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?
Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
Are these statements always true, sometimes true or never true?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Can you use this information to work out Charlie's house number?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
In 1871 a mathematician called Augustus De Morgan died. De Morgan
made a puzzling statement about his age. Can you discover which
year De Morgan was born in?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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?
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?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Can you make square numbers by adding two prime numbers together?
Use the interactivities to complete these Venn diagrams.
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?