Product Conquest: Claim the Grid with Multiplication
Product Conquest is an original strategy game that turns the multiplication table into a battlefield. Two sliders point at numbers along the bottom; their product marks a square on the grid that you claim as your territory. But there is a clever catch borrowed from a famous mathematical game: on each turn you may move only one slider, so your choices and your opponent are forever linked. It is a game of multiplication fluency and forward planning in equal measure.
The Mathematical Idea
Every square on the board is a product of two factors. Understanding the game means understanding how factors combine: the number 12 can be reached as 2 times 6, 3 times 4, or many other ways, while a prime product like 13 can only be made one way. Because you may move just one of the two pointers each turn, you must think about which products become reachable next – this is a gentle introduction to the idea of a game tree and to factor relationships. Players quickly discover that flexible numbers with many factor pairs give more options, while awkward numbers can trap an opponent.
How to Play
- Choose 2 Players to play against a friend, or 1 Player to practise claiming as many squares as possible.
- Two pointers sit on the factor row beneath the grid.
- On your turn, move exactly one pointer to a new factor, then the square equal to the product of the two pointers is claimed in your colour.
- You cannot claim a square that is already taken – choose a product that is still free.
- When no new product can be claimed, the player with the most squares wins.
A Worked Example
Suppose the pointers are on 3 and 4, giving the product 12, which you claim. Your opponent may now move only one pointer. If they slide the first pointer from 3 to 5, the product becomes 5 times 4, which is 20, and they claim square 20. You then might move a pointer to make 5 times 5, claiming 25. Notice how each move is constrained by where the pointers already sit – that constraint is the whole game.
Strategy Tips
Think one move ahead: after you claim a square, which products will your opponent be able to reach, and are any of them especially valuable? Try to steer the pointers toward regions of the grid you already control, and avoid handing your opponent easy access to large open areas. Numbers with many factor pairs, like 12, 18 and 24, are powerful hubs because they keep your options open.
Why It Helps Learners
Product Conquest reinforces multiplication facts, the concept of factors and products, and strategic forward thinking. Unlike rote times-table drills, it gives every multiplication a purpose, so students practise dozens of facts naturally while focused on winning. It also introduces the flavour of mathematical game theory in an accessible, hands-on way.