Objective: Welcome to Mrs. Harton’s Math Class; Date: 9/3/13• Bell Ringer: Sign up for email

• (2x+5) • Complete AP Grading Example• Homework Requests: Function evaluation and Writing equation of lines Check

solutions• In class:

• Discuss: Testing and Quizzes (Grading Example)• Rule of 4

• Go over this homework concepts; Review Evaluating and solving Factoring and Rational Expressions/Equations, Absolute Values Do odds

• Factoring power point available• Homework:

Finish Worksheets Factoring odds and Absolute Values [pg 1-2 #(1 +3’s ), pg 22 evens.Syllabus online Parent sign in sheet due Tues. 9/8If needed, bring in calculator loan contract 9/8 (online)Register on morganparkcps.org due Tues. 9/8 Email me your verification code.Bring in $15.00 fee by FRIDAY

• Announcements: Quiz: Friday Assigned Seating• Day for Mandatory Session

t (months 1 2 3 4 5 6 7

St (100’s) 1.54 1.88 2.32 3.12 3.78 4.90 6.12

The number of new software products sold is given by S(t), where S is measured inhundreds of units and t is measured in months from the initial release date of January 1. 2012. The software company recorded these sales data:

a) Estimate the number of units sold between April 1, 2012 through June 30, 2012.b) Assuming the data is linear, determine a the prediction equation estimating the number of units sold during months April and June.c) Using your prediction equation, predict the number of units sold in March and July?d) Graph the data and draw a quick sketch.e) Is your prediction equation accurate, why might it not be accurate?

(2x+5) = 4x2+16x+15

t (months 1 2 3 4 5 6 7St (100’s) 1.54 1.88 2.32 3.12 3.78 4.90 6.12

The number of new software products sold is given by S(t), where S is measured inhundreds of units and t is measured in months from the initial release date of January 1. 2012. The software company recorded these sales data:

a) Estimate the number of units sold between April 1, 2012 through June 30, 2012.Using the table data (4, 5, 6) , there were 1180 units sold

b) Assuming the data is linear, determine a the prediction equation estimating the number of product sold during months April and June. Using the point (4, 3.12) and (6, 4.9), the equation of the line is: y - 3.12 = .9(x-4) +2 ptsc) Using your prediction equation, predict the number of units sold in March and July? Evaluating the equation found in step (b), the number of units sold are for March x = 3 y = 2.22 units and for July x = 7, y = 4.92 unitsd) Graph the data and draw a quick sketch of your prediction equation. The red line is the graph of the original table data. The green line is the graph of the prediction equation found in (b). The graph was generated using Excel.e) Explain whether your prediction equation is accurate? What might make it be more accurate? Our initial assumption that the data was linear was incorrect. We can look at other regressions that might match the data more accurately. Challenge: Using your calculator, which regression yields the best fit?f) 1 pt b) 2 pts c)1 pts d) 2 pts 6) 5 pts

1 2 3 4 5 6 70

1

2

3

4

5

6

7

Series1Series2

Quizzes and Test• Show your work. This means I would like to

see the set up, the method used and the solution. Sometimes, no work is needed. However, explain your reasoning, why are you able to do what you are doing? If a formula is used, mention it.

Rule of 4The Rule of 4 refers to representing mathematical functions with graphs, tables, equations, and words. As learners discover how to represent functions in each of these ways, the mathematics becomes more meaningful. For example, consider the following cell phone plan offered by T-Mobile in 2011, represented using the Rule of 4.

1. Words Representation (from website) 3. Graph RepresentationEven More 1000 Talk + Unlimited Text$59.99 includes 1000 whenever minutesAdditional minutes $0.45 per minute

2. Table Representation

4. Equation Representation

Despite the fact that each of these representations of the cell phone cost function looks different, the same function is represented in each representation. All learners should practice to increase their ability to “see” the other forms mentally even when only one form is given.

Absolute Value

| x | = 5

Absolute Value Equations

x = 5 x = – 5Same Opposite

| x | = –2

No Solution

Two Solutions

Absolute Value PropertyIf |x| = a, where x is a variable or an expression and a 0, then x = a or x = a.

Solving Absolute Value Equations

1. Isolate the absolute value so that the equation is in the form |ax + b| = c. If c < 0, the equation has no solution.

2. Separate the absolute value into two equations, ax + b = c and ax + b = c.

3. Solve both equations.

3. Check your answers. Make sure they are not extraneous.

Absolute Value Equations

9523 x

423 x

55

Same Opposite

423 xDrop the absolute value bars!

