of study correlations imp units - wikispaces cig (2009).pdf... · with imp units course of study...

Alabama Course of Study Correlations

with IMP Units

Course of Study correlations for Algebra, Geometry, and Algebra II with Trigonometry

• Year 1 AMSTI units that address the COS standard

• Year 2 AMSTI units that address the COS standard

• Filling in the Holes – Additional resources that address COS standard

• Space for local systems to correlate their locally‐adopted textbooks to ACOS

In some instanced, a unit merely introduces a content standard but does not fully develop the concept. Additional resources would have to be utilized to fully address the standard.

Alabama Course of Study Correlation Document Algebra I

Course of Study Standard Year 1 IMP Unit Year 2 IMP Unit Filling in the Holes

Local Text

1. Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots, radical form, or decimal approximations.

• Applying laws of exponents to simplify expressions,

including those containing zero and negative exponents

Solve It (Days 6, 8, 9, 18, 19)Cookies (throughout) Patterns (Days 9‐10)

All About Alice (Days 1‐7)

Game of Pig (Day 27)

Small World (Days 19‐21)

ALEX

2. Analyze linear functions from their equations from their equations, slopes and intercepts.

• Finding the slope of a line from its equation or by applying the slope formula

• Determining the equations of linear functions given two points, a point and the slope, tables of values, graphs, or ordered pairs

• Graphing two‐variable linear equations and inequalities on the Cartesian plane

Solve It (Day 24‐26)Cookies (throughout) Patterns (throughout)

Overland Trail (Days 11‐25)

Meadows or Malls (Days 3‐4, 18, 19) Shadows (Days 13‐

14) High Dive (Day 23)

ALEX

3. Determine characteristics of a relation, including domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs.

• Finding the range of a function when given its domain

Solve It (Day 9‐12, 24‐26)Patterns (throughout)

Game of Pig (Day 7‐11) Overland Trail (Days 11‐25)



ALEX

4. Represent graphically common relations, including x = constant, y =

constant, ,y x= ,y x= 2 ,y x= and y x= .

• Identifying situations modeled by common relations,

including x = constant, y = constant, y = x, ,y x= , y =

x2, and y x=

Solve It (Day 5, 20‐23, 25‐29)Cookies (Day 2‐21)




ALEX

5. Perform operations of addition, subtraction, and multiplication on polynomial expressions.

• Dividing a polynomial by a monomial

Solve It (day 13‐17) Meadows or MallsWorld of Functions

Know How ALEX

6. Factor binomials, trinomials, and other polynomials using GCF,

difference of squares, perfect square trinomials, and grouping.

Solve It (Introduced)Fireworks (throughout)

Orchard Hideout

ALEX

7. Solve multistep equations and inequalities, including linear, radical, absolute value, and literal equations.

• Writing the solution of an equation or inequality in set notation

• Graphing the solution of an equation or inequality

• Modeling real‐world problems by developing and solving equations and inequalities, including those involving direct and inverse variation

Solve It (throughout)Cookies (throughout)

Game of Pig (Day 7‐21) Overland Trail (Days 11‐28)



ALEX

8. Solve systems of linear equations and inequalities in two variables graphically or algebraically.

• Modeling real‐world problems by developing and solving systems of linear equations and inequalities

Cookies (throughout) Overland Trail (Days 11‐25)



ALEX

9. Solve quadratic equations using the zero product property.• Approximating solutions of quadratic equations

graphically and numerically

Fireworks (throughout)Solve It (introduced)




ALEX

10. Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane.

• Deriving distance, midpoint, and slope formulas for line segments

Small WorldOrchard Hideout

ALEX

11. Solve problems algebraically involving area and perimeter of a polygon, area and circumference of a circle, and volume and surface area of right circular cylinders or right rectangular prisms.

• Applying formulas to solve real‐world problems

Solve It (Day 3) Game of Pig (Day 7‐26) Bees Build it Best (Day 11) ALEX

12. Compare various methods of data reporting, including scatterplots, stem‐and‐leaf plots, histograms, box‐and‐whisker plots, and line graphs, to make inferences or predictions.

• Determining effects of linear transformations of data

• Determining effects of outliers

• Evaluating the appropriateness of the design of a survey

Game of Pig (throughout)

Pit & PendulumOverland Trail (Days

17‐18) Small World

Is There Really a Difference? (throughout)

ALEX

13. Identify characteristics of a data set, including measurement or categorical and univariate or bivariate.

Game of Pig (Day 12‐21)

Pit & PendulumIs There Really a Difference? (throughout)

ALEX

14. Use a scatterplot and its line of best fit or a specific line graph to determine the relationship existing between two sets of data, including positive, negative, or no relationship.

Solve It (Line of Best Fit) Pit & PendulumIs There Really a Difference? (throughout)

ALEX

15. Estimate probabilities given data in lists or graphs.

• Comparing theoretical and experimental probabilities Solve It (introduced) Game of Pig

(throughout) Is There Really a Difference? (throughout)

ALEX

Alabama Course of Study Correlation Document Geometry

Course of Study Standard Year 1 IMP Unit Year 2 IMP Unit Filling in the Holes Local Text1. Determine the equation of a line parallel or perpendicular

to a second line through a given point.

Shadows (throughout)Patterns

Pit & Pendulum

Overland Trail

ALEX

2. Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles.

Shadows (Day 9‐16)Patterns (Day 20)

Bees Build It Best (Day 9)

Orchard Hideout (Day 3, 10)

3. Verify the relationships among different classes of polygons using their properties.

• Determining the missing lengths of sides or measures of angles in similar polygons.

Shadows (Day 11)Patterns

Bees Build It Best (Day 2‐10)

Orchard Hideout (Day 1) ALEX

4. Determine the measure of interior and exterior angles associated with polygons.

• Verifying formulas for measures of interior and exterior angles of polygons inductively and deductively

Shadows (Day 12, 14, 15)Bees Build It Best (Day 2‐

10) Patterns

5. Solve real‐life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes.

• Determining the equation of a circle given its

center and radius

Shadows (Day 10, 20‐Review)


Orchard Hideout (Day 5‐14, 19)

ALEX

6. Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations and using Pythagorean triples where applicable.

Shadows (Day 10, 20‐Review)



7. Use the ratios of the sides of special right triangles to find lengths of missing sides.

• Deriving the ratios of the sides of 30‐60‐90 and 45‐45‐90 triangles.

Shadows (throughout)Bees Build It best (throughout)

Orchard Hideout (Day 1)Suppl. Problem (Thirty‐

Sixty‐Ninety)

8. Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using the relationships to solve problems and to establish other relationships.

Shadows (Day 9‐16)Bees Build It Best (Day 9)

Suppl. Problem (Pythagorean Proof)

Orchard Hideout (Day 1, 3, 10)

Small World (Day 6‐10)

ALEX

• Determining the geometric mean to find missing lengths in right triangles

9. Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions.

• Recognizing the limitations of a conclusion through inductive reasoning

Shadows (Day 9‐16)Bees Build it Best (Day ‐

10, 21)


10. Find the missing measures of sides and angles in right triangles by applying the right triangle ratios of sine, cosine, and tangent.

Shadows (Day 13, 16, 20, 22‐25)

Bees Build It Best (Day 9) Patterns (Day 15‐20)

Orchard Hideout (Day 1)

11. Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.

Shadows (throughout)Bees Build It Best (Day 2‐

10)

Orchard Hideout (Day 5‐14)

Game of Pig (Day 7‐21)

ALEX

12. Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons.

Orchard Hideout (throughout)

ALEX

13. Identify the coordinates of vertices of the image of a given polygon that is translated, rotated, reflected, or dilated.


World of Functions As the Cube Turns

ALEX

14. Classify polyhedrons according to properties, including the number of faces.

• Identifying Euclidean solids


Orchard Hideout (Day 1) ALEX

15. Calculate measures of arcs and sectors of a circle from given information.


ALEX

16. Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids.

• Developing formulas for surface area and volume of spheres, cones, and pyramids

• Calculating specific missing dimensions of solid figures from surface area or volume

• Determining the relationship between surface areas of similar figures and volumes of similar figures


Suppl. Problems (Finding the Best Box, Another

Best Box, From Polygons to Prisms)


ALEX

17. Analyze sets of data from geometric contexts to determine what, if any, relationships exist.

• Distinguishing between conclusions drawn when using deductive and statistical reasoning

Shadows (introduced)Bees Build It Best (Day

11‐16)

Game of Pig (Day 7‐26)ALEX

• Calculating probabilities arising in geometric contexts 18. Construct with precision a circle graph to represent data

from given tables or classroom experiments.

Alabama Course of Study Correlation Document Algebra II with Trigonometry

Course of Study Standard Year 1 IMP Unit

Year 2 IMP Unit Filling in the Holes

Local Text

1. Determine relationships among the subsets of complex numbers.

Fireworks (Suppl. Prob)

Know How (Day 6‐7)

ALEX

2. Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value.

Know How (Day 6‐7) Meadows and Malls (Days

27‐33)

3. Analyze families of functions including shifts, reflections, and dilations

on families of functions including y = kx (inverse variation), y = kx

(direct variation/linear), y = x2 (quadratic), y = ax (exponential), and y = logax (logarithmic).

• Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains

• Identifying real‐world situations corresponding to families of functions

World of Functions (throughout)

Patterns (In/Out) Small World (Day 19‐

21) Fireworks

(throughout)

High Dive (throughout) Meadows and Malls (Days 10‐12, 20, 27‐33)

All About Alice (Day 10‐15)

ALEX

4. Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.

• Using completing the square, the zero product property and the quadratic formula

World of Functions (throughout) Fireworks

(throughout)


All About Alice (Day 10‐15)

5. Identify the characteristics of quadratic functions from their roots, graphs, or equations.

• Writing an equation when given its roots or graph

• Graphing a function when given its equation

• Determining the nature of the solutions of a quadratic equation

• Determining the maximum or minimum value of a quadratic functions both graphically and algebraically


(throughout) Small World

High Dive (throughout) Pit & Pendulum (Day 21‐24)

Meadows and Malls (Days 10‐12, 20, 27‐33) Orchard Hideout

6. Perform operations on functions, including addition, subtraction, multiplication, division, and composition.

• Determining the inverse of a function or a relation

• Performing operations on polynomial and rational expressions


(throughout)


Know How (Day 6‐7) All About Alice (Day 10‐15)

containing variables • Constructing graphs by analyzing their functions as sums of

differences

7. Solve equations, inequalities, and applied problems involving rational and irrational exponents, absolute values, radicals, and quadratics over the complex numbers as well as, exponential and logarithmic functions.

• Solving equations using laws of exponents, including rational and irrational exponents

• Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation


Fireworks (Suppl. Problems) Small World (throughout)

High Dive (Finding Release Time)

Meadows and Malls All About Alice (Day 10‐15)

Know How Bees Build it Best

ALEX

8. Solve systems of linear equations or inequalities in two and three variables using algebraic techniques, including those involving matrices.

• Calculating the determinant of a 2 x 2 and a 3 x 3 matrix

• Solving word problems involving real‐life situations

World of Functions Cookies (throughout) Meadows and Malls (Days

27‐33)

ALEX

9. Graph trigonometric functions of the form y = a sin(bx), y=a cos(bx), y=a tan(bx)

• Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations

• Determining specific unit circle coordinates associated with special angles


High Dive (throughout) Meadows and Malls

ALEX

10. Solve general triangles, mathematical problems, and real‐world applications using the Law of Sines and the Law of Cosines.

• Deriving formulas for Law of Sines and Law of Cosines • Determining area of oblique triangles

High Dive (throughout) Know How(Days 2‐3) As the Cube Turns (Days

13‐16) Bees Build It Best (throughout)

11. Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.

High Dive (throughout) Bees Build It Best Shadows

ALEX

12. Verify simple trigonometric identities using Pythagorean and reciprocal identities.

High Dive (Day 18‐20)

13. Use different forms of representations to compare characteristics of data gathered from two populations.

• Evaluating the appropriateness of the design of an experimental study.

• Describing how sample statistics reflect values of population parameters

Pit & Pendulum (Day 11‐15) Pollster’s Dilemma (Day 1‐3)

ALEX

14. Determine an equation of linear regression from a set of data.

• Examining data to determine if a linear, quadratic, or


Pollster’s Dilemma (Day 10)

exponential relationship exists, and predicting outcomes

ALEX

15. Calculate probabilities of events using permutations, combinations, and the laws of probability

• Using permutations and combinations to calculate probability

• Calculating conditional probability

• Calculating probabilities of mutually exclusive events, independent events, and dependent events

Pollster’s Dilemma (Day 3‐7)

Pennant Fever (throughout)


ALEX

FILLING IN THE HOLES

• Filling in the Holes with additional IMP units

• Filling in the Holes with ALEX activities • Filling in the Holes with TI activities

FILLING IN THE HOLES WITH IMP UNITS

The following IMP units may be purchased by the schools to address additional Alabama Course of Study objectives:

ALGEBRAUnit Title COS Standards Addressed

“The Overland Trail” 2, 3, 4, 7, 8, 12 “Meadows or Malls” 2, 4, 5, 7, 8

“Is There Really a Difference?” 12, 13, 14, 15

GEOMETRYUnit Title COS Standards Addressed

“As the Cube Turns” 13 “Overland Trail” 1

ALGEBRA II WITH TRIGONOMETRYUnit Title COS Standards Addressed

“Know How” 1, 2, 6, 7 “Meadows or Malls” 2, 3, 4, 5, 6, 7, 8, 9 “As the Cube Turns” 10

“The Pollster’s Dilemma” 13, 14, 15 “Pennant Fever” 15

FILLING IN THE HOLES WITH ALEX* LESSON PLANS – ALGEBRA

*Alabama Learning Exchange http://alex.state.al.us

ALGEBRA COURSE OF STUDY STANDARDS

ALEX LESSON PLANS DESCRIPTION

1. Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots, radical form, or decimal approximations.

• Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents

Title: You Mean ANYTHING To The Zero Power Is One?Overview: This lesson is a technology‐based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization. Title: Calendar Fun Operations Overview: This activity is designed to help students evaluate numerical expressions by using order of operations. The students will be provided a calendar for the current month of the year. Students will then be provided with a worksheet that contains 30 expressions and a different symbol for each expression. The students will manually calculate each expression using order of operations. Once the numerical value has been discovered for each expression, the symbol next to the expression will be drawn on the calendar for that date. Title: Color this Polynomial Simplified Overview: This lesson helps students of all levels visualize the process of polynomial simplification and replicate it with ease. Three alternate forms of assessment are given to accommodate any school's level of technology (Podcasting. Powerpoints or Poster Presentations). Title: Just the facts! Exploring Order of Operations and Properties of Real Numbers Overview: Students use their imagination while learning the importance of 'Order of Operations' and 'Properties of Real Numbers'. This lesson incorporates class discussions, wiki and/or online discussion threads (free at www.wikispace.com and/or quicktopic.com), art and puzzles. Title: Quadrilaterals Overview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson Title: Battle to the Death: Adding Integers Overview: The goal of this lesson is for students to use manipulatives to add integers, creating concepts rather than memorizing rules. This lesson will be related to the 300 Spartans who battled the invading Persians at the Battle of Thermopylae, inspiring the hit movie "300" and Stephen Pressfield’s historical fiction, The Gates of Fire. Interdisciplinary connections will be made to literature, theater, and history, discussing why Pressfield called this the most important battle in establishing and securing democracy in western civilization. This lesson is a base for many subsequent lessons including subtracting integers, combining like terms when simplifying algebraic expressions, and solving algebraic equations.

http://alex.state.al.us/lesson_view.php?id=5230






Title: Writing Word EquationsOverview: The students will learn to write word and formula equations. We will watch a web video about chemical equations. We will then complete the science in motion lab “The Color of Chemistry”. The students will also be required to write word and formula equations. Title: Bear Factory Probability Overview: Students will explore theoretical and experimental probability of an event.

