Holes
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
Always, sometimes or never? Number
Are these statements always true, sometimes true or never true?
Always, sometimes or never? Shape
Are these statements always true, sometimes true or never true?
Name that triangle!
Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?
More Dicey operations
In these multiplication and division games, you'll need to think strategically to get closest to the target.
Dicey operations
In these addition and subtraction games, you'll need to think strategically to get closest to the target.
Doplication
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Diagonally square
Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?
Treasure hunt
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Round the four dice
Round the three dice
What happens when you round these three-digit numbers to the nearest 100?
Number lines in disguise
Round and round the circle
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Four go
Counting cogs
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Button-up some more
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Three neighbours
Take three consecutive numbers and add them together. What do you notice?
Finding 3D stacks
Can you find a way of counting the spheres in these arrangements?
Making spirals
Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.