First session -- July 2

Today we developed class expectations:

1. Respect

• use respectful language when speaking to or about teachers, classmates, and yourself 
• listen (don't talk!) while another person is addressing the group
• save non-math-related talk for breaks
• leave quietly through the back door if you must leave before a break
• food and beverages are OK as long as they don't smell or make noise or leave a mess
•  turn off electronic devices in the school

2. Learning

• attend each class -- keep your goal in mind when you are tempted to skip class or slack off
• participate in class
• help each other to learn (except on quizzes and tests)
• do homework (even though it won't be marked -- it helps you prepare for quizzes and tests)

We decided that we would have either three 10-minute breaks or two 15-minute breaks per class, depending on how the lesson content divides most easily.

The first assignment was to draw a timeline of your life as it relates to this course, to identify obstacles to your succeeding in the course, and to develop strategies for overcoming these potential saboteurs.

We reviewed

• operations with signed numbers
• order of operations
• operations with fractions
• simplifying expressions
• basic algebra

We saved the graphing review for next class.

Here are some board shots:

Visualizing multiplication and division of whole numbers:

Three number sets -- of special interest were the integers, which include all the positive and negative whole numbers.
We forgot to add the set of rational numbers (those that can be written as fractions with an integer on top and bottom -- except no 0 on the bottom!)

We'll talk about the irrational numbers in a future class.

We used poker chips to visualize adding integers.

• blue (+1) stands for money.
• red (-1) stands for debt
• (+1) + (-1) =0  (you are paying off a debt)

Subtraction with integers can be changed to addition of the opposite sign.

It's even easier to change all double signs to a single one and then think of each term as an item to be added.

 Whenever possible, find pairs of opposite signs but same absolute value to cancel out to 0.  Then add up what you have left.

The multiplication and division rules are the same as we used to replace 2 signs in front of a number with one sign.
NOTE: when you divide, the result is called the QUOTIENT (not the product)




Thinking behind the rules in red:

• Repeatedly receiving money is good (makes you richer)
• Repeatedly having debt taken away is good (makes you richer)
• Repeatedly receiving debt is bad (makes you poorer)
• Repeatedly having money taken away is bad (makes you poorer) 

If you have more than one type of operation in an expression, follow the order of BEDMAS

Watch out for invisible brackets with the division bar.

Be careful with the exponents!

Multiplication is the easiest operation with fractions:  Multiply the tops, multiply the bottoms.

Then reduce the product by dividing top and bottom by the greatest common factor.  You can pre-reduce ONLY with multiplying.

For division, flip the second fraction and multiply.




Adding and subtracting fractions requires common denominators.
(Multiplying and dividing does NOT!)

You can find the sum of 2 terms only if they have the same units or variables or denominators or....
otherwise, you have to leave the 2 terms side by side or somehow force them to have the same units (not always possible)

Distribution can be thought of as opening up packages and combining the contents that are alike.

Here are guidelines for solving simple equations in one variable.