2. Analyze linear functions from their equations, slopes and intercepts.

• Determining the slope of a line from its equation or by applying the slope formula

• Determining equations of linear functions given two points, a point and the slope, tables of values, graphs, or ordered pairs

• Graphing two‐variable linear equations and inequalities on the Cartesian plane

Title: Math is FunctionalOverview: This lesson is a technology‐based activity in which students extend graphing of linear functions to the use of spreadsheet software. After students have become proficient in constructing a table of values, students are able to efficiently graph equations with more extensive computational requirements. Furthermore, inquiry and discovery about slope and y‐intercept will help students conceptualize material normally presented in Algebra I textbooks. Title: Finding the Slope of a Line Overview: This lesson will use a slide presentation to facilitate teaching students how to find the slope of a line when given the graph of the line or two points. Students will interact with the presentation in two ways: first, by taking notes and practicing examples, and second, by linking to a slope activity on the Internet. This lesson may be done in one ninety‐minute block or broken up over two fifty‐minute periods. This lesson would be incorporated in a unit on graphing linear equations. Title: We Love to Graph! Overview: The students will review plotting points on a Coordinate Plane through an interactive website. They will also practice changing the slope and y‐intercept on the website in order to see the effects. After this review, the students will work in groups to plot points and use slope to spell out letters of the alphabet. The students will then unscramble the letters to spell out "We Love to Graph!" Title: Graphing at all levels: It’s a beautiful thing! Overview: This lesson addresses the societal issue of the arts being eliminated in many public schools be employing graphs (at any level) as an artistic media. Review of all types of graphs is included through various interactive websites. Title: Graphing Stations Overview: This activity will be used to review all the forms of linear equations and to review graphing linear, their parallels and their perpendiculars. All the forms of linear equations will be reviewed for testing purposes. Students will participate in a round robin activity to help student’s master objectives before unit test. Title: Quadrilaterals Overview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson. Title: Human slope Overview: Students will participate in this discovery activity intended for them to uncover the role each variable plays in the graph of a line in the form y = mx + b. Students will actually demonstrate lines in slope intercept form on a life size graph. They will compare different graphs to see what effect adding negative signs and coefficients to the variables have on the graph. They will also analysis what happens to the graph when a constant is added or subtracted from the










variable.Title: 'There's Gold in Them There Hills' Overview: Students study the important characteristics of quadratic relationships by exploring the area of rectangles with a fixed perimeter. This lesson involves tables, graphing and patters. This Lesson is adapted from a Connected Math Unit: Frogs, Fleas, and Painted Cubes. Title: Take a Hike! An exploration into finding slopes of inclines Overview: Students will work in small groups to analyze a topographical map of the Fiery Gizzard hiking trail on the Cumberland Plateau in southeastern Tennessee. They will use the map key to determine distance traveled and elevation gained to determine the slope of a short portion of the trail with a steep incline.

3. Determine characteristics of a relation, including domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs.


Title: Math is FunctionalOverview: This lesson is a technology‐based activity in which students extend graphing of linear functions to the use of spreadsheet software. After students have become proficient in constructing a table of values, students are able to efficiently graph equations with more extensive computational requirements. Furthermore, inquiry and discovery about slope and y‐intercept will help students conceptualize material normally presented in Algebra I textbooks. Title: You Mean ANYTHING To The Zero Power Is One? Overview: This lesson is a technology‐based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization. Title: Marathon Math Overview: This unit on sequences and series is intended to help students make the connection from math to real life situations. Developing a marathon training program for a beginner runner is one simple way that students may use patterns in real life. The total mileage per week usually creates a pattern over time. Mathematical operations on patterns, sequences, and series enable students to do the calculations necessary for exploring the pattern. Students also explore nutrition information needed for a training program as proper nutrition is an important part of sports training.

4. Represent graphically common relations, including x = constant, y = constant, ,y x= ,y x=

and2 ,y x= y x= .

• Identifying

situations that are modeled by common relations,

Title: Math is FunctionalOverview: This lesson is a technology‐based activity in which students extend graphing of linear functions to the use of spreadsheet software. After students have become proficient in constructing a table of values, students are able to efficiently graph equations with more extensive computational requirements. Furthermore, inquiry and discovery about slope and y‐intercept will help students conceptualize material normally presented in Algebra I textbooks.







including x = constant, y = constant, y = x,

,y x , y = x2,

and

=

y x=

5. Perform operations of

addition, subtraction, and multiplication on polynomial expressions.

• Dividing a polynomial by a monomial

Title: "Like Terms", I Add Them Overview: Students will review the definition of 'like terms' and combining like terms. They will then learn to apply this to adding polynomials. Students will have an opportunity to work practice problems as they are viewing a PowerPoint presentation of the lesson. They will be adding polynomials using both the horizontal method and the vertical method. Title: Multiplying Polynomials Overview: Students will be introduced to multiplication of polynomials by looking at an area example. They will have an opportunity to use an interactive website to manipulate an area problem. (optional activity) A PowerPoint presentation will be used to demonstrate that the multiplication of polynomials is an extension of the distributive property. A worksheet is provided for skill practice. Title: Fortune Properties Overview: This lesson will teach students how to recognize and apply Identity and Equality Properties. Students will explore the use of properties in real life situations by hands‐on experience. Title: It's Around There Somewhere! Perimeter, and Circumference Overview: The purpose of this lesson is to review the concepts of perimeter, and circumference. Students will also use their knowledge to apply perimeter, and circumference formulas within practical applications such as in spatial design. Title: Bear Factory Probability Overview: Students will explore theoretical and experimental probability of an event. Title: What's The Real Cost of That Car? Overview: This is a Commerce and Information Technology lesson plan. A project requiring research, critical thinking and complex decision‐making about factoring all the costs of purchasing a large ticket item... a car.

6. Factor binomials, trinomials, and other polynomials using GCF, difference of squares, perfect square trinomials, and grouping.

Title: Factoring FanaticOverview: This activity is designed to give students practice in "finding" the correct factors to use when attempting to factor a trinomial. The students are provided with a Tic‐Tac sheet to help them discover the relationship or pattern between two numbers. Students then use their discovery to fill in a second Tic Tac sheet. At this point students have uncovered the mystery of how to locate the appropriate factors in a given trinomial. They can now factor any trinomial placed in front of them! Title: "Factoring by Mack" Overview: This strategy for factoring trinomials will eliminate the trial‐and‐error method used in most textbooks. The lesson will be a direct teaching lesson. With the teacher lecturing and the students taking notes and then having the









students break up into groups to solve sample problems.7. Solve multistep equations

and inequalities including linear, radical, absolute value, and literal equations.

• Writing the solution of an equation or inequality in set notation.

• Graphing the solution of an equation or inequality.

• Modeling real‐world problems by developing and solving equations and inequalities, including those involving direct and inverse variation.

Title: It’s a Party! Solving Multi‐step EquationsOverview: Often students are confused about ‘where to start’ when solving a multi‐step equation. In this lesson the equation is labeled as a ‘party’. The 'host' is labeled (x) with remaining operations being labeled according to their relationship to the host (friends, family, acquaintances, etc...). Technology assignments are used as one method to assess student understanding. Title: Solving Literal Equations Overview: This lesson contains a PowerPoint presentation about solving literal equations. There is an opportunity for the students to complete an interactive worksheet on the computer. There is also a worksheet provided for them to take home for extra practice if needed. Title: Systems of Linear Inequalities Project Overview: The systems of linear inequalities project was designed to be used in an Algebra IB class after a preliminary lesson on systems of linear inequalities. The project is to be graded per group based on the work completed and presentation to the class. Each group is required to use a graphing calculator in its presentation.


• Modeling real‐world problems by developing and solving systems of linear equations and inequalities

Title: QuadrilateralsOverview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be used in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson. Title: Systems of Linear Inequalities Project Overview: The systems of linear inequalities project was designed to be used in an Algebra IB class after a preliminary lesson on systems of linear inequalities. The project is to be graded per group based on the work completed and presentation to the class. Each group is required to use a graphing calculator in its presentation. Title: Systems of Equations: What Method Do You Prefer? Overview: The purpose of this lesson is to help students apply math concepts of solving systems of equations to real life situations. The students will use the three methods of graphing, substitution, and elimination to solve the system of







equations.Title: Systems on a Mission Overview: Students will solve systems of equations using 4 different methods. These methods include substitution, elimination by multiplication, elimination by addition or subtraction and graphing. Students will gain knowledge on how to use one method to solve a system of equations and another method to check their solution. Title: Quadrilaterals Overview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.

10. Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane.

• Deriving distance, midpoint, and slope formulas for line segments

Title: Finding the Slope of a LineOverview: This lesson will use a slide presentation to facilitate teaching students how to find the slope of a line when given the graph of the line or two points. Students will interact with the presentation in two ways: first, by taking notes and practicing examples, and second, by linking to a slope activity on the Internet. This lesson may be done in one ninety‐minute block or broken up over two fifty‐minute periods. This lesson would be incorporated in a unit on graphing linear equations. Title: Investigating School Safety and Slope Overview: Using a 'news report' approach, students investigate the slope of various stairways on the school campus and report on wheelchair accessibility and adherence to the Americans with Disabilities Act. (PowerPoint Included) An extension of this lesson includes the critique/design of existing/nonexistent ramps. Title: Trapezoids: What's Equal or Right About Them? Overview: This lesson will examine the properties of two trapezoids ‐ isosceles and right. The lesson will then use the properties to solve deeper analytical problems. Title: Quadrilaterals Overview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson Title: 'There's Gold in Them There Hills' Overview: Students study the important characteristics of quadratic relationships by exploring the area of rectangles with a fixed perimeter. This lesson involves tables, graphing and patters. This Lesson is adapted from a Connected Math Unit: Frogs, Fleas, and Painted Cubes.

11. Solve problems algebraically that involve area and perimeter of a polygon, area and circumference of a circle, and volume and surface area of right circular cylinders or right

Title: Swimming Pool MathOverview: Students will use a swimming pool example to practice finding perimeter and area of different rectangles. Title: It's Around There Somewhere! Perimeter, and Circumference Overview: The purpose of this lesson is to review the concepts of perimeter, and circumference. Students will also use their knowledge to apply perimeter, and circumference formulas within practical applications such as in spatial design. Title: Quadrilaterals Overview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students











rectangular prisms. • Applying

formulas to solve word problems.

explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.

12. Compare various methods of data reporting, including scatterplots, stem‐and‐leaf plots, histograms, box‐and‐whisker plots, and line graphs, to make inferences or predictions.




Title: Math is FunctionalOverview: This lesson is a technology‐based activity in which students extend graphing of linear functions to the use of spreadsheet software. After students have become proficient in constructing a table of values, students are able to efficiently graph equations with more extensive computational requirements. Furthermore, inquiry and discovery about slope and y‐intercept will help students conceptualize material normally presented in Algebra I textbooks. Title: I know what you did last summer: A data graphing project. Overview: This 'first day of class' lesson is designed to assist the teacher in establishing a 'community of learners' where both girls and boys learn to communicate mathematically. The lesson culminates with students presenting a graphical representation of their summer activities (or winter break) via a poster presentation. Title: Interpreting and Displaying Sets of Data Overview: The students will be able to take a set of given data and interpret the data into quartiles. Students should then be able to determine the parameters for a box and whisker plot by identifying outliers, interquartile range, and the five number summaries. Students will determine the best method for displaying data whether it be line plot, scatterplot, box and whisker plot, etc. Title: The State Capital of Stem and Leaf Overview: This lesson is a hands‐on, technology based math lesson. Students will create a stem‐and‐leaf plot and scatter plot both manually and using Microsoft Excel. Title: The Composition of Seawater Overview: This lesson develops student understanding of ocean water as a true solution. It demonstrates the differences of salinity and "salt" water. This lesson prepares the student to be able to apply the concepts of temperature, density, and layering of the oceans before conducting a lab dealing with these variables.


Title: I know what you did last summer: A data graphing project. Overview: This 'first day of class' lesson is designed to assist the teacher in establishing a 'community of learners' where both girls and boys learn to communicate mathematically. The lesson culminates with students presenting a graphical representation of their summer activities (or winter break) via a poster presentation.

14. Use a scatterplot and its line of best fit or a specific line graph to determine the relationship existing between two sets of data, including positive, negative,

Title: My Peanut Butter is Better Than Yours!Overview: The students will engage in the process of statistical data comparing data using tables and scatterplots. The students will compare data using measures of center (mean and median) and measures of spread (range). This lesson can be done with the worksheet or adapted to let the students use a graphing calculator to create their own scatter plot from the data table. This lesson is modified and adapted from Samples and Populations, Connected Math, Prentice Hall‐ Publisher. Title: Lines of Best Fit









or no relationship.

Overview: This lesson includes a teacher lead activity on gathering data and lines of best fit. Vocabulary is stressed (positive, negative or non‐existing correlations). In groups, students will demonstrate knowledge through podcasting and/or demonstrations. Options are available for schools with varying degrees of technology.


• Comparing theoretical and experimental probabilities

Title: Dice Roll ProjectOverview: This project is a fun way for students to observe the integration of a probability lesson with spreadsheet software. Students will record 36 rolls of a pair of dice. After they record their data, students will manually calculate the mean, median, mode and range. Students will then observe how quickly a computer can do those same calculations and many more things with that same data. Students will also compare experimental outcomes to the theoretical outcome. Title: Bear Factory Probability Overview: Students will explore theoretical and experimental probability of an event. Title: The Composition of Seawater Overview: This lesson develops student understanding of ocean water as a true solution. It demonstrates the differences of salinity and "salt" water. This lesson prepares the student to be able to apply the concepts of temperature, density, and layering of the oceans before conducting a lab dealing with these variables.




FILLING IN THE HOLES WITH ALEX* LESSON PLANS – GEOMETRY


GEOMETRY COURSE OF STUDY STANDARDS

ALEX LESSON PLANS

1. Determine the equation of a line parallel or perpendicular to a second line through a given point.

Title: Writing equations for parallel linesOverview: Students will complete a cooperative group assignment to discover that parallel lines have the same slope. They will view a PowerPoint presentation illustrating how to write an equation of a line parallel to a given line through a given point. Additional practice will be provided by means of a worksheet. Title: Quadrilaterals Overview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.

