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# National Curriculum - Numbers and the number system : Key Stage 3 : Mathematics Content Knowledge

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Key Stage 3
National Curriculum - Numbers and the number system
Question 1 of 8

# 1. How confident are you that you can explain:

## Example

The position of a digit in a number affects its value. Each place after the decimal point has a value one tenth of the value of the place to its left.

Pupils should be able to reason that in the number 4.763, the value of the digit 4 is four, the value of the digit 7 is seven tenths, the value of the digit 6 is six hundredths, and the value of the digit 3 is three thousandths. Using expanded notation, this can recorded as:

4.763 = 4 + 0.7 + 0.06 + 0.003

= 4 +710 + 6100 + 31000

Pupils should also be encouraged to explore situations involving numbers such as 5.001.

This is 5 units and 1 thousandth. The zeros are necessary place holders and their importance is significant.

5.001 = 5 + 010 + 0100 + 11000

## What this might look like in the classroom

#### Question 1:

In which of these numbers is the red 3 worth 30 (or 'three tens'):

310, 303, 34, 239, 33, 673, 133

34, 239 and 133

#### Question 2:

What numbers are represented by the following calculations:

1. 20 + 4 + 0.4 + 0.01 + 0.007
2. 1 + 910 + 7100 + 31000

1. 24.417

## Taking this mathematics further

Our decimal number system (base 10) is based on adding multiples of the powers of ten: ..., 1000, 100, 10, 1, 110, 1100, ... (or ..., 103, 102, 101, 100, 10-1, 10-2, ...)

The binary number system (base 2) is based on adding multiples of the powers of two: ..., 16, 8, 4, 2, 1, 110, 1100, ... (or ..., 24 , 23, 22, 21, 20, ...) In base 2, the number 19 would be written 10011. Can you see why?

Find out about the development of different number systems

'Program' a spreadsheet to break up any number in a given cell and present it in expanded decimal form

## Making connections

An understanding of place value can be built through the use of:

1. Place value blocks (or Diene's blocks)
2. A number line (by zooming in)
3. A calculator

and learners are likely to have encountered such approaches in the primary phase at least.

An understanding of place value is needed in order to genuinely understand rounding.

Adding fractions with different denominators is a significantly more advanced concept than place value in the decimal number system, but using an understanding of place value could be used to explore adding fractions such as the ones in question 2.

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