# Blog Posts alpha As I develop this page, the initial topics covered will simply be those that come to mind. Refinement will occur later. (I cannot get my 4TB MyBook unit to connect to this laptop. All files created over the past ten years are unavailable.)

• Factoring using the diamond method
• A demonstration of top ten (top seven?) tools
• Using the top ten tool bar
• Distributive property of real numbers
• Using the number line
• Adding positive and negative numbers
• Adding real numbers on one line and coefficiants on a different line
• The space betwee integers represents fractions
• 4 fifths of the way from 0 to 1 is the same amount as 4 fifths of the way from 100 to 101, from 150 to 151, from 171 to 172.
• Different lines for fractions with different denominators
• The many uses for the number one
• All numbers can be written as divided by one
• All numbers can be written as multiplied by one
• The number one can be written as any number divided by itself
• PEMDAS and variations
• The order of operations is part natural, part agreed upon convention.
• The order of operations informs the reason for solving  equations a certain way, but there are cases where you have a bit more freedom.
• How to apply the order of operations to complicated expressions
• How does x2 differ from x or x3?
• Introduction to prime factorization
• How rational functions are similar to fractions
• How rational functions differ from fractions
• A general approach to solving problems you haven’t see before.

1. Whatever you do to one side, must do to the other.
2. Multiplying an equality by -1 reverses all three part.
3. arguments to functions treated as a unit
4. recognize additive and multiplicative inverse
5. There are different number lines.
6. Thumbs up, thumbs down.
7. x^2 is not 2x
8. Translating symbols to action, expanding an expression
9. Prime factorization
10. FOIL is evil, use the x-box instead.

## Other Useful Things to Know

see next page

11 In word problems, list the info and attach notes
12 critical thinking skills
13 Squares and circles and other geometrical figures: using what you know to solve problems
14 Boolean algebra
15 Geometric construction