Problem
Marilyn needs to fertilise her front lawn. It measures 20 metres by 30 metres. Each bag of the fertiliser that she plans to use covers approximately 200m². How many bags should she buy?

Version 2: Marilyn needs to fertilise her front lawn. It measures 20 metres by 30 metres. She uses 3 bags of fertiliser to do the job. Roughly how large an area does each bag of fertiliser cover?

Version 3: Marilyn needs to fertilise her front lawn. It measures 20 metres by 35 metres. Each bag of the fertiliser that she plans to use covers approximately 200m². How many bags should she buy?

What is this problem about?
This is a fairly straightforward two-step problem. The children have to first be able to calculate the area of a rectangle given length and breadth. They then have to realize that the number of bags required is found by dividing the area of the lawn by the area that one bag will cover.

The point of Version 2 is to put the problem from a slightly different perspective.

Version 3 raises the dilemma of what to do in practice when there is a remainder in the division. Clearly Marilyn will have to buy another bag. This is an important aspect of practical problems. In real life, very few answers end up as whole numbers.

Achievement Objectives
Measurement (Level 4)
- calculate the areas of rectangles

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically ( make a drawing, be systematic)

Resources
piece of string formed into circle (about 6m long)
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- calculate the area of rectangles using m^2
- use remainders within the context of a problem

Teaching sequence

1. Using the piece of string and 4 children 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). This 5 minute introduction works well to capture the interest of the class and to focus their attention of the properties of shapes.
2. Read the problem to the class. Give the children time to think about the strategy they would select to solve the problem before getting them to work with a partner.
3. As the children 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?
4. Check that the children are recording their solutions so that they can be shared with others.
5. Display solutions for others in the class to read.
6. Discuss the different approaches taken.

Other contexts for the problem
Wallpapering a room.
Carpeting a floor.

Solution to the problem
First calculate the area of the garden. This is 20 x 30 = 600m². Since 200 goes into 600 three times, then Marilyn should buy 3 bags of fertiliser.

In version 1, divide the 600 by 3 to give an average cover of 200 m².