Scope and Sequence Algebra I 7th Grade

58

ALGEBRA I COURSE SCOPE AND SEQUENCE First Six Weeks GRADING PERIOD TEKS 8.2 Page 12 c1(C) Page 13

b1(C) Page 14 b1(D) Page 15 b3(A) Page 16 b4(B) Page 17

STUDENT EXPECTATIONS

First 6 Weeks

The student selects and uses appropriate operations to solve problems and justify solutions. The student translates among and uses algebraic, tabular, graphical, or verbal descriptions of linear functions. The student describes functional relationships for given problem situations and writes equations or inequalities to answer questions arising from the situations. The student represents relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, and equations and inequalities. The student uses symbols to represent unknowns and variables. The student uses the commutative, associative, and distributive properties to simplify algebraic expressions.

Introduced

Maintained

Resource Key PH – Prentice Hall PH-TE –Prentice Hall Teacher Ed. Sketchpad – Geometers Sketchpad Software AR – TEXTEAMS Algebraic Reasoning NR - TEXTEAMS Numeric Reasoning

59

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

ALGEBRA I COURSE SCOPE AND SEQUENCE Second Six Weeks

GRADING PERIOD TEKS

STUDENT EXPECTATIONS

b1(A)

The student describes independent and dependent quantities in functional relationships. The student gathers and records data, or uses data sets, to determine functional (systematic) relationships between quantities.

Page 19

b1(B) Page 20 b1(E) Page 21 b2(B) Page 22 b2(D) Page 23

c3(A) Page 24 c3(B) Page 26 c3(C) Page 27

8.9A Page 28

First 6 Weeks

The student interprets and makes inferences from functional relationships. For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations. In solving problems the student collects and organizes data, makes and interprets scatterplots, and models, predicts, and makes decisions and critical judgments. The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems. The student investigates methods for solving linear equations and inequalities using concrete models, graphs, and the properties of inequalities of equality, selects a method, and solves the equations and inequalities. For given contexts, the student interprets and determines the reasonableness of solutions to linear equations and inequalities. The student uses the Pythagorean Theorem to solve realworld life problems.

Introduced

Maintained

60

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

ALGEBRA I COURSE SCOPE AND SEQUENCE Third Six Weeks GRADING PERIOD TEKS

c2(G) Page 29 b2(A) Page 30 b2(C) Page 31 b3(B) Page 32 c1(A) Page 33 c1(B) Page 34 c2(A) Page 35 c2(B) Page 36 c2(C) Page 37 c2(D) Page 38 c2(E) Page 39 c2(F) Page 40

STUDENT EXPECTATIONS

First 6 Weeks

The student relates direct variation to linear functions and solves problems involving proportional change. The student identifies and sketches the general forms of linear (y = x and y = x + b) functions. The student interprets situations in terms of given graphs or creates situations that fit given graphs. Given situations, the student looks for patterns and represents generalizations algebraically. The student determines whether or not given situations can be represented by linear functions. The student determines the domain and range values for which linear functions make sense for given situations. The student develops the concept of slopes as rate of change and determines slopes from graphs, tables, and algebraic representations. The student interprets the meaning of slope and intercepts in situations using data, symbolic representations, or graphs. The student investigates, describes, and predicts the effects of change in m and b on the graph of y=mx + b. The student graphs and writes equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept. The student determines the intercepts of linear functions from graphs, tables, and algebraic representations. The student interprets and predicts the effects of changing slope and y-intercept in applied situations.

Introduced

Maintained

61

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

ALGEBRA I COURSE SCOPE AND SEQUENCE Fourth Six Weeks GRADING PERIOD TEKS

STUDENT EXPECTATIONS

d3(A) Page 42

The student uses patterns to generate the laws of exponents and applies them in problem-solving situations. The student analyzes data and represents situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

d3(C) Page 43 c4(A) Page 44

First 6 Weeks

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

The student analyzes situations and formulates systems of linear equations to solve problems.

Introduced

Maintained

Fifth Six Weeks

GRADING PERIOD TEKS

STUDENT EXPECTATIONS

c4(B) Page 46 c4(C)

The student solves systems of linear equations using concrete models, graphs, tables, and algebraic methods. For given contexts, the student interprets and determines the reasonableness of solutions to systems of linear equations. The student identifies and sketches the general forms of quadratic (y = x²) parent functions. The student finds specific function values, simplifies polynomial expressions, transforms and solves equations, and factors as necessary in problem situations.

Page 47

b2(A) Page 48 b4(A) Page 49

Introduced

First 6 Weeks

Maintained

62

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

ALGEBRA I COURSE SCOPE AND SEQUENCE Sixth Six Weeks GRADING PERIODS TEKS

STUDENT EXPECTATIONS First 6 Weeks

d1(A) Page 51 d1(B) Page 52

The student determines the domain and range values for which quadratic functions make sense for given situations. The student investigates, describes, and predicts the effects of changes in a on the graph of y = ax².

d1(C) Page 53 d1(D) Page 54

The student investigates, describes, and predicts the effects of change in c on the graph of y = x² + c. For problem situations, the student analyzes graphs of quadratic functions and draws conclusions.

d2(A) Page 55 d2(B) Page 56

The student solves quadratic equation using concrete models, tables, graphs, and algebraic methods. The student relates the solutions of quadratic equations to the roots of their functions.

d3(B) Page 57

The student analyzes data and represents situations involving inverse variation using concrete models, tables, graphs, or algebraic methods.

Introduced

Maintained

63

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

ALGEBRA I COURSE SCOPE AND SEQUENCE First Six Weeks GRADING PERIOD TEKS 8.2 Page 12 c1(C) Page 13

b1(C) Page 14 b1(D) Page 15 b3(A) Page 16 b4(B) Page 17

STUDENT EXPECTATIONS

First 6 Weeks

The student selects and uses appropriate operations to solve problems and justify solutions. The student translates among and uses algebraic, tabular, graphical, or verbal descriptions of linear functions. The student describes functional relationships for given problem situations and writes equations or inequalities to answer questions arising from the situations. The student represents relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, and equations and inequalities. The student uses symbols to represent unknowns and variables. The student uses the commutative, associative, and distributive properties to simplify algebraic expressions.

Introduced

Maintained

64

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

Mathematics Instructional Alignment Chart Student Expectations First Six Weeks TEKS #

8.2 A Grade 7th

Grade Level: Grade 8th

8.2 A Select and use 7.2 (F) Select appropriate operations and justify selection. appropriate operations and justify selection.

Eighth

Algebra I b.4.A Find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary.

Specific Student Expectations TLW use distributive property. TLW combine like terms. Instruction Strategies

Resources

Different strategies should be used to allow students to communicate through informal and formal mathematical language using various representations and models.

Manipulatives Cooperative Learning

Classroom

TEXTEAMS Alg. Reasonin: Swimming Pool Pipe Cleaners TEXTEAMS Numerical Reasoning: More or Less? TEXTEAMS Proportionality: Perplexing Puzzle Percent Bars What Does it Cost?

PH 3-6, Resource Pro Test Item Generator Assessment TAKS/Other Assessments

Test items Spring, 1999 Obj. 11, #21 Obj. 12, #22, 34, 38 Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Extensions Other NCTM 1, 2, 3 Students should justify their answers and interpret their meaning using correct units. For example, a student might write, “This is the amount of money, in dollars, it takes to pay for one hour of their trip Teacher made tests Self assessment, working in pairs Oral questions

65

Mathematics Instructional Alignment Chart Student Expectations

First Six Weeks TEKS #

c.1.C

Grade 7/8 7.11.A Select, use, and justify appropriate respresentation of selected data. 7.11 B Make inferences convincing arguments based on data 8.12.C Construct circle graphs, bar graphs, and histograms. 8.4 Generate different models for the same data. 8.12.B Make predictions from scatterplots.

Grade Level: Algebra I c.1.C The student translates among and uses algebraic, tabular, graphical, or verbal descriptions or linear functions.

Algebra I

Algebra II b.3.B Solve equations, inequalities and systems modeled by functions using graphs and tables d.3.C Compare and translate between algebraic and graphical solutions of quadratic equations.

Specific Student Expectations TLW translate from a word problem into an equation. TLW translate the equation into a table. TLW translate the table into a graph. TLW translate from a given graph into an equation. TLW translate from a table into an equation. TLW translate from word problems into graphs. Instruction Strategies Resources PH-TE , p. 269, Visual Learning TEXTEAMS Algebra I Assessment: Stacking Paper Cups Pg. 73 p. 271 Kinesthetic Learning 600-Meter Race Pg. 26 Translate word problems into equations. Make table Swimming Pool Problem Pg. 34 and graph. TEXTEAMS Algebra I 2000 and Beyond: The y-intercept. Going to Great Depths. TEXTEAMS Alg. Reasoning Cross Country Cycling. Assessment Classroom EOC/TAKS/Other Assessments In small groups have students work problems using EOC – Obj. 3 ; TAKS OBJ. 3 Fall 1998, Item #32, 36, 38, 39 different approaches, such as tables and graphs. Debrief as a whole group. Have students discuss the Spring 1999, Item #17, 18 different forms of solving the problems. Performance Assessment by TEKS go to:

www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other NCTM: 1, 2, 5, 6, 8 This TEKS introduces the AP Statistics concepts of analyzing patterns in scatter plots and the least squares of regression line. The concepts of interpolation and extrapolation are important in the AP Statistics curriculum. 66

Mathematics Instructional Alignment Chart Student Expectations

First Six Weeks TEKS #

b.1.C

Grade 7/8 7.3B Estimate and solve application problems involving proportional relationships. 8.3.A Compare and contrast proportional and nonproportional

Grade Level: Algebra I b.1.C The student describes functional relationships for given problem situations and writes equations or inequalities to answer questions arising from the situations.

