Copy the picture to draw this spiral. Then create your own elephant. The numbers in the centres of the squares give the radii of the quarter circles that you need to draw.
What do you notice about this sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21 … ? […]
What patterns do you notice in this table?
Continue the patterns to fill the empty squares.
Write a list describing all the patterns that you see.
What do you notice about the numbers on squares of the same colour?
Would the patterns continue for ever to […]
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Copy this pattern. You could use toothpicks or paper sticks or draw the pattern on isometric paper (download here).
Make or draw the next 3 patterns in the sequence. How would you explain to someone else on the telephone how to do this when you could not point to the diagram?
Work out the number of edge squares and the number of lines (matchsticks) needed to make the pattern with: side length 6 side length 25 side length 100 side length n.
Click here […]
How many lines are there in your diagrams? How many lines are there in the original diagram? Can you find a way of working out […]
Now shift the 4 times table up 3 to give 7, 11, 15, 19, 23, … 83, 87, 91, …
Which tables were shifted to give the following sequences? By how much? Explain […]
7, 10, 13, 16, 19, …
15, 18, 21, 24, 27, …
1, -2, -5, -8, -11, …
What do you notice?
The first two sequences come from a multiplication table shifted up. Which […]
This will be difficult to count, especially if you have a large class. Try the problem in small groups and then compare different methods for finding the answers, […]
How do you find the coordinates of the centre of square 1 if you know that (0, 3), (3, 4), (4, 1) and (1, 0) are vertices?
What are the coordinates of the centre of the 20th square?
Imagine the sequence of […]