Mia and Hunter call a cab. The taxi driver charges $1 flagfall when they get in the car.

The charge is then $2 for each kilometre they travel.

They have $23 between them.

How far can they travel?

The problem requires students to be systematic in their recording as they explore an add two pattern beginning at one.

1 and 2 dollar coins (pictures)

### Problem

Mia and Hunter call a cab. The taxi driver charges $1 flagfall when they get in the car. The charge is then $2 for each kilometre they travel. They have $23 between them. How far can they travel?

### Teaching Sequence

- Ask students who has travelled by taxi. Talk about the flagfall and the $2 per kilometre charges.
- Ask:
*If you want to travel 4 km how much would it cost?*Discuss solutions. - Pose problem for the students to work on in pairs.
- As the students 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? - Share solutions. Highlight examples of systematic recording.
- Conclude with some class practice counting forwards and backwards in twos using different starting numbers.

#### Extension to the problem

How far can Mia and Hunter travel if they have $40?

Pose problems with variations in the flagfall, $ rate /km, and amount of money.

### Solution

A table is an organized way to record the solution.

$ | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 |

km | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

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

#### Solution to the extension

19.5 km