Broadwater School Maths and Computing College Maths Homework Investigation

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Broadwater SchoolMaths and Computing
CollegeMaths Homework Investigation

• Tic-Tac-Toe

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Tic-Tac-Toe

• The final presentation can be hand written or
  word processed
• The best investigations will be displayed and
  rewarded with credits

• You have four weeks in which to complete this
  homework. The deadline, by which the
  investigation has to be handed in is Monday xth
  XXXX
• Read the instructions carefully then ask your
  Maths teacher to explain anything you do not
  understand
• Maths staff will be available to help you in this
  investigation every Tuesday during break, and
  Thursday from 12.40pm to 1.00pm in room 202
• The investigation should cover about 5 A4 sheets,
  and include all methods, graphs, workings etc.
• Some students will be able to extend the
  investigation and credit will be given for this
• A high standard of work will be expected, and
  work not of an appropriate standard will need to
  be completed during after school detentions
• GOOD
  LUCK

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InstructionsPlay a game of tic-tac-toe with a
partner.
Play two more games. Who won? How many different
ways are there to win on your 3 x 3 grid?
Now try playing a game on a 4 x 4 grid. This time
you need to get four in a line. How many ways
are there to win this time? What if you had a 5
x 5 grid?
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Finding a pattern to predict results

• Show your results in a table and look for a
  pattern in your answers.
• Fill in the answer for a 6 x6. Draw the grid to
  see if you are correct.
• Without drawing the grid, can you predict how
  many different ways are there to win on a 10 x 10
  grid?
• Explain how you worked out your answer.

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Finding a rule for your pattern

• Look across each line in your table.
• Find a rule that helps you to give the number of
  winning ways for each size of the grid. It must
  be the same rule for each one.
• Use your rule to work out how many ways there are
  to win on a 100 x 100 grid.
• Try to explain why your rule works.
• Can you express your rule using algebra?

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• Extending the investigation
• Can you look at the problem in a different
  way?
• Hint - Consider the number of lines drawn instead
  of the number of squares in the grid.
• What happens to your rule and results?

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Marking Criteria

• The investigation will be marked out of 21, and
  will be given a National Curriculum level
• A total of 7 marks will be awarded for the
  strategy used, is there a logical approach, what
  methods have been used?
• Up to 7 marks will be awarded for communication
  have the explanations been clear? Are any
  diagrams, tables or graphs labelled with reasons
  for using them?
• The final 7 marks are for reasoning and the
  standard of maths used in the investigation.

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Tic Tac Toe Marking Scheme