Conjecturing and generalising

problem

Counting Stick Conjectures

Age

5 to 11

Challenge level

How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?
game

Celebrate 25 Years of NRICH

Age

5 to 14

To celebrate NRICH's 25th birthday, why not play this special version of our classic game, Got It? Can you devise a strategy so that you will always win?
game

Nim-7 for Two

Age

5 to 14

Challenge level

Nim-7 game for an adult and child. Who will be the one to take the last counter?
problem

Window Frames

Age

5 to 14

Challenge level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.
problem

Spirals, Spirals

Age

7 to 11

Challenge level

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

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

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

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

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.