Objective

Suggested Student Activities

Days

Exam

1. Use a number line to graph and order real numbers.

2. Identify properties of and use operations with real numbers.

Psychic math

Identify then order numbers

1

1. Evaluate algebraic expressions.

Practice order of operations

1. Solve linear equations.

Practice solving linear equations of all types

2

2. Use linear equations to solve real-life problems.

Recall methods of solving equations using distributive property

1. Use a general problem-solving plan to solve real-life problems.

Construct and label a diagram for word problems

2. Use other problem-solving strategies to help solve real-life problems.

Create/evaluate a verbal model and -write an algebraic model

1-5 Real-Life Application

1. Solve simple inequalities.

Activity 1-6 Graphing Calculator (text) page 48

1

1

2. Solve “and” compound inequalities

3. Solve “or” compound inequalities

1. Solve absolute value equations

1

2

2. Solve and graph absolute value inequalities.

1

39

Review knowledge

Chapter 1 Review Games and Activities

1

Demonstrate knowledge

Test

1

Hook

Technology

Calculator

Project

Case study

1. Identify relations and functions.

2. Define, graph and evaluate linear functions.

Determine the domain and range

Scatter plots

1

1. Find slopes of lines and classify parallel and perpendicular lines.

2. Use slope to solve real-life problems.

Find the slope between two points

1

3

Recall the slopes of horizontal and vertical lines.

Real-Life Application: When Will I ever Use This?

Slope dance with the CBR

Project: Ski slope

1. Graph a slope-intercept linear function

2. Graph a standard form linear function

Review graphing vertical and horizontal lines

Recall finding the slope and y-intercept of a line given its equation

2

Determine the x-and y-intercepts of a linear equation in slope/intercept form

4

Use a graphing calculator to graph linear equations

Interdisciplinary Application (Resource Book)

Math & History (text)

1. Write linear equations.

2. Write direct variation equations.

Review writing an equation of a line given its graph, slope and y-intercept, slope and point, and two points.

3

Review writing an equation in standard form of a line given its graph

5

Review writing an equation of a line given two points.

Demonstrate writing an equation of a line that is parallel or perpendicular to a given line

6

35

Solve direct variation problems.

Fitting a Line to a Set of Data (text)

1. Use a scatter plot to identify the correlation shown by a set of data.

2. Approximate the best-fitting line for a set of data.

Determine the correlation of a scatter plot

2

7

Use a graphing calculator to find the linear regression equation for a given set of data

Using Linear Regression (text)

Do Standards Dissemination Project Activity, Take A Stand

1. Graph linear inequalities in two variables.

2. Use linear inequalities to solve real-life problems.

Determine whether a given ordered pair is a solution of an inequality

1

Graph a linear inequality in s/i form

9

Evaluate a piecewise function

2

Determine the equation of a piecewise function whose graph is given

Practice graphing piecewise functions

Explore the greatest integer function using a graphing calculator

Apply piecewise functions to solve real-life problems.

47

Activity 2.7 Graphing Piecewise Functions

1. Graph absolute value functions.

Graph absolute value functions.

1

26

Determine the vertex of the function

Find the symmetry line for the function

Hook

Technology

Calculator

Project

Case study

1. Graph and solve systems of linear equations in two variables.

Graphing Systems of Equations using calculator

2

1. Use algebraic methods to solve linear systems.

Demonstrate the substitution method of solving systems

2

Demonstrate elimination methods of solving systems

25

11

Use knowledge of systems – find many and no solutions

Real-Life Applications (Resource Book)

27

46

1. Graph a system of linear inequalities to find the solutions of the system.

2

10

1. Set up and solve linear programming problems.

Graph a set of constraints to a linear programming problem

2

Find the maximum and/or minimum values of an objective function for a set of constraints

13

1. Solve systems of linear equations in three variables.

Recall linear combinations to rewrite three variable systems.

Real-Life Applications (Resource Book)

2

12

Hook

Technology

Calculator

Project

Case study

1. Add and subtract matrices, multiply a matrix by a scalar, and solve matrix equations.

Matrix definitions

2

Add and subtract matrices

15

Multiply matrices by a scalar

Solve matrix equations

Technology Activity: (text)

Challenge: (text)

Challenge (Resource Book)

1. Multiply two matrices.

Determine whether matrix multiplication is possible and size of product

2

14

Know the procedure of matrix multiplication

Challenge: (text) page 213;

Challenge (Resource Book)

1. Do matrix arithmetic on the calculator

1

1. Evaluate determinants of 2x2 and 3x3 matrices.

Challenge: (text)

Challenge (Resource Book)

1

Find the determinant for a 2x2 matrix

16

1. Find and use inverse matrices.

Challenge: (text)

Challenge (Resource Book)

1

Solve a matrix equation

28

1. Solve systems of linear equations using inverse matrices.

Translate a linear system to a matrix equation and solve using inverse matrices

1

18

Hook

Technology

Calculator

Project

Case study

1. Graph quad functions.

• Practice graphing quad functions using vertex and axis of symmetry

48

• Analyze graph for points of symmetry

• Recall writing quads in standard form

1. Factor quad expressions and solve quad equations by factoring.

• Factor quad expression

8

• Factor quad expressions where a ≠ 0

42

• Factor to solve quad equations

• Find zeros of quad functions

1. Solve quad equations by finding square roots.

• Use properties of square roots

• Rationalize a denominator

29

• Use square roots to sollve a quad equation.

44, 43

• Using Technology – Solving Quad Equations (text page 271

1. Solve quad equations with complex solutions and perform operations with complex numbers.

5. Apply complex numbers to fractal geometry.

• Understand imaginary and complex numbers

• Add and subtract complex numbers

Multiply complex numbers

30

5-4 Activity Lesson Opener

1. Solve quad equations by completing the square.

2. Use completing the square to write quad functions in vertex form.

• Demonstrate how to find zeros when factoring is not possible

• Use/change the factored form of quads to vertex form.

• 5-5 Real-Life Application (Resource Book) page 75

• Using Technology – Finding Maximums and Minimums

1. Solve quad equations using the quad formula.

2. Use the discriminant to find the types and number of quad solutions.

• Solve quad equations using the quad formula.

• Select the best method to solve quads

19, 45

1. Write quad functions given characteristics of their graphs.

2. Use technology to find quad models for real-life data.

• Use characteristics of graphs to write quad functions

• Utilize technology to find quad model for data.

• 5-8 Challenge Skills and Applications

Hook

Technology

Calculator

Project

Case study

1. Use properties of exponents to evaluate and simplify expressions involving powers.

Practice evaluating numerical expressions

Apply the product and quotient of power rules to simplify algebraic expressions

1. Evaluate a polynomial function.

3. Graph a polynomial function.

Determine whether a function is a polynomial function

• Practice writing a function in standard form

• Use substitution or synthetic substitution to evaluate the polynomial function for a given value of x

22, 37

Describe the end behavior of a polynomial function

Use a graphing calculator to graph a polynomial function

Activity 6.2 Setting a Good Viewing Window (text) page 337

1. Add, subtract, and multiply polynomials.

Review special binomial products

6.4 Interdisciplinary Application (Resource Book) page 60

Add polynomials

Subtract polynomials

32

Multiply polynomials

1. Factor polynomial expressions.

5. Use factoring to solve polynomial equations.

• Review the factoring patterns of a general trinomial, a perfect square trinomial, the difference of two squares, common monomial factor

• Apply the special factoring patterns of the sum and difference of two cubes

33

6.4 Practice (Resource Book) pages 53, 54, 55

1. Divide polynomials and relate the result to the remainder theorem and the factor theorem.

Practice using long and synthetic division

• Evaluate f(k) to determine if a polynomial f(x) has a factor of (x-k)

• Determine the other zeros of a polynomial function when given one zero

36

6.5 Practice (Resource Book) Real-Life Application: When Will I Ever Use This? page 73

1. Find the rational zeros of a polynomial function.

Use the Rational Zero Theorem to find all real zeros of a polynomial function

1. Use the fundamental theorem of algebra to determine the number of zeros of a polynomial function.

2. Use technology to approximate the real zeros of a polynomial function.

Classify the solutions of a polynomial equation as rational, irrational, or imaginary

Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1

Use a graphing calculator to find the zeros of a function

1. Analyze the graph of a polynomial function.

Identify the x-intercepts

Locate the local maximums and local minimums

2. Use finite differences to determine the degree of a polynomial function that will fit a set of data.

Use finite differences to determine the degree of the polynomial function that will fit the data

optional

Hook

Technology

Calculator

Project

Case study

1. Evaluate nth roots of real numbers using both radical notation and rational exponent notation.

Familiarize how to determine real nth roots

Recall the definition of a rational exponent

Solve equations using nth roots

29?

1. Use properties of rational exponents to evaluate and simplify expressions.

Use properties of rational exponents to evaluate and simplify expressions.

23

31

1. Perform operations with functions including power functions.

1. Find inverses of linear functions.

2. Find inverses of nonlinear functions.

Determine the inverse of linear functions

20

Determine the inverse of non-linear functions

Verify the inverse of a function

Write an inverse model

Graph square root functions.

1. Graph square root and cube root functions.

2. Use square root and cube root functions to find real-life quantities.

Describe how to use translations to graph square root and cube root functions

Identify the domain and range of square root and cube root functions

7.5 Visual Approach Lesson Opener: (Resource Book) page 66

1. Solve equations that contain radicals or rational exponents.

Solve equations that contain radicals or rational exponents.

24

Check for extraneous solutions

Use the intersect feature on a graphing calculator to solve an equation

Math & History: Tsunamis (text) page 444

1. Use measures of central tendency and measures of dispersion to describe data sets.

3. Use box-and-whisker plots and histograms to represent data.

Find the measures of dispersion of a data set

Draw a histogram of a data set

Use a graphing calculator to find statistics and draw statistical graphs

Hook

Technology

Calculator

Project

Case study

1. Graph exponential growth functions.

Use exponential growth functions to model real life problems

Use the compound interest formula to compute compound interest

1

8.1 Real-life Application: When Will I Ever Use This?

1. Graph exponential decay functions.

Use exponential decay functions to model real life problems

36

Determine whether a function represents exponential growth or decay.

23

24

Activity 8.2 Exponential Growth and Decay

1. Use the number e as the base of exponential functions.

Define the natural base e

Simplify expressions containing e

2

Use a graphing calculator to graph functions with natural base e

Compute continuous compound interest.

8.3 Application Lesson Opener

1. Evaluate log functions.

6. Graph log functions.

Find the inverse of a log equation

Rewrite an exponential equation in log form

1. Use properties of logarithms.

Expand log expressions

Condense log expressions by using the change of base formula.

Math & History Logarithms (text) page 499

8.5 Graphing Log Functions (text) page 500

1. Solve exponential equations.

2. Solve log equations.

Determine whether a given x-value is a solution of the equation

1. Model data with exponential functions.

2. Model data with power functions.

Practice writing a power function of the form y=ab^x given two points

Draw a scatter plot of ln y versus x

Find an exponential model for given data

Hook

Technology

Calculator

Project

Case study

1. Write and use inverse variation models.

2. Write and use joint variation models.

• Recall definition of rational numbers

• Classify equations into direct, inverse or no variations

• Express variations as equations

• Recognize/solve joint variations

• Determine the constant of variation

3

1. Graph simple rational functions.

• Investigate rational functions in two forms

• Discover the characteristics of a hyperbola

• Determine direction of branches

• a > 0     I and/or III quadrant

• a < 0    II and/or IV quadrant

• Determine x-intercept and vertical/horizontal asymptotes

• Illustrate a graph of a simple rational function.

• Activity 9-2

• Graphing rational functions using graphing calculator in dot mode

1. Graph general rational functions.

• Investigate the characteristics of rational functions when m < n , m = n, m > n

• Determine x-intercept and vertical/horizontal asymptotes

• Illustrate the graph of general rational functions.

1. Multiply and divide rational expressions.

• Use factoring to simplify rational expressions

28

• Multiply rational expressions

5

• Divide rational expressions.

6

1. Add and subtract rational expressions.

4. Simplify complex fractions.

• Add/Subtract Expressions with common denominators

26

• Add/Subtract Expressions with unlike denominators

27

• Add/Subtract Expressions with common denominators/unlike denominators

• Simplify denominators by factoring to determine common denominator

• Recognize complex fractions and simplify by multiplying each denominator by the L.C.D.

