The commutative laws for addition and multiplication have a nice geometric aspect. This video introduces simple motions in the grid plane: translations and reflections, and then uses them to understand commutativity.

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.