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One offs

One offs. WMA Number and algebra. Michael Drake School of Educational Policy and Implementation. Starters. Write the next three terms of the sequence 3, 6, 9, 12, …. Write a sentence explaining how to get from one term to the next. Start with “To get the new term …”.  3  6  9  12. 

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One offs

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  1. One offs WMA Number and algebra Michael Drake School of Educational Policy and Implementation

  2. Starters • Write the next three terms of the sequence 3, 6, 9, 12, … Write a sentence explaining how to get from one term to the next. Start with “To get the new term …” •  3 •  6 •  9 •  12  Down rule  Across rule 

  3. Starters • Think of a number • Add 3 to it • Double it • Subtract two • Halve it • Subtract the number you started with • Add 6 • Multiply the number by 3

  4. Think of a number… • How do we write down that we are thinking of a number – without giving away the number we are thinking of? • What would one more than the number look like? • What would 3 less than the number look like? • What would double the number look like?

  5. Starters What is? 2  4 3  3 52 6  4 6  6 5  7 7  7 8  6 102 9  11

  6. Does this always work? Try some examples of your own… • How many examples do we need to convince ourselves if it works? • What sort of examples do we need to try? • What examples did you try and did it work?

  7. How about… • 29  31? • 299  301? • 4. 01  3.99?

  8. How does it work? • Let’s look at the structure underneath the problem by examining an example and copying it 4  4 3  5 What letter shall we use to show the number we are starting with? n - 1  n + 1 n  n

  9. n +1 n n2 +n -1 -n -1 Which is n2 – 1 (so one offs are always one less than the square number)

  10. Does it generalise? • Predict the answers to these problems • 27  33 • 3.8  4.2 • n2 – 16

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