3. Verify the relationships among different classes of polygons by using their properties.

Title: Geometrica Fights Back!Overview: This activity is designed to give students practice with the properties of special quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapezoids, and kites). The students are provided with a "murder mystery" sheet with descriptions of each "suspect" and a "line‐up" of twelve suspects (different quadrilaterals with their properties). The students must decide which suspect(s) from the line‐up meets the description. The "guilty" quadrilateral will be discovered at the end of the activity. Title: Polygons All Around Us! (This lesson is geared to a standard high school geometry class.) Overview: This is a hands‐on lesson that introduces students to polygons and their properties. It also promotes visual learning by having students identify how polygons are used in the world around us. Students will be given the opportunity to see the importance of geometry in the construction of almost everything in our world. Students will be able to state properties of different geometric figures. Title: Quadrilaterals Overview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.

5. Solve real‐life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric

Title: Geometrica Fights Back!Overview: This activity is designed to give students practice with the properties of special quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapezoids, and kites). The students are provided with a "murder mystery" sheet with descriptions of each "suspect" and a "line‐up" of twelve suspects (different quadrilaterals with their properties). The students must decide which suspect(s) from the line‐up meets the







shapes. D• etermining the equation of a circle given its center and radius

description. The "guilty" quadrilateral will be discovered at the end of the activity.Title: Applications of Area Abound Overview: The teacher will first provide direction instruction on area formulas and provide students an opportunity to practice using those formulas. Students will then apply their knowledge of area to real‐life situations. They will write a short story to go along with the area problem, and then record themselves "acting" it out, and finally add clip art images to illustrate their story. They will then turn all of this into a podcast using Photo Story 3, which can be uploaded to the Internet.



Title: Is it a Triangle?Overview: The purpose of this lesson is to help students investigate the relationships of the lengths of the sides of a triangle in order to discover the three triangle inequality theorems. Students will learn how to draw valid conclusions from the information obtained from the activity and apply those conclusions to real world geometry problems. This serves as an introduction into more advanced geometric theorems.

11. Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.

Title: Area and Perimeter of Various PolygonsOverview: In this lesson students will be engaged in an interactive online practice session using area and perimeter. Students will have to use critical thinking skills in order to unlock gates and learn more about the cups in the challenge. Title: Let’s Tessellate Overview: This lesson is a hands‐on, technology‐based project that will take place in the classroom and computer lab. Students will discover which regular polygons tessellate the plane by constructing polygonal tessellations. Students will also use a spreadsheet to calculate the area and perimeter of the polygons. Title: Applications of Area Abound Overview: The teacher will first provide direction instruction on area formulas and provide students an opportunity to practice using those formulas. Students will then apply their knowledge of area to real‐life situations. They will write a short story to go along with the area problem, and then record themselves "acting" it out, and finally add clip art images to illustrate their story. They will then turn all of this into a podcast using Photo Story 3, which can be uploaded to the Internet. Title: Pennies, Pennies and More Pennies Overview: Students will work in cooperative groups to determine the number of pennies to line the baseboard, cover the floor and fill the room. Students will determine the geometric probability that the head of pin will land on the penny and not the floor space between pennies. Title: Quadrilaterals Overview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts.








Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.


Title: What is the slope of the stairs in front of the school?Overview: The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally. Title: Trapezoids: What's Equal or Right About Them? Overview: This lesson will examine the properties of two trapezoids ‐ isosceles and right. The lesson will then use the properties to solve deeper analytical problems. Title: Quadrilaterals Overview: This is an inquiry lesson used to review Algebra 1 objectives by applying them to geometry concepts. Students explore the properties of quadrilaterals and classify them by definition. This lesson can be use in geometry classes. Students in geometry classes can apply theorems and definitions of quadrilaterals rather than as an inquiry lesson.

13. Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated.

Title: Let’s TessellateOverview: This lesson is a hands‐on, technology‐based project that will take place in the classroom and computer lab. Students will discover which regular polygons tessellate the plane by constructing polygonal tessellations. Students will also use a spreadsheet to calculate the area and perimeter of the polygons. Title: Investigation of Special Segments of Triangles Overview: This lesson will enable students to investigate three special segments of triangles in a very concrete way. The students will fold paper triangles to create the segments. This lesson would be a great way for students to explore the properties of the segments and their intersections.

14. Classify polyhedrons according to properties, including the number of faces. • Identifying Euclidean solids

Title: Platonic Solids Ornaments Overview: This is a hands‐on activity that introduces students to the five Platonic solids. Students will discover the special relationship between faces, vertices, and edges. Students will research the Platonic solids and then construct and decorate Platonic solids ornaments.

15. Calculate measures of arcs and sectors of a circle from given information.

Title: Water Tank Creations Part IOverview: In this lesson students will study the surface area and volume of three‐dimensional shapes by creating a water tank comprised of these shapes. Students will work in groups of 4‐5 to research water tanks, develop scale drawings and build a scale model. Teacher will evaluate the project using a rubric and students will assess one another’s cooperative skills using a rubric.


Title: Pennies, Pennies and More Pennies Overview: Students will work in cooperative groups to determine the number of pennies to line the baseboard, cover the floor and fill the room. Students will determine the geometric probability that the









• Deriving formulas for surface area and volume of spheres, cones, and pyramids


• Determining the relationship between surface areas of similar figures and volumes of similar figures

head of pin will land on the penny and not the floor space between pennies.

17. Analyze sets of data from geometric contexts to determine what, if any, relationships exist.


• Calculating probabilities arising in geometric contexts

Title: Golden Ratios of the Body, Architecture, and NatureOverview: Students will study the golden ratio as it relates to human body measurements, architecture, and nature. Students will use a desktop publishing program to create a poster. The poster will have digital photos of themselves, architecture samples, or nature examples. Students will also include a spreadsheet with the lengths, widths, and length/width ratios of the samples included in the photos. Title: Pennies, Pennies and More Pennies Overview: Students will work in cooperative groups to determine the number of pennies to line the baseboard, cover the floor and fill the room. Students will determine the geometric probability that the head of pin will land on the penny and not the floor space between pennies. Title: Let's Make A Pie Overview: The students will survey their classmates and construct circle graphs to display their results. Students will produce circle graphs using a compass and protractor, and then with an interactive computer program.




FILLING ON THE HOLES WITH ALEX* LESSON PLANS – ADVANCED MATH


ALGEBRA II W/ TRIGONOMETRY COURSE OF STUDY STANDARDS

ALEX LESSON PLANS

1. Determine relationships of subsets of complex numbers.

Title: Classifying Complex NumbersOverview: This lesson helps students distinguish between strictly complex numbers, strictly real numbers and strictly imaginary numbers while learning that real numbers and imaginary numbers are subsets of the set of complex numbers.

3. Analyze families of functions, including shifts, reflections, and dilations on families of functions including

y = kx (inverse variation), y = kx (direct

variation/linear), y = x2 (quadratic), y = ax (exponential), and y = logax (logarithmic). • Identifying the domain and range of a

relation given its graph, a table of values, or its equation, including those with restricted domains

• Identifying real‐world situations corresponding to families of functions

Title: We Are Family (Analyze Families of Functions)Overview: Students will be able to analyze and categorize families of functions. This should be a staggered lesson. Once a family of functions is introduced, the graphs can be explored using this lesson. Parent functions for this lesson include square root, absolute value, exponential, and logarithmic. Title: Predict the Future? Overview: Students will use data collected and a "best‐fit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression.

7. Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions. • Solving equations using laws of exponents,

including rational and irrational

Title: It’s a Party! Solving Multi‐step EquationsOverview: Often students are confused about ‘where to start’ when solving a multi‐step equation. In this lesson the equation is labeled as a ‘party’. The 'host' is labeled (x) with remaining operations being labeled according to their relationship to the host (friends, family, acquaintances, etc...). Technology assignments are used as one method to assess student understanding. Title: Graphing at all levels: It’s a beautiful thing! Overview: This lesson addresses the societal issue of the arts being eliminated in many public






exponents. • Expressing the solution of an equation,

inequality, or applied problem as a graph on a number line or by using set or interval notation.

schools be employing graphs (at any level) as an artistic media. Review of all types of graphs is included through various interactive websites

8. Solve systems of linear equations or inequalities in two and three variables using algebraic techniques, including those involving matrices. • Calculating the determinant of a 2 x 2 and a

3 x 3 matrix • Solving word problems involving real‐life

situations

Title: Systems of Equations: What Method Do You Prefer? Overview: The purpose of this lesson is to help students apply math concepts of solving systems of equations to real life situations. The students will use the three methods of graphing, substitution, and elimination to solve the system of equations.

9. Graph trigonometric functions of the form y = a sin(bx), y=a cos(bx), y=a tan(bx), y=a sec(bx), y=a csc(bx), and y=a cot(bx). • Determining period and amplitude of sine,

cosine, and tangent functions from graphs or basic equations


Title: Trapezoids: What's Equal or Right About Them?Overview: This lesson will examine the properties of two trapezoids ‐ isosceles and right. The lesson will then use the properties to solve deeper analytical problems. Title: Graphing at all levels: It’s a beautiful thing! Overview: This lesson addresses the societal issue of the arts being eliminated in many public schools be employing graphs (at any level) as an artistic media. Review of all types of graphs is included through various interactive websites.

11 . Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.

Title: I Can Determine The Height Of A Rocket!Overview: The lesson is intended to give students a fun real‐world experience in applying their math skills. They will use trigonometric ratios to calculate heights of tall structures. They will also use the Internet to convert their calculations from standard to metric units and vice versa.

13. Use different forms of representation to compare characteristics of data gathered from two populations.

• Evaluating the appropriateness of

Title: Predict the Future?Overview: Students will use data collected and a "best‐fit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression.






the design of an experimental study • Describing how sample statistics

reflect values of population parameters

14. Determine an equation of linear regression

from a set of data. • Examining data to determine if a linear,

quadratic, or exponential relationship exists, and to predict outcomes

Title: Predict the Future?Overview: Students will use data collected and a "best‐fit line" to make predictions for the future. The example the students will be working on for this lesson will demonstrate an exponential regression.

15. Calculate probabilities of events using the laws of probability.

• Using permutations and combinations to calculate probabilities

• Calculating conditional probability • Calculating probabilities of mutually

exclusive events, independent events, and dependent events.

Title: Bear Factory Probability Overview: Students will explore theoretical and experimental probability of an event.



TI* Calculator Activities Correlated to the Alabama Course of Study

These activities can be found at http://education.ti.com/educationportal/activityexchange

Algebra IDescription of Activity Course of Study Standard Addressed

Investigating Laws of Exponents (Algebra 1 Activity 6) TIalgebra.com• To investigate calculations with exponents on numerical bases • To investigate simplifying expressions with exponents

1

Cricket Thermometers • To investigate the relationship between temperature and the number of cricket chirps • To find the x‐value of a function, given the y value • To find the y value of a function, given the x value • To use technology to find linear regression • To use technology to plot a set of ordered pairs

2, 3, 14

Dog Days or Dog Years? (ID: 11682) TImath.com • To represent input/output values as ordered pairs • To analyze data from table of values and scatter plots • To determine functions to represent linear data

2

Dinner Party (ID: 8959) TIalgebra.com • To graph an equation of the form y = mx + b and display a table of values to find its y‐

intercept • To write the equation of a straight line given its slope • To use the point‐slope form to write the equation of a line when given the slope of a line

and a point on it

2

Transformations in the Coordinate Plane (Algebra 1 Activity 7) TIalgebra.com• To create a polygon using coordinate pairs in lists by setting up a connected scatter plot • To use operations on lists to translate, reflect, and dilate the polygon

3

http://education.ti.com/educationportal/activityexchange

GeometryDescription of Activity Course of Study Standard Addressed

Perimeters, Areas, and Slopes – Oh My! • To use analytic geometry to investigate the attributes of geometric figures • To use the Shading and Point‐of‐Intersection trace features of the Inequality Graphing

application

6

Give Me a Hand or Leaf Me Alone (Explorations Activity 5)• To find the surface area of an irregularly shaped object by relating area to mass • To find the y value of a function, given the x value • To use technology to find a best fit line • To use technology to plot a set of ordered pairs

17

Angles of a Triangle (Explorations Activity 13) • To investigate the sum of the angle measures of a triangle • To investigate the relationship between an exterior angle and the interior angles of a

triangle

5

Algebra II with TrigonometryDescription of Activity Course of Study Standard Addressed

Cell Phone Range (ID: 11599) TImath.com • To identify the domain and range of various real‐world step functions • To graphically explore numerical data points and observe step functions

3

Finding a Line of Best Fit (Algebra 1 Activity 4) • To create a scatterplot representing resting heart rate versus age • To graph vertical and horizontal lines to show Q1 and Q3 for both the ages and the heart

rates • To use the vertices of the Q1 and Q3 lines to calculate a line of best fit and graph it

16

Getting Triggy With It (ID: 9774) TIalgebra.com • To approximate the zeros, minima and period of the primary trigonometric functions by

graphing • To approximate the amplitude, frequency and phase shift of the primary trigonometric

functions by graphing • To state the range, amplitude, frequency, period and phase shift of a primary trig

function • To describe how the graph of a trigonometric function y = f(x) changes under

transformations

3

Introduction to Absolute Value (ID: 11305) TImath.com• To explore absolute values using the calculator by plotting points to graph y = ΙxΙ • To use the Transform application to perform transformations with absolute value

functions

9

Constant of Variation (ID: 11196) TImath.com • To explore how the constant of variation affects the graph of direct and inverse

variations. • To apply knowledge of variation to real‐world problems

3, 9

Determining Area (ID: 8747) TIalgebra.com • To apply a formula for the area of a triangle given the coordinates of the vertices • To divide polygons with more than three sides into triangles to find their areas • To develop a similar formula for the area of a convex quadrilateral

10

Operating on Matrices (ID: 11358) TImath.com • To add, subtract and multiply matrices • To find the determinant and inverse of matrices

10

Ain’t No River Wide Enough (ID: 9885) TIalgebra.com• To prove and apply the Law of Sines and Law of Cosines to find unknown sides or angles

of a triangle

14

Alabama High School Graduation Exam (AHSGE) Correlations

This document is an overview of the AHSGE standards and the AMSTI units that address those standards.

AHSGE Standards, Objectives & Eligible Content

Year 1 Units

Year 2 Units

Filling in the

Holes

Std. I: The student will be able to perform basic operations on algebraic expressions.

I-1. Apply order of operations • One, two, or no variables • One set of parenthesis • Determining the absolute value of a term • Suaring the quantity in parenthesis • No more than four terms • Adding or subtracting negative integers • Decimals to the tenths’ place

Solve It (throughout) Cookies (throughout) Patterns (Day 9-10) Small World (Day 19-21) Patterns (throughout)

Game of Pig (Day 27) All About Alice (Day 1-7)

I-2. Add and subtract polynomials Using the distributive property Unlike denominators

Solve It (Day 13-17) Cookies (throughout) Fireworks (throughout)

All About Alice (throughout)

Meadows or Malls

I-3. Multiply polynomials • Multiplying two quantities in parenthesis • Squaring a quantity in parenthesis • Adding or subtracting • Raising a quantity to a power • Fractions • Adding exponents

Solve It (Day 13-17) Cookies (throughout) Fireworks (throughout)

All About Alice (throughout)

Meadows or Malls

Alabama High School Graduation Exam Correlation with AMSTI Units

I-4. Factor polynomials • Difference of two squares • Greatest common monomial • Trinomial • Common binomials • Options will be factored completely

Solve It (Day 13-17) Fireworks (throughout)

Orchard Hideout

Std. II – The student will be able to solve equations and inequalities.