Algebra I

Algebra II b.3.A The student analyzes situations and formulates systems of equations or inequalities in two or more unknowns to solve problems.

Specific Student Expectations 7.15A, 7.15 B Allow students to validate conclusions using mathematical properties and relationships. 8.8B Connect models to formulas for volume of prisms, cylinders, pyramids, and cones.

TLW write and solve an equation/inequality given a real-world situation.

Instruction Strategies PH-TE, p. 290, Kinesthetic Learning p. 296, visual /Auditory Uses charts, tables, graphs manipulatives and calculators to discuss patterns, relationships, reasonableness. Emphasize fractional values

Resources TEXTEAMS Algebra I 2000 and Beyond Identifying more patterns Variable and Functions Valentine Day Idea Identifying Patterns Investigate Recursively TEXTEAMS Algebra I Assessment Mosaics PH Ch. 1 - 6 GTI Activity 17

Assessment Classroom Assesses students by asking questions such as, How did you solve this problem? Explain your strategy. Explain how you found your solution.

EOC/TAKS/Other Assessments EOC – 4; TAKS OBJ. 1 EOC Spring, 1999 Test Items #38, 30

Performance Assessment by TEKS go to: www.mathbenchmarks.org

Additional Support Activities/Other

Pre-AP Enrichment

NCTM: 1, 2, 5, 6, 8, 10

Emphasize fractional values. Justify reasonable window. Calculator: Table setup-Utilize “Ask” mode for independent variable. 67

Mathematics Instructional Alignment Chart Student Expectations

First Six Weeks TEKS #

b.1.D

Grade Level:

Grade 7/8 7.4A Generate formulas involving conversions, perimeter, area, volume, circumference, scaling. 7.4 B Graph data to demonstrate relationships. 8.4 Generate different models for the same data.

Algebra I b.1.D. Students represents relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.

Algebra I

Algebra II b.3.B The student use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities. d.4.B The student relates representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions.

Specific Student Expectations TLW use one method of representation to convert to other methods of representation.

7.2 A and 7.2 B Allow students the opportunity to represent multiplication and division situations involving fractions and decimals with concrete models, pictures, words, and numbers. 8.7A Draw solids from different perspectives.

Instruction Strategies

Resources

PH-TE , p. 215, ex. 1 and 2 p. 277, Auditory Learning p. 320, Auditory Learning

TEXTEAMS Algebra I Assessment: Mosaics Pg. 25 600-Meter Race Pg. 30 TEXTEAMS Alg. I 2000 and Beyond: Variables and Functions Valentine Day Idea TEXTEAMS Alg. Reasoning: Swimming Pool Movin’ on Down the Line PH Ch. 2, 7 and 10 Resource pro and manipulative kit

Assessment Classroom

EOC/TAKS/Other Assessments

In small groups have students work problems using different approaches, such as tables and graphs. Debrief as a whole group. Have students discuss the different forms of solving the problems.

EOC – Obj. 2 & 4 ; TAKS OBJ. 1 EOC Spring 1999, # 8, 12, 26 Fall 1998, # 34 Performance Assessment by TEKS go to: www.mathbenchmarks.org

Additional Support Pre-AP Enrichment

Activities/Other

PreAP students should be given the opportunity to explore the different mathematical representations with greater sophistication in their mathematical reasoning and communication.

68

NCTM: 1, 2, 4, 5, 6

Mathematics Instructional Alignment Chart Student Expectations

First Six Weeks TEKS #

b.3.A

Grade Level:

Grade 7/8 7.2C Add, subtract, multiply, and divide integers and connect to algorithms.

Algebra I

Algebra II

b.3.A.The student uses symbols to represent unknowns and variables.

7.2 F Select appropriate operations and justify.

Algebra I

b.3.A The student analyzes situations and formulates systems or equations or inequalities in two or more unknowns to solve problems

8.2A. Solve equations with models and use symbols to record. Specific Student Expectations TLW use symbols to represent unknowns and variables.

8.9A Find the surface area of prisms and cylinders using concrete models and nets.

Instruction Strategies PH-TE, p. 73, Auditory Learning, p. 74, Tactile p. 86, Kinesthetic Learning p. 85, Visual Learning

Resources TEXTEAMS Algebra I Assessment: Mosaic Bathing the Dog 600 Meter Race Swimming Pools TEXTEAMS Alg. I 2000 and Beyond: Variables and Functions Valentine Day Idea Investigate Recursively TEXTEAMS Alg. Reasoning: Stretching Sequences PH Ch. 1 - 10 GT I: 1, 3 Assessment Classroom EOC/TAKS/Other Assessments Have students calculate their own grades (averages) and determine grades needed to reach certain EOC : Obj 6 – TAKS OBJ. 2 plateaus.

Performance Assessment by TEKS go to: www.mathbenchmarks.org

PH-TE, pp. 81 and 87 Alternative Assessment

Additional Support Pre-AP Enrichment Evaluate expression using rational numbers.

Activities/Other

Ex: 3a – 4b when a = 5/6; b = -2/3

NCTM: 4, 5

69

Mathematics Instructional Alignment Chart Student Expectations

First Six Weeks TEKS #

b.4.B Grade 7/8

7.2 F Select and use appropriate operations and justify solutions. 8.2.A Select and use appropriate operations and justify selections.

Grade Level: Algebra I b.4.B. The student uses the commutative, associative, and distributive properties to simplify algebraic expressions.

Algebra I

Algebra II b.2.A Use tools including matrices, factoring, and properties of exponents to simplify expressions and transforms and solve equations.

Specific Student Expectations 7.2E Simplify numerical TLW define the commutative, associative, and expressions involving distributive properties. order of operations and TLW identify and apply the commutative, associative, exponents. and distributive properties. TLW simplify algebraic expressions use the commutative, associative, and distributive properties. Instruction Strategies Resources TEXTEAMS Algebra I Assessment: PH-TE, p. 35 Additional Problems CD’s For the Band Require students to show distribution arrow when Making Stuffed Animals using distributive property. Have students create Extracurricular Activities real-life examples of commutative and associative properties. TEXTEAMS Alg. Reasoning: Pipe Cleaners PH Ch. 1, 3 - 10 GT I: 16 Assessment Classroom EOC/TAKS/Other Assessments Assess students by asking them to justify each step as they work the problems out. TAKS OBJ. 2; EOC – OBJ #4

Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other This TEKS is developed throughout the Algebra I curriculum. Symbolic manipulation is a major component of Algebra I, and PreAP students should NCTM: 1, 2, 4, 5 have many meaningful opportunities to practice these skills.

70

ALGEBRA I COURSE SCOPE AND SEQUENCE Second Six Weeks

GRADING PERIOD TEKS

STUDENT EXPECTATIONS

b1(A)

The student describes independent and dependent quantities in functional relationships. The student gathers and records data, or uses data sets, to determine functional (systematic) relationships between quantities.

Page 19

b1(B) Page 20 b1(E) Page 21 b2(B) Page 22 b2(D) Page 23

c3(A) Page 24 c3(B) Page 25 c3(C) Page 26

8.9A Page 27

First 6 Weeks

The student interprets and makes inferences from functional relationships. For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations. In solving problems the student collects and organizes data, makes and interprets scatterplots, and models, predicts, and makes decisions and critical judgments. The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems. The student investigates methods for solving linear equations and inequalities using concrete models, graphs, and the properties of inequalities of equality, selects a method, and solves the equations and inequalities. For given contexts, the student interprets and determines the reasonableness of solutions to linear equations and inequalities. The student uses the Pythagorean Theorem to solve realworld life problems.

Introduced

Maintained

71

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

Mathematics Instructional Alignment Chart Student Expectations

Second Six Weeks TEKS #

b.1.A

Grade 7/8 7.4A Generate formulas involving area, conversions, perimeter, circumference, volume, scaling. 7.4B Graph data to demonstrate demonstrate relationships. 8.4 Generate different models from the same data.

Grade Level: Algebra I b.1.A. The student describes independent and dependent quantities in functional relationships.

Algebra I

Algebra II b.1.A For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations.

Specific Student Expectations TLW describe the independent and dependent quantities using the correct terminology and notation. Instruction Strategies PH-TE, p. 69, Auditory Learning p. 323, Tactile Learning p. 446, Visual Learning

Resources TEXTEAMS Algebra I Assessment: Explorer’s Glide Geothermal Energy TEXTEAMS Alg. I 2000 and Beyond: Valentine Day Idea Identifying Patterns TEXTEAMS Alg. Reasoning: Looking Back, Looking Forward PH Ch. 2, 7, 9, and 11 GTI Activity 8 AI: S2-A4 ; ACE: Appendix D Assessment EOC/TAKS/Other Assessments

Classroom Have students describe different sets of data by defining the independent and dependent variables. Compare the different descriptions of the same data.

EOC – OBJ. 1; TAKS: Obj. 1

Performance Assessment by TEKS go to: www.mathbenchmarks.org

Additional Support Pre-AP Enrichment Terms used interchangeably. Domain/abscissa/input/independent Range/ordinate/output/dependent Given a graph; determine range of function Given the range of function, find the elements of the domain.

72

Activities/Other NCTM: 2, 4, 5, 6

Mathematics Instructional Alignment Chart Student Expectations

Second Six Weeks TEKS #

b.1.B

Grade Level:

Grade 7/8

Algebra I

7.11A Select, use, and justify appropriate representations of collected data.

b.1.B. The student gathers and records data or uses data sets, to determine functional (systematic) relationships between quantities.

8.13.A Evaluate methods of s sampling. 8.12.B Make predictions from scatterplots.

Algebra I

Algebra II b.1.B In solving problems, the student collects data and records results, organizes the data, makes scatterplots, fits the curves to the appropriate parent function, interprets the results, and proceeds to model, predict, and make decisions and critical judgements.

