Scene: Me and my 3yo daughter Sophie are playing with toy animals (as usual).
She decides they want something to eat. I have the Cuisenaire rods close to hand. A child I was teaching the other day told me how she has given each one the name of a vegetable, so I say we could use them as food.
Then I say "That's seems about right... But wait, Pig has more..." and I lay the whites out next to the bar of chocolate.
Sophie says: "Panda needs two more," lays two more whites next to the brown rod and gives them to Panda.
I lay Hedgehog's strawberries next to the bar of chocolate. Sophie says: "She needs one more", and puts a red next to the other three.
Pig has five whites. I ask Sophie: "What colour can Pig have for five whites?" Sophie looks at the rods, and picks out a yellow. We line up the whites next to it. Yes, that's a fair exchange. I put the whites in the box, and Pig keeps the yellow rod.
Puppy's favourite colour is orange. I ask: "How many whites does Puppy need?" Sophie lines up the whites next to the orange rod. We count out ten together, and the exchange takes place. Hedgehog buys a blue.
Panda is last. There are eight whites remaining in the pile. I ask: "Which rod does Panda want?" Panda wants a pink (4cm). Sophie lines out four whites next to the pink, and says "four" (without counting out).
There are another four whites left in the pile. I say: "Can Panda buy another pink?" Sophie says no. I feel myself wanting to say yes, to show, but I don't. I say "Are you sure?" She re-states that Panda cannot have another pink. Then she gets another animal - Dragon - and says :"Dragon also likes pink!" and the exchange is made.
These events felt 'pedagogically' significant. I went with Sophie's imagination, whilst introducing mathematical ideas of sharing, equality and exchange.