This problem solving activity has a number (addition and subtraction) focus.
Millie needs to put her new fish into exactly one litre of water but she has just two measuring containers.
One holds seven litres and the other holds four litres.
How can she use these two containers to put exactly one litre of water into the fish tank?
The problem involves finding a solution to a practical problem using a mathematical process. The students have to first make the observation that the amount of water in one container cannot be transferred into the other evenly. The students also need to understand that these containers can be used together as opposed to just being separate entities. When they start solving this problem they will probably use a guess and check method directly related to the physical problem. They can then be encouraged to identify the mathematics that is behind what they have done.
The key to the solution actually involves finding the difference between the amounts in the containers. As the number one is the focus point, the students must devise a solution that has one as the difference. This can be achieved by the following formula: (2 x 4) – 7 = 1.
This problem should help students to become more flexible with number and be open to new ways to look at apparently old situations.
Millie needs to put her new fish into exactly one litre of water but she has just two measuring containers. One holds seven litres and the other holds four litres. How can she use these two containers to put exactly one litre of water into the fish tank?
Using the same scenario as above, can you put exactly four litres of water into the fish tank using a five litre and a three litre container?
As we said above, students will probably come to this by guess and check. The most direct answer to the problem is based upon the expression 2 x 4 – 7 = 1. However, it can be solved using the more complicated expression 3 x 7 – 5 x 4 = 1.
It may be worth noting that once you can get 1 litre you can get any amount simply by adding together enough ones. But there is often a more efficient way of doing things. For instance, 2 x 7 – 3 x 4 = 2, will provide the basis for getting two litres measured exactly.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/fishy-problem at 8:55pm on the 26th February 2024