Describing patterns and sequences

problem
Little squares

Age

5 to 7

Challenge level

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?
problem
Chain of changes

Age

5 to 7

Challenge level

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
problem
Amazing alphabet maze

Age

5 to 7

Challenge level

Can you go from A to Z right through the alphabet in the hexagonal maze?
problem
A city of towers

Age

5 to 7

Challenge level

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
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
Lost books

Age

7 to 11

Challenge level

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
problem
Lawn border

Age

5 to 11

Challenge level

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?
problem
Sticky triangles

Age

7 to 11

Challenge level

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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
Taking a die for a walk

Age

5 to 11

Challenge level

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.