Math 3 - Advanced Algebra W/Trigonometry

Math 3 - Advanced Algebra w/Trigonometry

Ms. Hahn 773-534-3954

Description:

Students extend their understanding of materials studied in preceding years of the curriculum, while learningabout and applying new topics such as derivatives, algebra of matrices, and circular functions. Populationgrowth, decision-making on land use, and a Ferris wheel circus act provide some of the contexts for themathematical concepts.

Expectations:

Be on time – Have all appropriate materials at your desk and be at your assigned seat when the bell rings.

Be prepared for class - Textbook, 3-ring binder, loose-leaf paper, graphing paper, ruler, protractor, pencils and red pens, graphing calculator (TI-84+ is recommended), etc.
Participate in all classroom activities and discussions - The activities and lessons we cover will be difficult and challenging, but I firmly believe that we will be able to accomplish them together.
Be respectful – Respect the people, equipment, and furnishings of the classroom. Also, listen while others are speaking and presenting.

Math Binder Guidelines:

Keep an organized math binder. DO NOT combine it with another subject.
Get a 3 ring binder and fill it with loose-leaf notebook paper and some tabs. This is more flexible than a spiral

notebook when you need to rearrange papers, add quizzes or handouts, or take out assignments to turn in or

include in your portfolio.

Write down the Date Assigned Assignment (Date, Title your work, HW#, page number, etc).

Use dividers to separate your notebook into sections – Class assignments and Notes / Homework
Within each section, keep materials in chronological order.

How to Do Homework:

Do your work in pencil.
SHOW ALL YOUR WORK – Just like on tests, quizzes, POW,etc.Keep your work so that you have it when it comes time to create unit portfolios.
If I give you a handout or worksheet write your name and date on them as soon as you get them.
Write each separate assignment on a new piece of paper.
If you do not know how to complete a particular assignment, contact someone from your group or from the class. If you still are havingdifficulties: write about what you understand andwhat you do not understand, as well as the

efforts that you have made.

Make homework corrections: Add corrections (notes and correct solutions) in red(no points will be taken off).

Missing class:

Students are expected to be in class every day it meets. When you are absent, you must check the website (accessed through the NCP school website) for the class assignments and home work that you missed. It is your responsibility to check in to find out what you missed. If you miss a test, you MUST make up the test within two days of your return. You must come to me to make an appointment. You will not be able to use class time to makeup tests. Late homework will be accepted for ½ credit until the end of the unit. You are responsible for presenting it to me.

What To Do in Class / Taking Notes in Class

Label and date your notes and class assignments.
Write down important problems, definitions, and theorems in your class notes – especially when I recommend it.
Do practice problems and clearly indicate the stepsof a solution.
After an assignment has been completed and discussed, reflect on its purpose. Write down the key ideas/points.

Doing so will help you see itsrelevance now and, as you write your portfolio, it will help you see how it fits into our

larger objectives.

Need Extra Help?

If you have any questions, I will be happy to work with you to arrange a time to meet either before or after school.

Math study tables are also available after school. Please do not hesitate to ask me to clarify an assignment or help

you improve a particularmathematical skill.

BRING YOUR MATH BINDER TO CLASS EACH DAY!

Other Rules:

Hats are not to be worn in the classroom at any time.
No eating!
To minimize disturbances in class, please use the restroom during the 8 minute passing periods.

Assessment:

All work is evaluated on a 4 point scale. Work that earns a four is outstanding and exceeds the requirements of

the assignment/assessment. A three indicates meeting the standards and showing proficiency without going

above the standard. A two represents a cursory understanding of or effort in the work. A one means that the

workis far below the standards and very little understanding is demonstrated.

Tests - 40% (final exams, unit tests and portfolios)
Quizzes - 25% (scheduled and pop quizzes on mathematical concepts in units)
Homework - 25% (homework assignments, supplemental problems and POW’s)
Participation - 10% (being prepared for class, presentations, questioning, group work)

Math Grade / School Grade / Letter Grade
3.6 - 4.0 / 90% - 100% / A
3.0 - 3.5 / 80% - 89% / B
2.0 - 2.9 / 70% - 79% / C
1.5 - 1.9 / 60% - 69% / D
0 - 1.4 / 0% - 59% / F

Course Outline: IMP 3

Fireworks:

The central problem involves sending up rockets to create a fireworks display. The trajectory of the rocket is a parabola; this unit continues the algebraic investigations with a special focus on quadratic expressions, equations, and functions. Students use algebra to find the vertex of the graph of a quadratic function by writing the quadratic expression in a particular form.

Meadowsand Malls:

SmallWorld, Isn’tIt?

This unit opens with a table of world population data over the last thousand years; it asks the following rather facetious question: If population growth continues to follow this pattern, how long will it be until people are squashed up against each other? To attack this problem, students study a variety of situations involving rates of growth, develop the concept of slope, and then generalize this to the idea of the derivative, the instantaneous rate of growth. In studying derivatives numerically, they discover that an exponential function has the special property that its derivative is proportional to the value of the function, and see that, intuitively, population growth functions ought to have a similar property. This, suggests that an exponential function is a reasonable choice to use to approximate their population data. They also learn that every exponential function can be expressed in terms of any positive base (except 1) and that scientists use as a standard basis the number for which the derivative of the exponential function equals the value of the function. They find this base, e, experimentally. Along the route of their study of exponential functions, they review logarithms, are introduced to the natural log function, and see that logarithms are a useful tool for answering questions raised by exponential functions.

High Dive:

The central problem of this unit involves a circus act in which a diver will fall from a turning Ferris wheel into a tub of water that is on a moving cart. Students are led to extend right-triangle trigonometric functions to the circular functions. They learn about the graphs of the sine and cosine functions and apply them both to geometric situations and to other contexts. In particular, they see how the graph of a sine-like function changes as various parameters such as period and amplitude are changed. Students then study the physics of falling objects and develop an algebraic expression for the time of the diver's fall in terms of his position. Along the way, students are introduced to several additional trigonometric concepts, such as polar coordinates, inverse trigonometric functions, and the Pythagorean identity.

PennantFever:

One team has a three-game lead over its closest rival for the baseball pennant. Each team has seven games to go in the season. What’s the probability that the team that is leading will win the pennant? Students set up a probability model for the problem. Their analysis requires an understanding of combinatorial coefficients and uses the tool of probability tree diagrams. Students work through the general topic of permutations and combinations, and develop the binomial theorem and properties of Pascal's triangle.

*ACT preparation will occur throughout the year.