Summary: Continuous and Discrete

Continuous and Discrete                                                                  October 27, 2011

OBJECTIVE: SWBAT DIFFERENCIATE BETWEEN CONTINUOUS/ DISCRETE

Today we learned about continuous and discrete. Discrete means that the item has to be a whole number. Discrete usually occurs when we are counting using whole numbers. Continuous can be fractional numbers and whole numbers. Basically, something that is measurable: height, weight, and time. If the numbers can be fractions and decimals then it is probably continuous. Some examples are shown below.

EXAMPLE:

Classify each set as discrete or continuous-

1. The number of suitcases lost by an airline.

2. The height of corn plants.

3. The number of ears of corn produced.

4. The number of green M&M’s in a bag.

5. The time it takes for a car battery to die.

6. The Production of tomatoes by weight.

1) Discrete. The number of suitcases lost must be a whole number.

2) Continuous. The height of corn plants can take on infinitely many values (any decimal is possible).

3) Discrete. The number of ears of corn must be a whole number. 

4) Discrete. The number of green M&M's must be a whole number. 

5) Continuous. The amount of time can take on infinitely many values (any decimal is possible).

6) Continuous. The weight of the tomatoes can take on infinitely many values (any decimal is possible). 

Summary: Shading Inequalities

Shading Inequalities                                                                 October 25, 2011

OBJECTIVE: SWBAT RECALL INEQUALITIES AND HOW TO SOLVE THEM

Today we learned more about inequalities and about how to shade the graph. For shading a graph, you either shade with or without the point you are using to substitute it in an equation. For example, let’s use the inequality y<4x-3. For x and y we will substitute in the points (0, 0). Now the equation reads 0<4(0)-3. Solve that and it reads 0<-3. If this inequality is true then you will shade the part that INCLUDES the points (0, 0). If the inequality is false then you would shade AWAY from the point.

EXAMPLE:

y<4x-3

Summary: Graphing Inequalities

Graphing Inequalities                                                                 October 25, 2011

OBJECTIVE: SWBAT RECALL INEQUALITIES AND HOW TO SOLVE THEM

Today we learned more about inequalities and about how to graph them. We learned that for inequalities with < and > that they had a dashed line. Then for ≤ and ≥ they have solid, as well as =. Graphing inequalities is actually easy. You graph it like a regular slope intercept equation. You just have to make the “y” an isolated variable as it is in slope intercept form. An example is shown below.

EXAMPLE:

y+3<4x à y<4x-3

Summary: Inequalities

Inequalities                                                                 October 24, 2011

OBJECTIVE: SWBAT RECALL INEQUALITIES AND HOW TO SOLVE THEM

Today we relearned inequalities. I actually remembered this from when we were in sixth grade and that all we had to do was just remember what the sign were. Those signs were: less than of equal to (≤), less than (<), greater than or equal to (≥), and greater than (>). We also learned that when you graph inequalities, you use a dashed line, not a regular line. Also we learned that when you’re writing inequalities on the number line there are open and closed circles. Open circles mean less than or greater than and closed circles mean it has the equal to part with it. An example is shown below.

EXAMPLE:

  3 ≤ x-2 ----------------------------> Your Problem

+2   +2-----------------------------> Add 2 to 3 and -2

5 ≤ x -----------------------> Answer used to graph on number line

Summary: Linear Equations

Linear Equations                                                                 October 13, 2011

OBJECTIVE: SWBAT WRITE, GRAPH, AND CREATE LINEAR EQUATIONS IN THE THREE FORMS

Basically all we did was review slope intercept (SI), point slope (PS), and standard form (STD). Along with that, we practiced changing from one form to another. For example, we did a problem for PS then changed it to SI then changed it to STD. Now, changing from PS to SI is quite easy actually but, changing from SI to STD. Now, that is a whole another story because I get it but, then I don’t get it. It looks hardier than it actually is but, I think I can manage to it.

