Converting Units

Video Link

One Reason to Understand Math...

http://www.youtube.com/watch?v=8jkri0AeZWQ

Someone forgot his Pythagorean Triple

Watch this...

And become SMARTER THAN HALF THE AUDIENCE!

Video Link

Algebra Dougie

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

Video Link

Repeat It (Algebra)

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

Have a little fun!

Video Link

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.

Video Link

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.

Pythagorean Triplets

Here are some more examples of Pythagorean Theorem problems.

Video Link

Linear Patterns

Here's a video explaining how to find a pattern based on a sequence.

Video Link

Most of you are fairly accomplished at this method.  What you have been having trouble at is understanding how to write the rule.  Mr. Khan shows a way to understand the rule in this video.

Video Link

Here's a more complicated example that actually gets Mr. Khan going into Algebra 1!

Video Link

Here's one more example.

Video Link

Hope these help you prepare.

Spaghetti and Meatballs For All

Video Link

Pythagorean Theorem

Here is a video explaining the Pythagorean Theorem.

Video Link

Dixit

How to play Dixit:  Also watch Wil Wheaton, Beth Riesgraf, Leo Chu, and Casey McKinnon.  A bit of bad language but not much.

Video Link

How to Think Big

Thinking about Infinity.

Video Link

Similar Figures

Sal Khan explains similar triangles much in the way I do.

Video Link

Proportions

I know I direct taught alot about proportions, but here's Sal Khan discussing proportions, so if you feel like you didn't understand, that's okay.  Just watch this video a few times to try to get it.

Watch this video first about why ratios are proportional:

Video Link

Video 2

Hope this helps you.

Ratios

Sal Khan explains ratios much like I would:

Video Link

Comedian and Juggler Puts Hand Percussionists to Shame

Video Link

Radicals

Radicals are the inverse operation of exponents.  The most common one is the square root, which asks you to find what number multiplies by itself in order to get the number under the radical.  Sometimes there won't be a clear answer, and in that case you will have to factor the number down into numbers that are squares and numbers that aren't.  Then you can pull the ones that are out by taking their square root and leave the numbers that aren't inside.

Here's a video explanation.

Video Link

Part 2: Examples

Video Link

Part 3: Estimating the value of a square root.

Video Link

3D Nets

I intended to put this up earlier.  Here's a video explaining nets if you had trouble reading what I wrote.  It also explains faces, edges, and vertices.