1. Solve rational equations.

• Solve rational proportions 

8

• Solve rational equations

9

1. 1. Find the distance between two points and find the midpoint of the line segment joining two points.

1. Apply midpoint formulas.

10

2. Apply distance formulas.

9

3. Helicopter Rescue

1. Graph and write equations of parabolas.

1. Identify the key attributes of a parabola

2. Demonstrate understanding of focus, directrix

3. Write the equation of a parabola given certain information

4. Graph a parabola given its equation

37

1. Graph and write equations of circles.

1. Identify the key attributes of a circle

2. Demonstrate understanding of center, radius

3. Write the equation of a circle given certain information

4. Write the equation of a circle given its graph

11

5. Graphing Calculator Activity with Keystrokes: (Resource Book) page

1. Graph and write equations of ellipses.

1. Identify the key attributes of an ellipse

2. Demonstrate understanding of foci, vertices, major axis, minor axis, co-vertices, center

3. Write the equation of an ellipse given certain vertices and co-vertices

4. Graph an ellipse given its equation

1. Graph and write equations of hyperbolas.

1. Identify the key attributes of a hyperbola

2. Demonstrate understanding of foci, vertices, transverse axis, asymptotes, center, central rectangle

3. Write an equation of a hyperbola given its foci and vertices

4. Graphing Calculator Activity with Keystrokes: (Resource Book) page 66

1. Write and graph an equation of a parabola with its vertex at (h, k) and an equation of a circle, ellipse, or hyperbola with its center at (h, k).

4. Classify a conic using its equation.

1. Identify a translated equation of a circle

4, 32

2. Analyze a general second-degree equation and determine which conic section the equation represents

33, 34

3. Reteaching with Practice: (Resource Book) pages 84–85;

4. History of Conic Sections (text) page 631

1. Solve systems of quad equations.

1. Recall algebraic methods of solving a linear system of equations and apply to quad systems

1. Use and write sequences.

2. Use summation notation to write series and find sums of series.

• Kow the language of sequences and series (finite, infinite, nth, a_n)

• Create a rule for the nth term of a sequence

• Find the nth term in a sequence

20

• Use sigma notation to write a series and formulate a sum

21

• Technology Activity: (text) page 658;

• Challenge: (text) page 657; (Resource Book) page 21

1. Write rules for arithmetic sequences and find sums of arithmetic series.

• Challenge: (text) page 665; (Resource Book) page 34

• Identify arithmetic sequences and series and the common difference

• Write a rule for the nth term and a sum of an arithmetic series

1. Write rules for geometric sequences and find sums of geometric series.

• Identify geometric sequences and series and the common ratio

• Write a rule for the nth term and a sum of a geometric series

• Challenge: (text) page 672; (Resource Book) page 48

• Extend a geometric sequence

?

1. Find sums of infinite geometric series.

• Determine if an infinite geometric series converges

• Write a repeating decimal as a fraction

• Construct an infinite series as a model

• Challenge: (text) page 680; (Resource Book) page 64

1. Evaluate and write recursive rules for sequences.

• Evaluate a recursive rule for a sequence

• Examine sequences and series which are neither arithmetic nor geometric

• Math & History: (text) page 687; (Resource Book) page 77

Hook

Technology

Calculator

Project

Case study

1. Use the fundamental counting principle to count the number of ways an event can happen.

2. Use permutations to count the number of ways an event can happen.

• Define/utilize the counting principle in relation to independent events

• Differentiate/use distinct formulas requiring all, some or repetition of objects

1. Use combinations to count the number of ways an event can happen.

2. Use the binomial theorem to expand a binomial that is raised to a power.

• Apply combination formula to events involving multiplying, adding or subtracting

• Upon investigating Pascal's Triangle, develop/use the binomial theorem to any power

Investigating Pascal's Triangle

page 710 (text).

1. Find theoretical and experimental probabilities.

2. Find geometric probabilities.

• Categorize probabilities as bounded from 0 (impossible) to 1 (certain)

• Use probability formula in given events, experiments and geometric events utilizing further formulas learned in geometry

Generating Random Numbers

page 723 (text).

