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Number Grids Lesson 2 Extensions

Number Grids Lesson 2 Extensions. Year 10 Deadline: Wednesday 3 rd November 2010. nxn square on grid. Find the difference between the products for squares from 2x2 up to 6x6. Try 3 of each. Create a table of results like this.

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Number Grids Lesson 2 Extensions

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  1. Number Grids Lesson 2 Extensions Year 10 Deadline: Wednesday 3rd November 2010

  2. nxn square on grid • Find the difference between the products for squares from 2x2 up to 6x6. Try 3 of each. • Create a table of results like this. • PREDICT what a 7 x 7 difference will be and CHECK to see if your prediction was correct. • What about an n x n square?

  3. Proof • Now you need to prove that the differences you have found work in any area of your 1-100 grid. • What could we write here to create a GENERAL square. • Now we need to multiply the opposite corners and find the difference. • What do you notice?

  4. Algebra Section • You need to prove that your differences of 10, 40, 90, 160 etc are always true on a 10x10 grid. • For each square from 2x2 upto 5x5 you need to multiply the brackets and get a final expression. • Explain what the final expression means.

  5. Extensions • How can this project be extended. So far we have proved that for an nxn square on a 1-100 grid the difference of the products of opposite corners is 10(n – 1)²

  6. General Points • To make this project good it needs to have; • Accurate and neat diagrams and writing (especially with algebra) • Linking commentary – Without LOTS of written comments algebra can be hard to follow. Explain at every stage what you have found and what you are going to do next. • Thorough extension – How can this project be extended further? • We will discuss this tomorrow but have a think tonight and bring in some ideas.

  7. Extensions • How can we extend this? • What is the general rule for an n x n square on an m x m grid? • Change from a 1-100 grid which is 10 x 10 to: • 9 x 9 grid/ 8 x 8 grid / 7 x 7 grid / etc • Change from a square to rectangles – Investigate 2 x 3/ 2 x 4 / 2 x 5 etc up to the general rectangle p x q. • Instead of finding difference, find the sum/product. • Change to a Number Stair see additional PowerPoint. • Change to a grid with the odd numbers/ even numbers/ multiples of 3/4/5 …. etc

  8. Important • It does not matter if you try an extension which does not seem to have a visible pattern even with algebra. Still include it in the project. The fact you tried will score you marks! • Try your own extension ideas! • Good Luck! • Remember worth 20% of semester grade.

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