- Maia plans to fertilise her front lawn. It measures 20 metres by 30 metres.

If each bag of the fertiliser covers approximately 200m^{2}, how many bags does Maia buy?

- Maia fertilises her front lawn. It measures 20 metres by 30 metres.

If she uses 3 bags of fertiliser how large an area does each bag of fertiliser cover?

- Maia fertilises her front lawn. It measures 20 metres by 35 metres.

If each bag of fertiliser covers approximately 200m^{2}, how many bags does she buy?

^{2}

This is a two-step problem that is presented in three ways. The students must know how to calculate the area of a rectangle given length and breadth, and apply their knowledge of division.

Copymaster of the problem (Māori)

Copymaster of the problem (English)

piece of string formed into circle (about 6m long)

### Problem

- Maia plans to fertilise her front lawn. It measures 20 metres by 30 metres. If each bag of the fertiliser covers approximately 200m
^{2}, how many bags does Maia buy? - Maia fertilises her front lawn. It measures 20 metres by 30 metres. If she uses 3 bags of fertiliser how large an area does each bag of fertiliser cover?
- Maia fertilises her front lawn. It measures 20 metres by 35 metres. If each bag of fertiliser covers approximately 200m
^{2,}how many bags does she buy?

### Teaching sequence

- Focus students' attention on the properties of shape by using a piece of string and 4 students, to form a number of shapes (square, parallelogram, rectangle). With each shape ask the class to explain how they would check if the shape was accurate. For example, how do they know that the parallel sides of the rectangle are equal? That the angles are 90 degrees? equal / parallel etc.
- Pose Maia's fertiliser problem and have the students suggest a strategy they might use.
- As the students work ask:

*What information have you found out? Why was that necessary?*

Explain your calcuations – especially the units that you are including (square metres)

How do you know that you are on the right track?

How do you know that your answer is reasonable? - Check that the students are recording their solutions so that they can be shared with others.
- Display solutions for others in the class to read.
- Discuss the different approaches taken.

#### Other contexts for the problem

Wallpapering a room.

Carpeting a floor.

#### Solution to the problem

1. First calculate the area of the garden. This is 20 x 30 = 600m^{2}. 600 divided by 200 = 3. Maia buy 3 bags of fertiliser.

2. Divide 600 by 3 to give an average cover of 200 m^{2}.

3. 20 x 35 = 700 and 700 divided by 200 gives 3 and 100 over. To cover that 100 m^{2} an extra bag will be needed. So Maia buys 4 bags. (Obviously she will only use half of the last bag. She can store the rest for the next time she has to fertilise her lawn.)