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.
  

ICT

• Pupils use computer models....

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
Resources - cubes of different colours - paper bags
Access to Santa's Sack

Learning activity

Make predictions about the cubes that are hidden in a bag. We find out that even when we can’t look in the bag we can still make a good guess about what is in it.

Put 5 cubes in a bag (3 red and 2 blue). Here is a bag with 5 cubes. The cubes are either red or blue and we’re going to try to find out what they are by picking one out one at a time. Shake the bag and ask a child to select one and show the class. Record the colour on the board and get the child to put the cube back in the bag. (Note: Each time a child takes a cube it must be returned before the next child draws a cube. Otherwise, the probabilities will change). Ask another child to select a cube. What colour have you got? If it is the same colour as the one previously drawn ask: Do you think that it is the same cube? Why or why not? Ask a third child to draw a cube but this time get them to predict what the cube might be. Why did you guess that? Do this five times altogether.

Do we know how many cubes there are of each colour? Why or why not? Would we find out more if we had more turns? Let another five children select a cube and record these on the board. Each time ask the child to predict the colour of the cube. Before we look in the bag I want us to think about all the possible combinations for the cubes. Record these on the board. How manay times do you have to repeat this before you can be pretty certain what's in the bag?

Try putting ten cubes of different colours in the bag. Keep drawing out cubes (remember to replace them each time). How many times do you have to do this to be sure you know what's in the bag?

Do you think that the more times you draw from the bag, the more you know about what’s inside?

Use Santa's Sack to find out what's in his sack. If you do 100 trials can all the class predict what's in the sack? How close to the expected results are the actual result?