Module 6 Handling data
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Can I list all the outcomes that may result from repeating an experiment?

Example review questions

  • A coin can land in two ways: Heads up or tails up.
    If you toss two coins, what are all the possible combinations of heads and tails?
    Rajat said, 'If I toss one coin twice, there are four possible outcomes. I think that if I toss the coin again, there will be 6 possible outcomes'. Is he right? Use a diagram to explain how you decided.
  • Karen and Huw each have three cards, numbered 2, 3 and 4. They each pick one of their own cards. They then add together the numbers on the two chosen cards. Draw a table to show all the possible outcomes.
  • Karen and Huw play the game again, but this time they have four cards numbered 2, 3, 4 and 5. How many possible outcomes are there? How do you know?

Teaching guidance

This teaching guidance document suggests some of the key vocabulary, models, images and practical equipment that children should experience and be able to use. It also includes some teaching tips to provide a few starting points for ways of supporting children with this area of mathematics.

PDF file Teaching guidance: Can I list all the outcomes that may result from repeating an experiment? | 216KB new window

Consolidation and practice

These resources are to support children in guided or independent work. Roll over the highlighted resource for a description.

PDF file How to use number spinners ITP | 139KB new window

SWF file Number spinners ITP | 38KB new window

XLS file Probability spreadsheet | 89KB new window

DOC file Year 9 Booster Kit – Lesson 11 | 117KB new window

Visit the nrich website new window for further activities to support practice and application.

Number spinners

itp_number_spinners.png

This interactive teaching program (ITP) is an ICT-based tool to support the exploration of number, reasoning and problem solving. Number spinners ITP allows the child or teacher to generate 3, 4, 5 or 6 random numbers on up to 3 spinners. Numbers from 0 to 99 can be displayed.

Opportunities to use and apply

Possible contexts include:

  • Devising games, e.g. Make up rules for a simplified lottery game – only numbers 1 to 3 are available and you can pick two numbers. How many possible outcomes are there? Can you devise a game where there are 12 possible outcomes?
  • Dice experiments, e.g. Throw two (or three) dice and find the total, identifying all the possible outcomes for the experiment.
  • Spinner and card experiments, e.g. Design an experiment using two different spinners and identifying the possible outcomes.

 

Confirming learning

Ask probing questions such as:

  • A door has a security lock. To open the door you must press the correct buttons. The code for the door is a letter followed by a single digit number, for example B6.
    How many different codes are there altogether?
    Explain how you are sure you have found all possibilities.
    Can you design a code that is harder to crack? How many different combinations does your code have?
    Security lock with code letters A, B, C and D and code numbers one to six.
  • These two spinners are spun at the same time.
    The two scores are added together. Record all the possible outcomes.
    Design two spinners that would give fewer possible outcomes for the experiment.
    Two spinners. One with minus three, plus two and minus one. The other with plus five, minus four and plus six.