Year 6 Conjecturing and generalising

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

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?

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

This activity involves rounding four-digit numbers to the nearest thousand.

What happens when you round these three-digit numbers to the nearest 100?

Are these statements always true, sometimes true or never true?

Are these statements always true, sometimes true or never true?

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

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.

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Can you find a way of counting the spheres in these arrangements?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Take three consecutive numbers and add them together. What do you notice?

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?