Keep the absolute value bars!

423 x33 12 x22

21x

33

22 72 x

27x

27

21

,

1. Isolate2. Two Cases3. Solve

Check your work!

Absolute Value Equations

6413 k

1013 k

44

Same Opposite

1013 kDrop the absolute value bars!

Keep the absolute value bars!

1013 k11

113 k33

311k

11

3393 k

3k

311

3,

1. Isolate2. Two Cases3. Solve

Check your work!

Absolute Value Equations

7127 x

57 x

1212

1. Isolate2. Two Cases3. Solve

No Solution

Absolute Value Equations

052 y

Same Opposite

052 y55 52 y

22

25y

25

1. Isolate2. Two Cases3. Solve

Check your work!

Absolute Value Equations with 2 Absolute Values

2342 ww

Same Opposite

2342 ww 2342 ww

6

52

,

ww 33 24 w44

6 w

6w

2342 ww

245 w

ww 33

44 25 w55

52w

Check your work!

Absolute Value Equations with 2 Absolute Values

332 kk

Same Opposite

332 kk 332 kk

21

45

,

kk 322 k33

k21

21k

332 kk

324 k

kk 33

22 54 k44

45k

22

Check your work!

Absolute Value Equations with 2 Absolute Values

xx 2392

Same Opposite

xx 2392 xx 2392

3

xx 22

394 x99

124 x

3x

xx 2392

39

xx 22

44No Solution

Factoring

Factoring a polynomial means expressing it as a product of other polynomials.

Factoring polynomials with a common monomial factor (using

GCF).

**Always look for a GCF before using any other factoring method.

Factoring Method #1

Steps:

1. Find the greatest common factor (GCF).

2. Divide the polynomial by the GCF. The quotient is the other factor.

3. Express the polynomial as the product of the quotient and the GCF.

3 2 2: 6 12 3Example c d c d cd

3GCF cdStep 1:

Step 2: Divide by GCF

(6c3d 12c2d2 3cd) 3cd

2c2 4cd 1

3cd(2c2 4cd 1)

The answer should look like this:

Ex: 6c3d 12c2d 2 3cd

Factor these on your own looking for a GCF.

1. 6x3 3x2 12x

2. 5x2 10x 35

3. 16x3y4z 8x2y2z3 12xy3z 2

23 2 4x x x

25 2 7x x

2 2 2 24 4 2 3xy z x y xz yz

Factoring polynomials that are a difference of squares.

Factoring Method #2

A “Difference of Squares” is a binomial (*2 terms only*) and it factors like this:

a2 b2 (a b)(a b)

To factor, express each term as a square of a monomial then apply the rule... a2 b2 (a b)(a b)

Ex: x2 16 x2 42

(x 4)(x 4)

Here is another example:1

49x2 81

1

7x

2

92 1

7x 9

1

7x 9

Try these on your own:

1. x 2 121

2. 9y2 169x2

3. x4 16

Be careful!

11 11x x

3 13 3 13y x y x

22 2 4x x x

End of Day 1

Sum and Difference of Cubes:

a3 b3 a b a2 ab b2 a3 b3 a b a2 ab b2

3: 64Example x (x3 43 )

Rewrite as cubes

Write each monomial as a cube and apply either of the rules.

Apply the rule for sum of cubes:

a3 b3 a b a2 ab b2

(x 4)(x2 4x 16)

(x 4)(x2 x 4 42 )

Ex: 8y3 125

Rewrite as cubes

((2y)3 53)

2y 5 4y2 10y 25

Apply the rule for difference of cubes:

a3 b3 a b a2 ab b2 2y 5 2y 2 2y5 5 2

Factoring Method #3

Factoring a trinomial in the form:

where a = 1 ax 2 bx c

Next

Factoring a trinomial:

ax 2 bx c

2. Find the factors of the c term that add to the b term. For instance, let

c = d·e and d+e = bthen the factors are

(x+d)(x +e ).

.

1. Write two sets of parenthesis, (x )(x ). These will be the factors of the trinomial.

xx

2: 6 8Example x x

x x

Factors of +8: 1 & 8

2 & 4

-1 & -8

-2 & -4

Factors of +8 that add to -6

2 + 4 = 6

1 + 8 = 9

-2 - 4 = -6

-1 - 8 = -9

-2-4

x2 6x 8

Check your answer by using FOIL

(x 2)(x 4)

(x 2)(x 4) x2 4x 2x 8

F O I L

x2 6x 8

Lets do another example:

6x2 12x 18

6(x2 2x 3) Find a GCF

6(x 3)(x 1) Factor trinomial

Don’t Forget Method #1.

