Key Stage 3: age 11-14

Links to the National Curriculum
Mathematics

• Collect data from a variety of suitable sources, including experiments.
• Interpret and discuss data
• Understand and use estimates of probability from theoretical models
• List all the outcomes for single events, and for two successive events in a systematic way.
• When dealing with a combination of two experiments, pupils identify all the outcomes, using diagrammatic, tabular or other forms of communication.
  

ICT

• Pupils use computer models of increasing complexity.

Duration
Two hours

Learning Objectives

Pupils will:

• Use the language associated with probability to discuss events including those with equally likely outcomes
• Collect data from a simple experiment and record in a frequency table: estimate probabilities based on this data
• Compare experimental and theoretical probabilities in simple contexts.
• Understand that if an experiment is repeated there may be, and usually will be, different outcomes. Also that increasing the sample size leads to better estimates of probability
• Identify all the mutually exclusive outcomes of an experiment; know that the sum of probabilities is one and use this when solving problems.
• Understand relative frequency as an estimate of probability and use this to compare outcomes of experiments.

Resources required
Access to coins simulation

Learning activity

Possible Introductory Activities:

“ How is it decided who kicks off in the FA Cup Final?”  or “Who serves first in a tennis match?”   Why is this method used?

In a France v England football match the referee can’t decide between using a Franc or a Fifty Pence piece - What would happen if he decides to use both coins instead of just one? What are the possible outcomes? Are they all equally likely?

Move into the cycle of Discussion > Prediction  >  Experimenting   >  Conclusions and back to Discussion etc.

Use the coins simulation for the experimentation part of the cycle.

Extend the investigation to more coins.

The worksheet gives a similar way of moving through the investigation into coin tossing.

Extension Work

This simulation can be used to illustrate any activity that has two equally likely outcomes and can be adapted to looking at repeated experiments as well.

For Example:

• What is the probability that in a three child family there will be exactly 1 girl?
• If I toss a coin 7 times what is the probability that I could correctly guess the outcome 4 or more times?
• If Beckham completes 50% of his passes successfully and makes 22 passes in a game what number of successes is most likely?
• Also moving onto simple tree diagrams is possible.