of Study Correlations IMP Units - Wikispaces CIG (2009).pdf... · with IMP Units Course of Study...
Transcript of 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)
Meadows or Malls (Days 3‐4, 18, 19) Shadows (Days 13‐
14) High Dive (Day 23)
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)
Overland Trail (Days 11‐25)
Meadows or Malls (Days 3‐4, 18, 19) Shadows (Days 13‐
14) High Dive (Day 23)
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)
Meadows or Malls (Days 3‐4, 18, 19) Shadows (Days 13‐
14) High Dive (Day 23)
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)
Meadows or Malls (Days 3‐4, 18, 19) Shadows (Days 13‐
14) High Dive (Day 23)
ALEX
9. Solve quadratic equations using the zero product property.• Approximating solutions of quadratic equations
graphically and numerically
Fireworks (throughout)Solve It (introduced)
Overland Trail (Days 11‐25)
Meadows or Malls (Days 3‐4, 18, 19) Shadows (Days 13‐
14) High Dive (Day 23)
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)
Bees Build It Best (Day 12‐16)
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)
Bees Build It Best (Day 12‐16)
Orchard Hideout (Day 5‐14, 19)
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)
Orchard Hideout (Day 1, 3, 10)
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.
Bees Build It Best (Day 11‐16)
World of Functions As the Cube Turns
ALEX
14. Classify polyhedrons according to properties, including the number of faces.
• Identifying Euclidean solids
Bees Build It Best (Day 21‐27)
Orchard Hideout (Day 1) ALEX
15. Calculate measures of arcs and sectors of a circle from given information.
Orchard Hideout (Day 5‐14)
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
Bees Build It Best (Day 21‐27)
Suppl. Problems (Finding the Best Box, Another
Best Box, From Polygons to Prisms)
Orchard Hideout (Day 5‐14)
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)
High Dive (throughout) Meadows and Malls (Days 10‐12, 20, 27‐33)
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
World of Functions (throughout) Fireworks
(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
World of Functions (throughout) Fireworks
(throughout)
High Dive (throughout) Meadows and Malls (Days 10‐12, 20, 27‐33)
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
World of Functions (throughout)
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
World of Functions (throughout)
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
World of Functions (throughout)
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)
Game of Pig (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.
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.
• Finding the range of a function when given its domain
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.
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
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.
• Determining effects of linear transformations of data
• Determining effects of outliers
• Evaluating the appropriateness of the design of a survey
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.
13. Identify characteristics of a data set, including measurement or categorical and univariate or bivariate.
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.
15. Estimate probabilities given data in lists or graphs.
• 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
*Alabama Learning Exchange http://alex.state.al.us
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.
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.
• Determining the geometric mean to find missing lengths in right triangles
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.
12. Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons.
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.
16. Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids.
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
• 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
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.
• Distinguishing between conclusions drawn when using deductive and statistical reasoning
• 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
*Alabama Learning Exchange http://alex.state.al.us
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
• Determining specific unit circle coordinates associated with special angles
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
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)
Orchard Hideout (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)
Orchard Hideout (throughout)
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)
Orchard Hideout (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.
Game of Pig (throughout)
• 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.
• Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents
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
values, graphs, or ordered pairs • Graphing two‐variable linear equations and inequalities on the Cartesian plane
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.
• Finding the range of a function when given its domain
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│.
• Identifying situations that are modeled by common relations, including x=constant, y=constant, y = x, y = √x, y = x2, and y = │x│.
V‐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
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.
• Deriving the distance, midpoint, and slope formulas
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
values, graphs, or ordered pairs • Graphing two‐variable linear equations and inequalities on the Cartesian plane
Cookies (throughout)
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│.
Cookies (Day 6‐13)
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
Cookies (throughout)
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
Cookies (throughout)
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
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.
• Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents
All About Alice (throughout) I‐1
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
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.
• Deriving the distance, midpoint, and slope formulas
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.
• Applying formulas to solve word problems
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
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.
• Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents
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.
• Finding the range of a function when given its domain
Game of Pig (Day 7‐11) III‐1 III‐2
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
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.
• Applying formulas to solve word problems
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
Game of Pig (throughout)
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.
Game of Pig (throughout)
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.
• Determining the geometric mean to find missing lengths in right triangles
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.*
Shadows (throughout)
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
Shadows (throughout)
*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
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 13‐25) 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.
Orchard Hideout (Day 3, 10)
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
Orchard Hideout (Day 5‐14, 19)
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.
