Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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?
Can you hang weights in the right place to make the the number balance balanced?
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you find all the different triangles on these peg boards, and find their angles?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
