The purpose of this activity is to engage students in solving a problem involving investigating with whole numbers using graphical means and/or generalising.

The background knowledge and skills that need to be established before and/or during this activity are outlined in the diagram below:

Click to show example questions for each heading

In approaching this activity, the students will need to make assumptions. Making different assumptions will mean that their final solutions are not likely to be exactly the same. The students might need to be reassured that this does not mean any solution is wrong, rather that it fits a different interpretation of the question. When discussing the assumptions the students will need to make, there is an opportunity to discuss the term average and to introduce the idea of central tendency and also discuss the likelihood of the mean, median and mode being very similar for a large sample size. This activity may be carried out with step by step guidance, or by allowing the student to follow their own method of solution. The approach should be chosen in sympathy with students' skills and depth of understanding.

The average person (with their partner) has two children before the age of 30 (that grow up to have their own….) and then lives to 75 years of age.

With approximately how many people living on the planet do you share a common ancestor/relative within seven generations?

### The arithmetic approach (show more)

- The student is able to make assumptions and to use a diagram to represent the pattern, in order to solve the problem.

### The conceptual approach (show more)

- The student is able to make assumptions, to use diagrams and/or to generalise in order to solve the problem.