Visualising and representing

problem
Perimeter expressions

Age

11 to 14

Challenge level

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
problem
Auditorium steps

Age

7 to 14

Challenge level

What is the shape of wrapping paper that you would need to completely wrap this model?
problem
Your number was...

Age

11 to 14

Challenge level

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
problem
Newspaper sheets

Age

14 to 16

Challenge level

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?
problem
Packing boxes

Age

14 to 16

Challenge level

Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.
problem
Reading from behind

Age

11 to 14

Challenge level

Can you find the time between 3 o'clock and 10 o'clock when my digital clock looks the same from both the front and back?
problem
Printing error

Age

11 to 14

Challenge level

Every third page number in this book has been omitted. Can you work out what number will be on the last page?
problem
Folding in half

Age

14 to 16

Challenge level

How does the perimeter change when we fold this isosceles triangle in half?
problem
Kangaroo hops

Age

11 to 14

Challenge level

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?
problem
Adjacent factors

Age

11 to 14

Challenge level

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?