honors algebra ii pacing guide - sharpschool...

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HONORS ALGEBRA 2 INSTRUCTIONAL GUIDE

Areas that are underlined and bolded are taught in each chapter.

CONTENT AND PACING

Time NC Standard Course of Study Note: HONORS objectives are in bold capitals.

ESSENTIAL QUESTIONS, SKILLS, TASKS

EQUATIONS AND INEQUALITIES • Absolute Value

Equations • Literal Equations

and Formulas RESOURCES: Glencoe: Chapter 1 Additional Resources: Prentice Hall: Chapter 1 McDougall-Littel: Chapter 1

PACING: 6 Days

Competency Goal 2: The learner will use relations and functions to solve problems. 2.04 Create, JUSTIFY, and use best-fit mathematical models of linear, exponential, quadratic, and CUBIC functions to solve problems involving sets of data. (a) Interpret the constants, coefficients, and bases in the context of the data. (b) Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions. 2.08 Use equations and inequalities with absolute value to model and solve problems; justify results. (a) Solve using tables, graphs, and algebraic properties. (b) Interpret the constants and coefficients in the context of the problem.

ESSENTIAL QUESTIONS: 1. Why is Algebra a universal

language? How does it facilitate problem solving?

ESSENTIAL SKILLS: 1. Students will be able to use a

graphing calculator to graph equations and inequalities and find solutions.

2. Students will be able to solve absolute value equations and inequalities graphically.

3. Students will be able to solve compound inequalities.

ESSENTIAL TASKS: 1. Find an example of a survey, poll,

etc. that contains a margin of error.

2. Find an industry that uses tolerance limits and investigate their uses.

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CONTENT AND PACING



LINEAR RELATIONS AND FUNCTIONS RESOURCES Glencoe: Chapter 2 Additional Resources: Prentice Hall: Chapter 2

PACING: 7 Days

Competency Goal 2: The learner will use relations and functions to solve problems. 2.01 Use the composition and inverse of functions to model and solve problems; justify results. 2.04 Create, JUSTIFY, and use best-fit mathematical models of linear, exponential, quadratic, and CUBIC functions to solve problems involving sets of data. (a) Interpret the constants, coefficients, and bases in the context of the data. (b) Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions. 2.08 Use equations and inequalities with absolute value to model and solve problems; justify results. (a) Solve using tables, graphs, and algebraic properties. (b) Interpret the constants and coefficients in the context of the problem.

ESSENTIAL QUESTIONS: 1. How do you determine the best-

fit model for a set of data? 2. How do you understand relations

and functions and select, convert flexibly among, and use various representations for them? (p, 395, PSSM)

3. How do you understand the meaning of equivalent forms of expressions, equations, inequalities, and relations? (p, 395, PSSM)

4. How do you draw reasonable conclusions about a situation being modeled? (p, 395, PSSM)

5. How can you analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior? (p, 395, PSSM)

6. How do you determine correlation coefficients and best-fit equations? What information do they provide? (p. 401, PSSM)

7. How are linear equations and direct variation related?

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CONTENT AND PACING


ESSENTIAL QUESTIONS, SKILLS, TASKS ESSENTIAL SKILLS: 1. Students will be able to describe

functions given a data tables, a graph, or an equation.

2. Students will be able to solve equations numerically, graphically, and algebraically and also be able to explain the process.

3. Students will be able to graph, on paper and with a calculator, a linear function from a set of data.

4. Students will be able to explain slope as a rate of change in the context of the given problem.

ESSENTIAL TASKS: 1. Collect data: Investigating

Polygons and Patterns (p. 19, Glencoe Algebra 2)

2. Lines of Regression (p. 87, Glencoe Algebra 2)

3. Falling Water: (p. 300, Glencoe Algebra 2)

4. Changing Area of Fractals (p. 611, Glencoe Algebra 2)

5. Make a collection of tables, graphs, and algebraic equations for several functions. Give groups of students one of each representation that does not

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CONTENT AND PACING



match and have them work with other groups of students to find the matching pieces. Initially, this can be done with only linear functions, but can be extended to other functions.

6. Use a motion detector to collect data and analyze rate of change over time. (Websites: www.education.ti.com; www.vernier.com)

7. Pressure in water depth. (p. 495, Glencoe Algebra 2)

SYSTEMS OF EQUATIONS AND INEQUALITIES RESOURCES Glencoe: Chapter 3 Additional Resources: Prentice Hall: Chapter 3

PACING: 6 Days

Competency Goal 2: The learner will use relations and functions to solve problems. 2.10 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, algebraic properties, and LINEAR PROGRAMMING.

