Maths GCSE Unit 1

Module 5 Foundation Number Grids Set 1

The aim is to achieve 665 - 888 (grade B - grade A*) . To achieve grade B pupils must:
          Change a feature of the box and use a variety of methods to achieve a fuller solution
          Find the differences using correct algebra - showing their method - explaining what the letter represents
          Predict and test and use algebra to justify their solutions
          To achieve 666 pupils will need to prove the result for a 2xw box, 3xw box etc.

To achieve grade A pupils must:

         Change 3 features: the length of the box, the width of the box and the size of the grid to find the algebraic rule
      for the difference of any size box on any size grid
          Results must be found algebraically with a clear and logical method

To achieve grade A* pupils must:

        Write a concise report with no unnecessary working but clear and well explained with perfect algebra
         Consider the conditions under which the rules are valid

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1
Calculate the difference for several 2x2 boxes and describe any patterns
Change a feature of the box e.g. the width
Show pupils how they could have used an algebraic approach to find the difference for a 2x2 box
Pupils try the algebraic approach for the 2x3 and 2x4 boxes and use this method to find the differences for boxes of width 5 and 6

2 Put the results in a table and find the nth term
Predict and test to see if it works
Guide pupils through algebraic way of finding the nth term i.e. start them off but pupils must be able to do this for themselves

3
Continue to investigate rectangular boxes by starting with boxes of length 3 e.g. 3 x 2, 3 x 3, 3 x 4, 3 x 5
Find the differences algebraically and find the nth term
Continue to investigate rectangular boxes by starting with boxes of length 4 e.g. 4 x 2, 4 x 3, 4 x 4, 4 x 5
Find the differences algebraically and find the nth term

4
Looking at your rules so far can you predict the difference for any length of box?
Test out your prediction
Can you prove it algebraically

5
Change the size of the grid e.g. a grid 9x9, 8x8
How do the differences change?
Can you find/prove the results algebraically?

6
What about a rectangular grid a x b?

Lesson	Details & links	Assessed work / further work / QMA	My Learning	My Thinking	My Research	My Feelings	My Peers
1	Calculate the difference for several 2x2 boxes and describe any patterns Change a feature of the box e.g. the width Show pupils how they could have used an algebraic approach to find the difference for a 2x2 box Pupils try the algebraic approach for the 2x3 and 2x4 boxes and use this method to find the differences for boxes of width 5 and 6
2	Put the results in a table and find the nth term Predict and test to see if it works Guide pupils through algebraic way of finding the nth term i.e. start them off but pupils must be able to do this for themselves
3	Continue to investigate rectangular boxes by starting with boxes of length 3 e.g. 3 x 2, 3 x 3, 3 x 4, 3 x 5 Find the differences algebraically and find the nth term Continue to investigate rectangular boxes by starting with boxes of length 4 e.g. 4 x 2, 4 x 3, 4 x 4, 4 x 5 Find the differences algebraically and find the nth term
4	Looking at your rules so far can you predict the difference for any length of box? Test out your prediction Can you prove it algebraically
5	Change the size of the grid e.g. a grid 9x9, 8x8 How do the differences change? Can you find/prove the results algebraically?
6	What about a rectangular grid a x b?