Specific Student Expectations TLW collect and record data in table form.

7.1A and 7.1B The student should be given the opportunity to represent and use numbers in a variety of equivalent forms.

Instruction Strategies

Resources TEXTEAMS Alg. I Assessment: Explorer’s Glide TEXTEAMS Alg. I 2000 and Beyond Have You Lost Your Marbles? Unidentified Circular Objects (UCO’s) Variables and Funcitons PH Ch. 1 – 3, 5,6, 8 - 11 GTI Activity 8; AI: S2-A 15-20 ACE: Appendix D

PH-TE, p. 20, Kinesthetic Learning Set tables of data horizontally as well as vertically

Assessment Classroom EOC/TAKS/Other Assessments In small groups have students work on math project, Tongue Twister, PH p. 57. EOC – Obj. 9; TAKS: Obj. 1 As a whole group compare and discuss the projects. Performance Assessment by TEKS go to:

www.mathbenchmarks.org Additional Support Pre-AP Enrichment

Activities/Other NCTM: 1, 2, 4, 5, 6

Data Collecting Project using CBR/CBL.

73

Mathematics Instructional Alignment Chart Student Expectations

Second Six Weeks TEKS #

b.1.E

Grade Level:

Grade 7/8

Algebra I

7.4A Generate formulas involving conversions, perimeter, area, circumference, volume, scaling. 8.4 Generate different models for the same data.

b.1.E. The student interprets and makes inferences from functional relationships.

Algebra I

Algebra II b.3.A The student analyzes situations and formulates systems of equations or inequalities in two or more unknowns to solve problems.

Specific Student Expectations TLW interpret data using real-world situations. TLW make inferences from a given problem situation involving functional relationships.

8.11A Find the probabilities of compound events.

Instruction Strategies Resources PH-TE, p.327, Kinesthetic Learning TEXTEAMS Alg. I Assessment Making Stuffed Animals p. 329, Tactile Learning Seeing the Horizon Have students create a table and construct a graph using data they have gathered. TEXTEAMS Alg. I 2000 and Beyond Developing Mathematical Models & Using Patterns to Identify Relationships TEXTEAMS Alg. Reasoning Speed Trap PH Ch. 1 – 3, 5, 7 - 11 GT II: 9 ACE: Appendix D Algebra I Assessment: Explorer’s Glide Pg. 46 Assessment Classroom EOC/TAKS/Other Assessments In small groups have students work problems using different approaches, such as tables and graphs. Debrief as a whole group. Have students discuss the different forms of solving the problems.

EOC – Obj. 8 & 9 ; TAKS: Obj. 1 Fall 1998, #24

Additional Support Pre-AP Enrichment Activities/Other Predict, make decisions, and critical judgements NCTM: 1, 2, 4, 5, 6 based on collected data.

74

Mathematics Instructional Alignment Chart Student Expectations

Second Six Weeks TEKS #

b.2.B

Grade Level:

Grade 8 7.2 G Determine reasonableness of solutions. 8.2.C Evaluate solutions for reasonableness.

Algebra I b.2.B. For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations.

Algebra I

Algebra II b.1.A For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations.

Specific Student Expectations TLW identify the domain and range given an equation. TLW determine the reasonable domain and range in realworld situations.

8.8C Estimate answers hnd use formulas to solve application problems involving surface area and volume.

Instruction Strategies PH-TE, p. 296, Visual/Auditory Learning p. 296, Ex. 1 Give a long list of examples and have students identify what represents domain and range.

Classroom

Resources TEXTEAMS Alg. I Assessment Explorer’s Glide Extracurricular Activities Hot-Air Balloon TEXTEAMS Alg. Reasoning Using Patterns to Identify Relationships Swimming Pools PH Ch. 1, 2 , 6 and 7 GT II: 10 ACE: Appendix D Assessment EOC/TAKS/Other Assessments

In small groups have students work problems using EOC – Obj. 1; TAKS: Obj. 2 different approaches, such as tables and graphs. Fall 1998 Test, Items 29, 31, 37 Debrief as a whole group. Have students discuss the Performance Assessment by TEKS go to: different forms of solving the problems. www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other Setting reasonable window (domain and range). NCTM: 1, 2, 4, 5, 6 Justify

75

Mathematics Instructional Alignment Chart Student Expectations

Second Six Weeks TEKS #

b.2.D

Grade Level:

Grade 7/8 7.11 B Make inferences and convincing arguments based on data. 8.12.B Make predictions from scatterplots.

Algebra I

Algebra I

Algebra II

b.2.D. In solving problems, the student collects and organizes data, makes and interprets scatterplots, and models, predicts, and makes decisions and critical judgments.

b.1.B In solving problems, the student collects data and records results, organizes the data, makes scatterplots, fits the curves to the appropriate parent function, interprets the results, and proceeds to model, predict, and make decisions and critical judgements.

Specific Student Expectations TLW solve problems using collected data.

7.10A Construct sample spaces for compound events (dependent and independent).

TLW interpret data and make decisions based on constructed models. Instruction Strategies Resources PH-TE, p. 59, Kinesthetic Learning TEXTEAMS Algebra I Assessment Stretched Spring p. 12, Auditory Learning Use charts, tables, graphs, manipulatives, and TEXTEAMS Alg. I 2000 and Beyond Going to Great Depths calculators to discuss patterns, relationships, and Identifying Patterns reasonableness. Assesses students using multiple formats (student PH Ch. 1 - 3, 5, 8 and 9 presentations, projects, observations, verbal statements, written responses).

Assessment Classroom EOC/TAKS/Other Assessments In small groups have students work problems using EOC – Obj. 9; TAKS: Obj. 2 different approaches, such as tables and graphs. Spring 1999 Test, Item 6, 37 Debrief as a whole group. Have students discuss the Fall 1998 Test, Item 14, 21 different forms of solving the problems. Performance Assessment by TEKS go to:

www.mathbenchmarks.org Additional Support Pre-AP Enrichment Create a problem situation; collect data & model through scatterplots. PH-TE, Technology, p. 240

Activities/Other NCTM: 1, 2, 3, 5

76

Mathematics Instructional Alignment Chart Student Expectations

Second Six Weeks TEKS #

c.3.A Grade 7/8

7.4A Generate formulas involving conversions, perimeter, area, scaling, circumference, and volume. 7.4B Graph data to demonstrate relationships 7.5A Solve equations with models and use symbols to record 7.5B Formulate problems from equations 7.10B Find probability of compound events through experimentation 8.4.BGraph data to demonstrate relationships. 8.5.A Solve equations with models and use symbols to record 8.5.B Formulate problems from equations 8.11.B Make inferences & convincing arguments based on data

Grade Level: Algebra I

Algebra I

Algebra II

c.3.A. The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems.

b.3.A Formulate equations, inequalities or systems to solve problems modeled by functions. c.1.A Identify and sketch graphs of parent functions, including linear, quadratic, square root and exponential.

Specific Student Expectations TLW translates word problems into linear equation or inequality TLW will study linear equation graphically to make inferences or predictions about two relationships. TLW study data graphically given a table of values to make inferences about a linear equation.

Instruction Strategies

Resources

PH-TE, p. 141, Kinesthetic Leaning p. 164, Tactile Learning p. 176, Visual Learning Key words for all 4 operations should be recognized Ex: more than, quotient, less than, increased by, etc.

TEXTEAMS Alg. I Assessment Motion Detector Problems Hot-Air-Balloon TEXTEAMS Alg. I 2000 and Beyond Solving Linear Inequalities PH Ch. 1 - 6 GT I: 23

Assessment Classroom PH-TE, p. 142 Alternative Assessment

EOC/TAKS/Other Assessments EOC – Obj. 2, 4 & 8; TAKS Obj. 4 Fall 1998, Item # 20 Spring 1999, Item # 2, 36, 40 Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Activities/Other

Pre-AP Enrichment Include systems of eq./ inequalities involving Dec./fractions and rewrite w/o dec./fractions. Ex: 2.50x + 1.75y = 40.50 1.25x + 1,25y = 20.50 Create a system of equations problem involving a real world situation. Solve and justify using various methods.

77

NCTM: 1, 2, 4, 5, 6

Mathematics Instructional Alignment Chart Student Expectations

Second Six Weeks TEKS #

c.3.B

Grade Level:

Grade 7/8 7.A Solve equations w/models and use symbols to record. 8.5.A Estimate, find, and justify solutions to application problems.

Algebra I c.3.B. The student investigates methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, selects a method, and solves the equations and inequalities.

Algebra I

Algebra II b.3.B Uses algebraic methods, graphs, tables, or matrices to solve systems. d.3.D Solves quadratic equations & inequalities. d.4.D Solves square root equations & inequalities. e.4 Solves rational equations & inequalities. f.4 Solves exponential and logarithmic equations & inequalities.

Specific Student Expectations TLW solve linear equations and inequalities using concrete models. TLW solve linear equations and inequalities using graphs. TLW solve linear equations and inequalities using the properties of equality.

7.14A Students should communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic models.

Instruction Strategies Resources PH-TE, p. 282, Visual Learning TEXTEAMS Alg. I Assessment Speeding Cars In small groups have students work problems using Geothermal Energy different approaches, such as tables and graphs. Debrief as a whole group. Have students discuss the TEXTEAMS Alg. I 2000 and Beyond Solving Linear Inequalities different forms of solving the problems. Stays the Same PH Ch. 3, 4, 5 and 6 GT I:24, 25;GT II: 24 Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments PH-TE, p. 278 Alternative Assessment EOC – Obj. 2, 4 & 8; TAKS OBJ. 4 Fall 1998, #19, 26 p. 283, Alternative Assessment Spring 1999, #34

Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Enrichment Give students the opportunity to experience how a question can be extended to provide them with a glimpse into an advanced topic. e.g. Although step functions will not be fully developed until later math courses, PreAP students can gain insight into linear functions by comparing them to functions that are not linear.

