Odd and even numbers

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

How will you complete these interactive Venn diagrams?

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

Are these statements always true, sometimes true or never true?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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?