Click on this link for topics covered in class, assignments made and a list of specific standards for October 26 - 30: Download Math II Calendar (October 26 - 30)
Students may view the following powerpoint: Download Finding Arc Measures Slideshow
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October 2009
October 26, 2009
October 21, 2009
AAT (October 26 - 30)
TEST THIS THURSDAY OVER (3.1-3-4) Quadratic Functions, Polynomial Functions of Higher Degree and Real Zeros of Polynomial Functions. . .We added 3.4 to the material for the test.
Friday - Worksheet on factoring, greatest common factor, binomials (difference of squares, difference of cubes, sum of cubes), trinomials and four terms by grouping. We will start rational functions Wednesday of next week. Calculator portion of test is Monday and we are out of school on Tuesday.
Thursday - First part of Polynomial Functions Test ( 3.1- 3.4/Non-Calculator). Students should arrive to class on time and get started immediately on the test in order to maximize classtime.
Standards:
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
M.AAT.2.7 Problem Solving: Relate
The learner will be able to solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
IMPORTANT NOTE: Download Review Sheet for Trig
Tuesday - We will discuss The Fundamental Theorem of Algebra (3.4). Students should be able to:
- Use The Fundamental Theorem of Algebra to determine the number of zeros of a polynomial function
- Find all zeors of polynomial functions, including complex zeros
- Find conjugate pairs of complex zeros
- Find zeros of polynomials by factoring
Homework: Page 269 #5,13,19,23,25,29,37,39,41,45,49,51,53,55,61,65
Monday - Real Zeros of Polynomial Functions (3.3). Continuation of the lesson we began on Friday.
- Use long division to divide polynomials
- Use synthetic division to divide polynomials by binomials of the form (x-k)
- Use the remainder theorem
- Use the factor theorem
- Use the Rational Zero Test to determine possible rational zeros of polynomial functions
- Determine upper and lower bounds for zeros of polynomial functions.
Homework: Finish Page 260 #7,9,19,21,29,35,37,41,43,47,49,53,57,59,65,67,71,75,77,89,90
Standards:
M.AAT.1.2 Polynomials: Solve
The learner will be able to solve polynomial equations over the field of complex numbers, using the following theorems: Remainder, Factor, Rational Root, and Fundamental Theorem of Algebra.
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
M.AAT.2.7 Problem Solving: Relate
The learner will be able to solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
Posted at 10:55 AM | Permalink | Comments (0)
Band Student Assignment Note (Math II and AAT)
I have given the band students in my Math II classes a copy of the assignments that they will miss while on the band trip and asked them to sign a copy stating they received the assignments.
The AAT assignment are already posted on the blog for this week and Monday of next week. We will have a test in AAT next Thursday and the band students will not be exempt from the test. If they need help with the material covered in class while they were away, they need to make sure to schedule time on Tuesday for extra help. Waiting until Wednesday is a bad option because it will force them to cram for the test. . . They should ask someone to be kind enought to share notes with them once they arrive back to school. The students can pick up a copy of the blog post outside my room and sign my copy stating they received the assignements.
Posted at 10:41 AM | Permalink | Comments (0)
October 19, 2009
AAT (October 19-23)
TEST next Thursday (3.1-3.3) See blog below for standards covered:
Friday - Real Zeros of Polynomial Functions (3.3). Students should be able to:
- Use long division to divide polynomials
- Use synthetic division to divide polynomials by binomials of the form (x-k)
- Use the remainder theorem
- Use the factor theorem
- Use the Rational Zero Test to determine possible rational zeros of polynomial functions
- Determine upper and lower bounds for zeros of polynomial functions.
Homework: Page 260 #7,9,19,21,29,35,37,41,43,47,49,53,57,59,65,67,71,75,77,89,90
Standards:
M.AAT.1.1 Graphing Functions: Concepts
The learner will be able to graph relations and functions using concepts including domain, range, rule of a function, symmetry, asymptotes, and periodicity and end behavior.
