Soft Drink Crates

Iceberg A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

There are many solutions to the first problem, as can be seen in the exciting From The Classroom section below. Some are reflections and rotations of others. There are also several ways to find the solution and the tendency of teachers and students alike is to use guess, check and improve as their first approach. However, this problem and all the other variations in the task will better resolve with the more ordered approach of breaking the problem into smaller parts. 1. Make the columns correct... 2. Keep cans in the same column but alter their row... 3. Until the rows are also correct... Similar reasoning leads to a solution for 18 cans. Again, there will be variations. This is a task that encourages high level thinking without a correspondingly high demand for mathematical skills. The emphasis is on the concept of proof and the application of strategies to achieve proof. That makes it accessible to all of our students and as a result we may find out things about their mathematical reasoning abilities that we would never discover through a diet of number or symbol driven text work. The last part of the card encourages trying all even numbers of cans. Clearly, 2 cans won't work and 24 cans must work. There is one other number of cans that doesn't work. Encourage your students to find it. 6, 10 and 14 cans are tricky, but will be found using the strategy above. Also, the strategy of 'have I solved a similar problem' is sometimes useful. For example if a block of 4, in 2 rows of 2, is added to the top right corner of the solution to 10 cans above, we will have a solution for 14 cans.

Whole Class Investigation Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

This task works beautifully as a whole class investigation if you have Poly Plug. The yellow/blue plugs even look like cans. If you don't have this resource you will have to find something appropriate - counters will do - and prepare a grid. There are two ways to use the plugs. Either two red boards can be masked to show the crate: and then the yellow/blue plugs are used as cans: or, the plugs can be used standing on this printable 'crate' (screw caps from bottled water will also work). Students can also record solutions on this Recording Sheet. The initial investigation is as above, but we can also ask: Are there any even numbers of cans that can be arranged as 'odd both ways'? Are there any odd numbers of cans that can be arranged as 'even both ways'? Are there any odd numbers of cans that can be arranged as 'odd both ways'? What happens if we start with a different crate shape? (Poly Plug can easily be changed into several different crate shapes.) For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 36, Soft Drink Crates, which includes an Investigation Guide. Visit Soft Drink Crates on Poly Plug & Tasks.

Is it in Maths With Attitude? Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Soft Drink Crates task is an integral part of: MWA Number & Computation Years 3 & 4 MWA Space & Logic Years 9 & 10 The Soft Drink Crates lesson is an integral part of: MWA Space & Logic Years 9 & 10

From The Classroom

St. Edmund's Junior School England Matthew Reames Year 5

Matthew's photos tell their own story. Words aren't really necessary to describe the involvement and enthusiasm of the children ...or who owns the problem.

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