Unit 5: Proportions and Lines. Activities: Resources:

Transcription

1 Timeline: 2 nd nine weeks Vocabulary: Slope Formula, Rate of Change, Y Intercept, Slope intercept form, Vertical, Horizontal Linear Function Slope Slope of a Line Unit 5: Proportions and Lines New State Standards: 8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. 8.EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. 8.F.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. 8.F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. College Readiness: (Range 13-15) Basic Operations and Applications: Perform one-operation computation with whole numbers and decimals (Range 16-19) Basic Operations and Applications: Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single-step percent (Range 13-15) Numbers: Concepts and Properties: Recognize equivalent fractions and fractions in lowest terms (Range 16-19) Numbers: Concepts and Properties: Recognize one-digit factors of a number (Range 20-23) Numbers: Concepts and Properties: Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor (Range 24-27) Numbers: Concepts and Properties: Find and use the least common multiple (Range 24-27) Numbers: Concepts and Properties: Order fractions (Range 24-27) Numbers: Concepts and Properties: Work with numerical factors (Range 13-15) Graphical Representations: Identify the location of a point with a positive coordinate on the number line (Range 24-27)Expressions, Equations and Inequalities: Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions) (Range 16-19) Graphical Representations: Locate points on the number line and in the first quadrant (Range 20-23) Graphical Representations: Exhibit knowledge of slope* (Range 24-27) Graphical Representations: Determine the slope of a line from points or equations* (Range 24-27) Graphical Representations: Match linear graphs with their equations* Activities: Concepts and Skills: Students will: Recognize equivalent fractions Solve proportions Calculate a rate of change from two points Understand that a constant rate of change is shown on a graph through the slope of a line. Use similar triangles to show the slope of a line Graph a line starting at the origin and using slope to find a second point Graph a line starting at a y intercept and using slope to find a second point Be led to discover y=mx+b as Slope Intercept form for a line. Graph vertical and horizontal lines. Determine an equation of a line from its graph Resources: Strategies: NCTM: Number and Operations: work flexibly with fractions, decimals, and percents to solve problems; understand the meaning and effects of arithmetic operations with fractions, decimals, and integers; understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems. select appropriate methods and tools for computing with fractions and decimals from

2 among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods; develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios. Algebra: represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; relate and compare different forms of representation for a relationship; identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. develop an initial conceptual understanding of different uses of variables; explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope; use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; recognize and generate equivalent forms for simple algebraic expressions and solve linear equations use graphs to analyze the nature of changes in quantities in linear relationships. Quality Core:

3 Timeline: 2 nd nine weeks Vocabulary: Solution to a system Elimination Method Substitution Method System of Equations Unit 6: Analyzing and Solving Linear Relationships New State Standards: 8.EE.8. Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. College Readiness: (Range 13-15) Basic Operations and Applications: Perform one-operation computation with whole numbers and decimals (Range 16-19) Basic Operations and Applications: Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single-step percent (Range 13-15) Numbers: Concepts and Properties: Recognize equivalent fractions and fractions in lowest terms (Range 16-19) Numbers: Concepts and Properties: Recognize one-digit factors of a number (Range 20-23) Numbers: Concepts and Properties: Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor (Range 24-27) Numbers: Concepts and Properties: Find and use the least common multiple (Range 24-27) Numbers: Concepts and Properties: Work with numerical factors (Range 13-15) Graphical Representations: Identify the location of a point with a positive coordinate on the number line (Range 24-27)Expressions, Equations and Inequalities: Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions) (Range 16-19) Graphical Representations: Locate points on the number line and in the first quadrant (Range 20-23) Graphical Representations: Exhibit knowledge of slope* (Range 24-27) Graphical Representations: Determine the slope of a line from points or equations* (Range 24-27) Graphical Representations: Match linear graphs with their equations* Range(20-23) Function: Evaluate quadratic functions, expressed in function notation, at integer (Range 28-32)Expressions, Equations and Inequalities: Find solutions to systems of linear equations Activities: Concepts and Skills: Students will: Solve a system of linear equations algebraically Estimate a solution of a system of linear equations by graphing Solve a system of linear equations in a real world context Understand that a solution to a system of linear equations is the point of intersections of the two graphs. Resources: Strategies: NCTM: Number and Operations: work flexibly with fractions, decimals, and percents to solve problems; understand the meaning and effects of arithmetic operations with fractions, decimals, and integers; understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems. select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods; develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

4 Algebra: represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; relate and compare different forms of representation for a relationship; identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. develop an initial conceptual understanding of different uses of variables; explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope; use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; recognize and generate equivalent forms for simple algebraic expressions and solve linear equations use graphs to analyze the nature of changes in quantities in linear relationships. Quality Core:

