Standards-Based Weekly Lesson Plan for Course/Content Area



TUTORING TUESDAY to THURSDAY ROOM 317. SCHOOL WIDE TUTORING IS ON TUESDAY AND THURSDAY ROOM 354 CHAPTER 3 SUMMARY IS PAST DUE! 4.1 4.2,4.3 are past due MINI QUIZ WED. 4.1-4.2 ACT algebra review sheet 1 due Tuesday Review sheet 2 due Wednesday Review sheet 3 due Thursday. 4.4 due Thursday. ACT algebra and geometry quiz Friday. (ACT algebra sheets will be collected together on Friday so you can study from them, but they should be completed as above) 4.5 due Monday 4/ 12

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|Unit Outcomes Chapter 4 |

|Students will be able to convert between radians and degrees, find arc lengths, convert to nautical miles and solve problems |

|involving angular speed |

|Students will be able to define the six trigonometric functions using the lengths of the sides of a right triangle |

|Students will be able to solve problems involving the trigonometric functions of real numbers and the properties of the sine and |

|cosine as periodic functions. |

|Students will be able to generate the graphs of the sine and cosine functions and explore various transformations of these graphs. |

|Students will be able to generate the graphs for the tangent, cot, secant and csc functions and to explore various transformations |

|of these graphs. |

|Students will be abel to graph sums, differences and other combinations of trig and algebraic functions. |

|Students will be able to relate the concept of inverse functions to trigonometric functions. |

|Students will be able to apply the concepts of trigonometry to solve real world problems. |

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|Unit Essential Questions |

|How do I use trigonometric functions to model situations to solve real world problems? |

|What are the 6 basic trigonometric functions and how do I find them from right triangles? |

|How do I graph and analyze graphs of trig functions? |

|How do I find and work with inverses of trig functions? |

|ACT GEOMETRY REVIEW ACT ALGEBRA REVIEW |

|Slope Linear equations |

|Midpoint formula Factoring |

|Distance Formula Problem solving |

|Systems of equations Substitution |

|Circles Evaluation of functions |

|Area and perimeter Quadratic equations |

|Equations of lines Simplification of algebraic expressions |

|Ratios and proportions |

|Essential questions: How do I use geometry and trig to find measures of lengths and angles, midpoints, slopes, areas and perimeters?|

|How do I use geometry to solve real life problems? How do linear equations help us solve problems? |

|COLLEGE READINESS STANDARDS for ACT review |

|24-27 Find midpoint of line segment. |

|28-32 Use distance formula |

|24-27 Determin the slope of line from points or equations |

|28-32 Interpret and use information from graphs in the coordinate plane. |

|24-27 Factor simple quadratics |

|24-27 Solve real world problems using first degree equations |

|24-27 Write expressions, equations, inequalites |

|28-32 Solve quadratic equations |

|33-36 Write expressions that require planning to model a situation |

|33-36 Write equations tht require planning |

|20-23 Evaluate algebraic expressions |

|PERFORMANCE DISCRIPTORS 7c 4a Make indirect measures using proportions. |

|9D 3 Compute distances,lengths and measures of angles using proportions, the Pythagorean theorem and its convers. |

|9A I Calculate distance, midpoint and slope |

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EXAMPLES OF INSTRUCTIONAL STRATEGIES: (i.e. demonstration, explanation, discussion, lecture, lecture—discussion, case studies, cooperative learning, discovery learning, problem based solving, scaffolding)

College Readiness Standards Chapter 4

GRE 704 Analyze and draw conclusions based on information from graphs in the coordinate plane 33-36

GR Identify characteristics of graphs based on a set of conditions

FUN 33-36 Match graphs of basic tirg functions with their graphs

EEI Write expressions that require planning and/or manipulation to accurately model a situation 33-36

NUM Apply rules of exponents 28-32

FUN Express the sine, cosine and tangent of an angle in a right triangle as a ratio of given side lengths. 24-27

Apply basic Trig ratios to solve right- triangle problems 28-32

Use trig concepts and basic identities to solve problems 33-36

FUN 33-36 Use trigonometric concepts and basic identities to solve problems.

Illinois Learning Standards- Performance descriptors. CHAPTER 4

8B4 Analyze functions by investigating by investigating domain, range, rates of change, intercepts, zeros, asymptotes, and local and global behavior.

8B Describe and perform transformations such as arithmetically combining, composing and inverting commonly used functions using technology to perform operations on more complicated symbolic expressions

8B Relate functions to their inverses and their reflections over the line y=x

8C Model and solve real problems using mathematical functions and relation

A8 Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships (I)

8A Describe the limiting process using numerical analysis, graphs, and algebra (J)

8C Identify essential quantitative relationships in a situation and determine the class or classes of functions (power, exponential, logarithmic) that might model the situation.(j)

8C Describe and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions. (

8B 3 Relate the effect of transformations on graphs and equations.

8B 8 Relate functions to their inverses and their reflections over the axes.

9D 2. Identify the basic trig ratios in terms of lengths of the sides of a right triangle and an acute angle.

9D 3. Solve for missing side lengths using the trig ratios for right triangles.

9D 4. Determine and justify the side length relationships present in 450 - 450 – 90o and 30o – 60o – 90o triangles.

RESOURCES NEEDED (for the week): Precalculus by Pearson/Addison Wesley 6th edition notebooks, pencils, calculators, board, overhead and overhead calculator. ACT practice sheet and quiz.