M.AAT.1.11 Graphing: Create/Transformations
The learner will be able to construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
M.AAT.2.7 Problem Solving: Relate
The learner will be able to solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
Thursday - We will finish our discussion of 3.2 Polynomial Functions of Higher Degree by addressing the Intermediate Value Theorem.
Homework: Page 247 #53,57,61,65,67,71,74,77,79,85,89,91,93,95,97 (Second period - don't forget to complete Page 247 #27, 31, 33, 37, 39, 45, and 47
Standards:
M.AAT.1.1 Graphing Functions: Concepts
The learner will be able to graph relations and functions using concepts including domain, range, rule of a function, symmetry, asymptotes, and periodicity and end behavior.
M.AAT.1.11 Graphing: Create/Transformations
The learner will be able to construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
M.AAT.2.7 Problem Solving: Relate
The learner will be able to solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
Wednesday - We will begin looking at (2nd period)/continue looking at (1st period) Polynomial functions of Higher Degree. This includes: Graphs of Polynomial Funcitons, The Leading Coefficient Test and Zeros of Polynomial Functions, and The Intermediate Value Theorem. We will save The Intermediate Value Theorem for tomorrow.
Homework:
- IMPORTANT NOTE REGARDING HOMEWORK: 1st period made it through the entire lesson because we started yesterday so these students should be able to complete the entire assignment 2nd period did not make it throught the entire lesson and will be allowed to omit #27, 31, 33, 37, 39, 45, and 47 tonight but add it to tomorrow's assignment.
- Page 239 - Complete the exploration excercise and be prepared to discuss this in class tomorrow if you happen to be called upon. Do the exploration using your calculator and then go back and make sure you could provide an accurate analysis of the end behavior of each function without using your calculator (HINT, HINT, HINT. . .)
- Page 246 #1-9,11,15,17,18,23,24,27,31,33,37,39,45,47,49,51
Standards:
M.AAT.1.1 Graphing Functions: Concepts
The learner will be able to graph relations and functions using concepts including domain, range, rule of a function, symmetry, asymptotes, and periodicity and end behavior.
M.AAT.1.11 Graphing: Create/Transformations
The learner will be able to construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
M.AAT.2.7 Problem Solving: Relate
The learner will be able to solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
1st period: Help with word problems and begin 3.2. We discussed Graphs and the LCT. We will continue the lesson tomorrow.
2nd period: Help with word problems
Homework - Complete/Correct word problems and be ready to turn them in tomorrow. . .
Standards:
M.AAT.1.1 Graphing Functions: Concepts
The learner will be able to graph relations and functions using concepts including domain, range, rule of a function, symmetry, asymptotes, and periodicity and end behavior.
M.AAT.1.11 Graphing: Create/Transformations
The learner will be able to construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
M.AAT.2.7 Problem Solving: Relate
The learner will be able to solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
Monday - Today, we will go over homework and answer questions the student may have. We will also go over the summary sheet for 3.1 and the answers to the test from last week. The students were supposed to try to correct the problems they missed before returning to class today. If time permits, we will begin looking at (3.2) Polynomial functions of Higher Degree. This includes: Graphs of Polynomial Funcitons, The Leading Coefficient Test and Zeros of Polynomial Functions, and The Intermediate Value Theorem. We will save The Intermediate Value Theorem for tomorrow.
Homework: Try to work on the word problems that were assigned Friday. (See this past Friday's blog page).
NOTE TO PARENTS: Many students are consistently failing to do their homework assignments. The students in AAT can't expect to do well in this class if they are not 1) attempting the homework problems and 2) asking for help with things that they do not understand. I will go over some of these problems in class tomorrow. The problems are all related to maximum and minimum values so I will not work every single homework problem in class. After going over these, and giving the students an opportunity to rework/complete the assignment, I will take them up on Wednesday and give each student a grade for accuracy. I will continue with 3.2 in class tomorrow after I spend the first 15 minutes working some of the homework problems.
