# Ice Cream Flavours

### Task 118 ... Years 2 - 10

#### Summary

Imagination is stimulated by the story shell of building your own triple-header ice cream - 3 scoops of ice-cream, but each scoop has to be a different flavour. If there are only 3 flavours, how many different triple-headers can be made? But that's only the beginning. What happens if...?

#### Materials

• 8 cubes in each of three flavours

#### Content

• counting
• algebraic patterns
• mathematical language of position and order
• visual patterns, including patterns of colour
• multiplication, multiplicative thinking, multiplication principle of counting
• permutations & combinations
• logical reasoning
• problem posing and solving
• recording mathematics

#### Iceberg

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

The solution to the task card is:

although in this case the student selected peppermint as one scoop instead of vanilla. The neat visual pattern indicates the thinking involved.

• Each flavour needs a 'turn' at sitting on the cone.
• The two flavours remaining must then be placed either 'this way' or 'this way'.
Now the door is open to any number of investigations. Ask the students what could be changed in the problem, suggesting that this is exactly what a mathematician does when they ask What happens if...? Likely responses are:
• number of flavours
• number of scoops
• whether or not flavours can be repeated
and you might even have some who suggest starting with a double cone and then making 'headers'. Since the double cone can be rotated in the hand, meaning that the left and right cone swap places, that brings up some challenging counting to get only unique solutions.

Assuming no repeats of flavours are allowed:

• If a fourth colour and triple headers are used, there are 24 different ice-creams.
• If a fourth colour and quadruple headers are used, there are also 24 different ice-creams!
• If a fifth colour and triple headers are used there, there are 60 ice-creams.
Challenge students to select and explore their own problem and present a report (written, poster, PowerPoint...) explaining their work.

#### 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.

The whole class lesson for this task is detailed in Maths300 Lesson 143, Ice-Cream Flavours. This lesson also extends the investigation with software. You will need a collection of cubes, similar to those shown, for the students and some A4 pieces of coloured paper for yourself to use as a floorboard introduction. If you use white and three other colours, the white can be quickly folded to a cone shape and the each other page is a scoop.

For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 143, Ice-Cream Flavours, which also includes student journal work in the Classroom Contributions and an exciting assessment approach.

#### 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 Ice Cream Flavours task is an integral part of:

• MWA Pattern & Algebra Years 3 & 4
• MWA Number & Computation Years 9 &10

The Ice-Cream Flavours lesson is an integral part of:

• MWA Number & Computation Years 9 &10
This task is also included in the Task Centre Kit for Aboriginal Students and the Primary Library Kit. Solutions for tasks in the latter kit can be found here.