Numbers are important for both counting and measurement, and today we start discussing measurement in the familiar context of time and the phases of a human life. This is not a bad place for young people to start learning about a scale and different units to measure something.

We begin by explaining how the fundamental units of a day, month and year come about from the relative motions of the earth, moon and sun. Then we lay out a linear scale representing 100 years, the rough potential life span of a human (although some people do live beyond that). On this time scale we can point out various important times and stages of life.

This is a good way for students to engage with numbers and their relation to their own lives and others around them. It is also a place to mention some interesting facts related to life spans of very long-lived creatures (like the bowhead whate), and also to talk about average life expectancies, such as 18 years for a domestic cat.

1. Counting using the grid plane
2. Arithmetic with rectangles
3. Number systems throughout history
4. The Hindu-Arabic number system
5. Laws of arithmetic using geometry
6. Fun with polyominoes
7. Addition and the names of numbers
8. Addition in practice
9. Multiples, and more names of numbers
10. Word problems using addition
11. Elementary projective (line) geometry
12. Pappus and Pascal
13. Logical reasoning with tic-tac-toe
14. The multiplication table
15. More multiplication: The 10x10 table
16. Some tricks to help with multiplication
17. Area problems using multiplication
18. The time scale of a human life
19. An introduction to measuring

Feel like learning mathematics from the ground up? Here is your chance: K-6 mathematics explained intuitively but accurately in a novel way by a professional pure mathematician.

The series is meant for those who are teaching public or high school, parents who have children in those years, and anyone who would like to strengthen their understanding of the subject.