Orchard Hideout (Day 5‐14, 19)
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. 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.
• Determining the geometric mean to find missing lengths in right triangles
Orchard Hideout (Day 1, 3, 10)
Std. 9: Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. • Recognizing the limitations of justifying a conclusion through inductive reasoning.
Orchard Hideout (Day 3, 10)
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.
Orchard Hideout (Day 5‐14)
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
Orchard Hideout (Day 5‐14)
• 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)
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.
• Determining the geometric mean to find missing lengths in right triangles
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)
Std. 10: Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine and tangent.
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 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 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
Fireworks (throughout)
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
Fireworks (throughout)
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.
• 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 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).
• 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 function
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
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).
• 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 function
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
Polynomials Unit Approximately 1.5 weeks
Polynomials Unit 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).
• 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 function
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
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).
• 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 function
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
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
Trigonometry (Including High Dive) Unit Approximately 4 weeks
Trigonometry (High Dive unit) 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).
• 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 function
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. 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
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
High Dive (throughout)
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
High Dive (Day 1‐20)
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.
High Dive (Day 1‐20)
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.
• Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents
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
GLENCOE/MCGRAW-HILL ALGEBRA 1 ©2003
CORRELATED TO
ALABAMA
COURSE OF STUDY: ALGEBRA I
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
5. Perform operations of addition, subtraction, and multiplication on polynomial expressions.
• Dividing by a monomial
SE: 417–423, 465, 664, 666–667 TWE: 417–423, 465, 664, 666–667
6. Factor binomials, trinomials, and other polynomials using GCF, difference of squares, perfect square trinomials, and grouping.
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
• Graphing the solution of an equation or inequality
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
GLENCOE/MCGRAW-HILL ALGEBRA 1 ©2003
CORRELATED TO
ALABAMA
COURSE OF STUDY: ALGEBRA I
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
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
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.
• Deriving the distance, midpoint, and slope formulas
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
GLENCOE/MCGRAW-HILL ALGEBRA 1 ©2003
CORRELATED TO
ALABAMA
COURSE OF STUDY: ALGEBRA I
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.
• Determining effects of linear transformations of data
SE: 56, 199–203, 298–300, 556–559 TWE: 56, 199–203, 298–300, 556–559
• Determining effects of outliers
SE: 733–736, 738, 747–748, 850 TWE: 733–736, 738, 747–748, 850
• Evaluating the appropriateness of the design of a survey
SE: 52, 708–714 TWE: 52, 708–714
13. Identify characteristics of a data set, including measurement or categorical and univariate or bivariate.
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
15. Estimate probabilities given data in lists or graphs.
• 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
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
SE: 289–296, 300–301, 308–309, 316, 318 TWE: 289–296, 300–301, 308–309, 316, 318
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
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
GLENCOE/MCGRAW-HILL GEOMETRY ©2004
CORRELATED TO
ALABAMA
COURSE OF STUDY: GEOMETRY
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
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
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
9. Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions.
• 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
GLENCOE/MCGRAW-HILL GEOMETRY ©2004
CORRELATED TO
ALABAMA
COURSE OF STUDY: GEOMETRY
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.
• Identifying Euclidean solids
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
GLENCOE/MCGRAW-HILL GEOMETRY ©2004
CORRELATED TO
ALABAMA
COURSE OF STUDY: GEOMETRY
OBJECTIVES PAGE REFERENCES
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
SE: 660–665, 666–669, 671–676, 696–700, 702–706
TWE: 660–665, 666–669, 671–676, 696–
700, 702–706
• Calculating specific missing dimensions of solid figures from surface area or volume
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.
• Distinguishing between conclusions drawn when using deductive and statistical reasoning
SE: 62–63, 82–87, 115, 117, 410 TWE: 62–63, 82–87, 115, 117, 410
• Calculating probabilities arising in geometric contexts
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
Glencoe/McGraw-Hill
Algebra 2 ©2003
ISBN# 0–02–827999–2
correlated to
Alabama Course of Study: Algebra II
GLENCOE/MCGRAW-HILL ALGEBRA 2 ©2003
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
2. Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value.
