Square numbers

problem
Picturing square numbers

Age

11 to 14

Challenge level

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
problem
Smith and Jones

Age

14 to 16

Challenge level

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!
problem
A square deal

Age

7 to 11

Challenge level

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
problem
Fitted

Age

7 to 11

Challenge level

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
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
Cycling squares

Age

7 to 11

Challenge level

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?
problem
Two primes make one square

Age

7 to 11

Challenge level

Can you make square numbers by adding two prime numbers together?
problem
Seven square numbers

Age

7 to 11

Challenge level

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.
problem
One wasn't square

Age

7 to 11

Challenge level

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
problem
Fractions in a box

Age

7 to 11

Challenge level

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.