1. Find probabilities of unions and intersections of two events.

2. Use complements to find the probability of an event.

• Define/recognize union/intersection of compound events

• Use accurate probability formula (OR) for compound events

• Define/utilize complements in relation to "all" outcomes of events

1. Find the probability of independent events.

2. Find the probability of dependent events.

• Use probability formula for independent events

• Recognize replacement/not replacement in calculating probabilities of dependent/independent events (conditional probability)

1. Find binomial probabilities and analyze binomial distributions.

2. Test a hypothesis.

• Identify success vs. failure probabilities and use in its application of binomial probabilities

• Differentiate between skewed and symmetric distributions in relation to analyzing binomial distributions

• Follow hypothesis testing procedures in accepting/rejecting claims

1. Calculate probabilities using normal distributions.

• Employ/interpret bell curves in regard to applied means, standard deviations and percents allocated to areas under the bell curve

• Use pertinent information in calculating accurate probabilities

1. Use trig relationships to evaluate trig functions of acute angles.

• Employ right triangle trigonometry (SOHCAHTOA) as it pertains to real life situations.

• Columbus' Voyage

• Identify trig ratios

15

1. Measure angles in standard position using degree measure and radian measure.

3. Calculate arc lengths and areas of sectors.

• Draw/identify angles in standard position (initial/terminal side)

• Use concept of coterminal angles (adding/subtracting multiples of 360) to sketch/state equivalent angles

16

• Define radian in relationship to angle measure

• Calculate angle measure in degrees/radians using 180/Π and Π/180 conversions

30

31

• Define/recognize sectors, arcs and radii in circles

• Apply arc length/area of sector formulas in evaluating real life situations

• Derivation of Arc Length

1. Evaluate trig functions of any angle.

• Evaluate trig functions given a point from a right triangle perspective

• Identify/define quadrantal angles

• Determine values of the six trig functions of quadrantal angles

• Memorize/utilize reference angle formulas (180 - θ, 180 + θ, 360 - θ) and mnemonic device ‘All Students Take Classes’ to determine if functions are positive/negative

17

1. Evaluate inverse trig functions.

• Identify/determine boundaries of inverse trig functions for sin,cos and tan

• Calculator practice to determine exact angles of given trig functions

19

1. Use the law of sines to find the sides and angles of a triangle.

3. Find the area of any triangle.

• Demonstrate/recognize how to solve oblique triangles using the Law of Sines (AAS,ASA,SSA)

• Identify/indicate when 1 triangle, 2 triangles or no triangles exist (Ambiguous Case-SSA)

• Demonstrate comprehension of finding the area of oblique triangles using K = 1/2 absinC (SAS)

1. Use the law of cosines to find the sides and angles of a triangle.

2. Use Heron’s formula to find the area of a triangle.

• Solve oblique triangles using the Law of Cosines (SAS, SSS)

• Practice finding the area of triangles using Heron's formula (SSS)

1. Graph sine and cosine functions.

2. Graph tangent functions.

• Memorize quadrantal angle values of the sine, cosine and tangent functions and use these 5 points to graph the basic curves

• Use y = a sin bx, y = a cos bx and y = a tan bx to determine/define amplitudes, periods and frequencies upon graphing results

29

1. Graph translations and reflections of sine and cosine graphs.

2. Graph translations and reflections of tangent graphs.

• Use the general equations y = a sin b(x-h) + k, y = a cos b(x-h) + k and y = a tan b(x-h) + k to find horizontal (phase) shift and vertical shift as they pertain to h,k respectively

• Translate graphs accordingly in relation to h,k

• *Reflect graphs in lines y = k upon performance of horizontal/vertical translations

1. Model data with a sine or cosine function.

2. Use technology to write a trig model.

• Write sinusoidal equations using the sine or cosine function by determining the amplitude, frequency, period, horizontal and vertical shifts of real life models

• Use graphing calculator to obtain models of sinusoidal regressions

1. Evaluate trig functions of the sum or difference of two angles.

• Assess trig functions, simplify trig expressions and solve trig equations using the accurate sum/difference formula

1. Evaluate expressions using double- and half-angle formulas.

• Assess trig functions, simplify trig expressions, solve trig equations and verify trig identities by choosing the accurate double/half angle formula

Hook

Technology

Calculator

Project

Case study