### Task 19 ... Years 2 - 6

#### Summary

Place any number of cookies on a plate ready to offer equal shares to guests. The problem is:
If I tell you any number of guests can you tell me the share they each receive?
This cameo includes an Investigation Guide.

#### Materials

A large number of counters and a paper plate.

#### Content

• 1:1 correspondence
• counting
• sharing and grouping
• partitioning wholes
• times tables facts
• multiples and factors
• fractions of a whole

#### 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 two variables in this problem - the number of cookies and the number of guests - and in choosing these the student creates their own iceberg. Some combinations of the numbers will give 'whole cookie sharing'; some will lead to the need to find fractional parts of some cookies. Even young children with little formal experience of fractions find ways to handle the second of these situations. Their desire to make fair shares is quite strong. It is not necessary to take the 'give the extras to the dog' approach.

If teachers wish they can set particular problems to limit the experience to whole numbers, or to encourage a search for patterns. For example:

1. There are 24 cookies. Work out the number of cookies for each guest in these cases: 1, 2, 3, 4, 6, 8, 12, 24 guests.
2. There are 24 cookies. Work out the number of cookies for each number of guests from 1 up to 24.
3. There are 3 guests. Work out the number of cookies for each guest in these cases: 1, 2, 3, 4, ..., 23, 24 cookies.
Backwards questions are another level of challenge. For example:
• When the children shared the cookies, everyone got some whole ones and 1/5. How many cookies and how many children do you think there were?

#### Extensions

Use this Investigation Guide shared by Toni Pfeiffer, Good Shepherd, Amaroo - or design your own and share it here.

#### 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 is easy to convert to a whole class investigation. You only need lots of counters and a paper plate for each group. No paper plates? A piece of paper will do. If you have Poly Plug, use them as cookies.