78

Activities/Other NCTM: 1, 2, 4, 5, 6

Mathematics Instructional Alignment Chart Student Expectations

Second Six Weeks TEKS #

c.3.C Grade 7/8

7.5A Solve equations with models and use symbols to record. 8.12B Use and justify appropriate measures to describe a set of data. 8.5.A Estimate, find, and justify solutions to application problems. 8.13.B Recognize misuses of data analysis and evaluate predictions.

Grade Level:

Algebra I

Algebra I

Algebra II

c.3.C. For given contexts, the student interprets and determines the reasonableness of solutions to linear equations and inequalities.

b.3.C Determines the reasonableness of solutions to systems of equations and inequalities d.4.C Determine the reasonableness of solution to square root equations & inequalities. d.1.A Determine the reasonableness of solution to quadratic equations and inequalities. e.3 Determines the reasonableness of solutions to rational equations and inequalities. f.3 Determines the reasonableness of solutions to exponential and logarithmic equations and inequalities.

Specific Student Expectations TLW check the solutions of linear equations and inequalities by substitution to determine if they are reasonable. TLW select from several graphs to find a reasonable answer to a linear equation or inequality and/or use calculator technology to help in the process. Instruction Strategies Resources PH-TE, p. 216, Tactile Learning TEXTEAMS Alg. I Assessment Motion Detector Problems p. 216, Ex. 4 Speeding Cars Identify slope and y-intercept. First Aid Supply Tactile Learning: Divide students into pairs. Have each student use the slope formula to find each slope TEXTEAMS Alg. I 2000 and Beyond while the other student finds the slope by plotting the Solving Linear Inequalities points on graph paper. Have students compare PH Ch. 3 – 6 answers. GT I: 28, 30 Assessment Classroom EOC/TAKS/Other Assessments In small groups have students work problems using EOC – Obj. 8; TAKS Obj. 4 different approaches, such as tables and graphs. Performance Assessment by TEKS go to: Debrief as a whole group. Have students discuss the www.mathbenchmarks.org different forms of solving the problems. Additional Support Pre-AP Enrichment Activities/Other TI-83 calculator: Refer to table to find rate of change NCTM: 1, 2, 3, 5, 6

79

Mathematics Instructional Alignment Chart Student Expectations Second Six Weeks TEKS #

8.9(A) Grade 7th

7.1(C) Represent squares and square roots using geometric models. 7.6(B) Use properties to classify shapes including triangles, quadrilaterals, pentagons, and circles.

Grade Level: Grade 8th 8.9 A Use the Pythagorean Theorem to solve real-life problems; and

Specific Student Expectations TLW use Pythagorean Theorem to solve real-life problems. TLW identify right angles.

Eighth

Algebra I d2B Relate solutions to quadratic equations to the roots of their functions.

7.6A, 7.6C, and 7.6D Student reviews geometric properties involving angles, properties of solids, and attributes of similarity. 8.6A Generate similar shapes using dilations including enlargements and reductions.

Instruction Strategies Cooperative Learning Tactile Learning Manipulatives

Classroom

Resources TEXTEAMS Alg. Reasoning Moving with Technology Grids Galore

PH 5-10, Resource Pro Test Item Generator Assessment TAKS/Other Assessments Performance Assessment by TEKS go to: www.mathbenchmarks.org

Teacher made tests Lesson Quiz/Checkpoint Self assessment/working in pairs

Additional Support Pre-AP Enrichment Other NCTM: 1, 2, 3, 5, 6 Pre-AP students should be able to use the Pythagorean Theorem in a variety of ways. Including but not limited to the derivative of the distance formula

80

ALGEBRA I COURSE SCOPE AND SEQUENCE Third Six Weeks GRADING PERIOD TEKS

c2(G) Page 29 b2(A) Page 30 b2(C) Page 31 b3(B) Page 32 c1(A) Page 33 c1(B) Page 34 c2(A) Page 35 c2(B) Page 36 c2(C) Page 37 c2(D) Page 38 c2(E) Page 39 c2(F) Page 40

STUDENT EXPECTATIONS

First 6 Weeks

The student relates direct variation to linear functions and solves problems involving proportional change. The student identifies and sketches the general forms of linear (y = x and y = x + b) functions. The student interprets situations in terms of given graphs or creates situations that fit given graphs. Given situations, the student looks for patterns and represents generalizations algebraically. The student determines whether or not given situations can be represented by linear functions. The student determines the domain and range values for which linear functions make sense for given situations. The student develops the concept of slopes as rate of change and determines slopes from graphs, tables, and algebraic representations. The student interprets the meaning of slope and intercepts in situations using data, symbolic representations, or graphs. The student investigates, describes, and predicts the effects of change in m and b on the graph of y=mx + b. The student graphs and writes equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept. The student determines the intercepts of linear functions from graphs, tables, and algebraic representations. The student interprets and predicts the effects of changing slope and y-intercept in applied situations.

Introduced

Maintained

81

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

c.2G

Grade Level:

Grade 7/8

Algebra I

7.3A Estimate and solve application problems involving percent 7.3 B Estimate and solve application problems involving proportional relationships. 8.3.A Compare and contrast proportional and nonproportional relationships. 8.3.B Estimate and solve application of proportional relationships.

c.2.G. The student rates direct variation to linear functions and solve problems involving proportional change.

Algebra I

Algebra II e.6 Use direct and inverse variation models.

Specific Student Expectations TLW relate direct variation to linear functions (vocabulary, direct variation, y = kx). TLW compare the contrast with the slope of linear equation. TLW solve problems involving proportional change. TLW analyze tables to see if the rate of change is proportional. Instruction Strategies Resources PH-TE, p. 158, Auditory Learning TEXTEAMS Alg. I Assessment p. 159, Making Connections Hull Pressure p. 225, Visual Larning TEXTEAMS Proportionality Perplexing Puzzle TEXTEAMS Alg. I 2000 and Beyond Height versus Arm Span PH Ch.4, 5 and 11 Assessment Classroom EOC/TAKS/Other Assessments In small groups have students work problems using EOC – Obj. 9; TAKS OBJ. 3 Fall 1998, Item #5 different approaches, such as tables and graphs. Debrief as a whole group. Have students discuss the Spring 1999, Item #33 different forms of solving the problems. Performance Assessment by TEKS go to:

www.mathbenchmarks.org Additional Support Pre-AP Enrichment

Activities/Other

Applications to real world situations.

A-1-2000 S. A. 4- Height versus Arm Span Alg. R. pgs 145-173; 184-200 NCTM: 1, 2, 4, 5

82

TEKS #

b.2.A

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks Grade Level:

Grade 7/8 7.7A Locate and name points using ordered pairs of integers on a coordinate plane.

Algebra I b.2.A. The student identifies and sketches the general forms of linear (y = x) and quadratic (y = x²) parent functions.

Algebra I

Algebra II b.2.C The student connects the function notation of y = and f (x) =. c.1.A The student identifies and sketches graphs of parent functions, including linear (y = x), quadratic (y = x²), square root (y = √x), inverse (y = 1/x), exponential (y = ax), and logarithmic (y =logax) functions.

8.7.D Locate and name points using ordered pairs of rationals on a coordinate plane.

Specific Student Expectations TLW identify the general form of linear and quadratic parent functions. TLW graph the function given the equation. Instruction Strategies PH-TE, p. 92, Kinesthetic Learning p. 225 Visual Learning Use multiple strategies of students’ choice. Use charts, tables, graphs, and manipulatives. Models instruction going from concrete to pictorial to abstract level.

Resources TEXTEAMS Alg. I Assessment Speeding Cars Transformations of Quadratic Functions TEXTEAMS Alg. I 2000 and Beyond The Linear Parent PH Ch. 2, 5, 7, and 11 GT II: 13, 27 TEXTEAMS Alg. Reasoning Cross-Country Cycling Making Connections Assessment Classroom EOC/TAKS/Other Assessments In small groups have students work problems using EOC – Obj. 1; TAKS: Obj. 2 different approaches, such as tables and graphs. Performance Assessment by TEKS go to: Debrief as a whole group. Have students discuss the www.mathbenchmarks.org different forms of solving the problems. Additional Support Pre-AP Enrichment Activities/Other Learn and use strategies that will allow them to NCTM: 1, 2, 3, 4 manipulate translations on a coordinate plane. PreAP students should be given the opportunity to explore graphs with greater sophistication in their mathematical reasoning and communication.

83

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

b.2.C Grade 7/8

8.7B Use geometric concepts and properties to solve problems.

Grade Level: Algebra I b.2.C. The student interprets situations in terms of given graphs or creates situations that fit the given graphs.

Algebra I

Algebra II b.1.B In solving problems, the student collects data and records results, organizes the data, makes scatterplots, fits the curves to the appropriate parent function, interprets the results, and proceeds to model, predict, and make decisions and critical judgements.

7.8C Use geometric concepts and properties to solve problems.

Specific Student Expectations TLW evaluate graphs relating to a real-life situation. TLW create a situation interpreting the given graph. Instruction Strategies Resources PH-TE, p. 56, Kinesthetic Learning TEXTEAMS Alg. I Assessment Summer Money Have students use newspapers, magazines or internet TEXTEAMS Alg. I 2000 and Beyond Interpreting Distance vs. Time Graphs that use graphs in certain real-life situations. Identifying Patterns TEXTEAMS Alg. Reasoning Pipe Cleaners PH Ch. 1 – 2, 4, 5, 7, and 11 ACE: Appendix D GT II: 31 Assessment Classroom EOC/TAKS/Other Assessments Have students work in small groups. EOC – Obj. 2 & 3 ; TAKS: Obj. 2 Debrief as a whole group. Performance Assessment by TEKS go to:

www.mathbenchmarks.org Additional Support Pre-AP Enrichment Group creates sketches of motions (CBR) and justify. Group will reproduce motion graphs. Learn and use strategies that will allow them to manipulate translations on a coordinate plane. PreAP students should be given the opportunity to explore graphs with greater sophistication in their mathematical reasoning and communication

Activities/Other NCTM: 1, 2, 5, 6

84

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

b.3.B

Grade Level:

Grade 7/8 7.5A Solve equations with models and use symbols to record.