ESSENTIAL QUESTIONS: 1. How can you solve an equation

graphically (geometrically)? 2. How is linear programming used

in the real world to solve problems?

ESSENTIAL SKILLS: 1. Students will be able to solve

equations and systems of equations graphically with a calculator.

2. Students will be able to solve a linear programming problem.

ESSENTIAL TASKS: 1. Veterinary Medicine (p. 131,

Glencoe Algebra 2)

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CONTENT AND PACING


ESSENTIAL QUESTIONS, SKILLS, TASKS 2. Systems of linear equations (p.

128, Glencoe Algebra 2) 3. Graphing Equations in Three Variables (p. 136, Glencoe Algebra 2)

MATRICES RESOURCES Glencoe: Chapter 4 Additional Resources: Prentice Hall: Chapter 4

PACING: 4 Days

Competency Goal 1: The learner will perform operations with complex numbers, matrices, and polynomials. 1.04 Operate with matrices to model and solve problems. Competency Goal 2: The learner will use relations and functions to solve problems. 2.10 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, algebraic properties, and LINEAR PROGRAMMING.

ESSENTIAL QUESTIONS: 1. How can matrices be used to

solve multivariable equations? 2. How are properties of matrices

similar to properties of the real number system? (p. 393, PSSM)

3. Why are matrices useful is displaying data and solving problems?

ESSENTIAL SKILLS: 1. The student will be able to

perform matrix operations by hand and with a graphing calculator.

ESSENTIAL TASKS: 1. Graphing Equations in Three

Variables (p. 136, Glencoe, Algebra 2)

2. Use matrices to model real-world data. (p. 161, Glencoe, Algebra 2)

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CONTENT AND PACING



POLYNOMIALS RESOURCES: Glencoe: Chapter 5 Sections 5-1 to 5-4 Additional Resources: Prentice Hall: Chapter 6

PACING: 5 Days

Competency Goal 1: The learner will perform operations with complex numbers, matrices, and polynomials. 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems.

ESSENTIAL QUESTIONS: 1. How do operations with real

numbers and polynomials compare and contrast?

ESSENTIAL TASKS: 1. Scientific Notation (p. 227,

Glencoe Algebra 2) 2. Synthetic Division (p. 234,

Glencoe Algebra 2) 3. Factoring with a graphics

calculator (p. 241, Glencoe Algebra 2)


explain the operational rules of exponents.

RADICAL EXPRESSIONS AND EQUATIONS RESOURCES: Glencoe: Chapter 5 Sections 5-5 to 5-9 Additional Resources: Prentice Hall: Chapter 7

PACING: 5 Days

Competency Goal 1: The learner will perform operations with complex numbers, matrices, and polynomials. 1.02 Define and compute with complex numbers. Competency Goal 2: The learner will use relations and functions to solve problems. 2.07 Use equations with radical expressions to model and solve problems; justify results. (a) Solve using tables, graphs, and algebraic properties. (b) Interpret the degree, constants, and coefficients in the context of the problem.

ESSENTIAL QUESTIONS: 1. How do properties of numbers

and number systems compare and contrast? (p. 393, PSSM)

2. How do complex numbers relate to other categories of numbers and how are operations performed with them?


simplify radicals and perform operations with them.

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CONTENT AND PACING



2. The students will be able to solve radical equations algebraically and with the graphing calculator.

ESSENTIAL TASKS: 1. Use a graphing calculator to solve

radical equations. Explore ways to find a proper domain and range for viewing.

2. Find the coordinates of the corners of a box and algebraically find the distance of several diagonals in the box. Measure the distance using a measuring device and compare with the algebraic solutions. Discuss validity. (p.417, Glencoe Algebra 2)

QUADRATIC FUNCTIONS AND INEQUALITIES RESOURCES: Glencoe: Chapter 6 Additional Resources: Prentice Hall: Chapter 5

PACING: 7 Days

Competency Goal 1: The learner will perform operations with complex numbers, matrices, and polynomials. 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. Competency Goal 2: The learner will use relations and functions to solve problems.

ESSENTIAL QUESTIONS: 1. How do families of parabolas

relate to families of lines? Examine the effect on the graph when changing coefficient values.