EXAMPLE:

(3, 4) b=-5

1. Point Slope (PS)-

*To find your slope do y1-y2 over x1-x2, when you have two points*

-5-4/0-3 equals -9/-3 which equals positive 3

Now just substitute the numbers into the formula-

y-4=3(x-3)

2. Slope Intercept (SI)-

*Substitute in the numbers for slope and y-intercept*

y=3x-5

3. Standard Form (STD)-

*If your slope is positive the y will be negative*

**If your y is negative then C might be positive**

3x 1y=

Now, just figure out the sign and if the C is negative or positive

3x-1y=5 or 3x-y=5

   -y is negative because it will then make -3x positive and make 5 negative

Summary: Perpendicular and Parallel Lines

Perpendicular and Parallel Line                          October 13, 2011

OBJECTIVE: SWBAT DESCRIBE THE SIMILARITIES OF ┴ (PERPENDICULAR LINES) AND ║ (PARALLEL LINES)

Today in class we learned about perpendicular and parallel lines. This was actually kind of easy. All you have to know for parallel lines is that lines are parallel if they have the same slope. For perpendicular lines, if they have the same y-intercept they will eventually intersect. Also, for perpendicular lines, you use multiplicative inverse for the slope. For example, 1/2, the inverse is -2/1 because you want the opposite of ½ so it has to be negative. Some examples are shown below.

EXAMPLES:

Parallel Lines-

~Remember to make lines parallel, they have to have the same slope~

y=2/3x+4

y=2/3x+6

*To make this parallel with the equation above, change the y intercept*

Perpendicular Lines-

~Remember to make lines perpendicular, you have to use multiplicative inverse~

y=3x+2

y=-1/3x+2

*If they have the same y-intercept, they will eventually intersect*

Summary: Standard Form

Standard Form                                                                  October 5, 2011

OBJECTIVE: SWBAT USE WHITE BOARDS TO GROUP LINES USING POINT SLOPE FORM

Today in class, we went over standard form again and learned how to actually do it this time. Another name for standard form is STD, not the disease though. The formula for standard form is Ax+By=C. Learning this was very confusing. It still is but, I can understand it better than before. An example is shown below about how to do this.

EXAMPLE:

Ax+By=C

***m= -Ax/B; b= C/B***

3x+2y=10

2y=-3x+10

    -Subtract 3x from both side

y=-3x/2+ 10/2

    -Divide everything by two

y=-3x/2+5

    -Reduce and you are done!

    -You know you are done if the answer looks like y=mx+b

Summary: Point Slope Countined

Point Slope Continued                                                                  October 3, 2011

OBJECTIVE: SWBAT GRAPH A LINE USING POINT SLOPE FORM

Today in class, we reviewed what point slope is. We practiced how to write point slope into slope intercept. It was actually pretty easy to understand. But it just took a long time to get it. We then took a quiz on this, which I failed. I know that I could have passed if Mr. Sudovsky gave us more time. But, I am just glad that he didn’t take it up as a grade.

EXAMPLE:

Slope- 1/10; Point- (10, 6)

y-6=1/10(x-10)----> Point Slope 

y=1/10(x-10)+6

y=1/10x-1{10/10}+6

y=1/10x+5----> Slope Intercept

Summary: Point Slope

Point Slope                                                                  September 30, 2011

OBJECTIVE: SWBAT REVIEW CFA TO GAIN BETTER UNDERSTANDING OF ALGEBRA USAGE IN REAL WORLD APPLICATIONS

Today in class we learned about point slope. Point slope is where they give you the point and the slope. The formula for point slope is y-y1=m(x-x1). It is hard to explain so; I will show you in the example instead. We also learned about quadratics, standard and some linear equations with how their graphs look like. The formula for standard is Ax+By=C. Some of the linear equations were y=x²+4, y=x³, y=x+2, and y=1x1.

EXAMPLE: