Fertiliser
Calculate the area of rectangles using m2
Use remainders within the context of a problem
This is a fairly straightforward two-step problem. The students 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.
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?
Teaching sequence
- Using the piece of string and 4 students 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.
- Read the problem to the class. Give the students time to think about the strategy they would select to solve the problem before getting them to work with a partner.
- 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
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.
In version 2, 20 x 35 = 700 and 700 divided by 200 gives 3 and 100 over. To cover that 100 m2 an extra bag will be needed. So Marilyn will have to by 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.)
| Attachment | Size |
|---|---|
| Fertiliseri.pdf | 38.38 KB |
| FertiliseriMaori.pdf | 45.52 KB |
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