Odd and even numbers

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?

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

In this game the winner is the first to make the total 37. Is this a fair game?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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