Key Stage 3: age 11 - 14

Again and Again is an investigation involving decimals and fractions. A knowledge of the equivalence of decimals and fractions is needed. The investigation also requires the pupil to make generalisations; this could be done algebraically using words or formulae.

The activity could also be used as an ICT activity using a spreadsheet to carry out the calculations again and again.

Links to the National Curriculum
Mathematics

• Collect data from a variety of suitable sources, including experiments.
• explore connections in mathematics to develop flexible approaches to increasingly demanding problems; select approproate strategies to use for numerical or algebraic problems.
• use fraction notation; understand equivalent fractions.
• use formulae to generalise a rule
  

ICT

• Pupils use computer models of increasing complexity.
• explore a given model with a numberof variables and create models of their own, in order to detect patterns and relationships.

Duration
Two hours

Learning Objectives

Pupils will:

• Use a given spreadsheet to investigate an iterative process by changing the variables.
• Collect results and communicate their findings.
• Design their own spreadsheet to investigate the iterative process.

Resources required
Access to Again and Again activity. Spreadsheet

Learning activity

Input a start number into the computer model. Try starting by dividing by 5 and adding 1. Pull the lever.
The computer will divide by 5 and add 1 again and again.....

Example:

Look at the result in the OUT box. Does it matter what number goes IN?

Try dividing by 6 and adding 1, dividing by 4 and adding 1...

Try dividing by 5 and adding 2, dividing by 5 and adding 3...

This activity could also be carried out using a spreadsheet.

Generalisations