5 Timeline: 2 nd nine weeks Vocabulary: Rate of Change, Input, Output, Function, Linear, Non-linear, Function rule Linear Function Discrete Data Nonlinear Function Parabola Proportional Relationship Quadratic Function Unit 7: Defining Functions New State Standards: 8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 8.F.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. 8.F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Activities: Concepts and Skills: Students will: Use input and output tables to describe functions Use rate of change comparisons from multiple representations of functions Model linear functions as tables, graphs and equations Compare functions that are not linear Create a rule for a function from a table or graph Resources: Strategies: College Readiness: (Range 13-15) Basic Operations and Applications: Perform one-operation computation with whole numbers and decimals (Range 16-19) Basic Operations and Applications: Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single-step percent (Range 13-15) Numbers: Concepts and Properties: Recognize equivalent fractions and fractions in lowest terms (Range 16-19) Numbers: Concepts and Properties: Recognize one-digit factors of a number (Range 20-23) Numbers: Concepts and Properties: Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor (Range 24-27) Numbers: Concepts and Properties: Find and use the least common multiple (Range 24-27) Numbers: Concepts and Properties: Order fractions (Range 24-27) Numbers: Concepts and Properties: Work with numerical factors (Range 13-15) Graphical Representations: Identify the location of a point with a positive coordinate on the number line (Range 24-27)Expressions, Equations and Inequalities: Write expressions, equations, or inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions) (Range 16-19) Graphical Representations: Locate points on the number line and in the first quadrant (Range 20-23) Graphical Representations: Exhibit knowledge of slope* (Range 24-27) Graphical Representations: Determine the slope of a line from points or equations* (Range 24-27) Graphical Representations: Match linear graphs with their equations* Range(20-23) Function: Evaluate quadratic functions, expressed in function notation, at integer values NCTM: Number and Operations:

6 work flexibly with fractions, decimals, and percents to solve problems; understand the meaning and effects of arithmetic operations with fractions, decimals, and integers; understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems. select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods; develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios. Algebra: represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; relate and compare different forms of representation for a relationship; identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. develop an initial conceptual understanding of different uses of variables; explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope; use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; recognize and generate equivalent forms for simple algebraic expressions and solve linear equations use graphs to analyze the nature of changes in quantities in linear relationships. Quality Core:

7 (V1) Vocabulary: slope formula, rate of change, y-intercept, slope intercept form, vertical, horizontal, slope, slope of a line, linear function Weekly Plan (1) Monday: Tuesday: Wednesday: Thursday: Friday: (4-1) Understanding Slope pgs (4-1) pgs (5-9) (4-1) pgs (5-10) (4-1) pgs (5-13) Review (4-1) Check(11) (Coach Book Lesson 11 Slope pgs ) (4-2) Graphing Linear Functions pgs (4-2) pg. 126 (6-17) (4-2) pg. 126 (6-20) (4-2) pg. 126 (6-23) Review (4-2) Check(12) (Coach Book Lesson 12 Slopes and y-intercepts pgs ) (3-3) Proportional Relationships pgs (3-3) pg. 94 (5-12) (3-3) pg. 94 (5-12) (3-3) pg. 94 (5-14) Review (3-3) Check(13) (Coach Book Lesson 13 Proportional Relationships pgs ) Coach Book: Lesson 14 Direct Proportions pgs Lesson 14 pg.104 Lesson 14 pg.104 Lesson 14 pg.104 Review Lesson 14 Check(14) (Coach Book Lesson 14 Direct Proportions pgs ) 40 min: Activity (4-2a) Activity Lab: Graphing Functions Using Calculators pg. 122 (1-6)

8 (V1) Vocabulary: slope formula, rate of change, y-intercept, slope intercept form, vertical, horizontal, slope, slope of a line, linear function Weekly Plan (2) Monday: Tuesday: Wednesday: Thursday: Friday: Review (4-1), (4-2), (3-3), Lessons Review (4-1), (4-2), (3-3), Lessons Review (4-1), (4-2), (3-3), Lessons Review (4-1), (4-2), (3-3), Lessons Review (4-1), (4-2), (3-3), Lessons Review over slope and y- intercept and how to graph linear functions 30 min: Practice/ Activity Create picture using lines. Lines will be created by determining the slope and the y-intercept for each of them. Students will create their own lines and they will need to label the slope, y- intercept, what kind of line it is, and the equation in slope-intercept form. Review over slope and y- intercept and how to graph linear functions 30 min: Practice/ Activity Continuing on with the activity: Create picture using lines. Lines will be created by determining the slope and the y-intercept for each of them. Students will create their own lines and they will need to label the slope, y- intercept, what kind of line it is, and the equation in slope-intercept form. Review over slope and y- intercept and how to graph linear functions 30 min: Practice/ Activity Continuing on with the activity: Create picture using lines. Lines will be created by determining the slope and the y-intercept for each of them. Students will create their own lines and they will need to label the slope, y- intercept, what kind of line it is, and the equation in slope-intercept form. 30 min: Practice Review Study Guide for Quiz in Coach Book pgs Review the other previous quizzes. 30 min: Assessment Quiz on (4-1), (4-2), (3-3), Lessons Coach Book pgs (3 problems on previous quizzes will be on the quiz)

