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
Spinners worksheet: print worksheet glue on to card and cut out. Access to spinner simulation

Learning activity

Begin by playing Odds and Evens using two spinners divided into quarters with the segments labelled 1, 2, 3 and 4.

Odds and Evens Players (in two teams or pairs) take turns spinning the spinner. One player (or team) wins if the sum is even. The other player or team wins if the sum is odd. Before the children start playing the game ask: Do you think this is a fair game? Why or why not? Let the teams or pairs play the game keeping track of the numbers of wins. Discuss the results and the children’s ideas about fairness. How did you decide if the game was fair? Why do some think it is fair and others think it isn’t fair? Can it be both? Deciding if the game is fair or not should lead into the idea that to predict fairness you need to know all possible outcomes, that is, all possible totals of numbers on the two spinners. From this you can see how many are odd and how many are even. How could we find all possible outcomes?

Share ideas If no one suggests tabulating the possible outcomes then introduce it as a useful technique when dealing with 2 variables. -see below. The sums can now be separated into even and odd numbers giving 8 even and 8 odd. Therefore the game is fair. Over a long series of trials (games) you would expect to get an even sum the same number of times as an odd one. Conclude by discussing the probability of getting an odd and an even total. - Probability of an even total = 8/16 =1/2 =Probability of an odd total.

Use the spinners simulation to do a long series of trials for different spinners. Would the game above be fair for any of the spinners in the simulation? Compare the experimental results with the expected results.

Use the spinners worksheet.