II-1. Solve multi-step equations of first degree • One set of parenthesis • Finding the sum or difference of terms containing

the same variable • Adding or subtracting a variable to or from both

sides of the equation • Finding the solution to the equation • Coefficients my be simple fractions

Solve It (throughout) Shadows (throughout) Cookies (throughout) Bees Build It Best (throughout)

Game of Pig (throughout) Overland Trail (Day 27-28)

II-2. Solve quadratic equations that are factorable

• Factoring of the type ax2 + bx = 0 • Difference of two squares • Factoring using GCF • Trinomials • Common binomials

Shadows (throughout) Solve It (introduced) Fireworks (throughout)

II-3. Solve systems of two linear equations. • Solving for values of both x and y • The options may be four graphs with lines plotted

and the intersection point labeled with its ordered pair.

Cookies (Day 6-12) Bees Do It Best (Day 18-20)

Baker’s Choice Meadows or Malls

II-4. Solve multi-step inequalities of the first degree • A negative coefficient may be used

Cookies (throughout) Bees Do It Best (Day 18-29)

Baker’s Choice

Std. III – The student will be able to apply concepts related to functions.

III-1. Identify functions. • Options may be graphs, ordered pairs, tables, or

mappings • Options may be equations when given a table of

values or ordered pairs • Options may be tables of values or ordered pairs

when given an equation • Functions may be expressed using either terminology

“f(x)=” or “y=”.

Solve It (Day 9-12) Shadows (Day 2-5) Patterns (throughout)

Game of Pig (Day 7-11) All About Alice (throughout)

III-2. Find the range of functions when given the domain.

• The domain of a function may be a single value or set of values

• A set of ordered pairs may be used • Functions may be expressed using either the

terminology “f(x)=” or “y=”.

Solve It (Day 9-12, 21-30, 24-26) Shadows (Day 2-5)

Pit and the Pendulum Game of Pig (Day 7-11)

Std. IV – The student will be able to apply formulas.

IV-1. Find the perimeter, circumference, area or volume of geometric figures.

• The value of pi (π) will be 3.14. • Options may be left in terms of π. • Unnecessary dimensions may be included. • Drawings may be used. • Finding volume or surface area of a rectangular prism

may be required. • Extracting a square root may be required. • Determining the area of a circle when given the

diameter in the drawing may be required. • The formulas will be given in the problem.

Solve It (Day 13-17) Bees Build it Best (throughout)


IV-2. Find the distance, midpoint, or slope of line segments when given two points.

• Radicals may be used. • Radicals will be simplified. • Lines graphed on the coordinate plane may be used • Determining the slope of a line given a line on the

coordinate plane with two points on a line on the coordinate plane without any coordinates labeled may be required

• The formulas will be given in the problem.

Shadows (Day 2-5) Solve It (Day 24-26) Bees Build It Best (Day 11-16) Small World (Day 3-10)


Overland Trail

Std. V – The student will be able to apply graphing techniques.

V-1. Graph or identify graphs of linear equations. • Equations may be expressed in terms of f(x)

Cookies Solve It (Day 24-26)

• The options may be four graphs • The options may be four equations

Shadows (Day 2-5)

V-2. Graph lines given certain conditions. • Two points may be included • X- and y- intercepts may be included • Point and slope may be included • Slope and y-intercept may be included

Solve It (Day 24-26) Shadows (Day 2-5)

V-3. Determine solutions sets of inequalities. • Compound inequality may be included. • Solving inequality may be required. • Options will be graphs.

Cookies (throughout) Baker’s Choice

V-4. Identify graphs of common relations. • Common relations are: x = constant, y = constant,

y = x, y = √x, y = x2, y = │x│. • The options may be four graphs • The options may be four equations.

Solve It (Day 24-26) Shadows (Day 2-5) World of Functions (throughout)

Pit and the Pendulum

Std. VI – The student will be able to represent problem situations.

VI-1. Translate verbal or symbolic information into algebraic expressions; or identify equations or inequalities that represent graphs or problem situations.

• Determining an equation or expression when given a verbal description.

• Graphing inequalities on a number line.

Cookies (throughout) Solve It (Day 29-30) World of Functions (throughout)

Game of Pig High Dive (Day 1-16)

Baker’s Choice

• Determining the equation of a line given two ordered pairs.

• Determining the equation of a line given the line graphed on the coordinate plane.

Std. VII – The student will be able to solve problems involving a variety of algebraic and geometric concepts.

VII-1. Apply properties of angles and relationships between angles.

• The following properties and relationships may be included: vertical angles, adjacent angles, supplementary angles, complementary angles, linear pair, relationships among the measures of angles formed by two parallel lines and a transversal.

• Word problems may be used. • The knowledge of the sum of measures of angles may

be used. • Determining measurements of angles when the

measurements of angles are expressed as algebraic expressions may be required.

Shadows (Day 9-16) Bees Build It Best (Day 9-11) Fireworks (throughout)


VII-2. Apply Pythagorean Theorem. • The Pythagorean Theorem will be given on the

reference page. • Diagrams, word problems, radicals will be used of

included. • All radicals will be simplified. • Drawings will be to scale.

Fireworks (Suppl. Problems) Shadows (Day 10, 20) Bees Build It Best (Day 11-15)

VII-3. Apply properties of similar polygons. • Diagrams will be included. • Drawings will be to scale. • The word ‘similar’ or the symbol “~” may be used. • Use of the scale factor will be required.

Shadows (Day 7-13, 17-19) Bees Build It Best (Day 2-8)

VII-4. Apply properties of plane and solid geometric figures.

• Diagrams will be included. • Word problems will be used. • The following content may be included: area and

perimeter of triangles, rectangles and squares – area and circumference of a circle, given radius or diameter – perimeter of a regular polygon, given one side – volume of rectangular prism or cylinder – sum of the measures of the angles in a triangle – sum of the measures of the angles in a rectangle.

• Determining any dimension of a figure • Determining any dimension of a figure when the

dimension is expressed as an algebraic expression may be required.

Shadows (Day 7-13, 17-19) Solve It (Day 13-17) Fireworks (throughout) Bees Build It Best (Day 2-8, 18-20)

Game of Pig (Day 7-26) Orchard Hideout (throughout)

VII-5. Determine measures of central tendency. • The word “mean” will be used for the arithmetic

average • The set of numbers used to assess the range will not

be in numerical order. • Decimals up to hundredths may be used. • Decimals with different numbers of decimal digits

may be used in the same item.


• Frequency diagrams may be used. VII-6. Determine probabilities.

• Both AND and OR situations may be included.

Bees Build It Best (Day 11) Game of Pig (throughout) High Dive (Day 1-16)

Pennant Fever

VII-7. Solve problems involving direct variation. • Diagrams may be used. • Verbal descriptions of proportions may be used.

Shadows (Day 7-13, 17-19)

Game of Pig

VII-8. Solve word problems involving algebraic concepts. • Word problems will be used. • Interpretation of figures may be required. • The following content may be included:

distance/rate/time problems – money problems, which may required a system of equations – numbers (sum, difference, product, quotient) – simple age problems referring only to the present – consecutive integers – area, volume, dimension problems – quantity problems – cost problems – wage problems

Cookies (throughout) Solve It (throughout) Fireworks (throughout) Small World (Day 6-10) World of Functions (throughout)

Game of Pig (throughout) High Dive (Day 1-16)

Pennant Fever Is There Really d Difference

SEQUENCING GUIDES Suggested sequencing guides are provided for Algebra I, Geometry, and Algebra II with Trigonometry. The first page of each sequencing guide is an overall plan for the year. The subsequent pages have each course broken down by ACOS standards that will be covered during a specific time frame. Many systems have their local pacing guides that the teachers are required to follow and this document is not intended to replace those local pacing guides. This document is meant only to provide the classroom teacher with

a general plan for implementing the AMSTI program.

Suggestions for using this sequencing guide: • Closely follow this guide the first time you implement IMP.

• As you teach through the guide, make written notes of units where students did not need as much time as well as units where students became ‘bogged’ down in

a topic or unit. These notes will allow for better planning next year.

• Keep records of any changes that would make your class run more smoothly.

• Record questions that ‘get your students going’ so that you will be sure to ask them the next time you teach the unit.

• Record the actual time you spent on a unit.

• Record what you would have done differently in a prior unit in order to facilitate learning in the current unit.

Suggested Sequencing Guide for Algebra I

Unit of Instruction Course of Study Standards Addressed

Full Year Schedule

Solve It unit 1, 2, 3, 4, 5, 6, 7, 9, 10, 11 5 weeks Relations & Functions unit

Linear Equations & Inequalities unit

2, 3, 4, 7, 10, 14

4 weeks Cookies unit 2, 4, 7, 8 6 weeks

Polynomials unit Factoring & Quadratics unit Fireworks unit activities

5, 6, 9

6 weeks

Radicals Unit All About Alice unit

1, 7, 10 5 weeks

Area, Perimeter & Volume Unit 11 4 weeks The Game of Pig unit 1, 3, 7, 11, 12, 13, 14, 15 6 weeks

*Activities from the Patterns unit should be added as needed to address additional course of study standards.

Suggested Sequence of Instruction – Algebra Solve It Unit

Approximately 25 days (5 weeks)

Solve It! Unit IMP Material AHSGE Local Text

COS Standards to be addressed: Std. 1: Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots, radical form, or decimal approximations.


Solve It (Day 6, 8, 9, 18, 19) I‐1

Std. 2: Analyze linear functions from their equations, slopes and intercepts. • Finding the slope of a line from its equation or by applying the slope formula • Determining the equations of linear functions given two points, a point and the slope, table of

values, graphs, or ordered pairs • Graphing two‐variable linear equations and inequalities on the Cartesian plane

Solve It (Day 24‐26) IV‐2V‐1 V‐2 V‐3

Std. 3: Determine characteristics of a relation, including its domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs. • Finding range of a function when given its domain

Solve It (Days 9‐12, 24‐26) III‐1III‐2

Std. 4: Represent graphically common relations, including x=constant, y=constant, y = x, y = √x, y = x2, and y = │x│.*

• Identifying situations that are modeled by common relations, including x=constant, y=constant, y = x, y = √x, y = x2, and y = │x│.

Solve It (Days 9‐12, 21‐30) V‐4

Std. 5: Perform operations of addition, subtraction, and multiplication on polynomial expressions.*

• Dividing by a monomial Solve It (Day 13‐17) I‐2

I‐3

Std. 6: Factor binomials, trinomials, and other polynomials using GCF, difference of squares, perfect square trinomials, and grouping.*

Solve It (Day 13‐17) I‐4

Std. 7: Solve multi‐step equations and inequalities including linear, radical, absolute value, and literal equations.

• Writing the solution of an equation in set notation • Graphing the solution of an equation or inequality • Modeling real‐world problems by developing and solving equations and inequalities, including those

involving direct and inverse variation

Solve It (throughout) II‐1II‐4 VII‐7 VII‐8

Std. 9: Solve quadratic equations using the zero‐product property. • Approximating solutions graphically and numerically

Solve It (Day 29‐30) II‐2

Std. 10: Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane.*

• Deriving the distance, midpoint, and slope formulas

Solve It (Day 24) IV‐2

Std. 11: Solve problems algebraically that involve area and perimeter of a polygon, area and circumference of a circle, and volume and surface area of right circular cylinders or right rectangular prisms.

• Applying formulas to solve word problems

Solve It (Day 3, 13‐17) IV‐1VII‐8

*Supplementary material needed

Relations & Functions Unit Linear Equations & Inequalities Unit

Approximately 4 weeks

Relations & Functions; Linear Equations & Inequalities IMP Material AHSGE Local Text

COS Standards to be addressed: Std. 2: Analyze linear functions from their equations, slopes and intercepts.

• Finding the slope of a line from its equation or by applying the slope formula • Determining the equations of linear functions given two points, a point and the slope, table of


Patterns unit activities IV‐2V‐1 V‐1 V‐2 V‐3

Std. 3: Determine characteristics of a relation, including its domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs.


Patterns unit activities III‐1III‐2

Std. 4: Represent graphically common relations, including x=constant, y=constant, y = x, y = √x, y = x2, and y = │x│.


V‐4


• Writing the solution of an equation in set notation

• Graphing the solution of an equation or inequality • Modeling real‐world problems by developing and solving equations and inequalities, including those


II‐1II‐4 VII‐7 VII‐8

Std. 10: Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane.


IV‐2

Std. 14: Use a scatterplot and its line of best fit or specific line graph to determine the relationship existing between two sets of data, including positive, negative, or no relationship.

Note: Many of these standards were introduced in the Solve It! Unit but were not fully developed.

Cookies Unit Approximately 30 days (6 weeks)

Cookies Unit IMP Material AHSGE Local Text

COS Standards to be addressed: Std. 2: Analyze linear functions from their equations, slopes and intercepts.

• Finding the slope of a line from its equation or by applying the slope formula • Determining the equations of linear functions given two points, a point and the slope, table of


Cookies (throughout)

Std. 4: Represent graphically common relations, including x=constant, y=constant, y = x, y = √x, y = x2, and y = │x│.


Cookies (Day 6‐13)





Std. 8: Solve systems of linear equations and inequalities in two variables graphically or algebraically. • Modeling real‐world problems by developing and solving systems of linear equations and

inequalities


Polynomials Unit Factoring and Quadratics Unit Approximately 30 days (6 weeks)

Polynomials Unit IMP Material AHSGE Local Text

COS Standards to be addressed: Std. 5: Perform operations of addition, subtraction, and multiplication on polynomial expressions.

• Dividing by a monomial

I‐2 I‐3

Std. 6: Factor binomials, trinomials, and other polynomials using GCF, difference of squares, perfect square trinomials, and grouping.

Fireworks unit activities I‐4

Std. 9: Solve quadratic equations using the zero‐product property. • Approximating solutions graphically and numerically

Fireworks unit activities II‐2

Radicals Unit All About Alice Unit Approximately 5 weeks

Radicals Unit IMP Material AHSGE Local Text



All About Alice (throughout) I‐1


• Writing the solution of an equation in set notation • Graphing the solution of an equation or inequality

• Modeling real‐world problems by developing and solving equations and inequalities, including those involving direct and inverse variation

II‐1II‐4 VII‐7 VII‐8

Std. 10: Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane.


IV‐2

Area, Perimeter & Volume Unit Approximately 4 weeks

Area, Perimeter & Volume Unit IMP Material AHSGE Local Text

COS Standards to be addressed: Std. 11: Solve problems algebraically that involve area and perimeter of a polygon, area and circumference of a circle, and volume and surface area of right circular cylinders or right rectangular prisms.


IV‐4VI‐1 VII‐8

NOTE: This standard was addressed in the Solve It! Unit but not fully developed.

The Game of Pig unit Approximately 30 days (6weeks)

Game of Pig unit IMP Material AHSGE Local Text



Game of Pig (day 27)

I‐1

Std. 3: Determine characteristics of a relation, including its domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs.


