Square numbers

problem
Square routes

Age

11 to 14

Challenge level

How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?
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
Numbers as shapes

Age

5 to 7

Challenge level

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
problem
Always, sometimes or never? Number

Age

7 to 11

Challenge level

Are these statements always true, sometimes true or never true?
problem
Swimming pool tiles

Age

7 to 11

Challenge level

This activity creates an opportunity to explore all kinds of number-related patterns.
problem
Graphing number patterns

Age

7 to 11

Challenge level

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?
problem
Odd squares

Age

7 to 11

Challenge level

Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?
problem
Up and down staircases

Age

7 to 11

Challenge level

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
problem
Cuisenaire squares

Age

7 to 11

Challenge level

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
problem
Making boxes

Age

7 to 11

Challenge level

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?