Problem
In Beltenup, taxi drivers charge $1 flag fall once you get in the car. Then they charge you $2 for each kilometre you travel. How far can you go if you and your friends have just $23 between you?

What is this problem about?
The children first have to see there’s a pattern here. The pattern is built in twos starting from one. When does the pattern hit 23?

Achievement Objectives
Algebra (Level 2)
- continue a sequential pattern and describe a rule for this

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (draw, use equipment, make a table).

Resources
1 and 2 dollar coins (pictures)
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- count in twos using odd numbers
- describe a repeating number pattern

1. Set the scene for the problem with a discussion about taxis. More specifically check that the children understand how taxis charge – flagfall and $ per km.
   Tell the children about the rates of "Beltenup" taxis.
   Ask: If you want to travel 4 km how much would it cost?
2. Discuss solutions.
3. Pose problem for the children to work on in pairs.
4. As the children work ask questions that focus their thinking on the repeating pattern of twos.
   What are you using to solve this problem? How is that helping you?
   What numbers are you using? Why?
   What is the next number? How do you know?
5. Share solutions.
6. Conclude with some class practice counting forwards and backwards in twos using different starting numbers.

Extension to the problem
How far could I travel in a Beltneup taxi if I had $40?

Solution
There are lots of ways of doing this. Let’s use a table.

So the friends can travel for 11 km in the taxi.