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Train for Two

Stage: 2 Challenge Level: Challenge Level:1

Here’s a game to play with a grown-up!



How do you play?
You'll need a grown-up to play with.
You'll also need one Cuisenaire rod of each length between 1 (white) and 10 (orange), or you can just write down the numbers on a piece of paper. You could use the interactive version here.
Decide who is going to go first, and choose a distance between 11 and 55. We'll use 25 as an example. The aim of the game is to make a train of length 25 (exactly).
Each player in turn puts down a Cuisenaire rod, putting them end to end so that there is a single train. The person who puts down the last rod to make 25 wins. If one player puts down a rod that makes the train longer than 25, then the other player wins. (If you aren't using rods, then you can use each of the numbers between 1 and 10, but only once.)

Does it make a difference who goes first?
Can you work out a winning strategy?
Notes for grown-ups
Train for Two helps to develop children’s fluency with simple addition. However, the real challenge is to find a winning strategy!

Easier version: Choose a smaller target, or use more rods.
Harder version: Choose a bigger target, or use fewer rods.

Repeat the game, aiming to find a winning strategy, then talk together about how it was found.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.