Algebra I b.3.B. Given situations, the student looks for patterns and represents generalizations algebraically.

8.5B Use an algebraic expression to find any term in a sequence.

Algebra I

Algebra II d.1.B The student relates representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions.

Specific Student Expectations TLW evaluate given situations and determine pattern(s). TLW write algebraic expressions.

7.4C Describe the relationship between the terms in a sequence and their positions in the sequence. 8.9B Use proportional relationships in similar shapes to find missing measurements.

Instruction Strategies PH-TE, p. 108, Tactile Learning p. 120, Visual/Auditory Learning

Resources TEXTEAMS Alg. I Assessment Stretched Spring TEXTEAMS Alg. Reasoning Making Connections Ups and Downs TEXTEAMS Alg. I 2000 and Beyond Show Me the Money! Graphs and Tables PH Ch. 1 - 10 ACE: Appendix D Resource pro and manipulative kit Assessment EOC/TAKS/Other Assessments

Classroom Small group discussion followed by whole group discussion where individual groups share in making generalizations.

EOC – Obj. 4, TAKS: Obj. 2

Performance Assessment by TEKS go to: www.mathbenchmarks.org

Additional Support Pre-AP Enrichment Show patterns vertically, horizontally & as a function rule.

Activities/Other NCTM: 4, 5, 6

85

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

7.11A

7.11B 8.12.B 8.12.C 8.13.B

c.1.A

Grade 7/8 Select, use and justify appropriate representations of collected data Make inferences and convincing arguments based on data Make predictions from scatterplots Gather information to make tables. Discuss and understand positive, negative, and no correlation in scatterplots.

Grade Level: Algebra I c.1.A. The student determines whether or not given situations can be represented by linear functions.

Algebra I

Algebra II c.1A Identifies and sketches graphs of parent functions, including linear, quadratic, square root, exponential. e(6) Uses direct and inverse variation functions as models to make predictions in problem situations.

Specific Student Expectations TLW analyze a graph to determine if the graph is linear. TLW analyze data in a table to determine if the table yields a linear function. TLW analyze a given equation to determine if the equation is linear. Instruction Strategies Resources PH-TE, p. 74, Tactile Learning TEXTEAMS Alg. I Assessment Which is Linear? p. 75, Kinesthetic Learning Graphing calculator; linear regression TEXTEAMS Alg. Reasoning Swimming Pool Ups and Downs TEXTEAMS Alg. I 2000 and Beyond Out for a Stretch Going to Great Depths PH Ch. 2 - 5 ACE: Appendix D Assessment Classroom EOC/TAKS/Other Assessments Small group discussion followed by whole group discussion where individual groups share in making EOC: Obj. 2, 3, and 4; TAKS: Obj. 3 generalizations. Performance Assessment by TEKS go to:

www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other Student should compare the change in independent variable to dependent variable. NCTM: 1, 2, 5, 6

86

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

c.1.B

Grade Level:

Grade 7/8 7.3A Estimate and solve application problems involving percents 7.3B Estimate and solve application problems involving proportional relationships 7.11B Make inferences and convincing arguments based on data 8.3.B Estimate and solve applications of percents and proportional relationships. 8.12.B Make predictions from scatterplots.

Algebra I c.1. B. The student determines the domain and range values for which linear functions make sense for given situations.

Algebra I

Algebra II b.1.A For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations.

Specific Student Expectations TLW determine domain and range for situational graphs. TLW determine domain and range from a table. TLW determine domain and range given ordered pairs. TLW determine range given equation (with set of domain). TLW determine domain given equation (with set of range). Instruction Strategies Resources PH-TE, p. 247, Visual Learning TEXTEAMS Alg. I Assessment T-Shirts Suggest that students make a table of values for the TEXTEAMS Alg. I 2000 and Beyond Identifying Patterns domain and range. Use table of values to graph coordinates. TEXTEAMS Alg. Reasoning Extend use of technology using table setup. Movin’ on Down the Line PH Ch. 2, 5 and 6 ACE: Appendix D Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments Small group discussion followed by whole group EOC – Obj. 1 & 9 ; TAKS: Obj. 2 discussion where individual groups share in making Spring 1998, Item # 31, 37 generalizations. Spring 1999, Item # 10, 13

Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Enrichment Justify window settings to given functions.

Activities/Other NCTM: 2, 5, 6 87

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

c.2.A Grade 7/8

7.11.B Make inferences and convincing arguments based on data.

Grade Level: Algebra I c.2.A. The student develops the concept of slope as rate of change and determines slopes from graphs, tables, and algebraic representations.

8.12.B Make predictions from scatterplots.

Algebra I

Algebra II d.2.B Uses slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons.

Specific Student Expectations 7.2D Use division to find unit rates TLW understands that slope is a rate of change. and ratios in proportional TLW find the slope from graphs. relationships such as speed, density, TLW find the slope from tables. price, recipes, and student-teacher TLW find the slope from algebraic relationships. ratio. Instruction Strategies Resources PH-TE, p. 216, Tactile Learning TEXTEAMS Alg. I Assessment Pool Problems p. 420, Auditory Learning p. 421, Visual Learning TEXTEAMS Alg. I 2000 and Beyond The y-intercept Have students come up with real-world examples Exploring Rates of Change illustrating slope (ex. Roof tops, staircases) Finite Changes Use a table to determine whether the relationship between sets of data is linear. TEXTEAMS Alg. Reasoning Cross-Country Cycling Ups and Downs PH Ch. 5 and 9 GT II: 1 ACE: Appendix D Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments Small group discussion followed by whole group EOC – Obj. 2& 3; TAKS Obj. 3 discussion where individual groups share in making Performance Assessment by TEKS go to: generalizations. www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other NCTM: 1, 2, 4, 5, 6, 8, 10 Understanding the relationship between rate of change and the slope of a line is a foundation for AP Calculus that is found in the Algebra I curriculum. Students can find a strong relationship between the EOC problem 21 and problem #2 of the 2000 AB Calculus AP Exam.

88

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks c.2.B Grade Level:

TEKS # Grade 7/8

Algebra I

Algebra II

c.2.B. The student interprets the meaning of slope and intercepts in situations using data, symbolic representations, or graphs.

7.7A

Locate and name points using ordered pairs of integers on a coordinate plane 7.11B Make inferences & convincing arguments based on data 8.7.D Locate and name points using ordered pairs of rationals on a coordinate plane 8.12.B Making predictions from scatterplots.

Algebra I

c.6

Use direct and inverse variation models. b.3.A Formulate equations, d.3.A inequalities, or systems to solve problems modeled by functions.

Specific Student Expectations TLW analyze the rate of change between two relationships given a table. TLW determine the slope and y-intercept given the graph of line by using the definition of slope (m=rise/run). TLW determine the slopes of vertical and horizontal lines. TLW determine the slope given two points by using the

y −y  m= 2 1  x2 − x1  TLW come up with the y-intercept given a point and the slope.

Instruction Strategies PH-TE, p. 231, Tactile Learning p. 231, Auditory Learning p. 231, Visual Learning

Resources TEXTEAMS Alg. I Assessment Pool Problems TEXTEAMS Alg. I 2000 and Beyond Height versus Arm Span The Y-Intercept What’s My Trend? Exploring Rates of Change TEXTEAMS Alg. Reasoning Making Connections

Assessment Classroom

EOC/TAKS/Other Assessments

Small group discussion followed by whole group discussion where individual groups share in making generalizations.

EOC – Obj. 2 & 3; TAKS Obj. Performance Assessment by TEKS go to: www.mathbenchmarks.org

Additional Support Pre-AP Enrichment

slope = m =

Activities/Other NCTM: 1, 2, 4, 5, 6

y2 − y1 ∆y rise ; ; ; rate of change x2 − x1 ∆x run

Understanding the relationship between rate of change and the slope of a line is a foundation for AP Calculus that is found in the Algebra I curriculum. Students can find a strong relationship between the EOC problem 21 and problem #2 of the 2000 AB Calculus AP Exam. 89

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

c.2.C

Grade 7/8 7.11B Make inferences and convincing arguments based on data.

Grade Level: Algebra I c.2.C. The student investigates, describes, and predicts the effects of changes in m and b on the graph of y = mx + b.

8.12.B Make predictions from scatterplots.

Algebra I

Algebra II c.1.B Extends parent functions with parameters such as m in y = mx and describes parameter changes on the graph of parent functions. d.2.B Uses the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x-h)² + k form of a function in applied and purely mathematical situations.

Specific Student Expectations TLW understand that m (slope) will change the steepness of the line. TLW understand the b (y-intercept) will translate the line up or down. Instruction Strategies Resources PH-TE, p. 227, Kinesthetic Learning TEXTEAMS Alg. Assessment Summer Money p. 231, Tactile/Auditory/Visual Learning The Submarine Have students translate the y-intercept and use the slope to draw the resulting line TEXTEAMS Alg. I 2000 and Beyond Lines Do It Too Linear Regression TEXTEAMS Alg. Reasoning Ups and Downs PH Ch. 5 Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments Small group discussion followed by whole group EOC – Obj. 1; TAKS – Obj. 3 discussion where individual groups share in making Fall 1998, Item #3 generalizations. Spring 1999, Item #7, 11

Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other Students generate equations given translations and NCTM: 2, 4, 5, 6 different slopes. 90

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

c.2.D

Grade 7/8 7.11.B Make inferences and convincing arguments based on data. 8.12.B Make predictions from scatterplots.

