Part II Day 2

State the daily objective: Area day 2 and introduce concept of scale (dilations).
Define: To find the area of a similar shape or scaled area you  want to use cross multiplication. An example is shown below:

 Here is a video to help you understand scale furthermore:

QUIZ
For the following figures find the area using the scale given
1) Scale factor= 1/2

area= 60 sq. in.

Area = x











2) Scale factor 1/6

Area = 120 sq. in.

 Area = x

3) Scale factor = 2

Area = 20 sq in.

Area = x

 

 

 

ANSWERS:

 

1) 1/2=60/x

60 x 1 = 60

60/2= 30

x=30 sq. inches

 

2) 1/6 = 120/x

120 x 1 = 120

120/6=20

x=20 sq. in.

 

3)2/1=20/x

20 x 2= 40

40/1= 40

x=40 sq. in.

Part ll Day 1

Daily objective- Area of squares, rectangles, triangles, trapezoids, parallelogram, circles, and polygons.
Definition- Students will be able to find the area of given shapes using my given equations and objectives.

VOCAB DEFINITIONS

Point- A point only respecify a location, it has no depth, nor length no width. We usually specify a point in geometry with a dot or a "point".

line- A long narrow mark or band that extends in both directions forever unless an end point is distinguished. "I drew a straight line."

Plane- A flat two dimensional surface

Line segment- A part of a line that is defined between two end points, and contains every point on the line between its end points.

Ray- A line which starts at a point with given coordinates, and  goes off in a particular direction to infinity, possibly though a second point.

Angle- The space (measured in degrees) between  two intersecting halves or surfaces at or close to the point where they meet.

Median- Middle value

Altitude- it it the height, or the distance from the base of a shape to the vertex

Perpendicular- A straight line at an angle of 90* to a given line, plane or surface

HOW TO FIND AREA OF DIFFERENT SHAPES

What are the formulas?

Squares- Area = width × height

Rectangles- Area= length x width

Triangles- Area = ½ × b × h

          b = base    h = vertical height

Trapezoid - Area= ((b1+b2)/2) h

Parallelograms-Area = b x a

 b is the length of any base

a is the corresponding altitude

Circles- Area=Πr²

Polygons- Area= 1/2 Perimeter * Apothem or 1/2(PA)

QUIZ

1.) What will the area of  a circle be given the radius is 5?

2.) What will the area be of a rectangle with a length of 4, and a width of 3?
3.) What is a median?

ANSWER KEY

1.) We know that the formula for finding the area of a circle is 3.14rsquared. If we plug in the numbers the the equation we come up with. 3.15 x 5squared. If the steps are followed correctly the answer will be 78.535...units squared.

2.) We know the formula for finding the area of a rectangle it length x width. Our length is 4 and our width is 3. All that's left is plugging the numbers to multiply them. 4x3=12. The area of the rectangle is 12units squared.
3.) A median is the middle value.

BELOW IS A GREAT AND SIMPLE VIDEO OF FINDING AREA, CHECK IT OUT!!

http://www.youtubehttp://www.youtube.com/watch?v=oApSNVkyTBE.

Day 4

 Daily objective- Students will be able to graph linear inequalities.


Definition- Taking a linear inequality and transferring the correct information and apply it to a properly formatted  graph to show given and sometimes un-given information.


What is a inequality?
        - A inequality is "When the two expressions are connected by 'greater than' or 'less than' sign, we get an inequality."

EXAMPLE- When operating in terms of real numbers, linear inequalities are the ones written in the forms

 or ,

How to graph the equation of a linear inequality

To understand how to graph the equations of linear inequalities such y ≥ x + 1, make sure that you have a good understanding of how to graph the equation of a line in slope intercept form.

A linear inequality is describes an area of the coordinate plane that has a boundary line. Every point in that region is a solution of the inequality.

VERY SIMPLE!!

STEP 1-Graph it as if its an equality
STEP 2- Look at the sign, less than you shade below the line, grater than you shade the area above the line the line.

EXAMPLE-

 In this case the line was shaded below the line because the equation has a less then inequality.

QUIZ!!!

1.)What is the equation 
of the line on the left?

2.)Now, what does the graph of y > x +3 look like?

3.)What would the graph of y ≤ -x + 1 look like?

ANSWER KEY

1.)Y=X+3

2.)

         

               

3.)

For another great way of looking at this, check out this video!

http://www.youtube.com/watch?v=kLfgjxmtfm8&sns=em

" Tips From The Pros" Part I

Day 5

Daily Objective: Students will be able to write a equation of a line given two data points.
Definition: Student will be able to find the slope and y-intercept to create an equation for two data points.
Step 1: use the equation below to find the slope ( m = slope in the equation y = mx + b)

  

Step 2: substitute x and y in the equation y = mx + b as well as the slope you solved for (m).

Step 3: Solve for b, the y-intercept and use that number and your slope to write out an equation. 

Example: y = 7x + 3

QUIZ

Write an equation using the following data points.

