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Writing up an investigation

Writing up an investigation. Diagonal Differences. What to include. I ntroduction . People should understand what your task was without having to look at anything else. M ethod . What was your approach to the problem and why?

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Writing up an investigation

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  1. Writing up an investigation Diagonal Differences

  2. What to include • Introduction. People should understand what your task was without having to look at anything else. • Method. What was your approach to the problem and why? • Results. Normally in table format, your results should be clear and easy to understand and laid out in the best possible way to enable patterns to be spotted. • Conclusions. From these results, what do you notice? Can you explain why (algebraically, maybe)? Can you come up with generalised rules or formulae to be able to work out the diagonal difference for a square in: • Any position • For any sized square • In any sized grid? • Limitations. Are there any situations when your formula won’t work?

  3. What you should be aiming for • Writing everything in a clear, unambiguous, mathematical way. • Use proper Maths terms but use them in the correct way and in the correct context. • Always introduce variables before referring to them. For example, don’t talk about n without saying what nis. • Use technology to enhance your task. • Demonstrate a thorough understanding of the task and why the results are as they are.

  4. Possible approaches • Define your variables, e.g. ‘In this investigation, I will refer to the following variable: x as the number in the top left hand corner, s as the length of the square and g as the length of the outer grid’ • Start with a fixed grid size (10) and fixed square size (3). Change the number in the top left hand corner. Show that the diagonal difference is always the same. Explain why this is algebraically

  5. Possible approaches (2) • Now investigate different grid sizes. Keep the square size fixed (3) and try grid sizes of 3, 4, 5, 6. Come up with a formula involving g. Try to prove this algebraically. • Now I would consider 2 possibilities: • Fix the grid size (10) and try square sizes of 2, 3, 4, 5. Come up with a formula involving s. Try to prove this algebraically • OR • Fix the square size differently and come up with formulae involving g. For example, come up with a formula when the square size is 2, 3, 4, 5

  6. What you’re aiming for… • Whichever approach you take, your result is two things: • To help you find an overall formula involving sand g • To convince the reader of how you came up with the formula and for them to understand how you came up with it. You should present this in a clear but concise way (e.g. not hundreds of tables)

  7. Task and time frame • You need, in your pair, to write up a full investigation. This can be done in poster format or like an assignment on several sheets of A4 paper. • Time to complete the task: • Thursday 17th Feb (double) • Monday 21st Feb (double) • Tuesday 22nd Feb (single)

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