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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
What happens when you add a three digit number to its reverse?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can all unit fractions be written as the sum of two unit fractions?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
There are lots of ideas to explore in these sequences of ordered fractions.
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Can you work out what step size to take to ensure you visit all the dots on the circle?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?