2. How do you understand complex numbers as solutions to quadratic equations that do not have real solutions? (p. 393, PSSM)

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CONTENT AND PACING



2.02 Use quadratic functions and inequalities to model and solve problems; justify results. (a) Solve using tables, graphs, and algebraic properties. (b) Interpret the constants and coefficients in the context of the problem. 2.04 Create, JUSTIFY, and use best-fit mathematical models of linear, exponential, quadratic, and CUBIC functions to solve problems involving sets of data. (a) Interpret the constants, coefficients, and bases in the context of the data. (b) Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

ESSENTIAL SKILLS: 1. Students will be able to examine

families of lines and parabolas and discuss the effect of changing values of coefficients.

2. Students will be able to “factor” a polynomial by finding the root values of the related equation.

3. Students will be able to efficiently collect data, find regression equations, determine whether the model is a good fit, and make reasonable predictions/conclusions.

ESSENTIAL TASKS: 1. Have the student bite down on a

piece of graph paper. Find the corresponding coordinate points, enter them in the graphics calculator, and find the equation that models the shape of their teeth. Discuss symmetry.

2. “Factor” a polynomial graphically on the TI 83/84 calculator.

3. Graphing Calculator Investigation: Families of Parabolas (p.320, Glencoe Algebra 2)

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CONTENT AND PACING



POLYNOMIAL FUNCTIONS TEXTBOOK / RESOURCES: Glencoe: Chapter 7 Additional Resources: Prentice Hall: Chapter 6

PACING: 7 Days

Competency Goal 1: The learner will perform operations with complex numbers, matrices, and polynomials. 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. Competency Goal 2: The learner will use relations and functions to solve problems. 2.01 Use the composition and inverse of functions to model and solve problems; justify results. 2.04 Create, JUSTIFY, and use best-fit mathematical models of linear, exponential, quadratic, and CUBIC functions to solve problems involving sets of data. (a) Interpret the constants, coefficients, and bases in the context of the data. (b) Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions. 2.06 Use POLYNOMIAL EQUATIONS (THIRD DEGREE AND HIGHER) to model and solve problems. (a) Solve using tables and graphs. (b) Interpret constants and coefficients in the context of the problem.

ESSENTIAL QUESTIONS: 1. How do you determine the

appropriate power of a polynomial function to fit a set of data?

2. Where are maximum/minimum values located on graphs of polynomial functions?

ESSENTIAL SKILLS: 1. Students will be able to determine

the maximum and minimum values of polynomial functions using a graphing calculator.

2. Students will be able to use a graphing calculator to determine the best-fit model for a set of data and use the equation to make predictions.

3. Students will be able to graph, on paper and with a graphing calculator, a polynomial function from a set of data and find solutions.

4. Student will be able to use finite differences to identify the degree of polynomial equations.

ESSENTIAL TASKS: 1. Seismic wave data: (p. 359,

Glencoe Algebra 2)

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CONTENT AND PACING


ESSENTIAL QUESTIONS, SKILLS, TASKS 2. Maximizing Volume: Make a

container by cutting squares from each corner of an 8.5” by 11” sheet of paper and folding up the resulting flaps. Algebraically and graphically find the size square that should be cut from each corner which will result in the largest volume of the container. Extension: Create a container with a lid flap. Extension: Box with Lid (p. 9-16, TI 83+ Handbook or Resources for Algebra)

CONIC SECTIONS RESOURCES: Glencoe: Chapter 8 Additional Resources: Prentice Hall: Chapter 10

PACING: 8 Days

Competency Goal 2: The learner will use relations and functions to solve problems. 2.09 IDENTIFY, COMPARE, AND CONSTRUCT THE CONIC SECTIONS to model and solve problems; justify results. (a) PRECISELY DESCRIBE PARABOLAS AND CIRCLES ALGEBRAICALLY ACCORDING TO DEFINITIONS, CHARACTERISTICS, AND CONSTITUENT PARTS. (b) Interpret the constants and coefficients of parabolas and circles in the context of the problem. (c) IDENTIFY AND DISTINGUISH AMONG THE CONIC SECTIONS USING TABLES, GRAPHS, AND ALGEBRAIC PROPERTIES.

ESSENTIAL QUESTIONS: 1. How do coefficients and signs of

equations change the graphs? ESSENTIAL TASKS: 1. Examine the graphs of similar

equations such as 2x + 3y = 4; 2x2 + 3y = 4; 2x2 + 3y2 = 4; 2x2 + 3y2 = 4; 2x2 + 8y2 = 4; 2x2 - 3y2 = 4; etc.