Game of Pig (Day 7‐11) III‐1 III‐2




Game of Pig (Day 7‐21) II‐1 II‐4 VII‐7 VII‐8

Std. 11: Solve problems algebraically that involve area and perimeter of a polygon, area and circumference of a circle, and volume and surface area of right circular cylinders or right rectangular prisms.


Game of Pig (Day 7‐26) IV‐1 VII‐8

Std. 12: Compare various methods of data reporting, including scatterplots, stem‐and‐leaf plots, histograms, box‐and‐whisker plots, and line graphs, to make inferences or predictions.

• Determining effects of linear transformations of data • Determining effects of outliers • Evaluating the appropriateness of the design of a survey


Std. 13: Identify characteristics of a data set, including measurement or categorical and univariate or bivariate.

Game of Pig (Day 12‐21) VII‐5

Std. 14: Use a scatterplot and its line of best fit or specific line graph to determine the relationship existing between two sets of data, including positive, negative, or no relationship.


Std. 15: Estimate probabilities given data in lists or graphs. • Comparing theoretical and experimental probabilities

Game of Pig (throughout) VII‐3

Suggested Sequencing Guide for Geometry

Unit of Instruction Course of Study Standards Addressed Full Year (1) Fundamentals of Geometry – Lines,

Angles and Logic (Shadows unit)

1, 2, 3, 4, 5, 8, 9, 10, 12, 17 9 weeks

(2) Triangles – Classification, Congruency, Similarity and Trigonometry

5, 6, 7, 8, 10 9 weeks

(3) Geometric Figures – Quadrilaterals, Transformations, and Circles

(Orchard Hideout unit)

3, 4, 5, 12, 13, 15, 18 9 weeks

(4) Area & Volume – Area of Polygons & Circles, Surface Area and Volume (Do Bees

Build It Best? unit)

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17 9 weeks

Suggested Sequence of Instruction – Geometry Shadows unit First Nine Weeks

Fundamentals of Geometry – Lines, Angles & Logic IMP Material AHSGE Local

Text COS Standards to cover: Std. 1: Determine the equation of a line parallel or perpendicular to a second line through a given point.

Shadows (unit)

Std. 2: Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles.

Shadows (Day 9‐16) VII‐1

Std. 3: Verify the relationships among different classes of polygons by using their properties. • Determine the missing lengths of sides or measures of angles in similar triangles.

Shadows (Day 11)

VII‐4VII‐3

Std. 4: Determine the measure of interior and exterior angles associated with polygons. • Verifying the formulas for the measures of interior and exterior angles of polygons inductively and

deductively.

Shadows (Day 12, 14‐15) Suppl. Problem: Exterior Angles

& Polygon Angle Sums

Std. 5: Solve real‐life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes.

• Determining the equation of a circle given its center and radius*

Shadows (Day 10, 20)

Std. 8: Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using the relationships to solve problems and to establish other relationships.


Shadows (Day 9‐16) VII‐3

Std. 9: Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. • Recognizing the limitations of justifying a conclusion through inductive reasoning

Shadows (throughout)

Std. 10: Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine and tangent.

Shadows (Day 13, 16, 20, 22‐25)

Std. 12: Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons.*


Std. 17: Analyze sets of data from geometric contexts to determine what, if any, relationships exist. • Distinguishing between conclusions drawn when using deductive and statistical reasoning • Calculating probabilities arising in geometric contexts


*Supplementary material needed

Suggested Sequence of Instruction – Geometry Second Nine Weeks

Triangles – Classification, Congruency, Similarity & Trigonometry IMP Material AHSGE Local Text

COS Standards to cover: Std. 5: Solve real‐life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes. ○ Determining the equation of a circle given its center and radius*

Shadows (Day 10, 20)

Std. 6: Apply the Pythagorean theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable**

Shadows (Day 10, 20) VII‐2

Std. 7: Use the ratios of the sides of special right triangles to find lengths of missing sides.** ○ Deriving the ratios of the sides of 30‐60‐90 and 45‐45‐90 triangles.

Shadows unit

Std. 8: Deduce relationships between two triangles, including proving the congruence or similarity of the triangles from given information, using the relationships to solve other problems and to establish other relationships.**

Shadows Appendix A: Triangular

Data

VII‐3


Shadows (Day 13‐25) Patterns (Day 15‐20)

*Supplementary material needed **This Std. is addressed in Bees unit

Suggested Sequence of Instruction – Geometry Orchard Hideout unit

Third Nine Weeks

Geometric Figures – Quadrilaterals, Transformations, and Circles IMP Material AHSGE Local Text

COS Standards to cover: Std. 2: Justify theorems related to pairs of angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles.


Std. 3: Verify the relationships among different classes of polygons by using their properties** ○ Determining the missing lengths of sides or measures of angles in similar polygons

Orchard Hideout (Day 1)Patterns unit VII‐3

VII‐4

Std. 4: Determine the measure of interior and exterior angles associated with polygons ○ Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively

Patterns (Day 18‐19)

Shadows : Suppl. Problem: “Exterior Angles & Polygon Angle Sums”

Std. 5: Solve real‐life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes**

○ Determining the equation of a circle given its center and radius


Std. 6: Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable.


Std. 7: Use the ratios of the sides of special right triangles to find lengths of missing sides. • Deriving the ratios of the sides of 30‐60‐90 and 45‐45‐90 triangles.

Orchard Hideout (Day 1); Supplementary Problems




Std. 9: Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. • Recognizing the limitations of justifying a conclusion through inductive reasoning.


Std. 10: Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine, and tangent.

Orchard Hideout (Day 1)

Std. 11: Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.


Std. 12: Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons*

Orchard Hideout(throughout)

Std. 13: Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected or dilated**

Std. 15: Calculate measures of arcs and sectors of a circle from given information.* Orchard Hideout (Day 5‐14) Std. 16: Calculate surface areas and volumes of solid figures, including spheres, cones and pyramids.

• Developing formulas for surface area and volume of spheres, cones and pyramids. • Calculating specific missing dimensions of solid figures from surface area or volume


• Determining the relationship between the surface area of similar figures and volumes of similar figures

Std. 18: Construct with precision a circle graph to represent data from given tables or classroom experiments*

*Supplemental material needed **This std. addressed in Bees unit

Suggested Sequence of Instruction – Geometry Do Bees Build It Best? unit

Fourth Nine Weeks

Area & Volume – Area of Polygons & Circles, Surface Area & Volume IMP Material AHSGE Local Text COS Standards to cover: Std. 2: Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles.

Bees (Day 9)

VII‐1

Std. 3: Verify the relationships among different classes of polygons by using their properties. • Determine the missing lengths of sides or measures of angles in similar triangles.

Bees (Day 2‐10) VII‐3VII‐4

Std. 4: Determine the measure of interior and exterior angles associated with polygons. • Verifying the formulas for the measures of interior and exterior angles of polygons inductively and

deductively.

Bees (Day 2‐10)

Std. 5: Solve real‐life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes.

• Determining the equation of a circle given its center and radius

Bees (Day 12‐16)

Std. 6: Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable.

Bees (Day 12‐16) VII‐2

Std. 7. Use the ratios of the sides of special right triangles to find lengths of missing sides. • Deriving the ratios of the sides of a 30‐60‐90 and 45‐45‐90 triangles

Bees (Day 11‐16)



Bees (Day 9) VII‐3

Std. 9: Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. • Recognizing the limitations of justifying a conclusion through inductive reasoning

Bees (Day 9)


Bees (Day 8‐10, 15‐20)

Std. 11: Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics*

Bees (Day 2‐10)

Std. 13: Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated.

Bees (Day 11‐16)

Std. 14: Classify polyhedrons according to their properties, including the number of faces. • Identifying Euclidean solids

Bees (Day 21‐27)

Std. 16: Calculate surface areas and volumes of solid figures, including spheres, cones and pyramids.* • Developing formulas for surface area and volume of spheres, cones and pyramids • Calculating specific missing dimensions of solid figures from surface area or volume • Determining the relationship between surface area of similar figures and volumes of similar figures

Bees (Day 21‐27)

Std. 17: Analyze sets of data from geometric contexts to determine what, if any, relationships exist. • Distinguishing between conclusions drawn when using deductive and statistical reasoning • Calculating probabilities arising in geometric contexts

Bees (Day 11‐16)

* Supplemental material needed

Note: You will have to supplement from other sources to fully cover the following topics: • Std. 15: Calculate measures of arcs and sectors of a circle from given information

• Std. 16: Calculate surface areas and volumes of solid figures, including spheres, cones and pyramids. (Must supplement Bees for spheres, cones, and pyramids.

Suggested Sequencing Guide for Algebra II (w/ Trig)

Unit of Instruction Course of Study Standards Addressed Full Year Schedule Fireworks Unit 1, 2, 3, 4, 5, 6, 7 2.5 weeks

Linear Functions & Equations Unit 3, 7 1 week Linear Systems w/ Inequalities Unit 8 1 week

Exponential & Logarithmic Functions Unit 3, 7

2 weeks

Polynomials Unit 3, 4 1 week Operations on Functions Unit 6 1 week

Rational Functions Unit 3, 6, 7 2 weeks Trigonometry Unit (including High Dive unit)

3, 5, 7, 9, 10, 11, 12

4 weeks Pit & Pendulum unit 5, 13, 14 2.5 weeks

Probability 15 1 week

Activities from World of Functions will be used to address standards in specific units.

Suggested Sequence of Instruction – Algebra II w/ Trigonometry Fireworks unit

Fireworks Unit IMP Material Local Text

COS Standards to be addressed: Std. 1: Determine the relationships among the subsets of complex numbers.

Fireworks (Imagined Solution)

Std. 2: Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value.

Fireworks (Imagined Solution)

Std. 3: Analyze families of functions, including shifts, reflections, and dilations of y=k/x (inverse variation), y =kx (direct variation), y = x2(quadratic), y = ax(exponential), and y = logax(logarithmic).


• Identifying real‐world situations corresponding to families of function

Fireworks (quadratic functions) World of Functions

Std. 4: Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.

• Using the zero product property, completing the square, and the quadratic formula • Deriving the quadratic formula

Fireworks (throughout)

Std. 5: Identify the characteristics of quadratic functions from their roots, graphs, or equations.• Generating an equation when given its roots or graph • Graphing a function when given its equation

• Determining the maximum or minimum values of quadratic function both graphically and algebraically.

• Applying functions to real‐world problems


Std. 6: Perform operations on functions, including addition, subtraction, multiplication, division and composition.

• Determining the inverse of a function or a relation • Performing operations on polynomial and rational expressions containing variables

• Constructing graphs by analyzing their functions as sums, differences, or products


Std. 7: Solve equations, inequalities, and applied problems involving absolute values, radicals, and Fireworks (Suppl. Problems)

quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions.



Linear Functions & Equations Unit Approximately 1 week

Linear Functions & Equations IMP Material Local Text

COS Standards to be addressed: Std. 3: Analyze families of functions, including shifts, reflections, and dilations of y=k/x (inverse variation), y =kx (direct variation), y = x2(quadratic), y = ax(exponential), and y = logax(logarithmic).



World of Functions

Std. 7: Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions.

• Solving equations using laws of exponents, including rational and irrational exponents • Expressing the solution of an equation, inequality, or applied problem as a graph on a number

line or by using set or interval notation

Linear Systems w/ Inequalities Unit

Approximately 1.5 weeks

Linear Systems w/ Inequalities Unit IMP Material Local Text COS Standards to be addressed: Std. 8: Solve systems of linear equations or inequalities in two or three variables using algebraic techniques, including those involving matrices.

• Evaluating the determinant of a 2x2 or 3x3 matrix • Solving word problems involving real‐life situations

Exponential & Logarithmic Functions Unit Approximately 2 weeks

Exponential & Logarithmic Functions IMP Material Local Text




World of Functions




Polynomials Unit Approximately 1.5 weeks

Polynomials Unit IMP Material Local Text




World of Functions

Std. 4: Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.

• Using the zero product property, completing the square, and the quadratic formula

• Deriving the quadratic formula

Operations on Functions Unit Approximately 1 week

Operations on Functions IMP Material Local Text

COS Standards to be addressed: Std. 6: Perform operations on functions, including addition, subtraction, multiplication, division and composition.

• Determining the inverse of a function or a relation • Performing operations on polynomial and rational expressions containing variables • Constructing graphs by analyzing their functions as sums, differences, or products

Rational Functions unit Approximately 2 weeks

Rational Functions IMP Material Local Text




World of Functions

Std. 6: Perform operations on functions, including addition, subtraction, multiplication, division and composition.

• Determining the inverse of a function or a relation • Performing operations on polynomial and rational expressions containing variables • Constructing graphs by analyzing their functions as sums, differences, or products




Trigonometry (Including High Dive) Unit Approximately 4 weeks

Trigonometry (High Dive unit) IMP Material Local Text




World of FunctionsHigh Dive (throughout)

Std. 5: Identify the characteristics of quadratic functions from their roots, graphs, or equations.• Generating an equation when given its roots or graph • Graphing a function when given its equation • Determining the maximum or minimum values of quadratic functions both graphically and

algebraically

• Applying functions to real‐world problems

High Dive (throughout)





Std. 9: Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y= tan(bx).• Determining period an amplitude of sine, cosine, and tangent functions from graphs or basic

equations • Determining specific unit circle coordinates associated with special angles


Std. 10: Solve general triangles, mathematical problems, and real‐world applications using the Law of Sines and the Law of Cosines.

• Deriving formulas for Law of Sines and Law of Cosines • Determining area of oblique triangles


Std. 11: Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.


Std. 12: Verify simple trigonometric identities using Pythagorean and/or reciprocal identities. High Dive (Day 18‐20)

Pit & Pendulum Unit

Approximately 2 weeks

Pit & Pendulum unit IMP Material Local Text

COS Standards to be addressed: Std. 5: Identify the characteristics of quadratic functions from their roots, graphs, or equations.

• Generating an equation when given its roots or graph • Graphing a function when given its equation • Determining the maximum or minimum values of quadratic functions both graphically and

algebraically • Applying functions to real‐world problems

Pit & Pendulum (Day 21‐24)

Std. 13: Use different forms of representation to compare characteristics of data gathered from two populations.

• Evaluating the appropriateness of the design of an experimental study • Describing how sample statistics reflect values of populations parameters

Pit & Pendulum (Day 11‐19)

Std. 14: Determine an equation of linear regression from a set of data• Examining data to determine if a linear, quadratic, or exponential relationship exists and to

predict outcomes

Pit & Pendulum (Days 7‐15, 21‐26)

Note: Supplementary material must be used to cover COS Std. 15

TEXTBOOK CORRELATIONS TO THE ALABAMA COURSE OF STUDY

The goal of each mathematics teacher is to ensure that her students are

introduced to all the content standards that are required in a given course by the state of Alabama. Concepts that are not addressed by an IMP unit must be

addressed with supplemental material. Locally‐adopted textbooks can provide this supplemental material. Included in this section are Glencoe/McGraw‐Hill,

McDougald Littell, and Prentice Hall correlations.

