1. Bernie Frankpitt

2. What is algebra?

3. “Algebra is the Language of Mathematics”

4. What is Algebra? “Algebra is the ‘Language of Mathematics’” – Yuck! – Languages of Mathematics are: Greek, Sanskrit, Arabic (Ancient) Latin (To 19 th Century) French, German, Russian (Present) English (Most Papers are published in English) Maori (Language for the Future?)

5. What is Algebra? “Algebra is the part of mathematics that deals with the abstraction of structure” You need to know something about the structure before you think of abstraction Pre-algebra is about identifying structure in concrete contexts Warning! I’m kind of opinionated about this

6. For Example Numeracy (arithmetic) is based on – Commutative Property – Associative Property – Distributive Property Structural Properties – Negatives of Fields – Reciprocals – Identities (0 and 1)

7. The key to understanding algebra is…

8. Strong concrete examples of the algebraic structure that you are trying to abstract

9. So ….

10. When using prime factorizations to calculate factorizations, lowest common denominators and largest common divisors.... One Answer

11. Teaching Sequence 1.Factor Trees and Prime Factorizations 2.Divisors 3.Simplifying Fractions 4.Multiples 5.Adding and Subtracting Fractions These are all ‘Hard Problems’

12. Prime Factorisations Calculate prime factorisations for all the numbers from one to 200 Use this as a table for conversions between positive integers and prime factorizations Sort Prime Factorizations in “Alphabetical order” for a reverse lookup table

13. Divisors

14. Simplifying Fractions

15. Multiples

16. Adding and Subtracting Fractions

17. Where’s the algebraic structure here? We’re digging into: Multiplicative structure of rings Polynomial rings Primes Rational Functions The prime factorization tables are more of a teaching aid than a useful mathematical idea.