Thursday+010410


 * L/I- To solve problems using patterns**

S/C; -I can identify patterns in problems -I can see the difference between arithmetic and geometric patterns -I can explain patterns using words and using examples (calculations/ method) -I can explain patterns using algebra to generalise -I can use inverse operations to use my understanding of the pattern to answer questions about it

=Multiplication Square=

Take a look at the multiplication square below: For example, if you take: 32 40 36 45 the numbers along one diagonal add up to  77   (   32  +4  5   ) and the numbers along the other diagonal add up to  76   (   36  +4  0   ).
 * Pick any 2 by 2 square and add the numbers on each diagonal.**

Try a few more examples. What do you notice? Can you show (prove) that this will always be true?

For example, if you take: 72 84 96 78 91 104 84 98 112 the numbers along one diagonal add up to  275   (   72  + 9  1  + 1  12   ) and the numbers along the other diagonal add up to  271   (   84  + 9  1  + 9  6   ).
 * Now pick any 3 by 3 square and add the numbers on each diagonal.**

Try a few more examples. What do you notice this time? Can you show (prove) that this will always be true?

Try a few more examples. What do you notice now? Can you show (prove) that this will always be true?
 * Now pick any 4 by 4 square and add the numbers on each diagonal.**


 * Can you predict what will happen if you pick a 5 by 5 square, a 6 by 6 square ... an n by n square, and add the numbers on each diagonal?**


 * Can you prove your prediction?**