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# National Curriculum - Algebra : Key Stage 2 : Mathematics Content Knowledge

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Key Stage 2
National Curriculum - Algebra
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# 1. How confident are you that you can:

## Example

#### Question 1

The perimeter of a rectangle is given by the formula

p = 2 × (l + w)

where l is the length and w is the width.

What is the perimeter of a rectangle of length 13 cm and width 6 cm?

l = 13 and w = 6, so l + w = 19

Therefore p = 2 × 19 = 38, so the answer is 38 cm.

#### Question 2

If a rectangle has a perimeter of 22 cm and all the edges are whole number of cm, what sizes could it be?

Using the formula p = 2 × (l + w), if p = 22, then (l + w) must equal 11. Therefore we need whole number pairs of l and w that add up to 11. There are five possible answers:
10 cm and 1 cm
9 cm and 2 cm
8 cm and 3 cm
7 cm and 4 cm
6 cm and 5 cm

## What this might look like in the classroom

One familiar context where formulae can be used is in converting between different metric and imperial units.

For example, 1 kg is approximately 2.2 pounds, so children could use the formula:

k ≈ 2.2 × p or pk ÷ 2.2

to convert between these units (≈ means ‘is approximately equal to’).

1 mile is approximately 1.6 km, so the conversion formula for converting these units would be:
k ≈ 1.6 × m or mk ÷ 1.6

Children could explore other conversions and devise and use their own formulae.

Another context that will be familiar for many children is converting currencies. Children could find out the current rate of conversion from pounds sterling to Euros, devise their own formulae and use them to answer questions such as:

The holiday that our family want to go on will cost €1,200. I can only afford to spend £1000. Can I afford this holiday?

## Taking this mathematics further

It’s easy to get these conversion formulae the wrong way round. It helps to think of the sentence ‘1 mile is approximately 1.6 kilometres’ . It then follows that the formula should be m ≈ 1.6 × k

 Miles Kilometres 1 16 2 3.2 3 4.8 5 8 10 16

you can see that ‘the number of kilometres is 1.6 times the number of miles’ and so the formula is k ≈ 1.6 × m

Getting children to say aloud sentences such as ‘the number of kilometres is 1.6 times the number of miles’ will help them avoid getting the formula the wrong way round.

Converting between degrees Fahrenheit and degrees Celsius is more complicated, partly because 0°C does not equal 0°F. The conversion formulae are:

C = (F-32) × 59

F = C × 59 + 32

These formulae allow higher-attaining children the chance to explore negative numbers. If the temperature is 21°F, what is this in degrees Celsius?

Children could explore using formulae like this in a spreadsheet.

## Making connections

These sorts of conversion formulae can also be shown as line graphs. For example the conversion from miles to kilometres as a graph is:

The conversion graph for Fahrenheit to Celsius is:

If children have experience of using formulae, of making conversion tables and of drawing the related graphs they will be helped to develop their conceptual understanding of this important aspect of mathematics, and is likely to make it easier for them to cope with more complex algebra in Key Stage 3.

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