# 3.3 Recognise, classify, represent and describe numbers

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## To recognise and use equivalent forms of numbers [lo 1.5.2]

1. You have just completed a learning unit on ordinary fractions. Let us do some revision.

What fraction in each of the following figures is coloured in?

1.1

1.2

1.3

2. Write the answers above as decimal fractions.

## Tenths

We read 0,3 as nought comma three and we call it a decimal fraction .

The comma is called the decimal sign and it separates the whole numbers from the fractions.

Do you still remember?

$\frac{1}{\text{10}}$

3. Look at the number line and fill in the missing numbers.

4. Work together with a friend. Count aloud and complete the following:

4.1 0,2 ; 0,4 ; 0,6 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.2 4,7 ; 4,5 ; 4,3 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.3 0,5 ; 1,5 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.4 3,6 ; 3,2 ; .............. ; .............. ; .............. ; .............. ; .............. ;

4.5 9,2 ; 9,1 ; .............. ; .............. ; .............. ; .............. ; .............. ;

Do you still remember?

If I want to add 0,3 to the previous number repeatedly I can programme my calculator in this way: Number + 0,3 + = = =

## To use a series of techniques to do mental arithmetic [lo 1.10.5]

By now you know that we can use the pocket calculator very effectively to find or check answers. Now that you have seen how to programme your pocket calculator or to add on, try to complete the following activity without making any mistakes. Programme your pocket calculator and write the first 10 answers to the following:

1.1 Start at 3,7 and add 0,6 each time:

1.2 Start at 9,3 and subtract 0,4 each time:

## Activity 3:

• To recognise, classify and represent numbers in order to describe and compare them [LO 1.3.3]
• To recognise and use equivalent forms of numbers [LO 1.5.2]
• To use a series of techniques to do mental arithmetic [LO 1.10.5]

In this activity we would like to see whether you can determine which ordinary fractions (mixed numbers) fit in with which decimal fractions. It is important for you to be able to see that 0,2kg is actually exactly the same as $\frac{2}{\text{10}}$ kg !

1. Link the ordinary fractions to their decimal fraction partners. Connect column A to the correct answer in column B.

 A B E.g. 0,2 kg 1 $\frac{5}{\text{10}}$ / 1 $\frac{1}{2}$ km 1.1 0,5 m 152 $\frac{7}{\text{10}}$ km 1.2 17,6 litre $\frac{2}{\text{10}}$ kg 1.3 8,4 seconds 8 $\frac{4}{\text{10}}$ sec 1.4 152,7 km 17 $\frac{6}{\text{10}}$ ℓ 1.5 1,5 km $\frac{5}{\text{10}}$ / $\frac{1}{2}$ m

Challenge!

2. Work with a friend. Write the following fractions as decimal fractions:

2.1 $\frac{4}{5}$ 2.2 $\frac{2}{\text{20}}$

2.3 $\frac{3}{5}$ 2.4 $\frac{7}{\text{20}}$

2.5 $\frac{\text{18}}{\text{30}}$ 2.6 $\frac{\text{48}}{\text{60}}$

3. Explain what must be done to get the above answers.

5. Now use a calculator to check your answers in no. 2.

## To be capable of doing mental arithmetic [lo 1.9]

1. You now have the opportunity of improving your mental arithmetic skills and applying your newly acquired knowledge. Complete the following mental arithmetic test as quickly and as accurately as possible: