This problem solving activity has a measurement focus.

PSTV is planning to show **wildlife films** in the time slot between 1 o'clock and 5 o'clock on Thursdays.

If each programme lasts **half an hour**, how many **different programmes** will they need to buy to fill the time slot?

- Read time in half-hours.
- State that there are 2 half-hours in an hour.
- Count in 2s to 8.
- Devise and use problem solving strategies to explore situations mathematically.

This problem helps explore the idea of half-hours. This is both an important concept in time and a useful application of the simple fraction one-half.

- Copymaster of the problem (English)
- Copymaster of the problem (Māori)
- List of wildlife films
- Clock (preferably analogue - you could also show a digital representation)

### The Problem

PSTV is planning to show wildlife films in the time slot between 1 o'clock and 5 o'clock on Thursdays.

If each programme lasts half an hour, how many different programmes will they need to buy to fill the time slot?

### Teaching Sequence

- Show the students the list of wildlife films. Explain to them that some of these films will be purchased by PSTV to be shown between 1 o'clock and 5 o'clock on Thursdays.
- Introduce the problem by displaying half past three on the clock and asking what programme, from the list provided, might be on PSTV at that time. Display the title students choose on the board and write 'half past three' and 3:30 next to it.
- Move the hands to 4 o'clock and ask what programme would now be on. Display the title students choose on the board and write '4 o'clock' and 4:00 next to it.
- Pose the problem.
- Ask the students questions that focus their thinking on telling the time in ½ hours.
*What time is this?**How do you know?**Tell me what the time would be in half an hour from then?**Can you show me that time on the clock?* - Encourage the students to plan ways to keep track of their solution so that they can share it with others.
- Share solutions.

#### Extension

How many programmes would PSTV need from 11 o'clock in the morning until 6 o'clock in the evening?

### Solution

This might be done with rods or by using a clock face. It might also be another chance to practice counting in 2s.

There are four hours to fill in. Each hour has two half-hour programmes. So PSTV needs 2 + 2 + 2 + 2 equals 8 programmes. Any combination of 8 films could be used to solve this problem.

#### Solution to the Extension

This can be proven using the same methods that were used to prove the solution to the original problem. There are seven hours to fill in between 11 o'clock in the morning until 6 o'clock in the evening. Each hour has two half-hour programmes. So PSTV needs 2 + 2 + 2 + 2 + 2 + 2 + 2 equals 14 programmes. Any combination of 14 films could be used to solve this problem.