Conjecturing and generalising

problem

Spirals, Spirals

Age

7 to 11

Challenge level

1 out of 3

Here are two kinds of spirals for you to explore. What do you notice?
problem

The Great Tiling Count

Age

7 to 11

Challenge level

1 out of 3

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
problem

Broken Toaster

Age

7 to 11

Challenge level

1 out of 3

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
problem

Number Tracks

Age

7 to 11

Challenge level

1 out of 3

Ben's class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
problem

Tables Without Tens

Age

7 to 11

Challenge level

1 out of 3

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
problem

Tiling

Age

7 to 11

Challenge level

1 out of 3

An investigation that gives you the opportunity to make and justify predictions.
problem

Snake Coils

Age

7 to 11

Challenge level

1 out of 3

This challenge asks you to imagine a snake coiling on itself.
problem

Sums and Differences 1

Age

7 to 11

Challenge level

1 out of 3

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
problem

Sums and Differences 2

Age

7 to 11

Challenge level

1 out of 3

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
problem

Surprising Split

Age

7 to 11

Challenge level

1 out of 3

Does this 'trick' for calculating multiples of 11 always work? Why or why not?