Soft Drink Crates
Task 211 ... Years 2 - 10
SummaryThe story shell is a worker packing cans into a standard 6 x 4 crate. The worker notices that when the crate has a given number of cans in it, they are arranged so that the rows and columns are all even numbers. Given 10 cans as a starting point, the initial investigation revolves around the question:
IcebergA 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...
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 InvestigationTasks 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:
The initial investigation is as above, but we can also ask:
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:
The Soft Drink Crates lesson is an integral part of:
From The Classroom
Winkie Primary School
This journal entry from Brodie and Tyson shows the quality of work that can be expected from primary students
... and that these two need to do a bit more exploring into which numbers of cans can and can't be placed in even rows and columns.
You can read here about the influence of our 6 day professional development course Engineering 'aha' Moments in Number on Nic's teaching practice.
St. Edmund's Junior School
Words aren't really necessary to describe the involvement and enthusiasm of the children