Focus on Math

Helping children become mathematicians!

Problem Solving Question: Intermediate — Water Jugs February 15, 2011

Filed under: Intermediate Math Ideas & Problems — Focus on Math @ 4:00 pm

I had a great time in Melissa’s grade 5/6 class yesterday doing a logic problem. Melissa had mentioned that she had done a few logic problems with her class and wanted me to facilitate one for her to observe.

I chose a classic “Water Jug” problem, one which, according to one story, was the inspiration for the 19th Century mathematician Simeon Denis Poisson’s pursuit of mathematics:

  • Two friends have and eight-litre jug of water and wish to share it evenly. They also have two empty jugs, one which holds exactly five litres and another which holds exactly three litres. How can they measure four litres using these jugs?

The students went to work on the problem, but clearly some were having more difficulty than others (as is often the case). After a short while we stopped to have a quick discussion about which operations were likely to be used in solving the problem (addition and subtraction, and not multiplication or division). A second discussion a bit later focused on how students might organize their thinking to keep track of the “pouring”. This is a perfect example of when making a chart is a useful problem-solving strategy. Some students got stuck in a “cycle” of pouring, where they would have a line on their charts exactly like a previous line (or stage in the pouring) and they could not figure out how to get out of the cycle. Still, a number of students were able to find solutions in the time we had — and there was a real excitement in the air.

There are many variations of this problem — different sized jugs, different numbers of jugs, different target measure — something to fit nearly every level! If you haven’t yet tried logic problems with your class, I encourage you to give it a go!

I’ll not post the solution here (it is always good for YOU to practice your problem solving skills, too!), but would love to hear what your students do with the problem.

Mathematically yours,


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