Any lesson in a traditional textbook can be adapted to the “AMSTI method of teaching” by incorporating the following elements into the lesson:

• Students working collaboratively in groups

• Students working on long‐term, open‐ended problems

• Students using graphing calculators

• Students being assessed based on a variety of criteria

• Students writing about mathematics and the processes they are using to determine an answer

• Students making class presentations explaining the reasoning behind their solutions to problems

Glencoe/McGraw-Hill

Algebra 1 ©2003

ISBN# 0–07–825083–8

correlated to

Alabama Course of Study: Algebra I

GLENCOE/MCGRAW-HILL ALGEBRA 1 ©2003

CORRELATED TO

ALABAMA

COURSE OF STUDY: ALGEBRA I

OBJECTIVES PAGE REFERENCES Number and Operations Students will: 1. Simplify numerical expressions using properties of real numbers and order of operations,

including those involving square roots, radical form, or decimal approximations.


SE: 7, 410, 417–423, 425–430, 444–449, 450–453, 469

TWE: 7, 410, 417–423, 425–430, 444–449,

450–453, 469

Algebra 2. Analyze linear functions from their equations, slopes, and intercepts.

• Finding the slope of a line from its equation or by applying the slope formula

SE: 256–262, 269–270, 275–277, 831–832 TWE: 256–262, 269–270, 275–277, 831–832

• Determining the equations of linear functions given two points, a point and the slope, tables of values, graphs, or ordered pairs

SE: 218–223, 272–277, 280–286, 287–292 TWE: 218–223, 272–277, 280–286, 287–292

• Graphing two-variable linear equations and inequalities on the Cartesian plane

SE: 218–221, 248–249, 273–274, 352–359, 369–374, 394–398

TWE: 218–221, 248–249, 273–274, 352–

359, 369–374, 394–398

3. Determine characteristics of a relation, including its domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs.

• Finding the range of a function when

given its domain

SE: 45, 206, 209, 216, 219, 221, 223, 248, 323, 344, 443

TWE: 45, 206, 209, 216, 219, 221, 223, 248,

323, 344, 443

1


CORRELATED TO

ALABAMA


OBJECTIVES PAGE REFERENCES 4. Represent graphically common relations, including x = constant, y = constant, y = x, y =√x, y

= x2, and y = x.

• Identifying situations that are modeled by common relations, including x = constant, y = constant, y = x, y =√x, y = x2, and y = x

SE: 218–223, 226–231, 256–262, 264–267, 524–530, 533–538

TWE: 218–223, 226–231, 256–262, 264–

267, 524–530, 533–538



SE: 417–423, 465, 664, 666–667 TWE: 417–423, 465, 664, 666–667


SE: 476–478, 482, 487–488, 489–500, 501–506, 508–509, 512, 515, 518, 544, 552, 649

TWE: 476–478, 482, 487–488, 489–500,

501–506, 508–509, 512, 515, 518, 544, 552, 649

7. Solve multistep equations and inequalities including linear, radical, absolute value, and literal

equations.

• Writing the solution of an equation or inequality in set notation

SE: 212–213, 318–320, 326–328, 333–334, 339–341, 346–348

TWE: 212–213, 318–320, 326–328, 333–

334, 339–341, 346–348


SE: 218–221, 248–249, 273–274, 345–351, 352–357, 352–359, 369–374, 394–398

TWE: 218–221, 248–249, 273–274, 345–

351, 352–357, 352–359, 369–374, 394–398

2


CORRELATED TO

ALABAMA


OBJECTIVES PAGE REFERENCES • Modeling real-world problems by

developing and solving equations and inequalities, including those involving direct and inverse variation

SE: 139, 146, 157, 176, 258–260, 267, 302, 330, 341, 350, 395, 559, 563, 644

TWE: 139, 146, 157, 176, 258–260, 267,

302, 330, 341, 350, 395, 559, 563, 644


• Modeling real-world problems by

developing and solving systems of linear equations and inequalities

SE: 372, 374, 378–379, 385, 391, 395, 397 TWE: 372, 374, 378–379, 385, 391, 395, 397

9. Solve quadratic equations using the zero product property.

• Approximating solutions graphically and numerically

SE: 488–494, 495–500, 535–537 TWE: 488–494, 495–500, 535–537

Geometry 10. Calculate length, midpoint, and slope of a line segment when given coordinates of its

endpoints on the Cartesian plane.


SE: 196, 256–259, 261, 264–265, 611–615 TWE: 196, 256–259, 261, 264–265, 611–615

Measurement 11. Solve problems algebraically that involve area and perimeter of a polygon, area and

circumference of a circle, and volume and surface area of right circular cylinders or right rectangular prisms.

• Applying formulas to solve word

problems

SE: 8, 14, 34, 124–125, 183–184, 196, 256, 261, 412, 414–415, 456, 554–560, 566, 596, 611–615

TWE: 8, 14, 34, 124–125, 183–184, 196,

256, 261, 412, 414–415, 456, 554–560, 566, 596, 611–615

3


CORRELATED TO

ALABAMA


OBJECTIVES PAGE REFERENCES Data Analysis and Probability 12. Compare various methods of data reporting, including scatterplots, stem-and-leaf plots,

histograms, box-and-whisker plots, and line graphs, to make inferences or predictions.


SE: 56, 199–203, 298–300, 556–559 TWE: 56, 199–203, 298–300, 556–559


SE: 733–736, 738, 747–748, 850 TWE: 733–736, 738, 747–748, 850


SE: 52, 708–714 TWE: 52, 708–714


SE: 731–736 TWE: 731–736

14. Use a scatterplot and its line of best fit or a specific line graph to determine the relationship existing between two sets of data, including positive, negative, or no relationship.

SE: 298–307, 312, 323, 729, 857 TWE: 298–307, 312, 323, 729, 857


• Comparing theoretical and experimental probabilities

SE: 777–778, 782–784, 792, 852 TWE: 777–778, 782–784, 792, 852

4

Glencoe/McGraw-Hill

Geometry ©2004

ISBN# 0–07–829637–4

correlated to

Alabama Course of Study:

Geometry

GLENCOE/MCGRAW-HILL GEOMETRY ©2004

CORRELATED TO

ALABAMA

COURSE OF STUDY: GEOMETRY

OBJECTIVES PAGE REFERENCES Algebra Students will: 1. Determine the equation of a line parallel or

perpendicular to a second line through a given point.

SE: 146–147, 241–242 TWE: 146–147, 241–242

Geometry 2. Justify theorems related to pairs of angles,

including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles.

SE: 37–40, 107–114, 126–130 TWE: 37–40, 107–114, 126–130


• Determining the missing lengths of sides or measures of angles in similar polygons

SE: 289–296, 300–301, 308–309, 316, 318 TWE: 289–296, 300–301, 308–309, 316, 318


• Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively

SE: 404–410 TWE: 404–410

5. Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes.

• Determining the equation of a circle

given its center and radius

SE: 47, 178, 188, 193, 209–210, 250, 270, 290–292, 300–301, 310, 318, 344, 351, 358, 371–372, 379–380, 387, 405, 418, 433, 440, 537, 563, 570, 575–577, 596–597, 612, 618

TWE: 47, 178, 188, 193, 209–210, 250, 270,

290–292, 300–301, 310, 318, 344, 351, 358, 371–372, 379–380, 387, 405, 418, 433, 440, 537, 563, 570, 575–577, 596–597, 612, 618

1


CORRELATED TO

ALABAMA


OBJECTIVES PAGE REFERENCES 6. Apply the Pythagorean Theorem to solve

application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable.

SE: 28, 349, 350–356 TWE: 28, 349, 350–356


• Deriving the ratios of the sides of 30–60–90 and 45–45–90 triangles

SE: 357–363 TWE: 357–363

8. Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using them to solve problems and to establish other relationships.

• Determining the geometric mean to

find missing lengths in right triangles

SE: 192–194, 200–203, 207–210, 214–215, 298–301, 316–319, 342–344

TWE: 192–194, 200–203, 207–210, 214–

215, 298–301, 316–319, 342–344


• Recognizing the limitations of justifying a conclusion through inductive reasoning

SE: 62–64, 68–69, 76–77, 82–83, 88, 115, 255–257

TWE: 62–64, 68–69, 76–77, 82–83, 88, 115,

255–257

10. Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine, and tangent.

SE: 364–370, 371–373 TWE: 364–370, 371–373

2


CORRELATED TO

ALABAMA


OBJECTIVES PAGE REFERENCES 11. Determine the areas and perimeters of

regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.

SE: 47–49, 180, 241–244, 302, 305–306, 390, 432, 442–445, 528, 595–598, 601–603, 610–616, 617–618, 642, 732–733

TWE: 47–49, 180, 241–244, 302, 305–306,

390, 432, 442–445, 528, 595–598, 601–603, 610–616, 617–618, 642, 732–733

12. Apply distance, midpoint, and slope

formulas to solve problems and to confirm properties of polygons.

SE: 48–49, 295, 315, 415, 420–422, 442–448, 472, 488, 495, 597, 599, 603, 605–606, 618–621

TWE: 48–49, 295, 315, 415, 420–422, 442–

448, 472, 488, 495, 597, 599, 603, 605–606, 618–621

13. Identify the coordinates of the vertices of

the image of a given polygon that is translated, rotated, reflected, or dilated.

SE: 465, 467–468, 470, 472–474, 479, 481, 492, 495, 497, 600

TWE: 465, 467–468, 470, 472–474, 479,

481, 492, 495, 497, 600

14. Classify polyhedrons according to their properties, including the number of faces.


The opportunity to address this objective is available. See the following:

SE: 636–642 TWE: 636–642

Measurement 15. Calculate measures of arcs and sectors of a

circle from given information.

SE: 529–535, 536–543, 623–626 TWE: 529–535, 536–543, 623–626

3


CORRELATED TO

ALABAMA


OBJECTIVES PAGE REFERENCES


• Developing formulas for surface area and volume of spheres, cones, and pyramids

SE: 660–665, 666–669, 671–676, 696–700, 702–706

TWE: 660–665, 666–669, 671–676, 696–

700, 702–706


SE: 656, 707–713 TWE: 656, 707–713

• Determining the relationship between the surface areas of similar figures and volumes of similar figures

SE: 707–713 TWE: 707–713

Data Analysis and Probability 17. Analyze sets of data from geometric contexts to determine what, if any, relationships exist.


SE: 62–63, 82–87, 115, 117, 410 TWE: 62–63, 82–87, 115, 117, 410


SE: 20, 622–627 TWE: 20, 622–627

18. Construct with precision a circle graph to represent data from given tables or classroom experiments.

The opportunity to address this objective is available. See the following:

SE: 534 TWE: 534

4


CORRELATED TO

ALABAMA

COURSE OF STUDY: ALGEBRA II

OBJECTIVES PAGE REFERENCES Number and Operations Students will: 1. Determine the relationships among the

subsets of complex numbers.

SE: 270–275, 280, 315, 374–375 TWE: 270–275, 280, 315, 374–375


SE: 270–275, 315–316, 372, 374–375 TWE: 270–275, 315–316, 372, 374–375

3. Analyze families of functions, including shifts, reflections, and dilations of y = k/x (inverse variation), y = kx (direct variation/linear), y = x2 (quadratic), y = ax (exponential), and y = logax (logarithmic).

• Identifying the domain and range of a

relation given its graph, a table of values, or its equation, including those with restricted domains

SE: 56–61, 93–95, 99–101, 104, 181, 397–398, 416, 523, 527–528, 830–831

TWE: 56–61, 93–95, 99–101, 104, 181, 397–

398, 416, 523, 527–528, 830–831

• Identifying real-world situations corresponding to families of functions

SE: 93–94 TWE: 93–94


• Using completing the square, the zero

product property, and the quadratic formula

SE: 301–305, 306–312, 313–319, 345, 361–362, 370, 460, 841

TWE: 301–305, 306–312, 313–319, 345,

361–362, 370, 460, 841

1


CORRELATED TO

ALABAMA


OBJECTIVES PAGE REFERENCES 5. Identify the characteristics of quadratic functions from their roots, graphs, or equations.

• Writing an equation when given its roots or graph

SE: 303, 374–376 TWE: 303, 374–376


SE: 110–115, 123–127, 286–293, 294–299, 335–337, 348–349, 353–358, 395–396, 397–399, 420–423, 428–429, 435–437, 523–524, 762–768, 846–847

TWE: 110–115, 123–127, 286–293, 294–

299, 335–337, 348–349, 353–358, 395–396, 397–399, 420–423, 428–429, 435–437, 523–524, 762–768, 846–847

• Determining the nature of the solutions

of a quadratic equation

SE: 313–319, 326–329, 339 TWE: 313–319, 326–329, 339

• Determining the maximum or minimum values of quadratic functions both graphically and algebraically

SE: 288–290, 354–356, 358, 364 TWE: 288–290, 354–356, 358, 364

6. Perform operations on functions, including addition, subtraction, multiplication, division, and composition.

• Determining the inverse of a function

or a relation SE: 390–394, 399, 404–405, 521, 531,

617, 699, 749, 844, 859 TWE: 390–394, 399, 404–405, 521, 531,

617, 699, 749, 844, 859

• Performing operations on polynomial and rational expressions containing variables

SE: 390–394, 399, 404–405, 521, 531, 617, 699, 749, 844, 859

TWE: 390–394, 399, 404–405, 521, 531,

617, 699, 749, 844, 859

2


CORRELATED TO

ALABAMA


OBJECTIVES PAGE REFERENCES • Constructing graphs by analyzing their

functions as sums or differences

The opportunity to address this objective is available. See the following: SE: 383, 387 TWE: 383, 387

7. Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as exponential and logarithmic functions.

• Solving equations using laws of

exponents, including rational and irrational exponents

SE: 222–228, 257–262, 264–267, 279–280, 361–362, 526, 532, 535–536, 570, 604–607

TWE: 222–228, 257–262, 264–267, 279–

280, 361–362, 526, 532, 535–536, 570, 604–607

• Expressing the solution of an equation,

inequality, or applied problem as a graph on a number line or by using set or interval notation

SE: 35, 37, 40–41, 44, 46, 51, 829 TWE: 35, 37, 40–41, 44, 46, 51, 829

Algebra II 8. Solve systems of linear equations or inequalities in two variables using algebraic techniques,

including those involving matrices.

• Evaluating the determinant of a 2x2 or 3x3 matrix

SE: 182–188, 189–191, 212, 835 TWE: 182–188, 189–191, 212, 835

• Solving word problems involving real-life situations

This objective is addressed throughout. See, for example:

SE: 26, 72, 122, 194, 237, 319, 334, 425,

438, 459, 490, 550, 642, 670, 737, 795, 869

TWE: 26, 72, 122, 194, 237, 319, 334, 425,

438, 459, 490, 550, 642, 670, 737, 795, 869

3


CORRELATED TO

ALABAMA


OBJECTIVES PAGE REFERENCES Geometry 9. Solve coordinate geometry problems using

algebraic techniques.

SE: 175–178, 185, 390–391, 412–413, 417–418, 433–434

TWE: 175–178, 185, 390–391, 412–413,

417–418, 433–434

Data Analysis and Probability 10. Use different forms of representation to compare characteristics of data gathered from two

populations.