Grade Level: Algebra I c.2D. The student graphs and writes equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept.

Algebra I

Algebra II d.1.C Determines a quadratic function from its root or a graph.

Specific Student Expectations TLW graph and write equations of lines given two points. TLW graph and write equations of lines given a point and a slope. TLW graph and write equations of lines given a slope and y-intercept. Instruction Strategies Resources PH-TE, p. 231, Auditory Learning TEXTEAMS Alg. I Assessment Graph It p. 237, Auditory Learning Speeding Cars p. 269, Visual Learning Use floor tiles as coordinate plane and use students TEXTEAMS Alg. I 2000 and Beyond Linear Differences as points. Determine slope, y-intercept and write Lines Do It Too function. Exploring Rates of Change TEXTEAMS Alg. Reasoning Making Connections PH Ch. 5 and 6 GT II: 17 Resource pro and manipulative kit

Performance Assessment by TEKS go to: www.mathbenchmarks.org Assessment Classroom EOC/TAKS/Other Assessments Small group discussion followed by whole group EOC – Obj. 2; TAKS: Obj. 3 Fall 1998, Item #36, 39, 40 discussion where individual groups share in making Spring 1999, Item #20 generalizations. Additional Support Pre-AP Enrichment Activities/Other Understanding the relationship between rate of change NCTM: 1, 4, 5, 6, 8, 10 and the slope of a line is a foundation for AP Calculus that is found in the Algebra I curriculum. Students can find a strong relationship between the EOC problem 21 and problem #2 of the 2000 AB Calculus AP Exam.

91

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

c.2.E

Grade Level:

Grade 7/8

Algebra I c.2.E. The student determines the intercepts of linear functions from graphs, tables, and algebraic representations.

7.7.A Locate and name points using ordered pairs of integers on a coordinate plane.

Algebra I

Algebra II d.1.C Determines a quadratic function from its roots or graph. NOTE: First find the roots given a quadratic function.

8.7.D Locate and name points using ordered pairs of rationals on a coordinate plane. Specific Student Expectations TLW find the intercepts of linear functions from graphs. TLW find the intercepts of linear functions from tables. TLW find the intercepts of linear functions from algebraic representations.

7.14B Evaluate the effectiveness of different representations to communicate ideas. This TEK should be addressed throughout the Algebra I course.

Instruction Strategies PH-TE, p. 232, Kinesthetic Learning p. 269, Visual Learning

Resources TEXTEAMS Alg. I Assessment Summer Money TEXTEAMS Alg. I 2000 and Beyond The Y-Intercept TEXTEAMS Alg. Reasoning Cross-Country Cycling Speed Trap PH Ch. 5 and 6 Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments Small group discussion followed by whole group EOC – Obj. 3 TAKS: OBJ. 3 Fall 1998, Item #35 discussion where individual groups share in making Spring 1999, Item #14 generalizations.

Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Enrichment Identify intercepts as critical points.

Activities/Other NCTM: 1, 2, 4, 5, 6, 8

92

Mathematics Instructional Alignment Chart Student Expectations Third Three Weeks TEKS #

c.2.F

Grade Level:

Grade 7/8 7.7.B Graph translations 7.9 Estimate measurements and solve problems with lengths, area, and volume 8.6.B Graph dilations, reflections and translations. 8.10.A Describe effect on perimeter and area when dimensions are changed. 8.6.B Describe effect on volume when dimensions are changed.

Algebra I c.2.F. The student interprets and predicts the effects of changing slope and y-intercept in applied situations.

Algebra I

Algebra II c.1.B Extends parent functions with parameters and describes parameter changes. d.2.B Investigate, describe, and predict effects of changes in a, h, and k on the graphs of y = a(x – h)2 + k form of a function. c.2.B Sketch graphs of conic sections by relating parameter changes in the equation to corresponding changes in the graph.

Specific Student Expectations TLW analyze and describe effects caused by changed in parameters. TLW translate linear equations in order to find the new y-intercept TLW predict the outcome of a graph when the slope or y-intercept changes.

8.10B Describe the resulting effect on volume when dimensions of a solid are changed proportionally.

Instruction Strategies PH-TE, p. 301, Auditory Learning p. 225, Visual Learning p. 227, Kinesthetic Learning

Resources TEXTEAMS Alg. I Assessment Summer Money TEXTEAMS Alg. I 2000 and Beyond Lines Do It Too TEXTEAMS Alg. Reasoning Movin’ on Down the Line Stretching Sequences Pipe Cleaners PH Ch. 5 and 6 GT II: 16 Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments Small group discussion followed by whole group EOC – Obj. 1; TAKS: Obj. 3 discussion where individual groups share in making Performance Assessment by TEKS go to: generalizations. www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other Students are able to compare maximum and minimum values (justify). NCTM: 1, 2, 4, 5, 6, 8, 10 93

ALGEBRA I COURSE SCOPE AND SEQUENCE Fourth Six Weeks GRADING PERIOD TEKS

STUDENT EXPECTATIONS

d3(A) Page 42

The student uses patterns to generate the laws of exponents and applies them in problem-solving situations. The student analyzes data and represents situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

d3(C) Page 43 c4(A) Page 44

First 6 Weeks

The student analyzes situations and formulates systems of linear equations to solve problems.

Introduced

Maintained

94

Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

Mathematics Instructional Alignment Chart Student Expectations Fourth Three Weeks TEKS #

d.3.A

Grade Level:

Grade 7/8 7.2.F Select appropriate operations and justify selections. 7.2.G Determine reasonableness of solutions. 8.2.A Select and use appropriate operations and justify selection. 8.2.C Evaluate solutions for reasonableness.

Algebra I d.3.A. The student uses patterns to generate laws of exponents and applies them in problem-solving situations.

Algebra I

Algebra II f.3 For given contexts, the student determines the reasonable domain and range values of exponential and logarithmic functions, as well as interprets and determines the reasonableness of solutions to exponential and logarithmic equation and inequalities.

Specific Student Expectations TLW demonstrate laws of exponents using patterns. Instruction Strategies PH-TE, p. 381, Kinesthetic Learning p. 386, Auditory Learning Use manipulatives and calculations to discuss patterns, relationships. Use correct mathematical language.

Classroom

Resources TEXTEAMS Alg. I Assessment Bright Lights The Marvel of Medicine What is Reasonable? PH Ch. 8 GT I: 16 GT II: 12 Resource pro and manipulative kit Assessment EOC/TAKS/Other Assessments

Consistently make statements and questions such as: What law did you use to simplify the statement? Is there another way of simplifying it?

EOC – Obj. 7; TAKS: Obj. 5 Spring 1999 Test, Item #32, 35 Fall 1998 Test, Item 17, 23, 28

Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Enrichment Students should be allowed to investigate the laws of exponents on their own or in groups of 2 to 3 students. Although this type of problems look like exponential equations found in Algebra II, PreAP students can use properties of exponents to solve these type of equations.

95

Activities/Other NCTM: 1, 4, 5, 6, 8

TEKS #

d.3.C

Mathematics Instructional Alignment Chart Student Expectations Fourth Three Weeks Grade Level:

Grade 7/8 7.12.B Use and justify appropriate measures to describe a set of data 7.11.B Make inferences and convincing arguments based on data 8.12.A Select appropriate measure of central tendency to describe data. 8.12.B Make predictions from scatterplots.

Algebra I d.3.C. The student analyzes data and represents situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

Algebra I

Algebra II f.4 The student solves exponential and logarithmic equations and inequalities using graphs, tables, and algebraic methods.

Specific Student Expectations TLW analyze situations involving exponential growth and decay using graphing calculators. TLW use a table on calculator and graph to see the difference of exponential, growth and decay. Instruction Strategies Resources PH-TE, p. 369, Visual Learning TEXTEAMS Alg. I Assessment Bright Lights p. 374, Kinesthetic Learning The 600-meter Race TEXTEAMS Alg. I 2000 and Beyond Exponential Relationships Radioactive Decay Identifying Patterns TEXTEAMS Alg. Reasoning Ups and Downs PH Ch. 8 Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments Small group discussion followed by whole group EOC – Obj. 7; TAKS: Obj. 5 discussion where individual groups share in making Performance Assessment by TEKS go to: generalizations. www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other Students should be able to generate their own exponential problems and equations when data is NCTM: 1, 2, 4, 5, 6, 8, 10 provided. 96

TEKS #

c.4.A

Mathematics Instructional Alignment Chart Student Expectations Fourth Three Weeks Grade Level:

Grade 7/8 7.5.B Formulate problems from equations. 8.5.A Estimate, find, and justify solutions to application problems.

Algebra I c.4.A. The student analyzes situations and formulates systems to linear equations to solve problems.

Algebra I

Algebra II b.3.A The student analyzes situations and formulates systems of equations or inequalities in two or more unknowns to solve problems.

Specific Student Expectations TLW translate verbal expressions to algebraic expressions. Instruction Strategies

Resources TEXTEAMS Alg. I Assessment Bonnie’s Dilemma PH-TE, p. 269, Visual Learning Four Cars p. 271, Kinesthetic Learning TEXTEAMS Alg. I 2000 and Beyond Systems of Linear Equations and Inequalities TEXTEAMS Alg. Reasoning Stretching Sequences Grids Galore PH Ch. 6 Assessment Classroom EOC/TAKS/Other Assessments Small group discussion followed by whole group EOC – Obj. 4 and 8 TAKS - Obj. 4 discussion where individual groups share in making Fall 1998, Item #2, 8, 12 generalizations. Spring 1999, 33, 9, 24

Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Enrichment Choose the most appropriate method and justify solutions. Pre-AP students should show greater sophistication in their mathematical reasoning and communication.

