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 Chase Me game

Learning activity
Chase Me

The aim of the game is for the tortoise to catch up with the hare or vice versa. Moves are decided by throwing two dice. Adding  together the numbers on the two dice tells you which animal moves one place clockwise.

Initially the game is set up so that the tortoise or the hare will move one place clockwise based on the following table.

1. Which of the following statements do you think is true?

The tortoise is more likely to win than the hare.

The hare is more likely to win than the tortoise.

Both are equally likely to win ( the game is fair)

2. Play the game by clicking on the throw the dice once/again button until there is a winner. Which animal won?

3. Repeat (2) a few times until you have played several games. How many times did each animal win?

4. Do you want to change your answer to question 1? Why do you think your answer is now correct?

5. Complete the following table to show all possible ways of combining the two dice and the scores that are obtained.:

6. Use this table to find the probability that the tortoise moves on any given throw.

7. Is the probability that the hare wins the game greater or less than this? Why?

8. Use the table to devise a fair game. Click on the numbers to set up your fair game. Play your game several times. Do the results seem to show that it is fair?

9. Devise a game so that the probability that the tortoise moves is 2/3. Set up this game and play it a few times. Estimate the probability that the tortoise wins the game

10. Click on play again original game and play the original game once and record how many moves it takes for an animal to win.

11. Use the button throw until there is a winner and record which animal wins and how many throws it takes.

12. Do this several times. To do this click play again keep these scores and throw until there is a winner. Record your results and draw a bar chart to show how many throws it takes to get a winner.

13. Can you explain the gaps in your bar chart?

14. Calculate the mean, median and mode of the number of throws it takes to get a winner.

15. Repeat (10) to (14) with a fair game and then with the game where the probability that the tortoise wins is 2/3.

16. What do you notice about the distribution of the number of throws in a game as the probability of winning changes? Which gives the longest game? Which gives the shortest?

17. Make up your own investigations and carry them out.