces – instead, he’s trapped. If you do this, it’s checkmate! It’s also great to hear decision-making, ‘Miss I’m going to use the same piece twice’ or ‘Miss it doesn’t work because I used the King. We plan and model good mathematical vocabulary, and variation in questioning and explanations.

Reasoning and discovery

I particularly like using the ‘4 missing boxes that must be equal to the Queen’s value’ problem with pupils because, through this trial and error, children discover that in fact, it’s not possible! They’re shocked that I dared to give them such a question. Using mathematical reasoning, they discover that if two odd numbers always make an even number, then four odd numbers will also make an even number; therefore, four pieces cannot make a queen as she has an odd point value. Numicon is great for showing this more visually.

You can also represent some questions as balancing scales, asking questions such as, ‘If I had a queen on the right, which pieces would be on the left?’ We’re seeing the = sign as ‘the same as’ or ‘is equal to’ and not just ‘find the total’.

What next?

There are so many great activities for chess + maths. Try these number tasks and, as a final thought, I’ll leave you with chess + investigations idea… Imagine a chess + Cluedo mystery!​​

Author

  • Hari Neocleous

    Hari is a primary maths SEN teacher who has over twenty years of experience teaching in London schools. Hari is also a primary school chess teacher, ‘Curious Maths’ teacher and LogiqBoard teacher. She is the maths column writer for Cherubs Family Magazine.
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