#15 Thursday, July 22

Solving radical equations  (start at slide 4)
 video with extraneous root


Solving rational equations

#14 Wednesday, July 21

The discriminant


Quadratic inequalities
another video 

#13 Tuesday, July 20

Quadratic formula -- I couldn't believe how many musical versions there are out there!
-- pop goes the weasle tune
--lego music video
-- a group song and dance
--a rap
--another music video
...and many more....

How to use it:
-- to music (includes information about the discriminant)
-- tutorial

-- projectile problems


Maximum/minimum problems

#12 Monday, July 19

 If you try searching for videos on completing the square, you will find that what we call the "standard form" is often called the "vertex form" and what we call "general form" is called "standard form".   Sigh.
Converting a quadratic function to vertex form by completing the square video

Tutorial -- completing the square starts at slide #8



By the way, I'm sad but somewhat relieved that I won't have to buy pizza for everyone after weekly test #2....

#11 Friday, July 16

Simplifying radicals -- click here for another method

Finding zeros as exact values

 Finding the equation of a quadratic function from the graph or clues -- see slides 15 and 16

#10 Thursday, July 15

Two-fifths of the way through the course!

Composition of functions video     printed lesson

Inverse of a linear function
Inverse of a quadratic function

Class #9 Wednesday, July 14

Finding the zeros of a function or the roots of an equation by factoring

Graphing quadratic functions

Class #8 Tuesday, July 13

Factoring trinomials with leading coefficient greater than one
-- box method 

 --BUM method, criss cross method and decomposition (Grouping method)  
 This video is similar to the BUM method 

Relations and Functions -- domain and range
Function notation
Adding and subtracting functions
Multiplying and dividing functions

Class #7 Monday, July 12

One test down!

Factoring

--removing common factors

--difference of squares

-- trinomials with a lead coefficient of 1

A Pledge

After all the quizzes and tests have been written, if no one has committed a certain math crime, I will buy a slice of pizza for every remaining student in the class on the last day of class.

Remember that the square of a binomial (2-term expression) is a trinomial -- don't forget the middle term!!!

6. Friday, July 9

 Board shots:

Video showing multiplying with algebra tiles

Remember Unit 1 test on Monday!

5 Thursday, July 8

We're a fifth of the way through the course!

Click here for instructions for solving a system of equations with the graphing calculator

Video on solving coin problems (second way is closer to the rate problem method we did in class)

Word problem handout key

4. Wednesday, July 7

Resources for the method of elimination to solve a system of equations:
Video -- one-step elimination
Video -- multiplication before elimination
Print lesson

System of 3 equations in 3 variables:
Video(male voice)
Video (female voice)

Bring your graphing calculator tomorrow!

3. Tuesday, July 6

 Some resources if you want to review today's material -- also, try Googling for more videos.
Number of solutions to a linear system
Solving inequalities   Lots more worked examples, some fancy ones
Graphing inequalities on the number line
Graphing linear inequalities
Graphing a system of inequalities

Board shots:

Review of substitution.
When you solve by substitution, there are a couple of steps that need extra notation -- either use arrows to guide the reader visually through the flow, or  label the 2 equations and keep the labels with them through their transformations and use words like "substitute x from A into B"
(note not all the steps are listed on this example -- see the handout)

 
Here is a more complicated example -- it's easier to simplify each equation first to x-term, y-term, and constant term.

Open circles mean the end point is not included.  A coloured circle means that point is included.
To decide which side to colour, you can use a test point -- if it satisfies the inequality statement, that's the correct side.   Also, if the variable is on the left, the inequality sign will mirror the arrowhead of the coloured region.

When solving inequalities, just leave the inequality sign alone unless you divide or multiply each side by the same negative number -- then the sign flips horizontally.  You can avoid this scenario by planning to throw the x-terms to the side that will result in a positive coefficient of x.  Then the last step will be to turn the whole inequality statement around (including the sign) to get the x on the left.

                     

For an inequality with 2 variables, graph the boundary line solid if there is an "...or equal to" sign.  If it's just > ("greater than") or < ("less than"), make the boundary a broken line.  Use a test point to determine which side to colour.
 Otherwise, if the inequality statement starts with "y is greater than....", colour above the line.  "Y is less than..." means colour below the line.







With a system of inequalities, graph each on the same grid and heavily colour the overlapping region.

Here's the Number of Solutions handout filled in.  To find how many solutions a system has, you just have to compare the slopes (different = 1 solution), and if they are the same, look also at the y-intercepts (same slope, same intercept = same line, so infinite number of solutions)  (same slope, different y-intercept means parallel lines, so 0 solutions.)

If you try to solve a system using algebra and the letters disappear, examine the resulting statement.  If it is true (eg 0=0), there is an infinite number of solutions.  If false (eg 0=6), there is no solution.

2. Monday, July 5

Another great on-line resource is bcmath.ca.
It has some powerpoint animations that you can control by pressing your arrow keys.

• Solving a system of linear equations by graphing (there's a little error in this one -- "point-slope form" should be "slope-intercept form" )

• Solving systems by substitution  

Board shots from today:

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.