/ACCOMMODATIONS (for the week): The special education student has no modifications for math. The following are his accommodations:

Give verbal directions in clearly stated steps. Give concrete examples, Provide visual aids. Model the instruction, as possible, provide vocabulary, word banks, as possible. Allow peer tutoring.

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Monday ACT GEOMETRY REVIEW and 4.3- trig

Daily objective:

Knowledge: Students will know necessary formulas and procedures for solving Geometry problems on ACT. Will know 6 trig functions

Skills: Students will solve problems involving trig functions( evaluate trig functions given an angle)

Skills: Effectively solve problems dealing with the following topics

• Slope

• Midpoint formula

• Distance Formula

• Systems of equations

• Circles

Activities and Strategies (Include do now, instructional activities, student activities [guided/independent], and closure)

1. Do now- Students work on geometry packet. In cooperative groups

2. Students ask questions on geometry packet.

3. Collect packets

4. Hand back and go over midterm

5. Go over geometry review sheet given as homework

6. If time, students take notes on how to find 6 trig functions given angle. Do guided practice and then independent practice.

7. Closure Students state midpoint, distance formula, area of triangle.

8. Hand out algebra review sheet (ACT) as homeowork.

Alternative Instructional Activities and Strategies: (anticipating student confusion, please include other strategies to help students who do not understand after the first set of instructional activities and strategies)

Homework: ACT algebra review sheet : 4.3 p 382 QR 3,6,10/3-48(X3), 58,59,63-66

Tuesday 4.4 Graphs of sine and cosine

OBJECTIVES:

Knowledge: Students will know shapes and characteristics of sine and cosine curves. Will know basic algebraic procedures to evaluate, solve and set up expressions.

Skills: Students will be able to generate sine and cosine graphs and explore transformations and state period. Students will know how to factor, solve linear and quadratic equations, evaluate polynomials, solve problems involving linear equations.

Activities and Strategies (Include do now, instructional activities, student activities [guided/independent], and closure):

1. Do now Second sheet of ACT algebra review. Students work in cooperative groups.

2. Homework 4.2 and 4.3 and ACT sheet 1 of algebra review.

3. Teacher explains how to develop sine graph and find period, phase shift, amplitude and vertical shift. Do guided and independent practice.

4. Closure Students state what amplitude, period, phase shift and vertical shift are and do.

5. Hand out third ACT algebra sheet

Homework: 4.4 p 394QR 3,8,10/ 3-39 (x3),48,50,54,57,58,61,73,74 Third algebra review sheet. Finish review sheet 2.

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Wednesday 4.3

Daily Objective:

Knowledge: Students will know shapes and characteristics of sine and cosine curves. . Will know basic algebraic procedures to evaluate, solve and set up expressions.

Skills: Students will be able to generate sine and cosine graphs and explore transformations and state period. Students will know how to factor, solve linear and quadratic equations, evaluate polynomials, solve problems involving linear equations.

Activities and Strategies (Include do now, instructional activities, student activities [guided/independent], and closure):

1. Do now Multiple trig questions to prepare for mini quiz find cos 225, solve cosx = .5, sin x = 8/17 tan< 0 find cos.

2. Students ask questions on ACT algebra review sheets and 4.3 and 4.4

3. Closure- mini quiz

Homework 4.4 p 394QR 3,8,10/ 3-39 (x3),48,50,54,57,58,61,73,74

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Thursday 4.5-4.6

Daily Objective:

Knowledge: . Will know basic algebraic procedures to evaluate, solve and set up expressions. Will recognize tan, cot and sec, csc graphs and know their properties and solve trig equations involving tan,cot, sec and csc.

Skills: Students will know how to factor, solve linear and quadratic equations, evaluate polynomials, solve problems involving linear equations. Students will be able to recognize tan, cot, sec, csc graphs and state properties of tan. Students will able to graph sums, differences of trig and algebraic functions and identify sinusoid functions.

Activities and Strategies (Include do now, instructional activities, student activities [guided/independent], and closure):

Alternative Instructional Activities and Strategies: (anticipating student confusion, please include other strategies to help students who do not understand after the first set of instructional activities and strategies)

1. Do now- practice problems for ACT algebra/geometry quiz

2. Go over 4.4 and answer questions on ACT algebra sheets

3. Students state procedure for solving trig equations.

Homework: Be sure all Act algebra sheets are finished, 4.5 p 402 QR 3,6,9,10/1.3.5,8.13.14,17-22,2529,30,35,36,41

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Friday – ACT quiz

Daily objective:

Knowledge: Students will know necessary formulas and procedures for solving Geometry problems on ACT and procedures for solving algebra problems

Skills:: Effectively solve problems dealing with the following topics:

• Midpoint formula Factoring

• Distance Formula Problem solving

• Systems of equations Substitution

• Circles Evaluation of functions

• Area and perimeter Quadratic equations

• Equations of lines Simplification of algebraic expressions

Activities and Strategies (Include do now, instructional activities, student activities [guided/independent], and closure)

1. ACT geometry and algebra quiz

lternative Instructional Activities and Strategies: (anticipating student confusion, please include other strategies to help students who do not understand after the first set of instructional activities and strategies)

Homework: 4.5 p 402 QR 3,6,9,10/1.3.5,8.13.14,17-22,2529,30,35,36,41

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