1) (3, 2) (7, -4)

2) (3,2) (7,4)

3) (4,2) (3,6)

ANSWERS

1) y = -3/2x + 13/2

-4 - 2 = -6 over 7 - 3 = 4

Reduce - 6/4 to - 3/2

y = - 3/2x + b

2= - 3/2(3) + b

b = 13/2

Final equation is y = -3/2x + 13/2

 

2) y = 1/2x + 1/2

4-2=2

7-4=3

slope (m)= 2/3

2=2/3(3) + b

b= 1/2

Final equation is y = 1/2x + 1/2

 

3) y = -4x + 18
6-2=4
3-4=-1
slope (m) = -4
2= -4 (4) + b
b= 18
Final equation is y = -4x + 18

Day 3 extra

Daily Objective- Students will be able to find the number of outcomes for compound events, identify independent and conditional events, and compute probability and odds.

Definitions-
Compound event- An event that consists of two or more events that are not mutually exclusive.
Independent event-An outcome that is not affected by previous outcomes.
Conditional event-An outcome that is affected by previous outcomes.
Probability- Is the measure of how likely an event is.
Odds- Is the ratio that compares the number of favorable outcomes of an event to the number of unfavorable out comes.

-HOW TO FIND THE NUMBER OF OUT COMES FOR COMPOUND EVENTS-

Consider two different events.  Rolling a six sided dice and spinning a 5 position game spinner.

First, determine the number of possible outcomes for each of the events.
     The dice has 6 possible outcomes.
     The spinner has 5 possible outcomes.
Next, multiply the outcomes together to get the total number of possible outcomes.
     6 * 5 = 30 possible outcomes.

-HOW TO IDENTIFY CONDITIONAL AND INDEPENDENT EVENTS-


The key to determining if an outcome or probability of an event has an affect on the outcome or probability of an event occuring.  For example if I have two dice and one outcome is to roll a 1 on each die we can see that if any one of the die is NOT a one, the probability that you will roll two ones is zero.  So, the event, rolling two ones, is dependent on one of the dice being a one.  Another example may help.  If you determine that 65% of bicycle owners have a mountain bike and that 20% of bicycle owners have a mountain bike with full suspension it is easy to see that the second event (mountain bikes with full suspension) is dependent on the event of having a mountain bike.

Independent events do NOT have any effect on the outcome or probability of each other.  A classic example of this is flipping a coin.  If I flip a coin, there is a 50% probability that it will come up heads.  Flipping the coin again, regardless of how many coin flips have proceeded it and what the outcome of those flips was does NOT change the probability of it coming up heads.  Each coin flip is therefore independent because the outcome and probability doesn't based on another event.

The question that must be answered is:  What other events will affect the outcome or probability of another event?  If the answer is NONE, then you have an Independent event - otherwise it is conditional.

-HOW TO CALCULATE PROBABILITY AND ODDS-

Simply defined, probability is the likelihood of a specific outcome for a given event. This can be calculated mathematically, generally as a percent, by giving the number of outcomes divided by the total number of possible outcomes.  We'll use rolling a dice as an example.

The probability of rolling a 6 on a six sided dice.  There is one 6 on the dice, so the number of specific outcomes is 1.  The total possible is 6.  The probability is 1/6 or 16.6666%.  If you change the specific outcome to rolling an even number, the number of specific outcomes is 3 and the total possible is 6.  Using our formula, 3/6 = 50% probability.

Odds are the first cousin of probability.  However, odds define the number of disireable outcomes vs the undesireable outcomes and is expressed as a ratio.

So, to determine odds, define the number of desired outcomes.  Then determine the number of undesirable outcomes.  Express this as ratio Desireable:Undesireable.

You go to a baseball game. The desirable outcome is getting a hit or a walk.  The undesirable is getting an out.  Now, lets say that this batters on base average (percentage of the time he gets a desirable outcome) is 40%.  This implies that 60% of the time he get an undesirable outcome.  Desirable (40)/Undesirable(60) results in a ratio 40:60, which reduces to 2:3.  The odds for this batter yielding a good result is 2:3.

QUIZ

1.  Calculate the number of outcomes for the following:  A dice with 6 sides and a spinner with 5 possible outcomes.

2.  Independent events do NOT have any affect on the outcome or probability of occurrence of each other.

               a) True

               b) False

               c) 50% chance of not never happening

3.  What is the probability of rolling either a 4 or a 6 on a six sided die.  Here is another great way to look at probabilities See video tutorial on probability.

Answer Key

1.  Multiply the number of possible outcomes of the each event by each other.  In this case there are 6 outcomes possible on the die and 5 for the spinner.

       6 x 5 = 30 possible outcomes.

2.  a) True.  Independent events are events that do NOT effect each other.

More about Independent events 

3.  Probability is calculated by dividing the number of desired outcomes by the total possible outcomes.  In this case, there are two desired outcomes: 4 or 6.  The total number possible is 6.

      2/6 = 1/3 = 0.33333 or 33.333% probability of rolling a 4 or a 6

More about probability

Day 3

•  Daily Objective: Students will define the y-intercept in math as well as translate it to real world meaning.
• Definition: Students will be able to define the y-intercept in math and understand how it is used in the real world.

  

  This picture captures a perfect example of the y-intercept used in math.
  The y-intercept is the point on a linear line where the line crosses the y-axis.
  Now when you define this using a real world equation such as: y= 40x + 10,
  the y equals the total cost if x is the variable(hours) and 10 is the initial fee.
  
  
  

  QUIZ

  Give the y-intercept shown in each of the following graphs.

  1)

  

  2)
  

  

  3)
  

  

  
  

  ANSWERS

  1) -6

  2)  5

  3) -1