Exploring and noticing

problem

The Great Tiling Count

Age

7 to 11

Challenge level

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

Great Squares

Age

7 to 11

Challenge level

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
problem

It's All About 64

Age

7 to 11

Challenge level

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
problem

Calendar Patterns

Age

7 to 11

Challenge level

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
problem

The Clockmaker's Birthday Cake

Age

7 to 11

Challenge level

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
problem

Number Tracks

Age

7 to 11

Challenge level

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

Polo Square

Age

7 to 11

Challenge level

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
problem

Tables Without Tens

Age

7 to 11

Challenge level

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

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

Cubes Here and There

Age

7 to 11

Challenge level

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?