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
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
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
GLENCOE/MCGRAW-HILL ALGEBRA 2 ©2003
CORRELATED TO
ALABAMA
COURSE OF STUDY: ALGEBRA II
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
• Graphing a function when given its equation
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
GLENCOE/MCGRAW-HILL ALGEBRA 2 ©2003
CORRELATED TO
ALABAMA
COURSE OF STUDY: ALGEBRA II
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
GLENCOE/MCGRAW-HILL ALGEBRA 2 ©2003
CORRELATED TO
ALABAMA
COURSE OF STUDY: ALGEBRA II
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.
• Using permutations and combinations to calculate probabilities
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
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.
(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
5. Perform operations of addition, subtraction, and multiplication on polynomial expressions.
(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
6. Factor binomials, trinomials, and other polynomials using GCF, difference of squares, perfect square trinomials, and grouping.
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
8. Solve systems of linear equations and inequalities in two variables graphically or algebraically.
(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
13. Identify characteristics of a data set, including measurement or categorical and univariate or bivariate.
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
15. Estimate probabilities given data in lists or graphs.
(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
3. Verify the relationships among different classes of polygons by using their properties.
(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
4. Determine the measure of interior and exterior angles associated with polygons.
(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
5. Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes.
(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
7. Use the ratios of the sides of special right triangles to find lengths of missing sides.
(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)
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.
(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
9. Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions.
(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
11. Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.
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
12. Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons.
SE & TE: 52, 66-67, 244-248, 365, 481, 483
13. Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated.
SE & TE: 396, 399, 400, 404, 408, 414, 417, 422-423, 426, 429, 451, 507, 509, 510, 620, 635, 816, 818
14. Classify polyhedrons according to their properties, including the number of faces.
(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
18. Construct with precision a circle graph to represent data from given tables or classroom experiments.
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
2. Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value.
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
4. Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.
(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
5. Identify the characteristics of quadratic functions from their roots, graphs, or equations.
(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
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.
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
ALABAMA COURSE OF STUDY:
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.
• Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents
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
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
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│.
• Identifying situations that are modeled by 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
5. Perform operations of addition, subtraction, and multiplication on polynomial expressions.
• Dividing by a monomial
9-1: Adding & Subtracting Polynomials 9-2: Multiplying & Factoring 9-3: Multiplying Binomials 9-4: Multiplying Special Cases
6. Factor binomials, trinomials, and other polynomials using GCF, difference of squares, perfect square trinomials, and grouping.
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
• 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
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
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
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.
• Deriving the distance, midpoint, and slope formulas
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.
• Applying formulas to solve word problems
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 linear transformations of data
• 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
13. Identify characteristics of a data set, including measurement or categorical and univariate or bivariate.
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
15. Estimate probabilities given data in lists or graphs.
• Comparing theoretical and Experimental probabilities
4-5: Applying Ratios to Probability 4-6: Probability of Compound Events Real-World Snapshots: Applying Probability
PRENTICE HALL MATHEMATICS
GEOMETRY 2004
CORRELATED TO ALABAMA COURSE OF STUDY: GEOMETRY
ALABAMA COURSE OF STUDY:
MATHEMATICS SECTIONS WHERE TAUGHT
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
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.
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
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.
3-3: Parallel Lines & the Triangle Angle-Sum Theorem 3-4: The Polygon Angle-Sum Theorems
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
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
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
7-3: Special Right Triangles
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.
• Determining the geometric mean to find missing lengths in 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
9. Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions.
• 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
11. Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.
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
12. Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons.
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
13. Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated.
12-1: Reflections 12-2: Translations 12-3: Rotations 12-4: Compositions of Reflections 12-5: Symmetry 12-6: Tessellations 12-7: Dilations
14. Classify polyhedrons according to their properties, including the number of faces.
• Identifying Euclidean solids
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
• 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
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.
• Distinguishing between conclusions drawn when using deductive and statistical reasoning
• Calculating probabilities arising in geometric contexts
7-8: Geometric Probability
18. Construct with precision a circle graph to represent data from given tables or classroom experiments.
7-6: Circles and Arcs
PRENTICE HALL MATHEMATICS
ALGEBRA 2 © 2004
CORRELATED TO ALABAMA COURSE OF STUDY: ALGEBRA 2 with TRIGONOMETRY
ALABAMA COURSE OF STUDY:
MATHEMATICS SECTIONS WHERE TAUGHT
Number and Operations 1. Determine the relationships among the subsets of complex numbers.
5-6: Complex Numbers
2. Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value.
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 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 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
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
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
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
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.
• 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
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
• Determining specific unit circle coordinates associated with special angles
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
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.
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
• Using permutations and combinations to calculate probabilities
• 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