9 x 14 9 x 12 Calculate the value of the following: 1 8 × 14 = Starter: Answer the questions below in your books Calculate the value of the following: 1 8 × 14 = (9 - 7) × 5 = (54 ÷ 3) × (42 – 16) = 25 × (24 ÷ 8) = 20 × 37 = 25 × 185 = 12 + 17+ 17 = 15 + 15 +14 = 200 – 38 = 51 – 32 = 333 + 111 + 555 + 2 How many days are there in a leap year? 1 to 6 : hard questions 7 to 12 easier questions. 9 x 14 9 x 12

9 x 14 9 x 12 Calculate the value of the following: 1 8 × 14 = 112 1 8 × 14 = 112 (9 - 7) × 5 = 10 (54 ÷ 3) × (42 – 16) = 468 25 × (24 ÷ 8) = 75 20 × 37 = 740 25 × 185 = 4625 12 + 17+ 17 = 46 15 + 15 +14 = 44 200 – 38 = 162 51 – 32 = 19 333 + 111 + 555 + 2 = 1001 How many days are there in a leap year? 366 Starter: Answer the questions below in your books 9 x 14 9 x 12

Work out Pascal’s Triangle Investigating Pascal’s Triangle Calculate Pascal’s Triangle Explore some of the patterns using Pascal’s Triangle Sort out the even and odd numbers to form Sierpinski’s Triangle Work out Pascal’s Triangle

If you look at the even numbers and their locations in Pascal’s triangle, you get a slightly more complex triangle called the Sierpinsky Triangle. You will need to colour in only the boxes with even numbers in them. Remember that even numbers end in 0, 2, 4, 6 and 8. To make Pascal’s Triangle, you just add up the two numbers above any box. One group of you is going to look at building up Pascal’s Triangle from scratch. Blaise Pascal started with the number 1 at the edges of his triangle. Choose a different number and see what happens. You might discover a miracle… Lots of mathematicians have found different patterns in the boxes that form Pascal’s Triangle. Explore some of the diagonal patterns by looking at the differences between each of the numbers. See if you can use this knowledge to predict the next few numbers in each sequence.

To the left is a section of Pascal’s Triangle. Begin by filling in the gaps in the version of Pascal’s Triangle that you have been given. You do this by adding together the two numbers above each oblong to find the contents of that oblong. Things to look for. To the left is a section of Pascal’s Triangle. Note that if you add the 1,3,6 and 10, it adds up to 20 (as shown by the 20 that goes in the other direction). Can you find anymore examples of where this happens within the triangle? Go down each diagonal, counting the distance between this and the next. Another thing you could do is look at the gaps within each sequence. Can you use this to predict what comes next?

See if you can find some more. Begin by filling in all the gaps in the triangle you have been given. Add the two numbers diagonally above each box together to get the contents of the box. If you add the numbers diagonally in the way shown, you will get a very special collection of numbers… Fibonacci Numbers. See if you can find some more. If you add the numbers along each row, you should start to see a pattern very quickly. Can you figure out which is the largest number, the 64th Fibonnacci number or the 64th number in the sequence where you just double the answer each time?

The normal Pascal’s Triangle is made up of odd and even numbers The normal Pascal’s Triangle is made up of odd and even numbers. I have coloured in some of Pascal’s Triangle below so you can see what it might look like. Make your colouring as neat as possible. We call the odd or even attribute of a number, its parity. If two numbers have the same parity, they are either both odd or both even; if two numbers had different parities, one would be odd and the other, even. Remember that the even numbers all end in 0, 2, 4, 6 and 8. If you record all these occasions, you can find if someone is cheat. If you started the triangle having 1, 1---1, 1-----1, what do you think would happen if it started 2, 2---2, 2-----2? What about if you started with 3 instead? Do you think different things would happen if you had odd or even numbers? If so, what?

What have you found?