Introducing algebra

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing 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?

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?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Can you replace the letters with numbers? Is there only one solution in each case?

Use the information about Sally and her brother to find out how many children there are in the Brown family.