Math Anxiety

http://math.about.com/od/reference/a/anxiety.htm

Many of the students I've encountered with math anxiety have demonstrated an over reliance on procedures in math as opposed to actually understanding the math. When one tries to memorize procedures, rules and routines without much understanding, the math is quickly forgotten and panic soons sets in. Think about your experiences with one concept - the division of fractions. You probably learned about reciprocals and inverses. In other words, 'It's not yours to reason why, just invert and multiply'. Well, you memorized the rule and it works. Why does it work? Do you really understand why it works? Did anyone every use pizzas or math manipulatives to show you why it works? If not, you simply memorized the procedure and that was that. Think of math as memorizing all the procedures - what if you forget a few? Therefore, with this type of strategy, a good memory will help, but, what if you dont' have a good memory. Understanding the math is critical. Once students realize they can do the math, the whole notion of math anxiety can be overcome."

When Students Fail...

I just read this article about when students fail math.  It was very insightful.

http://www.slate.com/articles/health_and_science/science/2013/04/math_teacher_explains_math_anxiety_and_defensiveness_it_hurts_to_feel_stupid.html

What I'd Tell My Teenage Self

I saw this on TED and wanted to share it with you.

http://blog.ted.com/2013/11/13/what-id-tell-my-teenage-self-life-and-career-advice-from-the-ted-staff/

As for me? I'm not sure what I would say.  Probably, "Don't put too much stock in what others think of you.  In a few years, you won't be around them anyway."

Someone forgot his Pythagorean Triple

Watch this...

And become SMARTER THAN HALF THE AUDIENCE!

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Algebra Dougie

One more, this time to Teach Me How to Dougie.

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Repeat It (Algebra)

MJ's classic Beat It with different lyrics that apply to what we're learning.

Have a little fun!

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Something Funny...

And now for something completely different!

Brought to you from the deep dark recesses of youtube:  Hint: Stick with it and you'll hear Thrift Shop.

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Graphing Linear Equations

Most of you know what a linear equation is.  You've not heard it called this, but you know what it is.  All the sequences we've had so far form linear equations.  So what are some things you can take away from what we've done with sequences?

1.  All linear equations have a constant rate of change.  As in, when x goes up by 1, y goes up by the same number each time, whether it's up by 2, 3, 5, etc.

We call this rate of change m.  In equation form, it's the number that is multiplied by x (remember inverses mean that it could be the number you're dividing by, too!).

These equations also have a constant number where x crosses the y-axis, called the y-intercept.  You find this by setting x to zero.  Then when you multiply by the change, the change falls out, leaving the intercept.  This intercept is called b.

A linear equation has a few different forms, but the most workable form is called the slope-intercept form.  This means we are solving for y by doing stuff to x.  So y = m * x + b

We can then graph the line on a coordinate plane based on using a process table for y = m * x + b.

You can see that demonstrated here:

Properties of Equality

The properties of equality are basic algebraic facts that help us solve equations.  We are already using these, we just haven't put names to them yet.  So in this video this teacher puts the name with the concept.  You will cover this again in 9th grade and refresh it in 10th and 11th grade.  So you might as well learn it now so that it's faster in 9th grade and an old concept in 11th grade.

To see this concept in more detail, watch this video.

The major takeaway are the properties of equality for the operations.  Used in conjunction with the additive and multiplicative identities and inverses, we can solve for variables.

Here is the list of properties:

Additive identity: a + 0 = a (or 4 + 0 = 4, etc)

Multiplicative identity:  a * 1 = a  (or 4 * 1 = 4, etc)

Additive inverse: a + -a = 0 (or 4 + -4 = 0, etc)

Multiplicative inverse a * 1/a = 1 (or 4 * 1/4 = 1, etc)

Addition property of equality: if a = b, then a + c = b + c  (if 4 = 4, then 4 + 2 = 4 + 2)

Subtraction property of equality: if a = b, then a - c = b - c (if 4 = 4, then 4 - 2 =  4 - 2)

Multiplication property of equality: if a = b, then a * c = b * c (if 4 = 4, then 4 * 2 = 4 * 2)

Division property of equality: if a = b, then a / c = b / c (if 4 = 4, then 4 / 2 = 4 / 2)

Using these properties, we can solve any equation with 1 variable.  We can simplify any equation with 2 variables.  Understanding these properties will help you write equations for word problems, or pick the correct equation out of a list.

Properties of Arithmetic

I'm sure some of you have wondered "how does Mr. V. know all these tricks?"  One reason is because I have learned this set of arithmetic properties here:

http://www.coolmath.com/prealgebra/06-properties/

Many of you are already using these without knowing it.  The multiplicative inverse property is used in solving proportions through butterfly method.

The additive inverse property is used to solve for x in linear relationships when y is constant.

I just like the way the concepts are presented at coolmath. I hope you do too.

Oh, and if you don't learn them now, you will continue to struggle and will probably have trouble in the rest of your math career through high school and possibly beyond.

Scientific Notation Flow Chart

This flow chart should help you figure out how to write scientific notation and convert it back to standard notation.