(Moved to Tuesday - we didn't cover 3.2 yet. . .) Page 246 #1-9,11,15,17,18,23,24,27,31,33,37,39,45,47,49,51
Standards:
M.AAT.1.1 Graphing Functions: Concepts
The learner will be able to graph relations and functions using concepts including domain, range, rule of a function, symmetry, asymptotes, and periodicity and end behavior.
M.AAT.1.11 Graphing: Create/Transformations
The learner will be able to construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
M.AAT.2.7 Problem Solving: Relate
The learner will be able to solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
Posted at 12:13 AM | Permalink | Comments (0)
October 18, 2009
Math II (October 19 - 23)
Monday - Review for Test (Special Right Triangle and Trig Ratios/Inverses Trig Ratios) Classwork/Homework: Pages 179-180 #1-21
Tuesday - Test (Special Right Triangle and Trig Ratios/Inverses Trig Ratios)
Homework: Read pages 182-185 and study the examples
Wednesday - SlideShow: http://www.geometrycrusher.com/Documents/GCH11L1%20SlideShow.ppsx There is a momentary delay in opening the slideshow - be patient.
Complete pages 192-193 in your workbook before class on Thursday Wednesday - Early Release Day - Go over answers to quiz
Homework: Read pages 194-195 and study the examples
Complete pages 196-197 in your workbook before class on Thursday
Thursday - Use Properties of Tangents
Homwork: Complete Pages 196-197 in Workbook befoe class tomorrow.
Friday - Pages 186 -187 #1-22
Standards Wednesday - Friday:
Grade: 9,10,11,12
Description: MM2G3. Students will understand the properties of circles.
Elements:
a. Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
b. Understand and use properties of central, inscribed, and related angles.
c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.
d. Justify measurements and relationships in circles using geometric and algebraic properties.
b. Understand and use properties of central, inscribed, and related angles.
c. Use the properties of circles to solve problems involving the length of an arc and the area of a sector.
d. Justify measurements and relationships in circles using geometric and algebraic properties.
Grade: 9,10,11,12
Description: MM2G4. Students will find and compare the measures of spheres.
Elements:
a. Use and apply surface area and volume of a sphere.
b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.
b. Determine the effect on surface area and volume of changing the radius or diameter of a sphere.
Posted at 11:50 PM | Permalink | Comments (0)
October 12, 2009
AAT (October 12 - 16)
Friday - Word problems involving the quadratic equation, finding minimum and maximum values.
Homework: Pages 234-236 #61,63,65,68,69,71,73,74,75,76
Thursday - Today we will begin our study of Polynomial and Rational Functions. We will:
- discuss how to sketch and analyze graphs of quadratic functions
- define polynomial functions (giving special attention to quadratics)
- state the standard and general forms of quadratic equations
- discuss the vertex, axis of symmetry, and maximum and minimum values of a quadratic equation
Homework:
- Complete 3.1 Study Guide
- Pages 233-234 #1-7odd,13,15,17,19,23, 29,31,35,37,39,41,43,57,59
We will review these concepts again in first period tomorrow. The seniors missed the majority of the class period. We will look at graphing equations involving shrinks/stetches (most everyone has a good grasp on horizontal/vertical shifts) and work example #4 by hand. We will also discuss minimum and maximum a bit more including the importance of knowing what x and y coordinates represent in specific problems. We will answer homework questions and look at some of the word problems the students will have for homework over the weekend.
Link for help with completing the square: http://www.jamesbrennan.org/algebra/quadratics/Completing%20the%20Square.htm
Standards (Thursday and Friday):
M.AAT.1.1 Graphing Functions: Concepts
The learner will be able to graph relations and functions using concepts including domain, range, rule of a function, symmetry, asymptotes, and periodicity and end behavior.
M.AAT.1.11 Graphing: Create/Transformations
The learner will be able to construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
Wednesday - PSAT (First and Second Periods did not meet today.)
Monday - Tuesday: The students will take a test over functions, parent graphs, domain, transformations, combinations and compositions of functions and inverse functions. This will be a two day test (10 problems on the first day and 10 problems on the second day) so the students should have ample time to finish the test.
