March 30th - Homework

March 30, 2011

Coefficient

Variable:

• Unknown
• Symbols/Letters
• Changed
• Live in a variable world....things constantly change

The word equation comes from the word "equality"

• 4x + 2 = 6x + 4
• A common misconception by students "part of an equation".  Each equation has at least two sides.  If you add something to one side of the equal sign, you have to do the same to the other sign, to keep the sides equal.

Hands on Equations System

For this activity you need 8 blue pawns, 8 white pawns 4 green blocks and 4 red blocks.  Two of each of those blocks need to be low numbers and the other two need to be high.....for each color.  The white pawns are negative variables, and the red cubes are negative numbers....although in my pictures the red cubes are being used as positive numbers.

This represent the equation 2x = 10.  The blue pawn is the variable.  2 x 5 = 10.  x = 5

This picture represent x + 2 = 9.  The blue pawn is the variable.  What plus 2 = 9? x = 7.

This picture represents 2x = x + 3.  x = 3.

Picture below shows the solution

Picture below shows the solution

 

This is the solution of the above two pictures

No picture to go with this explanation.  But it will show you the process.

This example should have been done with the pawns and blocks.  The x is the blue pawns.

2(x+3) = 10.......the 2 tells us how many times we are going to build (x+3).  So is becomes (x+3) (x+3) = 10.  2x + 6 = 10.  x = 2.  See picture above

Types of Equations

1. One step equations
1. Adding/subtracting equations
2. multiplying/dividing equations
3. Do the opposite of whatever is happening to the x (or variable)
2. Two step equations
1. Either add/subtract and then mutiply/divide
2. Do the opposite of whatever is happening to the x (or variable), but do it twice.
3. Multi step equations
1. Variables on both sides
2. Distributive property 
3. Combine like terms
4. Applying the distributive property...... a(b + c) = ab + ac 

 One Step Equations

• x + 4 = 6
• x hates people, wants to be alone. He hates things that are adding or subtracting to  him.  He also hates when things are multiplying and dividing to him.  We need to get x by himself.  In this problem 4 is being added to x.  apply -4 to each side.  X is now happy all by himself.  x = 2
• x - 12 = 4
• Get x by himself.  12 is being subtracted from the x.  What is the opposite of -12?  +12.  Add 12 to each side.  x = 16
•  - 4 = x +6
• What is the opposite of +6?  -6. Subtract 6 to each ide.  -10 = x.
• 3x = 15
• Get x by himself to make him angry.  3 is being multiplied to x.  Opposite of multiplication is division.  Divide each side by 3.  x = 5.
• 2/3x = 4 (two-thirds)x = 4.  
• How do you undo division? Multiply.  Multiply each side by 3.  3(2/3)x = 4(3).  The 3's cross out.  2x = 12.  Divide two to each side. x = 6.

Sorry the picture is sideways.  I'm too lazy to fix it.

Two Step Equations

• 3x + 4 = 22
• Step one:  deal with the addition or the subtraction first.
• What is the opposite of +4?  Subtract the 4 from each side.
• We now have 3x = 18
• Step 2: deal with the multiplication or division
• 3 is being multiplied to x.  What is the opposite of multiplication?
• Divide 3 ....both sides
• x = 6
• Two step equation examples:



I don't know why my pics keep coming in sideways.






Multi Step Equations:








Combining Like Terms






Putting it ALL together...."the Pinnacle"






What students need to know to be successful

• Integers
• Order of Operations
• Equality (What the = means)
• Distributive Property
• Like terms
• Companion/Inverse Operations

March 23, 2011

The Golden Rectangle

The Golden Spiral
Take the rectangle and "spiral" it counter-clockwise



Fibionacci Number Sequence

Link to Video: TeacherTube Videos - The Fibonacci Sequence-Rabbit Story





Pascal's Triangle

Sierpinski Triangle



Triangular Numbers

Square Numbers

Exponential Growth

Link to Video:  Exponential Growth

March 16th Reflection

During this class I found myself struggling with function machines.  I can easily figure out the input and output when given the function machine.  I am so glad that Steve showed us how to figure out the function machine for linear functions using the rate of change.  Once he showed us that, it got easier for me, and I was able to figure out the function machine every time.

I can tell this class is going to be a little challenging for me, but in my opinion that's a good thing.

March 16, 2011

Homework Check

How Much do I Weigh?

Algebra is about taking what we know and being able to recognize patterns and describe it.  Allows us to open up mathematics.

In this example, we know that a black square would come next, followed by a green triangle.

If we assigned letters it would look like this:

AA B AA B AA

Here is another example credit taken by Danae:

AA B C AA B C

What makes something a function?

• an input has one specific output

Here is an example of a "function machine."
4 goes in for x and a 6 comes out

Sequences: http://www.interactivestuff.org/sums4fun/sequences.html

This works with linear functions.

Terms are built/linked together by multiplication or division and separated by addition and subtraction

• 7x -2
• There are two terms in this problem.
• 1) 7x
• 2) -2
• 
• Another example:
• 
• 
  

Homework
No Reading!
Beckman Hard-Back pg 394 #1 a, &b, #2 a, b, & c
Reflection

Reflection

So, after taking the pre test for algebra I have decided that this class is going to be tough for me.  It has been a long time since I have done more than basic algebra.  I remember learning about slope, x and y intercepts, graphing the functions and inequalities and solving equations, but I don't remember how to do those things let alone teach them.  Hopefully it will all come back to me, but this class might be a challenge for me.

The assignment "How Much Do I Weigh" was challenging.  I was able to figure out the first page no problem, but really struggled with pages 2 and 3.  Is there a trick or a simpler way to do those problems that I am missing?  Is there some algebraic expression that I should have picked up on to the those pages less painful?  If yes, I'd like to know what I should have done to solve those problems.

What is Algebra

What is Algebra - a brainstormed list done by the group.

(Screenshots taken from A Maths Dictionary for Kids 2011)

Terms we need to know
Expression


Equation - number sentence with numbers and symbols.  You have to have an equal sign, and the problem has to be solvable.

Operation -  What you do to the numbers. Add, multiply, subtract, divide
Variable - sumbol that represents the unknown.  Usually a letter, in lower grades its a box, shape or line.  Example - 5x (x is the variable)
Constant - Doesn't change.   A 3 is always a 3, 5 is always a 5

Inequality - not equal in size, amount or value

Function - For each input, there is one output.

Order of Operations

Homework:

Read 254 - 256 in Van de Wall

Problems on the worksheets

1/2 gal cardboard - start collecting