# Integrated Math 320 (Frothingham)

**Course Description**

This course will work at an accelerated pace and introduce more sophisticated topics originally addressed in last year’s Integrated Math 210/220 courses. Using a problem set developed and implemented at Phillips Exeter Academy as our main curricular resource, students will work to develop math concepts, skills, techniques and theorems. Skill development will also be supported by targeting topics and using the McDougal Littell Algebra II textbook series.

The choice to pursue developing math knowledge using the problem set is deliberate as it offers opportunities for students to think deeply about math concepts and problem solving, develop strong habits of mind, as well as increase their ability to investigate, conjecture, predict, analyze, verify and communicate mathematically. It is expected that students will struggle with some of the problems. Asking questions and participating in a class conversation are critical to this curriculum, and expected of all students. In addition, students will likely need to employ different strategies in their problem solving. Students should try a variety of methods, which can include: sketching a picture, cutting out a diagram and manipulating pieces, general coordinate proofs and solving simpler known example as a first step to understanding problems that they find difficult. It is important that students keep their work organized in a notebook or binder and should keep all of their work (including any attempts) in a orderly, easily accessible way.

Time in class will be spent in a combination of sharing solutions, assessment and skill development. Students will be expected to present solutions to the class and while this may not occur every single class, it will be very regular. For this reason preparation for class is critical and students can expect roughly 10-15 problems assigned over the course of a week.. The amount of time it takes to complete these problems will vary depending on the content and student, however, students should come to class having attempted (and documented these attempts) all assigned problems. As the class discusses assigned problems, students should made notes, corrections or additions to the work in their notebooks. Notebooks will be collected periodically to assess homework completion. Assessments will be given on a regular basis, on which students will be asked to solve problems similar to those done as homework.

The Phillips Exeter Math Department offer the following information to new students:

CONTENTS: Members of PEA Mathematics Department have written the material in this book. As you work through it, you will discover that algebra, geometry and trigonometry have been integrated into a mathematical whole. There is no Chapter 5, nor is there a section on tangents to circles. The curriculum is problem-centered, rather than topic-centered. Techniques and theorems will become apparent as you work through the problems, and you will need to keep appropriate notes for your records - there are no boxes containing important theorems. There is no index as such, but the reference section that will be provided should help you recall the meanings of key words that are defined in the problems (where they usually appear italicized).

COMMENTS ON PROBLEM-SOLVING: You should approach each problem as an exploration. Reading each question carefully is essential, especially since definitions, highlighted in italics, are routinely inserted into the problem texts. It is important to make accurate diagrams whenever appropriate. Useful strategies to keep in mind are: create an easier problem, guess and check, work backwards, and recall a similar problem. It is important that you work on each problem when assigned, since the questions you may have about a problem will likely motivate class discussion the next day.

Problem-solving requires persistence as much as it requires ingenuity. When you get stuck, or solve a problem incorrectly, back up and start over. Keep in mind that you’re probably not the only one who is stuck.. If you have taken the time to think about a problem, you should bring to class a written record of your efforts, not just a blank space in your notebook. The methods that you use to solve a problem, the corrections that you make in your approach, the means by which you test the validity of your solutions and your ability to communicate ideas are just as important as getting the correct answer.

TECHNOLOGY: Some of the problems in this book require the use of technology (graphing calculators or online software) in order to solve them. Moreover, you are encouraged to use technology to explore, and to formulate and test conjectures. Keep the following guidelines in mind: write before you calculate, so that you will have a clear record of what you have done; store intermediate answers in your calculator for later use in your solution; pay attention to the degree of accuracy requested; refer to your calculator manual when needed; and be prepared to explain your method to your classmates. Also if you are asked to “graph y=(2x-3)/(x+1)”, for instance, the expectation is that, although you might use your calculator to generate a picture of the curve, you should sketch that the picture in your notebook or on the board with correctly scaled axes.

Recommendations for technology:

● TI-83 Graphing Calculators (the school has a class set which may be used during class and there are cell phone apps available that work very similarly.

● http://www.meta-calculator.com/online/ (Also available on the App store)

__Schedule of Major Topics__

Students will have regular assessments over the course of the semester to monitor their mastery of course topics. The frequency of these assessments may increase or decrease with the nature of the current material, but it is reasonable to expect at least one every three weeks. Project works will also occur during the semester and students can expect to complete at least two unit projects in each semester.

__Semester 1__

September/October Problem Set Math 2 Pages 1-15

Unit Project #1: Modeling with Quadratic Functions

November/December/January Problem Set Math 2 Pages 16-40

Unit Project #2: Exeter Reflection

__Semester 2__

January/February Problem Set Math 2 Pages 41-50

Unit Project #1: Changing Dimensions

March/April Problem Set Math 2 Pages 51-60

Unit Project #1: Exeter Reflection Project

May/June Problem Set Math 2 Pages 61-65,

MCAS Exam

**SYLLABUS: Math Syllabus for Math 320 **

https://docs.google.com/document/d/1rNzZvW7bF-W0q9CzzSVQlJCFwUX7w_10CCKhtdF1Q8w/edit

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