9 (V2) Vocabulary: Solution to a system, system of equations, substitution method, elimination method Weekly Plan(3) Monday: Coach Book: Lesson 15 Pairs of Linear Equations pgs Lesson 15 pg. 110 Lesson 15 pg. 110 Lesson 15 pg. 110 Tuesday: Review Lesson 15 Check(15) (Coach Book Lesson 15 Pairs of Linear Equations pgs ) (5-1) Solving Systems by Graphing pgs (5-1) pg. 150 (5-13) (5-1) pg. 150 (5-13) (5-1) pg. 150 (5-15) Wednesday: Review (5-1) Check(16) (Coach Book Lesson 16 Solve Systems of Equations Graphically pgs ) (5-2) Solving Systems by Substitution pgs (5-2) pg. 156 (4-9) (5-2) pg. 156 (4-9) (5-2) pg. 156 (4-11) Thursday: Review (5-2) (5-3) Solving Systems by Elimination pgs (5-3) pgs (3-8) (5-3) pgs (3-8) (5-3) pgs (3-9) (11-12) Friday: Mad Minutes Review (5-3) Check(17) (Coach Book Lesson 17 Solve Systems of Equations Algebraically pgs ) 30 min: Activity (5-3b) Activity Lab pg. 162 (1-3)

10 (V2) Vocabulary: Solution to a system, system of equations, substitution method, elimination method Weekly Plan (4) Monday: Review (5-1), (5-2), (5-3) (5-4) Systems in the Real World pgs (5-4) pg. 169 (5-10) (5-4) pg. 169 (5-13) (5-4) pg. 169 (5-15) Tuesday: Review (5-4) Coach Book: Lesson 18 Use Systems of Equations to Solve s pgs Lesson 18 pg. 130 Lesson 18 pg. 130 Lesson 18 pg. 130 Wednesday: Review Lesson 18 Check(18) (Coach Book 18 Use Systems of Equations to Solve s pgs ) 30 min: Activity Students will get into groups and work on problems using systems of equations. They can choose their own method, but they must explain on how they solved the problem. The problems will be word problems. They must set it up and than solve for the missing number in order to come up with the solution. Thursday: Review (5-1), (5-2), (5-3), Lessons min: Activity Continuing the activity: Students will get into groups and work on problems using systems of equations. They can choose their own method, but they must explain on how they solved the problem. The problems will be word problems. They must set it up and than solve for the missing number in order to come up with the solution. Friday: Mad Minutes Review (5-1), (5-2), (5-3), Lessons min: Assignment Students will get into groups. They will be given a word problem which they will have to solve using system of equations. They must write the problem, set the problem up, work it out, and explain in their own words on how they came up with the answer.

11 (V2) Vocabulary: Solution to a system, system of equations, substitution method, elimination method Weekly Plan (5) Monday: Review (5-1), (5-2), (5-3), Lessons min: Practice Review Study Guide for Quiz in Coach Book pgs Review the other previous quizzes. Tuesday: Review (4-1), (4-2), (3-3), Lessons min: Assessment Quiz on (4-1), (4-2), (3-3), Lessons Coach Book pgs (3 problems on previous quizzes will be on the quiz) Wednesday: (3-2) Functions pgs (3-2) pg. 89 (5-11) (3-2) pg. 89 (5-12) (3-2) pg. 89 (5-14) Remaining Time: Activity Thursday: Review (3-2) Coach Book: Lesson 19 Introduction to Functions pgs Lesson 19 pg. 146 Lesson 19 pg. 146 Lesson 19 pg. 146 Friday: Mad Minutes Review Lesson 19 Check(19) (Coach Book Lesson 19 Introduction to Functions pgs ) 30 min: Activity Math Game: What s My Output? Pg. 91