Please let me continue to stress the importance of remaining on task during class, taking good notes, attempting homework problems (the day they are assigned), and coming back into class and asking questions related to specific homework problems. I always ask students if they have questions regarding the previous assignment. I will spend at least the first 10-15 minutes of class answering questions over homework provided the students ask questions. I will also document my gradebook regarding whether or not students are actually completing their assignments on time. In the past, I had given student's the opportunity (with the homework packet) to go back and rework things they missed on their assignments for full credit but apparently this encouraged many students to simply procrastinate in actually getting their homework done on time. My logic was that if a student didn't understand a problem, they'd come back into class the next day and ask about things they had not understood and go back and reattempt/correct specific problems before the packet was due on the day of the test. This was also an effort on my part to help prepare the students for what they would need to do when they arrived at their respective colleges. Professors will not check student's homework at all. I will no longer take up the packet on the day of the test and all homework grades will be logged the day after the assignment is announced in class. If a student does not do their homework on time, a grade of zero will be entered into the gradebook and late work at this point will not be accepted. Since answers are available to students, sufficient work must be shown if credit is to be awarded. Hopefully, these changes will encourage student mastery of the standards.
STANDARDS COVERED ON THE FUNCTIONS TEST:
PS1: PATTERNS, RELATIONS, AND FUNCTIONS
The learner will be able to use functions to represent and analyze patterns and quantitative relationships.
M.AAT.1.1 Graphing Functions: Concepts
The learner will be able to graph relations and functions using concepts including domain, range, rule of a function, symmetry, asymptotes, and periodicity and end behavior.
M.AAT.1.10 Functions: Define/Graph
The learner will be able to define and graph by hand and calculate the following functions: identity, constant, absolute value, step, greatest integer, polynomial (including linear and quadratic), square root, and piecewise.
M.AAT.1.11 Graphing: Create/Transformations
The learner will be able to construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
PS2: ALGEBRAIC PROBLEM SOLVING: The learner will be able to use a variety of functions to model and solve problems.
M.AAT.2.7 Problem Solving: Relate
The learner will be able to solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
Posted at 06:00 AM | Permalink | Comments (0)
October 11, 2009
Math II (October 12-16)
- County Benchmark Test Tuesday (10-13-09) over The Great Quadratic Unit
- Test Next Tuesday (10-20-09) over The Right Triangle Unit
Monday - Review "The Great Quadratic" for the county's benchmark test. The student's should participate in the class review and look back over their Unit One Test and ask any unresolved questions they may have still have.
Tuesday - County Benchmark Test: "The Great Quadratic". The student's should have participated in the class review on Monday and also looked back over their Unit One Test and asked any questions they may have still had on problems missed.
Wednesday - Review/Practice of Special Right Triangles and Trig functions.
Homework: Worksheets 5.1 (Special Right Triangles), 5.2(Tangent Ratio), 5.3(Sine and Cosine Ratios)
Thursday - Today we learned about the Inverse Trig Ratios: Inverse Tangent, Inverse Sine and Inverse Cosine. We use these ration to find missing angle measures in Triangles.
Classwork/Homework: Worksheet Solving Right Triangles (More Practice)
Friday -Practice with Inverse Trig Functions:
Classwork/Homework: Pages 176-177 #1-27 all
Standards:
Wednesday - Friday
MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.
a. Discover the relationship of the trigonometric ratios for similar triangles.
b. Explain the relationship between the trigonometric ratios of complementary angles.
c. Solve application problems using the trigonometric ratios.
Posted at 10:09 AM | Permalink | Comments (0)
October 06, 2009
Math II (October 5 - 9)
Monday - Today we finished our discussion of the tangent ratio which we began on Friday.
Homework: Page 160 #14-21
Many of the students did not do their assignment from Friday. . . They had three days and at least half the class period on Friday to complete this assignment (13 problems). We will have a quiz over Special Right Triangles and the Tangent Ration on Wednesday.
