Problem
Manu was singing a song. It went "one, two, three, one, two, …" What are the next three numbers? What is the tenth number he’ll sing?

What is this problem about?
This problem is about recognising number sequences and then being able to use them in some way. In this question the number sequence is 1, 2, 3, 1, 2, 3, …. The children first have to recognise this and then use it to find the tenth number in Manu's song.

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 (guess and check, make a drawing, use equipment)

Resources
number tiles (many 1's, 2's, 3's)
counters (3 colours)
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- describe and continue a repeating number pattern
- use ordinal numbers

Teaching sequence

1. Start the following pattern: snap, clap, snap, clap....Join my pattern when you know how it goes.
2. After the all the children can follow the pattern ask them if they can use counters (2 colours) to show the pattern.
   Ask if they can use numbers to show this pattern: 1, 2, 1, 2...
3. Read the problem to the class.
4. As the children work on the problem ask questions that focus on their description of patterns:
   What number comes next? How do you know?
   How will you find the tenth number? (ways of keeping track)
5. Share solutions.

Extension to the problem
Find other ways to show the pattern (counters, actions ...)

Solution
The next three numbers are 3, 1, and 2 in that order.

To find the tenth number Manu will sing it may be easiest to write out all the numbers. (It can be done by drawing or by using counters numbered 1, 2, 3.) We have listed the first ten numbers with their ‘number’ underneath.
1,   2,   3,   1,   2,   3,    1,   2,   3,   1
1    2    3    4    5     6    7     8    9    10
So the tenth number that Manu sings is one!