12 (V3) Vocabulary: Rate of Change, input, output, function, linear, nonlinear, function rule, domain, range, linear function, discrete data, nonlinear function, parabola, proportional relationship, quadratic function Monday: (3-1) Relating Graphs to Events pgs (3-1) pg. 84 (6-9) (3-1) pg. 84 (6-11) (3-1) pg. 84 (6-11) (13-16) Tuesday: Review (3-2) (3-4) Linear Functions pgs (3-4) pg. 101 (4-8) (3-4) pg. 101 (4-8) (3-4) pg. 101 (4-10) Remaining Time: Activity Weekly Plan (6) Wednesday: Review (3-4) (3-5) Nonlinear Functions pgs (3-5) pg. 106 (4-13) (3-5) pg. 106 (4-13) (3-5) pg. 106 (4-15) Remaining Time: Activity Thursday: Review (3-5) Coach Book: Lesson 20 pgs Lesson 20 pg. 152 Lesson 20 pg. 152 Lesson 20 pg. 152 Friday: Mad Minutes Review Lesson 20 Check(20) (Coach Book 20 Work with Linear Functions pgs ) 30 min: Activity (3-5b) Activity Lab Using Linear and Nonlinear Graphs pg. 108 (1-4)

13 (V3) Vocabulary: Rate of Change, input, output, function, linear, nonlinear, function rule, domain, range, linear function, discrete data, nonlinear function, parabola, proportional relationship, quadratic function Monday: (NO SCHOOL) Tuesday: (NO SCHOOL) Weekly Plan (7) Wednesday: (NO SCHOOL) Thursday: (NO SCHOOL) Friday: (NO SCHOOL) Review Lesson 20 Coach Book Lesson 21 Use Functions to Solve s pgs Lesson 21 pg. 160 Lesson 21 pg. 160 Lesson 21 pg. 160 Review Lesson 21 Check(21) (Coach Book Lesson 21 Use Functions to Solve s pgs ) (4-3) Writing Rules for Linear Functions pgs (4-3) pg. 130 (3-8) (4-3) pg. 130 (3-8) (4-3) pgs (3-8) (10-13)

14 (V3) Vocabulary: Rate of Change, input, output, function, linear, nonlinear, function rule, domain, range, linear function, discrete data, nonlinear function, parabola, proportional relationship, quadratic function Weekly Plan (8) Monday: Review (4-3) Coach Book Lesson 22 Use Graphs to Describe Relationships pgs Lesson 22 pg. 166 Lesson 22 pg. 166 Lesson 22 pg. 166 Tuesday: Review Lesson 22 Check(22) (Coach Book Lesson 22Use Graphs to Describe Relationships pgs ) (4-4) Comparing Functions pgs (4-4) pg.137 (6-11) (4-4) pg. 137 (6-11) (4-4) pgs (6-11) (13-14) Wednesday: Review (4-4) 30 min: Lesson Coach Book Lesson 23 Compare Relationships Represented in Different Ways pgs Lesson 23 pg. 172 Lesson 23 pg. 172 Lesson 23 pg. 172 Thursday: Review Lesson 23 Check(23) (Coach Book Lesson 23 Compare Relationships Represented in Different Ways pgs ) 30 min: Practice Review Study Guide for Quiz on (1-3), (1-4), (1-5), (4-3), (4-4), Lessons in Coach Book pgs Review the other previous quizzes Friday: Mad Minutes Review (1-3), (1-4), (1-5), (4-3), (4-4), Lesson 21, Lesson 22, Lesson min: Assessment Quiz on (1-3), (1-4), (1-5), (4-3), (4-4), Lessons Coach Book pgs (3 problems on previous quizzes will be on the quiz)

15 Vocabulary: All vocabulary from above Weekly Plan (9) Monday: Tuesday: Wednesday: Thursday: Friday: Review for Test pgs , , Previous Reviews(Q1): pgs , 76-77, min: Review Chapter Reviews pgs (1-15) pgs (1-24) pgs (1-21) Previous Chapter Reviews(Q1) pgs (6-19) pgs (4-33) pgs (2-49) Unfinished work/activity Review for Test pgs , , Previous Reviews(Q1): pgs , 76-77, min: Review Chapter Reviews pgs (1-15) pgs (1-24) pgs (1-21) Previous Chapter Reviews(Q1) pgs (6-19) pgs (4-33) pgs (2-49) Unfinished work/activity Review for Test pgs , , Previous Reviews for Test(Q1) pgs , 76-77, min: Assessment Chapter Tests/ Test Preps pg. 112 (1-17) pg.113 (1-4) pg. 144 (1-22) pg. 145 (1-7) pg. 174 (1-20) pg. 175 (1-5) Previous Chapter Tests/ Test Preps(Q1) pg. 44 (1-18) pg. 78 (4-33) pg. 79 (1-12) pg. 210 (1-53) pg. 211 (1-12) Test will be composed of 20 problems Unfinished work/activity 45 min: 2nd Quarter Short Cycle Assessment 45 min: 2nd Quarter Short Cycle Assessment: Review over Assessment