Describing patterns and sequences

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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?

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?

Can you go from A to Z right through the alphabet in the hexagonal maze?

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?

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?

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?

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?

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

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.