• Evaluating the appropriateness of the design of an experimental study

SE: 682–685 TWE: 682–685

• Describing how sample statistics reflect values of population parameters

SE: 682–685 TWE: 682–685

11. Determine an equation of linear regression from a set of data.

• Examining data to determine if a linear or quadratic relationship exists and to predict outcomes

SE: 81–87, 95, 99, 103, 598, 831 TWE: 81–87, 95, 99, 103, 598, 831

12. Calculate probabilities of events using the laws of probability.


SE: 644–647, 651–654, 658–660 TWE: 644–647, 651–654, 658–660

• Calculating conditional probability

SE: 653–656 TWE: 653–656

• Calculating probabilities of mutually exclusive events, independent events, and dependent events

SE: 632–635, 651–654, 658–659, 661, 670, 687–690, 854–855

TWE: 632–635, 651–654, 658–659, 661,

670, 687–690, 854–855

4

McDOUGAL LITTELL ALGEBRA I © 2004

CORRELATED TO

ALABAMA COURSE OF STUDY: ALGEBRA I

ALABAMA COURSE OF STUDY: MATHEMATICS

PAGE REFERENCES

Number and Operations 1. Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots, radical form, or decimal approximations.

(a) Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents

SE & TE: 10, 13, 16-22, 38, 39, 52, 54,55, 57, 58, 196, 390, 797 (a) SE & TE: 9-15, 22, 27, 28, 30, 38, 39 52, 54, 57, 58, 449-455, 456-462, 463-469, 470-476, 477, 482, 484-491, 494-496, 498-499, 516 , 553, 697, 797

Algebra 2. Analyze linear functions from their equations, slopes and intercepts.

(a) Finding the slope of a line from its equation or by applying the slope

formula (b) Determining the equations of linear

functions given two points, a point and the slope, table of values, graphs, or ordered pairs

(c) Graphing two-variable linear equations and inequalities on the Cartesian plane

SE & TE: 218-224, 226-233, 241-249, 265, 266, 267, 268, 390, 800 (a) SE & TE: 226-233, 244, 246, 247, 265, 267, 268, 390, 800 (b) SE & TE: 273, 276-278, 279-284, 285-291, 292-298, 300-306, 308-314, 322, 324-325, 327, 328-329, 339, 390, 391, 801 (c) SE & TE: 210-217, 219-220, 221, 224, 244, 247, 248-249, 264, 265, 266, 267, 332, 360-366, 385, 387, 390, 800, 802


(a) Finding the range of a function when given its domain

SE & TE: 46-42, 56, 59, 77, 256-262, 266, 267, 391, 772, 797, 800 (a) SE & TE: 46-51, 52, 56, 59, 77, 257, 259, 260, 262, 266, 267, 268

4. Represent graphically common relations, including x=constant, y=constant, y = x, y = √x, y = x2, and y = │x│.

(a) Identifying situations that are modeled by common relations, including x=constant, y=constant, y = x, y = √x, y = x2, and y = │x│.

SE & TE: 213-215, 267, 390, 800 (a) SE & TE:213-215, 267, 709


(a) Dividing by a monomial

SE & TE: 100-107, 124, 125, 127, 576-582, 548-589, 590-596, 634, 635, 637, 638, 639, 798, 806 (a) SE & TE: 684, 687, 697, 702, 703, 807


SE & TE: 603, 604-609, 610, 611-617, 618, 619-624, 625-632, 635, 636, 637, 639, 655, 806

7. Solve multi-step equations and inequalities including linear, radical, absolute value, and literal equations.

(a) Writing the solution of an equation in set notation (b) Graphing the solution of an equation or inequality (c) Modeling real-world problems by

developing and solving equations and inequalities, including those involving direct and inverse variation

SE & TE: 145-152, 154-159, 190, 191, 193, 194, 197, 340-345, 353-358, 384, 385, 387, 388, 391, 722-728, 767, 769, 770, 799, 802, 808 (a) SE & TE: 145-152 (b) SE & TE: 334-338, 346-347, 349, 355, 357, 359, 360-367, 374, 384, 385, 387, 802 (c) SE & TE:134, 135, 136, 140, 141, 142, 143, 147, 149, 150, 151, 152, 158, 160-165, 169, 170, 191, 193, 195, 197, 237, 238, 339, 343, 350, 389, 660, 703, 800


(a) Modeling real-world problems by developing and solving systems of linear equations and inequalities

SE & TE: 398-404, 405-410, 411-417, 418- 424, 426-431, 432-438, 440-442, 443, 444-445, 461, 475, 568, 773 (a) SE & TE: 400-402, 407, 409, 410, 413, 415, 417, 419, 420, 421, 422, 423, 424, 428, 430, 434, 436, 441, 443, 445, 803

9. Solve quadratic equations using the zero- product property.

(a) Approximating solutions graphically and numerically

SE & TE: 606-608, 613, 615, 616, 617, 620- 621, 623, 628, 630, 632, 625, 636, 637, 638, 773, 806 (a) SE & TE: 292-299, 318, 458, 573, 839-841

Geometry 10. Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane.

(a) Deriving the distance, midpoint, and slope formulas

SE & TE: 226-228, 230-231, 247, 265, 267, 390, 745-750, 768, 769, 770, 800, 808 (a) SE & TE: 225, 226, 745, 747

Measurement 11. Solve problems algebraically that involve area and perimeter of a polygon, area and circumference of a circle, and volume and surface area of right circular cylinders or right rectangular prisms.

(a) Applying formulas to solve word problems

SE & TE: 11, 13, 14, 21, 22, 23, 29, 174, 177, 178, 197, 569, 627, 630, 637 (a) SE & TE: 11, 13, 14, 21, 22, 29, 178, 197, 569, 627, 630, 637, 791

Data Analysis and Probability 12. Compare various methods of data reporting, including scatterplots, stem- and-leaf plots, histograms, box-and- whisker plots, and line graphs, to make inferences or predictions.

(a) Determining effects of linear transformations of data

(b) Determining effects of outliers (c) Evaluating the appropriateness of the design of a survey

SE & TE: 42, 43, 44, 45, 56, 204-205, 207, 208, 264, 368-374, 375-381, 387, 792-793 (a) SE & TE: 373, 379 (b) SE & TE: 376, 379-380 (c) SE & TE: 207, 647


SE & TE: 827-832

14. Use a scatterplot and its line of best fit or specific line graph to determine the relationship existing between two sets of data, including positive, negative, or no relationship.

SE & TE: 292-299, 306, 325, 327, 801


(a) Comparing theoretical and Experimental probabilities

SE & TE: 316-322, 326, 801 (a) SE & TE: 114-120, 124, 125, 127, 172, 568, 798

McDOUGALD LITTELL GEOMETRY © 2004

CORRELATED TO

ALABAMA COURSE OF STUDY: GEOMETRY

ALABAMA COURSE OF STUDY: MATHEMATICS

PAGE REFERENCES

Algebra 1. Determine the equation of a line parallel or perpendicular to a second line through a given point.

SE & TE: 167-178, 182-183, 185, 808

Geometry 2. Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles

SE & TE: 109-112, 113-114, 120, 135, 142, 143-144, 147, 148, 150-151, 153- 155, 156


(a) Determine the missing lengths of sides or measures of angles in similar triangles.

SE & TE: 321, 329, 330-332, 333, 337, 338- 340, 342-344, 347-349, 351, 353, 356-358, 359, 364, 366-369, 383, 385, 386, 389, 814 (a) SE & TE: 472-479, 519, 817


(a) Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively.

SE & TE: 324, 327, 661-665, 666-668, 682, 708, 711, 823 (a) SE & TE: 661, 666, 667


(a) Determining the equation of a circle given its center and radius

SE & TE: 333, 335-336, 339, 343-345, 350, 354, 357, 361, 600-601, 606, 609, 614, 619, 631, 633, 634, 664, 665 (a) SE & TE: 636-640, 652, 654, 822

6. Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable.

SE & TE: 537, 539-541, 547


(a) Deriving the ratios of the sides of a 30-60-90 and 45-45-90 triangles

SE & TE: 550-554 (a) SE & TE: 551-553 (TE) 556 (SE)


(a) Determining the geometric mean to find missing lengths in right triangles

SE & TE: 202-230, 232-235, 238-241, 250, 253-257, 480-505, 513, 517-520, 527-534, 549, 566, 582, 809-810, 818-819 (a) SE & TE: 529-534, 549, 566, 582, 819


(a) Recognizing the limitations of justifying a conclusion through inductive reasoning

SE & TE: 4-8, 33, 43, 60, 65-67, 78, 87-93, 94, 108, 110, 121, 142, 155, 193, 228, 236, 294, 329, 395, 403, 472, 497, 514, 542, 612, 628, 641, 676, 727, 750-751, 803 SE & TE: 4-9, 71, 74-78, 107, 121, 162-163

10. Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine and tangent.

SE & TE: 558-565, 566-572


SE & TE: 51-53, 55-57, 62, 65, 78, 370-379, 384, 444, 539, 669-675, 690-691, 695, 710, 726, 734, 741, 749, 804, 814, 823-824


SE & TE: 52, 66-67, 244-248, 365, 481, 483


SE & TE: 396, 399, 400, 404, 408, 414, 417, 422-423, 426, 429, 451, 507, 509, 510, 620, 635, 816, 818


(a) Identifying Euclidean solids

SE & TE: 719-726, 742, 758, 777, 825 (a) SE & TE:714-715

Measurement 15. Calculate measures of arcs and sectors of a circle from given information.

SE & TE: 603-604, 607-608, 613, 616-617, 620, 651, 683-687, 689, 692, 695- 696, 705, 709-712, 821, 824

16. Calculate surface areas and volumes of solid figures, including spheres, cones and pyramids.

(a) Developing formulas for surface area and volume of spheres, cones and pyramids (b) Calculating specific missing dimensions of solid figures from surface area or volume (c) Determining the relationship between surface area of similar figures and volumes of similar figures

SE & TE: 727-765, 772, 775-778, 825-826 (a) SE & TE: 736-737, 752-753, 759, 761 (b) SE & TE: 731, 733, 739-741, 745-747, 756, 772 (c) SE & TE: 766-771, 776-778, 826

Data Analysis & Probability 17. Analyze sets of data from geometric contexts to determine what, if any, relationships exist.

(a) Distinguishing between conclusions drawn when using deductive and statistical reasoning (b) Calculating probabilities arising in geometric contexts

SE & TE: 65, 115, 122, 184, 242, 256, 301, 315, 367, 386, 428, 472, 495, 521, 542, 548, 654, 668, 675, 712, 741, 778 (a) SE & TE: 86-95 (b) SE & TE: 699-704, 706, 710, 713


Must supplement text on this objective

McDOUGAL LITTELL ALGEBRA 2 © 2004

CORRELATED TO ALABAMA COURSE OF STUDY: ALGEBRA 2 with TRIGONOMETRY

ALABAMA COURSE OF STUDY:

MATHEMATICS PAGE

REFERENCES Number and Operations 1. Determine the relationships among the subsets of complex numbers.

SE & TE: 123


SE & TE: 5, 8-11, 12-13, 15-24, 123-129, 637

Algebra 3. Analyze families of functions, including shifts, reflections, and dilations of y=k/x (inverse variation), y =kx (direct variation), y = x2(quadratic), y = ax(exponential), and y = logax(logarithmic).

(a) Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains (b) Identifying real-world situations corresponding to families of function

SE & TE: 187-228, 239-246, 260-283, 309- 312, 314-317, 390-410 (a) SE & TE:187, 191, 194-195, 197-200, 201, 209-210, 212-216, 218, 228, 232, 234-238, 241-242, 332, 342, 347- 348, 482-483, 487, 502, 504-505, 510, 512-514 (b) SE & TE: 192-193, 198-200, 209-210, 217- 218, 227-228, 233-236, 245-246, 265, 268-270, 282, 308-319, 335- 336, 338-340, 345, 348-349, 395- 400, 407, 409-410, 486-487, 494, 496-498, 508-509, 517-519


(a) Using the zero product property, completing the square, and the quadratic formula (b) Deriving the quadratic formula

SE & TE: 151, 203, 207-208, 210, 275-283, 291, 293-307 (a) SE & TE: 8, 109, 111-122 (b) SE & TE: 112


(a) Generating an equation when given its roots or graph (b) Graphing a function when given its equation (c) Determining the maximum or minimum values of quadratic functions both graphically and algebraically (d) Applying functions to real-world problems

SE & TE: 109-122, 260-270 (a) SE & TE: 122, 224-226, 264, 266-267, 280-281, 282, 292 (b) SE & TE: 79, 81, 86, 110, 118, 212, 219- 221, 225, 260-269 (c) SE & TE: 79, 85, 110, 205, 208, 261-270 (d) SE & TE: 114-117, 119-122, 210, 228, 265, 268-270, 282, 305-306

6. Perform operations on functions, including addition, subtraction, multiplication, division and composition.

(a) Determining the inverse of a function or a relation (b) Performing operations on polynomial and rational expressions containing variables (c) Constructing graphs by analyzing their functions as sums, differences, or products

SE & TE: 229-236 (a) SE & TE:237-246 (b) SE & TE: 25-32, 42-50, 55-56 (c) SE & TE: 234

7. Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions.

(a) Solving equations using laws of exponents, including rational and irrational exponents (b) Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation

SE & TE: 109-121, 127-129, 132, 134, 137- 139, 143-150, 152, 154, 203, 207, 210, 264, 267, 269, 402, 417-427, 429-440, 558-567, 571, 573, 575, 579, 581-583 (a) SE & TE: 419 (b) SE & TE: 3, 5, 9, 141, 143-150, 152, 154, 158-160

8. Solve systems of linear equations or inequalities in two or three variables using algebraic techniques, including those involving matrices.

(a) Evaluating the determinant of a 2x2 or 3x3 matrix (b) Solving word problems involving real- life situations

SE & TE: 664-682, 687-710, 735-746, 778- 780, 787, 789 (a) SE & TE: 770-771, 773, 775-777 (b) SE & TE: 666, 669-670, 672-674, 681-682, 684-686, 693-694, 696-698, 715- 716, 708-710, 745-746

Geometry 9. Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y= tan(bx).

(a) Determining period an amplitude of sine, cosine, and tangent functions from graphs or basic equations (b) Determining specific unit circle coordinates associated with special angles

SE & TE: 488-491, 495-496, 499-500, 506 (a) SE & TE: 483, 490-500, 523-525, 529 (b) SE & TE: 485

10. Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines.

(a) Deriving formulas for Law of Sines and Law of Cosines (b) Determining area of oblique triangles

SE & TE: 598-601, 603-609, 611-613 (a) SE & TE: 656-657 (b) SE & TE: 602, 604, 606, 610-611, 613-614


SE & TE: 465-466, 468, 477, 482-486, 543

12. Verify simple trigonometric identities using Pythagorean and/or reciprocal identities.

SE & TE: 550-556

Data Analysis and Probability 13. Use different forms of representation to compare characteristics of data gathered from two populations.

