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.

Copymaster of the problem (Māori)

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