Always check for GCF before you do anything else.

When a>1, let’s do something different!

2: 6 13 5Example x x

Step 1:

Multiply a · c

Step 2: Find the factors of a·c (-30) that add to the b term

= - 30

Factors of 6 · (-5) : 1, -30 1+-30 = -29

-1, 30 -1+30 = 29

2, -15 2+-15 =-13

-2, 15 -2+15 =13

3, -10 3+ -10 =-7

-3, 10 -3+ 10 =7

5, -6 5+ -6 = -2

-5, 6 -5+6 =1

2: 6 13 5Example x x

Step 2: Find the factors of a·c that add to the b term

Let a·c = d and d = e·fthen e+f = b

d = -30e = -2f = 15

-2, 15 -2+15 =13

2: 6 13 5Example x x

Step 3: Rewrite the expression separating the b term using the factors e and f

-2x+15x -5 13x

-2x + 15x -5

Step 4: Group the firsttwo and last two terms.

2: 6 13 5Example x x

Step 4: Group the firstTwo and last two terms.

Step 5: Factor GCF from each groupCheck!!!! If you cannotfind two common factors,Then this method does not work.

Step 6: Factor out GCF

- 2x + 15x - 5

3x - 1) + 5(3x - 1)

3x - 1) (2x + 5)

Common factors

Step 3: Place the factors inside the parenthesis until O + I = bx.

6x2 30x x 5F O I L

O + I = 30 x - x = 29xThis doesn’t work!!

2: 6 13 5Example x x

6x 1 x 5 Try:

I am not afan of guessand check!

6x2 6x 5x 5F O I L

O + I = -6x + 5x = -xThis doesn’t work!!

2: 6 13 5Example x x

6x 5 x 1

Switch the order of the second termsand try again.

Try another combination:

(3x 1)(2x 5)

6x2 15x 2x 5F O I L

O+I = 15x - 2x = 13x IT WORKS!!

(3x 1)(2x 5)6x2 13x 5

Switch to 3x and 2x

Factoring Technique #3continued

Factoring a perfect square trinomial in the form:

a2 2ab b2 (a b)2

a2 2ab b2 (a b)2

Perfect Square Trinomials can be factored just like other trinomials (guess and check), but if you recognize the perfect squares pattern, follow the formula!

a2 2ab b2 (a b)2

a2 2ab b2 (a b)2

Ex: x2 8x 16

x2 8x 16 x 4 2

2

x 2 4 2

Does the middle term fit the pattern, 2ab?

Yes, the factors are (a + b)2 :

b

4

a

x 8x

Ex: 4x2 12x 9

4x 2 12x 9 2x 3 2

2

2x 23 2

Does the middle term fit the pattern, 2ab?

Yes, the factors are (a - b)2 :

b

3

a

2x 12x

Factoring Technique #4

Factoring By Groupingfor polynomials

with 4 or more terms

Factoring By Grouping1. Group the first set of terms and

last set of terms with parentheses.2. Factor out the GCF from each group

so that both sets of parentheses contain the same factors.

3. Factor out the GCF again (the GCF is the factor from step 2).

Step 1: Group

3 2

3 4 12b b b Example 1:

b3 3b2 4b 12 Step 2: Factor out GCF from each group

b2 b 3 4 b 3 Step 3: Factor out GCF again

b 3 b2 4

3 22 16 8 64x x x

2 x3 8x2 4x 32 2 x3 8x2 4x 32 2 x 2 x 8 4 x 8 2 x 8 x2 4 2 x 8 x 2 x 2

Example 2:

Try these on your own:

1. x 2 5x 6

2. 3x2 11x 20

3. x3 216

4. 8x3 8

5. 3x3 6x2 24x

Answers:

1. (x 6)(x 1)

2. (3x 4)(x 5)

3. (x 6)(x2 6x 36)

4. 8(x 1)(x2 x 1)

5. 3x(x 4)(x 2)

Objective: Welcome to Mrs. Harton’s Calculus Class• Homework:

• Complete handout Complex Fractions/Composition of Functions• Look at Section 1.1-1.3 Be prepared to ask questions about this material.• Interest Survey (online) due Fri. 9/2• Syllabus online Parent sign in sheet due Fri. 9/2• If needed, bring in calculator loan contract 8/27 (online)• Register on morganparkcps.org due Fri. 9/2