(a) Evaluating the appropriateness of the design of an experimental study (b) Describing how sample statistics reflect values of populations parameters

SE & TE: 59, 65-67, 87, 104, 149, 182, 185, 218 (a) Must supplement text book (b) Must supplement textbook

14. Determine an equation of linear regression from a set of data

(a) Examining data to determine if a linear, quadratic, or exponential relationship

exists and to predict outcomes

SE & TE: 185, 200, 235, 245, 308, 423 (a) SE & TE: 200, 235, 245, 269-270, 308, 399, 409

15. Calculate probabilities of events using the laws of probability

(a) Using permutations and combinations to calculate probabilities (b) Calculating conditional probability (c) Calculating probabilities of mutually exclusive events, independent events, and dependent events

SE & TE: 861-872 (a) SE & TE: 852-859 (b) 864-865, 868-872 (c) 864-866, 868-872

PRENTICE HALL MATHEMATICS

ALGEBRA I © 2004

CORRELATED TO ALABAMA COURSE OF STUDY: ALGEBRA I


MATHEMATICS SECTIONS WHERE TAUGHT

Number and Operations 1. Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots, radical form, or decimal approximations.


1-2: Exponents and Order of Operations 1-4: Adding Real Numbers 1-5: Subtracting Real Numbers 1-6: Multiplying and Dividing Real Numbers 1-7: The Distributive Property 8-1: Zero & Negative Exponents 8-2: Scientific Notation 8-3: Multiplication Properties of Exponents 8-4: More Properties of Exponents 8-5: Division Properties of Exponents

Algebra 2. Analyze linear functions from their equations, slopes and intercepts.

• Finding the slope of a line from its equation or by applying the slope

formula • Determining the equations of linear

functions given two points, a point and the slope, table of values, graphs, or ordered pairs

• Graphing two-variable linear equations and inequalities on the Cartesian plane

5-1: Relating Graphs to Events 5-2: Relations and Functions 5-3: Functions Rules, Tables & Graphs 5-4: Writing a Function Rule 5-5: Direct Variation 5-6: Describing Number Patterns 6-1: Rate of Change and Slope 6-2: Slope-Intercept Form 6-3: Standard Form of a Line 6-4: Point-Slope Form and Writing Linear Equations 6-5: parallel and Perpendicular Lines



5-2: Relations and Functions 5-3: Functions Rules 5-4: Writing a Functions Rule 5-6: Describing Number Patterns

4. Represent graphically common relations, including x=constant, y=constant, y = x, y = √x, y = x2, and y = │x│.


5-2: Relations and Functions 5-3: Function Rules, Tables & Graphs 5-4: Writing a Functions Rule



9-1: Adding & Subtracting Polynomials 9-2: Multiplying & Factoring 9-3: Multiplying Binomials 9-4: Multiplying Special Cases


9-5: Factoring Trinomials of the Type x2 + bx + c 9-6: Factoring Trinomials of the Type ax2 + bx + c 9-7: Factoring Special Cases 9-8: Factoring by Grouping

7. Solve multi-step equations and inequalities including linear, radical, absolute value, and literal equations.

• Writing the solution of an equation in set notation


• Modeling real-world problems by developing and solving equations and inequalities, including those involving direct and inverse variation

2-2: Solving Two-Step Equations 2-3: Solving Multi-Step Equations 2-4: Equations Having Variables on Both Sides 2-5: Equations & Problem Solving 3-4: Solving Multi-Step Inequalities 3-6: Absolute Value Equations & Inequalities 4-3: Proportions and Percent Equations 6-7: Graphing Absolute Value Equations 11-5: Solving Radical Equations 12-7: Solving Rational Equations


• Modeling real-world problems by developing and solving systems of linear equations and inequalities

7-1: Solving Systems By Graphing 7-2: Solving Systems Using Subtraction 7-3: Solving Systems Using Elimination 7-4: Applications of Linear Systems 7-5: Linear Inequalities 7-6: Systems of Linear Inequalities

9. Solve quadratic equations using the zero- product property.

• Approximating solutions graphically and numerically

10-4: Solving Quadratic Equations 10-5: Factoring to Solve Quadratic Equations 10-6: Completing the Square 10-7: Quadratic Formula 10-8: Using the Discriminant 10-9: Choosing a Model

Geometry 10. Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane.


6-1: Rate of Change and Slope 6-2: Slope-Intercept Form 6-3: Standard Form of a Line 6-4: Point Slope Form and Writing Linear Equations 6-5: Parallel & Perpendicular Lines

Measurement 11. Solve problems algebraically that involve area and perimeter of a polygon, area and circumference of a circle, and volume and surface area of right circular cylinders or right rectangular prisms.


Problems are found on pages: 9, 14, 15, 51, 63, 70, 75, 79, 85, 92, 97, 98, 100, 103, 108, 109, 111, 114, 126, 144, 156, 158, 165, 166, 179, 190, 193, 194, 215, 250, 251, 265, 288, 296, 302, 316, 322, 349, 350, 366, 367, 375, 382, 388, 408, 409, 414, 428, 459, 460, 464, 468, 470, 471, 477, 492, 494, 500, 504, 505, 506, 515, 532, 533, 535, 538, 539, 545, 551, 571, 572, 589, 593, 594, 595, 596, 604, 610, 632, 640, 660, 663, 664, 690, 699

Data Analysis and Probability 12. Compare various methods of data reporting, including scatterplots, stem- and-leaf plots, histograms, box-and- whisker plots, and line graphs, to make inferences or predictions.


• Determining effects of outliers • Evaluating the appropriateness of

the design of a survey

1-9: Graphing Data on the Coordinate Plane 2-7: Using Measures of Central Tendency 5-1: Relating Graphs to Events 5-5: Direct Variation 6-6: Scatter Plots and Equations of Lines


1-9: Graphing Data on the Coordinate Plane 2-7: Using Measures of Central Tendency 5-1: Relating Graphs to Events

14. Use a scatterplot and its line of best fit or specific line graph to determine the relationship existing between two sets of data, including positive, negative, or no relationship.

1-9: Graphing Data on the Coordinate Plane 6-6: Scatter Plots and Equations of Lines


• Comparing theoretical and Experimental probabilities

4-5: Applying Ratios to Probability 4-6: Probability of Compound Events Real-World Snapshots: Applying Probability


GEOMETRY 2004

CORRELATED TO ALABAMA COURSE OF STUDY: GEOMETRY



Algebra 1. Determine the equation of a line parallel or perpendicular to a second line through a given point.

3-6: Slopes of Parallel & Perpendicular Lines

Geometry 2. Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles

2-5: Proving Angles Congruent


• Determine the missing lengths of sides or measures of angles in similar triangles.

6-1: Classifying Quadrilaterals 6-2: Properties of Parallelograms 6-3: Proving That a Quadrilateral is a Parallelogram 6-4: Special Parallelograms 6-5: Trapezoids and Kites 6-6: Placing Figures in the Coordinate Plane 8-2: Similar Polygons 8-3: Proving Triangles Similar 8-4: Similarity in Right Triangles 8-6: perimeter and Areas of Similar Figures


• Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively.

3-3: Parallel Lines & the Triangle Angle-Sum Theorem 3-4: The Polygon Angle-Sum Theorems


• Determining the equation of a circle given its center and radius

5-1: Mid-segments of Triangles 5-2: Bisectors in Triangles 5-3: Concurrent Lines, Medians, & Altitudes 5-4: Inverses, Contrapositives, and Indirect Reasoning 5-5: Inequalities in Triangles 6-1: Classifying Quadrilaterals 6-2: Properties of Parallelograms 6-3: Proving That a Quadrilateral is a Parallelogram 6-4: Special Parallelograms 6-5: Trapezoids and Kites 6-6: Placing Figures in the Coordinate Plane 7-6: Circles and Arcs 7-7: Areas of Circles and Sectors

6. Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable.

7-2: The Pythagorean Theorem and Its Converse


• Deriving the ratios of the sides of a 30-60-90 and 45-45-90 triangles

7-3: Special Right Triangles



4-1: Congruent Figures 4-2: Triangle Congruence by SSS and SAS 4-3: Triangle Congruence by ASA and AAS 4-4: Using Congruent Triangles 4-5: Isosceles and Equilateral Triangles 4-6: Congruence in Right Triangles 4-7: Using Corresponding Parts of Congruent Triangles


• Recognizing the limitations of justifying a conclusion through inductive reasoning

2-1: Conditional Statements 2-2: Biconditionals and Definitions 2-4: Reasoning in Algebra 2-5: Proving Angles Congruent

10. Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine and tangent.

9-1: The Tangent Ratio 9-2: Sine and Cosine Ratios


1-7: Perimeter, Circumference & Area 7-1: Areas of Parallelograms & Triangles 7-2: The Pythagorean Theorem & Its Converse 7-3: Special Right Triangles 7-4: Areas of Trapezoids, Rhombuses & Kites 7-5: Areas of Regular Polygons 7-6: Circles and Arcs 7-7: Areas of Circles and Sectors 8-6: Perimeter and Areas of Similar Figures


1-4: Measuring Segments and Angles 1-6: The Coordinate Plane 3-6: Slopes of Parallel & Perpendicular Lines Distance Formula: pp. 63, 244, 362, 615, 629, 727 Midpoint Formula: pp. 333 Slope Formula: pp. 151, 154


12-1: Reflections 12-2: Translations 12-3: Rotations 12-4: Compositions of Reflections 12-5: Symmetry 12-6: Tessellations 12-7: Dilations



10-1: Space Figures and Nets 10-2: Space Figures and Drawings

Measurement 15. Calculate measures of arcs and sectors of a circle from given information.

7-6: Circles and Arcs 7-7: Areas of Circles & Sectors 11-2: Chords and Arcs

16. Calculate surface areas and volumes of solid figures, including spheres, cones and pyramids.

• Developing formulas for surface area and volume of spheres, cones and pyramids


• Determining the relationship between surface area of similar figures and volumes of similar figures

10-1: Space Figures and Nets 10-2: Space Figures and Drawings 10-3: Surface Areas of Prisms and Cylinders 10-4: Surface Areas of Pyramids and Cones 10-5: Volumes of Prisms and Cylinders 10-6: Volumes of Pyramids and Cones 10-7: Surface Areas and Volumes of Spheres 10-8: Areas and Volumes of Similar Solids

Data Analysis & Probability 17. Analyze sets of data from geometric contexts to determine what, if any, relationships exist.



7-8: Geometric Probability


7-6: Circles and Arcs


ALGEBRA 2 © 2004

CORRELATED TO ALABAMA COURSE OF STUDY: ALGEBRA 2 with TRIGONOMETRY



Number and Operations 1. Determine the relationships among the subsets of complex numbers.

5-6: Complex Numbers


5-6: Complex Numbers

Algebra 3. Analyze families of functions, including shifts, reflections, and dilations of y=k/x (inverse variation), y =kx (direct variation), y = x2(quadratic), y = ax(exponential), and y = logax(logarithmic).


• Identifying real-world situations corresponding to families of function

2-1: Relations and Functions 2-5: Absolute Value Functions and Graphs 2-6: Vertical & Horizontal Translations 5-1: Modeling Data with Quadratic Functions 5-2: Properties of Parabolas 5-3: Translating Parabolas 7-8: Graphing Radical Functions 8-1: Exploring Exponential Models 8-2: Properties of Exponential Functions 8-3: Logarithmic Functions as Inverses 9-2: Graphing Inverse Variations 9-3: Rational Functions & Their Graphs 13-7: Translating Sine and Cosine Functions


• Using the zero product property, completing the square, and the quadratic formula

• Deriving the quadratic formula

5-5: Quadratic Equations 5-7: Completing the Square 5-8: The Quadratic Formula 6-2: Polynomials and Linear Factors 6-4: Solving Polynomial Equations 6-5: Theorems About Roots of Polynomial Equations 6-6: The Fundamental Theorem of Algebra 9-3: Rational Functions & Their Graphs 9-6: Solving Rational Equations


• Generating an equation when given its roots or graph


• Determining the maximum or minimum values of quadratic functions both graphically and algebraically

• Applying functions to real-world problems

5-1: Modeling Data with Quadratic Functions 5-2: Properties of Parabolas 5-3: Translating Parabolas 5-7: Completing the Square

6. Perform operations on functions, including addition, subtraction, multiplication, division and composition.

• Determining the inverse of a function or a relation

• Performing operations on polynomial and rational expressions containing variables

• Constructing graphs by analyzing their functions as sums, differences, or products

2-6: Vertical & Horizontal Translations 5-3: Translating Parabolas 6-3: Dividing Polynomials 7-6: Function Operations 7-7: Inverse Relations and Functions 8-2:Properties of Exponential Functions 8-3: Logarithmic Functions as Inverses 9-2: Graphing Inverse Variations 9-4: Rational Expressions 9-5: Adding & Subtracting Rational Expressions

7. Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions.



1-4: Solving Inequalities 1-5: Absolute Value Equations & Inequalities 2-7: Two-Variable Inequalities 5-5: Quadratic Equations 5-6: Complex Numbers 5-7: Completing the Square 5-8: The Quadratic Formula 7-5: Solving Radical Equations 8-4: Properties of Real Numbers 8-5: Exponential and Logarithmic Functions 8-6: Natural Logarithms 14-2: Solving Trigonometric Equations Using Inverses

8. Solve systems of linear equations or inequalities in two or three variables using algebraic techniques, including those involving matrices.

• Evaluating the determinant of a 2x2 or 3x3 matrix

• Solving word problems involving real-life situations

3-2: Solving Systems Algebraically 3-2: Systems of Inequalities 3-4: Linear Programming 3-6: Systems with Three Variables 4-5: 2x2 Matrices, Determinants & Inverses 4-6: 3x3 Matrices, Determinants & Inverses 4-7: Inverse Matrices and Systems 4-8: Augmented Matrices and Systems

Geometry 9. Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y= tan(bx).

• Determining period an amplitude of sine, cosine, and tangent functions from graphs or basic equations


13-2: Angles & the Unit Circle 13-4: The Sine Functions 13-5: The Cosine Function 13-6: The Tangent Function 13-7: Translating Sine and Cosine Functions

10. Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines.

• Deriving formulas for Law of Sines and Law of Cosines

• Determining area of oblique triangles

14-3: Right Triangles and Trigonometric Ratios 14-4: Area and the Law of Sines 14-5: The Law of Cosines


13-2: Angles and the Unit Circle 13-8: Reciprocal Trigonometric Functions 14-3: Right Triangles and Trigonometric Ratios

12. Verify simple trigonometric identities using Pythagorean and/or reciprocal identities.

13-6: The Tangent Function 13-7: Translating Sine and Cosine Functions 14-4: Trigonometric Identities

Data Analysis and Probability 13. Use different forms of representation to compare characteristics of data gathered from two populations.

• Evaluating the appropriateness of the design of an experimental study

• Describing how sample statistics reflect values of populations parameters

12-5: Working with Samples

14. Determine an equation of linear regression from a set of data

• Examining data to determine if a linear, quadratic, or exponential relationship exists and to predict outcomes

2-4: Using Linear Models 6-1: Polynomial Functions

15. Calculate probabilities of events using the laws of probability


• Calculating conditional probability • Calculating probabilities of mutually

exclusive events, independent events, and dependent events

1-6: Probability 6-7: Permutations and Combinations 9-7: Probability of Multiple Events 12-1: Probability Distributions 12-2: Conditional Probability

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