Activities/Other NCTM: 1, 2, 4, 5, 6, 8. 10

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ALGEBRA I

SCOPE AND SEQUENCE Fifth Six Weeks

GRADING PERIOD TEKS

STUDENT EXPECTATIONS

c4(B) Page 46 c4(C)

The student solves systems of linear equations using concrete models, graphs, tables, and algebraic methods. For given contexts, the student interprets and determines the reasonableness of solutions to systems of linear equations. The student identifies and sketches the general forms of quadratic (y = x²) parent functions. The student finds specific function values, simplifies polynomial expressions, transforms and solves equations, and factors as necessary in problem situations.

Page 47

b2(A) Page 48 b4(A) Page 49

Introduced

First 6 Weeks

Maintained

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Second 6 Weeks

Third 6 Weeks

Fourth 6 Weeks

Fifth 6 Weeks

Sixth 6 Weeks

Mathematics Instructional Alignment Chart Student Expectations

Fifth Three Weeks TEKS #

c.4.B

Grade Level:

Grade 7/8 7.5.B Formulate problems from equations. 8.5.A Estimate, find, and justify solutions to application problems.

Algebra I c.4.B. The student solves systems of linear equations using concrete models, graphs, tables, and algebraic methods.

Algebra I

Algebra II b.3.B The student uses algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities.

Specific Student Expectations TLW use concrete models to demonstrate possible solutions. TLW use graphing calculator to solve for point of intersection. TLW use table on calculator to check on possible solutions. TLW use algebraic methods:(substitution, linear combination, addition/subtraction) to solve systems of equations. Instruction Strategies Resources TEXTEAMS Alg. I Assessment: Bonnie’s Dilemma PH-TE, p. 301, Kinesthetic Learning Four Cars Students should be seated with plenty of elbow room to work with algebra tiles. TEXTEAMS Alg. I 2000 and Beyond Systems of Linear Equations and Inequalities Work through several examples with students. Concrete Models and Systems of Linear Eq. Explain that you need to choose one tile shape to PH Ch. 6 represent the variable x, a different tile shape to GT II represent the variable y, and a different tile shape to AI: S2-A27, 28 represent one unit. ACE: Module 3 Activities/Other Assessment Classroom Have students work in small groups. Have each individual group demonstrate on the overhead a sample problem.

EOC/TAKS/Other Assessments EOC – Obj. 4; TAKS - Obj. 4 Fall 1998, Item #11

Performance Assessment by TEKS go to: www.mathbenchmarks.org

Additional Support Pre-AP Enrichment Activities/Other In reference to real world applications have students A-1, 3.4 (Systems of Linear Equations and Linear justify meaning of intersection. It is important to Inequalities). discuss the different approaches to solving problems. The variety of methods will help students feel more NCTM: 1, 2, 4, 5, 6, 8, 10 comfortable taking risks and trying new methods with more difficult problems.

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TEKS #

c.4.C Grade 7/8

7.2.G Determine reasonableness of solutions.

Mathematics Instructional Alignment Chart Student Expectations Fifth Three Weeks Grade Level: Algebra I c.4.C. For given contexts, the student interprets and determines the reasonableness of solutions to systems of linear equations.

8.2.C Evaluates solutions for reasonableness.

Algebra I

Algebra II b.3.C For given contexts, the student interprets and determines the reasonableness of solutions to systems of linear equations.

Specific Student Expectations TLW determine whether solutions are for real-world situations or just solving for the solutions of systems. TLW real-world situations; solutions would be limited to positive real numbers. Instruction Strategies Resources TEXTEAMS Alg. I Assessment: PH-TE, p. 296, Visual/Auditory Learning Bonnie’s Dilemma p. 301, Kinesthetic Learning Four Cars TEXTEAMS Alg. I 2000 and Beyond Systems of Linear Equations and Inequalities PH Ch. 6 GT II: 20, 21, 22 Assessment Classroom EOC/TAKS/Other Assessments Have students work in small groups. Debrief as a whole group. EOC – Obj. 8; TAKS - Obj. 4 Fall 1998, #3, 18, 22, 25, 27 Spring 1999, #23, 27, 39

Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other Have students justify meaning of intersection in relation to real-world applications, and look at graphs & tables to prove which is the NCTM: 1, 2, 4, 5, 6, 8, 10 “Better Deal”. Have students write their own application problems to systems of equations.

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TEKS #

b.2.A

Grade 7/8 7.7.A Locate and name points using ordered pairs of integers on a coordinate plane.

Mathematics Instructional Alignment Chart Student Expectations Fifth Three Weeks Grade Level: Algebra I b.2.A. The student identifies and sketches the general forms of linear (y = x) and quadratic (y = x²) parent functions.

8.7.D Locate and name points using ordered pairs of rationals on a coordinate plane.

Algebra I

Algebra II b.2.C The student connects the function notation of y = and f(x) =. c.1.A The student identifies and sketches graphs of parent functions, including linear (y = x), quadratic (y = x²), square root (y = √x), inverse (y = 1/x), exponential (y = ax), and logarithmic (y =logax) functions.

Specific Student Expectations TLW identify the general form of linear and quadratic parent functions. TLW graph the function given the equation. Instruction Strategies Resources PH-TE, p. 92, Kinesthetic Learning TEXTEAMS Alg. I Assessment Investigating the effects of a and c on the graph p. 225, Visual Learning of y = ax2 + c Use multiple strategies of students choice. Use charts, tables, graphs, manipulatives. TEXTEAMS Alg. I 2000 and Beyond Models instruction going from concrete to pictorial The Linear Parent Function to abstract level. Age Estimates Identify and sketch variations of the parent functions Sales Goals PH Ch. 2, 5 , and 7 GT II: 13, 27 ACE: Appendix D Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments Have students work in small groups defining the meaning of the important characteristics of a linear EOC – Obj. 1 TAKS: Obj. 2 or quadratic functions. Debrief as a whole group. Performance Assessment by TEKS go to:

www.mathbenchmarks.org Additional Support Pre-AP Enrichment This TEKS is developed throughout the Algebra I curriculum. Symbolic manipulation is a major component of Algebra I and PreAP students should have many meaningful opportunities to practice these skills. 101

Activities/Other A-1, 1.1 (The Linear Parent Function). AR, pp. 80 – 144. NCTM: 1, 2, 4, 5, 6

TEKS #

b.4.A

Grade 7/8 7.2.F Select appropriate operations and justify selection. 8.2.A Select and use appropriate operations and justify selections.

Mathematics Instructional Alignment Chart Student Expectations Fifth Three Weeks Grade Level: Algebra I b.4.A The student finds specific function values, simplifies polynomial expression, transforms and solves equations, and factors as necessary in problem situations.

Algebra I

Algebra II b.2.A The student uses tools including matrices, factoring, and properties of exponents to simplify expressions and transform and solve equations.

Specific Student Expectations TLW solve functions with specific values. TLW simplify polynomials. TLW solve equations. TLW solve by factoring. Instruction Strategies Resources PH-TE, p. 329, Kinesthetic/Auditory Learning TEXTEAMS Alg. I Assessment Home Improvement Models instruction going from concrete to pictorial The Marvel of Medicine to abstract levels. TEXTEAMS Alg. Reasoning Swimming Pool PH Ch. 3, 4, 5 and 10 GT I: 15, 30, 33, 35 GT II: 29 Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments EOC – Obj. 6 TAKS: Obj. 2 Use questions such as: How did you solve this Spring 1999 Test, Item 5, 15, 16, 29 problem? Explain your strategy. Explain how you Fall 1998 Test, Item, 1, 5, 6, 7 found a solution in a different way. What are some Performance Assessment by TEKS go to: patterns you noticed? www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other This TEKS is developed throughout the Algebra I curriculum. Symbolic manipulation is a major AR, pp. 80 – 173, 184 – 200. component of Algebra I and PreAP students should have many meaningful opportunities to practice NCTM: 1, 2, 4, 5, 6, 8, 10 these skills.

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ALGEBRA I SCOPE AND SEQUENCE SIXTH SIX WEEKS d1(A) Page 51 d1(B) Page 52

The student determines the domain and range values for which quadratic functions make sense for given situations. The student investigates, describes, and predicts the effects of changes in a on the graph of y = ax².

d1(C) Page 53 d1(D) Page 54

The student investigates, describes, and predicts the effects of change in c on the graph of y = x² + c. For problem situations, the student analyzes graphs of quadratic functions and draws conclusions.

d2(A) Page 55 d2(B) Page 56

The student solves quadratic equation using concrete models, tables, graphs, and algebraic methods. The student relates the solutions of quadratic equations to the roots of their functions.

d3(B) Page 57

The student analyzes data and represents situations involving inverse variation using concrete models, tables, graphs, or algebraic methods.

103

Mathematics Instructional Alignment Chart Student Expectations Sixth Three Weeks TEKS #

d.1.A

Grade Level:

Grade 7/8

Algebra I d.1.A The student determines the domain and range values for which quadratic functions make sense for given situations.

7.5.A Solve equations with models and use symbols to record. 8.4.A

Estimate, find, and justify solutions to application problems.

Algebra I

Algebra II d.1.A For given contexts, the student determines the reasonable domain and range values of quadratic functions, as well as interprets and determines the reasonableness of solutions to quadratic equations and inequalities.

Specific Student Expectations TLW determine the range from a table when domain is given. TLW given domain, find range on x, y table. TLW explain parameters for given real situations.

