Problem
Katie was given a marble on Tuesday. Then she was given two marbles every day for a long time. When did she get her 11th marble?

What is this problem about?
This problem gives a good opportunity to reinforce counting in twos, using different starting points (eg 1..3..5 or 4..6..8).

This problem mixes several things together. First the children have to realise that Katie has a sequence of 1, 2, 2, … and that that adds up to 1, 3, 5, 7, … on each successive day. They then have to work out when this sequence gets to 11. The final step is to convert that number of days into a day of the week.

All these steps by themselves are not too hard. The difficult thing is to find a way to record all the steps and then put them all together.

Achievement Objectives
Algebra (Level 1)
- make and describe repeating and sequential patterns
- continue a repeating and sequential pattern

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (be systematic, use equipment, make a drawing)

Resources
marbles or counters
Blackline master of the problem

Specific learning outcomes
The children will be able to:
- identify and continue a repeating number pattern (1..3..5..7)
- state the days of the week in order (measurement objective)

Teaching sequence

1. Introduce the problem by "acting" the start of the problem using a child.
2. Brainstorm for ways to solve the problem (use equipment -counters or bottletops, draw).
3. As the children work on the problem in pairs ask questions about the patterns they are using?
   How do you know how many marbles to add each day?
   Can you count the counters you have put out?(note if they count in twos)
   How could you convince the others in the class that you are correct?
4. Share solutions to the problem.

Extension to the problem
When did Katie get her 30th marble?

Solution
One way to do this is to put out 11 counters and have some cubes ready. We will use the cubes to count the days. Count out 1 for the first day and record a single cube. Then count out two and record by adding a second cube. Then count out another two counters and record a third block. We show the count in the diagram.

Here it can clearly be seen that it takes 6 days for Katie to get 11 marbles.
This could perhaps be done more easily by:

1     + 2     + 2     + 2     + 2    + 2
Tu     We       Th      Fr       Sa      Su