Tuesday: Review for Quiz
Quiz over Special Right Triangles and the Tangent Ratio on Wednesday.
Link to Reveiw for Quiz: Download Math 2 Unit 2 quiz review
Wednesday: Quiz - Special Right Triangles (45-45-90 and 30-60-90) and Tangent Ratio
Thursday: Sine and Cosine Ratios - This topic should come easy to the students if they understood the Tangent Ratio.
Homework: Page 166 #1-12
Friday: Solving Triangles Using the Sine and Cosine Ratios.
Homework: Page 167: #15-17 and 21-26
Standards for the Week:
MM2G2. Students will define and apply sine, cosine, and tangent ratios to right triangles.
a. Discover the relationship of the trigonometric ratios for similar triangles.
b. Explain the relationship between the trigonometric ratios of complementary angles.
c. Solve application problems using the trigonometric ratios.
Posted at 06:50 AM | Permalink | Comments (0)
AAT (October 5 - 9)
STANDARDS FOR THE WEEK (See bottom of post):
Monday - Today we defined inverse functions and discussed finging them graphically and algebraically.
Link for power point: http://www.slideworld.com/slideshows.aspx/Inverse-Functions-p.-242-247-2.7-ppt-941008#
Quiz on Tuesday! (1.3 - 1.6)
Homework: Section 1.7 Page 145 #1,7,11,15-27odd,31,33,41,42,43,45,49,51,55,57
Tuesday- Quiz (Functions, Graphs of Functions, Shifts, Reflections, and Stretches, Combinations, Compositions, Inverses)
Homework:
- Review Sheet
- Page 146 #59,63,69,71,73,75,79,81,83,85,89,90
Wednesday: Review for Test -Students will get their quizzes back and we will work problems on the board in preparation for the test tomorrow.
Homework (Optional but great practice) -
Page 150 #63,65,67,78,69,73,75,77,81,83,87,89,91,93,95,97,100,101,
102,103,105,115,117,119,123,127,129,131,133,141,143,145,147,153,155
Thursday: Test over Functions has been rescheduled for Monday and Tuesday of next week.
Friday: Test over Functions will be Monday and Tuesday of next week. Students should go back over the problems that they missed on the quiz. We spend Wednesday and Thursday working problems and discussing error analysis. Students continue to make many careless errors which include errors with distributive property, trying to reduce when their is no common factor, failing to use formulas when beginning problems. . .I often times put links on the blog that will be beneficial to the students if they choose to view them. It will also be beneficial for the students to look over any examples in their book that relate to the standards being taught.
STANDARDS FOR THE WEEK:
PS1: PATTERNS, RELATIONS, AND FUNCTIONS
The learner will be able to use functions to represent and analyze patterns and quantitative relationships.
M.AAT.1.1 Graphing Functions: Concepts
The learner will be able to graph relations and functions using concepts including domain, range, rule of a function, symmetry, asymptotes, and periodicity and end behavior.
M.AAT.1.10 Functions: Define/Graph
The learner will be able to define and graph by hand and calculate the following functions: identity, constant, absolute value, step, greatest integer, polynomial (including linear and quadratic), square root, and piecewise.
M.AAT.1.11 Graphing: Create/Transformations
The learner will be able to construct an equation or graph that results from transformations, (translation, dilation, reflection) using a parent equation or graph.
M.AAT.1.12 Graphing Functions: Methods
The learner will be able to graph polynomial, rational, and algebraic functions using appropriate techniques and tools.
PS2: ALGEBRAIC PROBLEM SOLVING: The learner will be able to use a variety of functions to model and solve problems.
M.AAT.2.7 Problem Solving: Relate
The learner will be able to solve problems throughout this course that involve selecting appropriate approaches and tools using estimating strategies to predict computational results, and judging reasonableness of results. Solves problems that relate concepts to practical applications and to other concepts using appropriate tools.
Posted at 06:46 AM | Permalink | Comments (0)
