About cookies

The NCETM site uses cookies. Read more about our privacy policy

Please agree to accept our cookies. If you continue to use the site, we'll assume you're happy to accept them.

 

Personal Learning Login






Sign Up | Forgotten password?
 
Register with the NCETM

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


Key Stage
Key Stage
Topic
Topic
Questions

Next Question
Next

Enter the Self-evaluation Tools
Self-evaluation Tools
Currently viewing
Key Stage 3
National Curriculum - Numbers and the number system
Question 1 of 8

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

a. a. the place value of decimals using expanded notation and decimals or fractions?


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

Answer 1:

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

Answer 2:

  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.

Related information and resources from the portal

Related information and resources from other sites

 
 
Add to your NCETM favourites
Remove from your NCETM favourites
Add a note on this item
Recommend to a friend
Comment on this item
Send to printer
Request a reminder of this item
Cancel a reminder of this item
Share |