When the Christmas excitement in school peaks, we are often looking for alternative ways to engage our children in meaningful maths activities. I have to admit, though, I tend to avoid ‘Christmas maths’ activities. Perhaps it’s my lack of imagination, but the activities always feel a bit contrived.
This is a question that I’ve often used in the last week of term instead. I like the way that it generates curiosity and readily engages children whilst being mathematically complex.
You have two containers, one of which will hold three gallons of water, the other five gallons of water. You need exactly four gallons of water.
How do you use these two containers to measure out the four gallons?
So children talk, draw, experiment, struggle and theorise. They will need to realise that you have to empty the contents of one container into the other to measure out different quantities of water. Eventually, either by luck or by judgement, the children are likely to find a solution.
Then the thinking can begin. I use this task to highlight the importance of seeing maths problems from the last step and working backwards. Here, you can identify that there are two possible last moves:
1. Have two gallons of water in the three gallon container, and pour one gallon from the five gallon container into it.
2. Have one gallon of water in the five gallon container, and pour an extra three gallons into it.
So essentially, you need to find a way of getting either one or two gallons of water in the correct container. And now the problem is easier. You can fill the 5 gallon container, pour 3 gallons in the other container and you have two gallons. Or, using the smaller container, you can pour 3 gallons into the five gallon container, then two more gallons. That will leave one gallon in the smaller container. In both cases, you will need to swap the water into the other container so you can complete the final step.
Lots of great reasoning, and there are so many ‘standard’ maths problems that you could draw parallels between. All we need is a powerful context. Maybe Santa and his reindeer could need 4 gallons of water…