7.13A Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems

Instruction Strategies

Resources TEXTEAMS Alg. I Assessment Fireworks Celebration PH-TE, p. 323, Tactile Learning Mathematical Domain and Ranges of Non-linear p. 329, Visual/Tactile Learning Functions Teacher demonstrates solving quadratic function PH Ch. 7 using the graphing calculator, using table. GTII: 27 Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments Have work in small groups and debrief as a whole EOC – Obj. 1, 7 TAKS: Obj. 2 group. Spring 1999 Test, Item #32, 35 Fall 1998 Test, Item #17, 23, 28

Performance Assessment by TEKS go to: www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other Find critical points (minimum, maximum values and NCTM: 1, 2, 4, 5, 6, 10 intercepts). Quadratic functions in PreAP Algebra I can be used to introduce optimization problems found in AP Calculus.

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Mathematics Instructional Alignment Chart Student Expectations Sixth Three Weeks TEKS #

d.1.B

Grade Level:

Grade 7/8

Algebra I d.1.B The student investigates, describes, and predicts the effects of changes in a on the graph of y = ax².

7.7.b Graph translations. 8.6.b Graph dilations, reflections and translations.

Algebra I

Algebra II d.2.B The student uses the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(xh)² + k form of a function in applied and purely mathematical situations.

Specific Student Expectations TLW investigate the effect of having integers as coefficient of a in the parent equation of y = ax². TLW investigate the effect of having fractions as the coefficient of a in the parent equation of y = ax².

7.13C Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

Instruction Strategies PH-TE, p. 351, Auditory Learning p. 318, Visual Learning

Resources TEXTEAMS Alg. I Assessment Investigating the Effects of a and con the graph of y = ax2 + c Transformations of Quadratic Functions PH Ch. 7 GT II: 27 Resource pro and manipulative kit Assessment Classroom EOC/TAKS/Other Assessments Have students investigate the effects of the different components of a quadratic function. Debrief as a EOC – Obj. 1; TAKS - Obj. 5 whole group. Performance Assessment by TEKS go to:

www.mathbenchmarks.org Additional Support Pre-AP Enrichment Explain verbally the changes in y = ax2. Quadratic functions in PreAP Algebra I can be used to introduce optimization problems found in AP Calculus

105

Activities/Other A-1, 1.2 (Transformations). NCTM: 1, 2, 4, 5, 6, 10

Mathematics Instructional Alignment Chart Student Expectations Sixth Three Weeks TEKS #

d.1.C

Grade Level:

Grade 7/8 7.7.b Graph translations. 8.6.b Graph dilations, reflections and translations.

Algebra I

Algebra I

Algebra II

d.1.C The student investigates, describes, and predicts the effects of changes in c on the graph of y = x² + c.

d.2.b The student uses the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x-h)² + k form of a function in applied and purely mathematical situations.

Specific Student Expectations TLW investigate and describe the changes in “c” on the graph if y = x² + x by using a calculator. Instruction Strategies PH-TE, p. 323, Tactile Learning p. 339, Visual Learning Illustrations of graphs on overheads using different values of “c”.

Resources TEXTEAMS Alg. I Assessment Transformation of Quadratic Functions Investigating the Effects of a and c on the graph of y = ax2 + c TEXTEAMS Alg. I 2000 and Beyond Transformations PH Ch. 7 GT II: 27 Resource pro and manipulative kit

Assessment Classroom

EOC/TAKS/Other Assessments

Have students re-sketch a y = x² + c equation starting EOC – Obj. 1; TAKS – Obj. 5 with a new value of c and the corresponding graph Performance Assessment by TEKS go to: using different c values. www.mathbenchmarks.org Additional Support Pre-AP Enrichment Explain verbally the changes in y = x2 + c

Activities/Other NCTM: 2, 4, 5, 6, 10

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Mathematics Instructional Alignment Chart Student Expectations Sixth Three Weeks TEKS #

d.1.D Grade 7/8

7.5.A Solve equations with models and use symbols to record.

Grade Level: Algebra I d.1.D. For problem situations, the student analyzes graphs of quadratic functions and draws conclusions.

8.5.A Estimate, find, and justify solutions to application problems.

Algebra I

Algebra II d.1.B The student relates representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions. d.3.A The student analyzes situations involving quadratic functions and formulates quadratic equations or inequalities to solve problems.

Specific Student Expectations TLW analyze and graph quadratic functions to determine the maximum or minimum (vertex).

7.13B Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

TLW determine the number of solutions (roots) of a quadratic function by graphing. Instruction Strategies Resources TEXTEAMS Alg. I Assessment Golfing PH-TE, p. 91, Tactile Learning p. 322, Tactile Learning TEXTEAMS Alg. Reasoning p. 499, Tactile Learning Swimming Pool PH Ch. 2, 7 and 10 GT II: 28

Assessment Classroom EOC/TAKS/Other Assessments Have students describe graphs. Explain what values are reasonable for the domain and range in the EOC – Obj. 9 TAKS: Obj. 5 problem situation. Describe the relationship Performance Assessment by TEKS go to: between the height of the object and the time. www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other Quadratic functions in PreAP Algebra I can be used NCTM: 1, 2, 3, 5, 6, 10 to introduce optimization problems found in AP Calculus

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Mathematics Instructional Alignment Chart Student Expectations Sixth Three Weeks TEKS #

d.2.A

Grade Level:

Grade 7/8 7.11.B Making inferences and convincing arguments based on data. 7.4.A Generate formulas involving conversions, perimeter, circumference, area and volume and scaling. 8.12.B Make predictions from scatterplots. 8.4 Generate different models for the same data.

Algebra I d.2.A The student solves quadratic equations using concrete models, tables, graphs, and algebraic methods.

Algebra I

Algebra II d.3.D The student solves quadratic equations and inequalities.

Specific Student Expectations TLW use algebra tiles to solve quadratic equation. TLW create and solve a quadratic equation from a table. TLW factor and solve a quadratic equation by algebraic methods. Instruction Strategies PH-TE, p. 327, Kinesthetic Learning p. 339, Visual Learning The teacher uses examples from the newspaper or pictures of parabolas from magazines to write the quadratic equation.

Resources TEXTEAMS Alg. I Assessment Golfing Home Improvement TEXTEAMS Alg. I 2000 and Beyond Identifying More Patterns Quadratic Relationships Investigating Completing the Square PH Ch. 7, 9, 10 and 11 GT I: 31 Assessment Classroom EOC/TAKS/Other Assessments Students should make connections between the roots of quadratic functions and the solutions to quadratic EOC – Obj. 5 TAKS: Obj. 5 Spring 1999, Item #21, 25, 31, 19, 22 equations and the factors of quadratic polynomials and the x-intercept of a parabola. They connect this Fall 1998, Item #3, 4, 9, 10 understanding to the vertex, polynomial, and Performance Assessment by TEKS go to: factored form of the equation of a parabola www.mathbenchmarks.org Additional Support Pre-AP Enrichment Activities/Other Quadratic functions in PreAP Algebra I can be used to introduce optimization problems found in AP NCTM: 2, 4, 5, 6, 10 Calculus.

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Mathematics Instructional Alignment Chart Student Expectations Sixth Three Weeks TEKS #

d.2.B

Grade Level:

Grade 7/8 7.5.A Solve equations with models and use symbols to record.

Algebra I d.2.B The student relates the solutions of quadratic equations to the roots of their functions.

Algebra I

Algebra II d.1.C The student determines a quadratic function from its roots or a graph.

8.5.A Estimate, find, and justify solutions to application problems. Specific Student Expectations TLW relate the solutions to the roots (zeros) or x-intercepts of a quadratic equation. TLW find and compare the roots of x-intercepts algebraically and graphically with calculator.

7.13A Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.

Instruction Strategies PH-TE, p. 491, Visual Learning p. 499, Tactile/Visual Learing

Resources TEXTEAMS Alg. I Assessment Golfing Home Improvement TEXTEAMS Alg. I 2000 and Beyond Quadratic Functions PH Ch. 7 and 10

Assessment Classroom EOC/TAKS/Other Assessments Students should make connections between the roots of quadratic functions and the solutions to quadratic EOC – Obj. 5 TAKS: Obj. 5 Fall 1998, Item #9, 10 equations and the factors of quadratic polynomials and the x-intercept of a parabola. They connect this Performance Assessment by TEKS go to: understanding to the vertex, polynomial, and www.mathbenchmarks.org factored form of the equation of a parabola Additional Support Pre-AP Enrichment Activities/Other Given the vertex & one root, student finds the other NCTM: 2, 4, 5, 6 root. (line of symmetry, x ≠ 0.)

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Mathematics Instructional Alignment Chart Student Expectations Sixth Three Weeks TEKS #

d.3.B

Grade Level:

Grade 7/8 7.3.B Estimate and solve application problems involving proportional relationships.

Algebra I

Algebra I

Algebra II

c.6 The student uses direct and d.3.B The student analyzes data inverse variation functions and represents situations as models to make involving inverse variation using predictions in problem concrete models, tables, graphs, or situations. algebraic methods.

8.3.A Compare and contrast proportional and nonproportional relationships. Specific Student Expectations TLW interpret and analyze situations involving inverse variation using tables or graphs.

7.14A Describe a set of data using mean, median, mode, and range.

Instruction Strategies PH-TE, p. 511, Visual /Tactile Learning p. 519, Tactile/Auditory Learning

Resources TEXTEAMS Alg. Reasoning Swimming Pool Pipe Cleaners TEXTEAMS Algebra Assessment Constructing Houses PH Ch. 8 and 11 Assessment

Classroom

EOC/TAKS/Other Assessments

Students should make connections between the roots of quadratic functions and the solutions to quadratic EOC – not tested; TAKS –not tested equations and the factors of quadratic polynomials Performance Assessment by TEKS go to: and the x-intercept of a parabola. They connect this www.mathbenchmarks.org understanding to the vertex, polynomial, and factored form of the equation of a parabola. Additional Support Pre-AP Enrichment Activities/Other It is important to discuss the different approaches to finding the roots of a quadratic function. The variety of methods will help students feel more comfortable NCTM: : 2, 3, 4, 5, 6, 10 taking risks and trying new methods with more difficult problems.

110