2. Investigating Ellipses (p. 432, Glencoe Algebra 2)

3. Conic Sections (p. 453, Glencoe Algebra 2)

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CONTENT AND PACING


ESSENTIAL QUESTIONS, SKILLS, TASKS ESSENTIAL SKILLS: 1. Students will be able to

distinguish the type of conic by examining the coefficients and signs in the algebraic equation.

2. Students will be able to graph conics by transforming the equation into an equivalent form that allows them to identify the intercepts and sketch the graph.

RATIONAL EXPRESSIONS AND FUNCTIONS RESOURCES: Glencoe: Chapter 9 Additional Resources: Prentice Hall: Chapter 9

PACING: 7 Days

Competency Goal 1: The learner will perform operations with complex numbers, matrices, and polynomials. 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. 1.05 Model and solve problems using direct, inverse, combined and joint variation. Competency Goal 2: The learner will use relations and functions to solve problems. 2.01 Use the composition and inverse of functions to model and solve problems; justify results. 2.05 Use rational equations to model and solve problems; justify results. (a) Solve using tables, graphs, and algebraic properties. (b) Interpret the constants and coefficients in the context of the problem. (c) Identify the asymptotes and intercept graphically and algebraically.

ESSENTIAL QUESTIONS: 1. What are the characteristics of a

rational function? 2. What are the similarities and

differences of rational functions and inverse variation?

ESSENTIAL SKILLS: 1. Students will be able to graph

rational equations using the graphing calculator.

2. Students will be able to solve direct, joint, and inverse variation problems and identify whether they are linear, polynomial, rational, or other.

ESSENTIAL TASKS: 1. Graphing Rational Functions (pp.

491, 512, Glencoe Algebra 2) 2. Apparent length of an object is

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CONTENT AND PACING



inversely proportional to one’s distance from the object. (p. 494, Glencoe Algebra 2)

EXPONENTIAL AND LOGARITHMIC RELATIONS AND FUNCTIONS RESOURCES: Glencoe: Chapter 10 Additional Resources: Prentice Hall: Chapter 8

PACING: 13 Days

Competency Goal 1: The learner will perform operations with complex numbers, matrices, and polynomials. 1.01 Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems. Competency Goal 2: The learner will use relations and functions to solve problems. 2.03 Use exponential functions to model and solve problems; justify results. (a) Solve using tables, graphs, and algebraic properties. (b) Interpret the constants, coefficients, and bases in the context of the problem. 2.04 Create, JUSTIFY, and use best-fit mathematical models of linear, exponential, quadratic, and CUBIC functions to solve problems involving sets of data. (a) Interpret the constants, coefficients, and bases in the context of the data. (b) Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

ESSENTIAL QUESTIONS: 1. How are inverse functions related

to exponential and logarithmic equations?

2. How can the properties of classes of functions, including exponential, polynomial, rational, and logarithmic functions, be compared and understood? (p. 395, PSSM)

3. How are exponential equations used to model problems involving growth and decay?

ESSENTIAL SKILLS: 1. The student will be able to use

the graphing calculator to analyze and solve exponential and logarithmic equations.

2. The student will be able to apply the definition of logarithms to solve problems.

ESSENTIAL TASKS: 1. Collect temperature data of a hot

cup of water cooling to room

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CONTENT AND PACING



temperature over time. Find the regression equation. Extension: Take the natural log (ln) of the y coordinates and find the linear equation: ln y= (slope) x + y-intercept to (time, ln (temp)) and then find the equivalent exponential equation.

2. Explore the growth of money. Examine data when $1000 is put in savings at 5% for 10 years. Compare with a lesser percent or a larger initial contribution. Use data analysis, equation (formulas) and FINANCE APP on the graphing calculator. Explore an initial investment of $1000 at 5% with an additional $200 added per month. Is this an exponential function? Explain.

3. Explore Amortizing of Loans (p. 605, Glencoe Algebra 2)

4. Collect and analyze data by repeatedly cutting a sheet of paper in half. (cuts, sheets) (p. 522, Glencoe Algebra 2)

5. Analyze population data and explore implications with density, trash disposal, food needs, etc. (p. 539, Glencoe Algebra 2)

6. Explore the connections between

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CONTENT AND PACING



a geometric sequence such as 20, 10, 5, 2.5 and an exponential function.

7. Use the graphing calculators, including data analysis, formulas, graphing, and FINANCE APP, to explore exponential and logarithmic functions. (p. 552, Glencoe Algebra 2)

honors algebra ii pacing guide - sharpschool...

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