Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
What's the greatest number of sides a polygon on a dotty grid could have?
Watch the video to see how Charlie works out the sum. Can you adapt his method?
Which of these pocket money systems would you rather have?
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Can you find a way to identify times tables after they have been shifted up or down?
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?