• Agenda: Enter email address on computer• Congrats! Overdue!• Introductions (Who is Mrs. Harton?)• What is Calculus and why study it? • Http://www.youtube.com/watch?v=ismnD_QHKkQ• Course and Class requirements and procedures• Diagnostic – Assignment Closure

Electrical Engineering Research• Graduated from Tennessee State University, B.S., Electrical Engineering• Graduated from the Massachusetts Institute of Technology (MIT), S.M., Electrical

Engineering• Started career at Motorola, Inc. in Research in Speech Telephony.• Patents/PublicationsTeaching• Graduated from Northwestern University, MSEd. , M.S. in Education and Social Policy• IB Training Math (IB)• AP Calculus Training (College Board)

PersonalMarried since 1980, with two daughters both in Grad School (Physics, Chemistry)

Who is Mrs. Harton?

What is Calculus?

• Calculus is a process of applying limits to pre-calculus topics.

• Calculus is mathematics in motion!

http://media.wiley.com/product_data/excerpt/84/07645249/0764524984.pdf

http://media.wiley.com/product_data/excerpt/84/07645249/0764524984.pdf

http://media.wiley.com/product_data/excerpt/84/07645249/0764524984.pdf

About this course - Calculus SpecificThe AB course - equivalent of one semester of college calculus.

Goals:1. Give students an understanding of and appreciation for topics in

Calculus.2. Prepare students for success in their future mathematics courses.3. Prepare students for success on the AP Calculus AB exam.

• AP Calculus exam will be given on Wednesday May 7, 2014• Calculators Mandatory

• Course Fees:• Course Packets- $30• AP Calculus Exam - $89 (Free/Reduced Lunch Waivers available)

Required Materials:• Notebook/ Dividers –

4 dividers (Homework, Bell Ringers/Exit Tickets, Tests/Quizzes, Handouts)

• Spiral notebook for Notes only Don’t hand in spiral paper• Loose leaf Paper and Graph Paper• Pens and No. 2 Pencils, Colored Pencils• Graphing calculator (TI83+ or TI84 required, TI 89- TI Inspire Suggested)

No calculator sharing – Sharing calculators considered cheating Calculator loan program available• Text book (Book is online)• Course Packets• Internet Access

About this course Calculus Specific- Calculator • Students make extensive (and appropriate) use of their

calculator. • All students MUST have an AP approved graphing

calculator with the capabilities of the following:• Graphing equations in an arbitrary window• Finding the zeros of a function (solve an equation numerically)• Calculate numerical derivatives• Calculate numerical integrals

• Students are taught how to use graphing calculators to help solve problems, experiment, interpret results and support conclusions.

Cheating and Academic Honesty

• Integrity, once lost, is difficult to be regained. • The work you submit for credit is your own. • Any student either duplicating the efforts of another or

supplying another with the fruits of their labors will be given no credit for that assignment.

• Obviously, in group situations collaboration is encouraged; however, each student is expected to make a genuine contribution.

)Quizzes 20%

Tests 20%Mid-term/Semester Finals 20%Class work 20%Homework 20%

Evaluation Policy (Grade weighting)

• Quizzes - Given almost daily. Homework quizzes, take home quizzes, exit tickets and bell ringers.

• Tests- given at the end of each chapter on the cumulative topics examined to that point in time.

• Tests will be composed of free response and/or multiple-choice questions, some with calculator, and some non-calculator to model the form of the AP Exam.

NO ELECTRONICS!

If I ask you for anything,Not producing anything I ask you for

is an offense for write up!

Give it upOr get written up!

Tardy: Once the door is closed, You are late! No entry without a tardy pass!!!!No entry until after class start and set up!Do NOT KNOCK on my Door.I will see you and let you in at my earliest convenience, only with a tardy pass.

NO ID___NO ENTRY!Hat___NO ENTRY!

Don’t have an ID, get one before coming to class.And No hats allowed!

No purses or bags on your desk or in your lap. Put them on the floor or underneath your desk or

BETTER YET, Don’t bring them in here.

Attention SignalWhen I need to get the attention of the class I will use an attention signal.

Teacher action: I will raise my fist in the air and say:“Class- Come to center. Education is Power”

Student Action: Students stop all talking and/or any activities. Each student raises fist and looks at teacher.

Class Dismissal

Do not leave your seats until I dismiss you.Class is not officially over until I say, “Class dismissed. You may leave.”

Leaving the Classroom?

Once you are here,You are here!

Use the bathroom before you get here!Get your homework before you get here!

Go to your locker before you get here!Don’t ask me if you can leave!

Once you are here,You are here!

