Year 6 Exploring and noticing

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?

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

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

How do you know if your set of dominoes is complete?

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.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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?

A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.

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