Week 1: - Kent



Chapter 1 Suggestions:

Sec. 1.1, Day 1: Intro to Graphing

Goals for students:

• graph equations in the coordinate plane

• derive and use distance formula

Review syllabus with students; discuss grading policies, etc.

Give students a problem to work on in small groups, such as the following:

The quarterback of the KSU football team throws a pass from the KSU 30 yard line. He is 10 yards in from the sideline and his receiver catches the ball right on the sideline at the opponent’s 46 yard line. How far did he throw the pass?

Use this problem as a springboard for deriving the distance formula. Let students figure it out first if they can and use their ideas as you work through it. Be sure they understand that the distance formula derives directly from the Pythagorean Theorem.

Then do several routine examples.

Review basic graphing in coordinate plane, emphasizing x and y intercepts.

Introduce graphing calculator skills if time.

Suggested homework: pp. 70- 71: 3, 5, 7, 11, 15, 19, 25, 27, 31, 35, 39, 41, 45, 47, 50, 51, 55, 115, 116, 117

Graphing calc: p. 72: 93, 95, 99, 103, 105

Sec 1.1, Day 2: Intro to Graphing, cont’d

Goals for students;

• derive and use circle equation

• complete the square on an equation of a circle in general form; name center and radius

After taking questions on the homework, you might give students a problem like the following:

Given the following sketch, how would you express the distance between an arbitrary point

(x,y) on the given circle, and the origin, (0,0)?

Then do the same for a circle with center (h,k), not the origin; derive the standard form of the

circle (p. 67)

This new edition of the text moved the problems involving completing the square to section 6.2, p. 542. I plan to cover that skill here because we do not study conics in this course. Please note that p. 542 is NOT printed in the students’ custom edition, but is available to you as a pdf file on the MATH 11010 Instructor webpage ( ) under “Extra Worksheets or Activities” on the left side of the page, after the Chapter Suggestions. You’ll need to email it to your students, post it on your course website, or write the few problems on the board.

Suggested homework: p. 72-73: 57, 59, 63, 67, 69, 71-79 all, 81, 83, 85, 118, 121, 123, 125, 127 and

p. 542: 11, 13, 15, 17.

Sec 1.2 Intro to Functions

Goals for students:

• Determine whether a correspondence is a relation or function

• Find function values, or outputs, using a formula

• Vertical line test

• Find domain and range of a function

You might start with application, informally, like #74, p. 88, perhaps without using function notation right away. You might say something like “Value = “ then gradually introduce [pic]notation, perhaps joking that it is the “lazy way out.” (less writing).

Then all the traditional stuff. Be sure to emphasize reading function values from a graph.

You might introduce domain of function informally to start, perhaps with an application, again using #74 on p.88: “What values of x make sense in the problem?”

Be sure to also emphasize reading domain and range from a graph.

Suggested homework: pp. 84 - 87: 3, 5, 7, 11, 13, 17, 19, 21-61 odd, 54, 73, 75

Bonus/challenge problems: 87, 89, 91, 93

Sec 1.3 and 1.4: Linear functions; Equations of lines

Goals for students

• Understand that linear functions are functions with a constant rate of change

• Find slope from two points and in context

• Interpret slope in context of a real-world situation

• Write linear models

• Write equations for lines

This material is supposed to be a review for students. Be sure to emphasize that a linear function is a function with a constant rate of change. Briefly review finding the slope of a line from two points, then focus on the applications in 1.3. Be sure students can interpret the slope in context: e.g. in example 6 on p. 98: for the function M : [pic], or in words, “for each added cm in the length of the humerus, the height of a male increases 2.89 cm.”

Refresh writing equations for lines, a skill that we hope is a review.

Suggested homework: pp. 99 – 102: 1 –39 every other odd; 41 - 57 odd;

pp. 115-119: 23-47 odd; 51, 53, 57, 61-67 odd

Section 1.5, Day 1: More on Functions

Goals for students:

• Given the graph of a function, student can name intervals over which it is increasing or decreasing.

• Estimate the relative maximum or minimum values of a function, given its graph

• Write a function that models a real world scenario

Finding intervals of increasing or decreasing function values is not difficult for students, though they need to understand that we’re dealing with the OUTPUTS that are increasing or decreasing, yet identifying the values of the INPUTS for which this occurs. Though introducing it informally, do ask students to try to understand the more formal definition on p.120.

Modeling is another issue. As you probably know, modeling is difficult for students. Certainly emphasize the area type, like example 4 on p. 123. The Instructor website has a worksheet with extra modeling problems. You might let students work in groups and try to figure it out. Another option is to guide them through it, then let them work on the rest of the problems on the sheet, offering help as needed. The goal of the sheet is writing the models.

Suggested homework: p. 127 - 130: 1-27 odd, 28, 31, 32, 33 and maybe some from worksheet .

Sec. 1.5: Day 2: More on Functions

Goals for students

• Find function values of piecewise functions given the input

• Graph piecewise functions by hand, including the greatest integer function

• Given the graph of a piecewise linear function, write a function formula for it.

Here’s one way to introduce piecewise functions: You might let students work in small groups on the following.

The normal length L of a giant earthworm (measure in cm) is approximately a function of its age, t (measured in weeks). This function can be represented by the following piecewise function rule:

[pic]

a) What is the normal length of a giant earthworm that is 4 weeks old? Express this information using function notation.

b) Evaluate L(8) and interpret this value in the context of the problem.

c) What is the domain of L? What does this domain tell you about the normal life span of a giant earthworm?

Then ask students to graph this function.

Suggested homework: p. 130-131: 35 – 63 odd.

EXAM I

Sample on the website

Study guide for students on the website too. Feel free to distribute it to students (maybe early in the week), then answer questions. During the class before the exam, you might let students work in groups on Review exercises, p. 169ff. OR on the sample exam on p. 173.

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