Question about the rules or a consequencesPlease do make an appointment to see me after school or briefly after class. I do want to answer your questions and hear and allay your concerns.

Order of Operations

1.Beginning of class including Bell Ringer

2.Homework Requests3.Today’s Lesson4.Guided and Independent Practice5.End of Class (Closure) Possible Exit

Ticket6.Class Dismissal

In Class:

Review Section 1.1

• Homework: • Interest Survey (online) due Fri. 9/2• Syllabus online Parent sign in sheet due Fri. 9/2• If needed, bring in calculator loan contract 8/27• Register on morganparkcps.org due Fri. 9/2• Pg 9- #27-38 Calculator needed https://

epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=100841 • Read Section 1.2

Course Requirements

1. Attend class daily and on time.2. Bring necessary learning supplies daily. Keep brand new text in

excellent condition ($25 damage fee). 3. Participate in class by paying attention, taking notes, contributing

to discussions and meeting all classroom expectations. 4. Read and study the textbook as you work on completion of all

homework and classwork assignments.5. Work hard independently, and work effectively with other

students and with me.6. Follow directions the first time.7. Turn in all assignments and projects on time. 8. Study for and complete all tests and quizzes.9. Seek outside assistance as needed.

School Requirements

1. Bring a reinstatement form from the attendance office within 3 days for all excused absences.

2. Wear ID at all times while in the building. ID’S must be worn and visible before upon entering class.

3. Wear appropriate clothing at all times.4. Drinking water is permitted but otherwise, no

eating or drinking in class.5. Follow Uniform Discipline Code.

What is Calculus?

• http://www.youtube.com/watch?v=ismnD_QHKkQ

• Limits• http://www.youtube.com/watch?v=lCSk4Df2x-A• http://www.youtube.com/watch?annotation_id

=annotation_314822&feature=iv&src_vid=lCSk4Df2x-A&v=oA6kdSi9_EA

• http://www.youtube.com/watch?feature=player_embedded&v=GGQngIp0YGI#at=123

Classroom Procedures Achieve—To succeed in something!

Transition: Beginning the class 5-7 minutes (until all homework is checked)

Students will come in from the hallway to the classroom:• Show me your ID, Remove hat • Go to their assigned seating. • Get their class book and, if needed, sharpen pencil. Get pencils and recycled

paper• Get graded papers from graded paper (Out) bin. • Check missing assignments folder if neededStudents will:• Take out homework and prepare for homework check. Homework is due

immediately.• Write homework requests on board along with name.• Write down today’s homework assignment in HW calendar• Work on the Bell Ringer.• Share a class book with an assigned partner. • Open book to page shown on overhead.

Classroom Procedures Achieve—To succeed in something!

Transition: Beginning the class 5-7 minutes (until all homework is checked)

What behaviors would indicate a student is not participating in this transition? • Moving around the room without a purpose.• Not taking out homework and preparing for homework

check. • Not working on the bell ringer. • Talking loudly yelling, or continuing to react to a

situation that occurred outside the classroom in the hallway or another class.

Transition: Ending the class (5 minutes or less)

Students will prepare for departure from the class. Students should:• make sure they have copied down all homework

assignments. • listen for Instructor to make final announcements. • Put all materials away and are seated in their assigned

seats prior to the bell ringing to end the period. • Wait for instructor will dismiss the class.

Welcome to Mrs. Harton’s Class

• What is Algebra? And why study them? Refer to figure.

• Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them.

Welcome to Mrs. Harton’s Class

• What is Geometry? And why study them? Refer to figure.

• Geometry - branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

Welcome to Mrs. Harton’s Class

• What is PreCalculus?

• Precalculus prepares students for calculus the same way as pre-algebra prepares students for Algebra I. While pre-algebra teaches students many different fundamental algebra topics, precalculus does not involve calculus, but explores topics that will be applied in calculus.

• Calculus – the study of Change.

Studying ProcessWhat does it mean to study in Mrs. Harton’s Class? Studying begins At Home• Before coming to class:• Read the section and start your notes. • Write down the definitions of words and

copy theorems. • Work through each example.• Make note of what you don’t understand.

Studying continues In Class• Listen to Teacher led instruction• Take Notes• Ask Questions• Do in class work

Studying continues with HomeworkTo do Assigned Homework• Write Header -Name, Date, Section number,

page numbers, problem numbers• Copy Question and figures• Look at notes and the text to see how to

apply definitions and theorems• Mark up the figure and solve the problem. Studying continues In Class: • Request to see problems you don’t

understand and make corrections to Homework