Week 1 of the First Quarter

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Weeks: 1- 6

Instructional Unit Plan Unit 5 Georgia Performance Standards M8A3d Recognize functions in a variety of representations and a variety of contexts. M8A3e Identify relations and functions as linear or nonlinear. M8A3f Translate among verbal, tabular, graphic, or algebraic representations of functions. M8A4a Interpret slope as a rate of change. M8A4b Determine meaning of the slope and y-intercept in a given situation. M8A4c Graph equations in the form y = mx +b M8A4d Graph equations in the form ax + by = c M8A4e Graph the solution set of an inequality, identifying whether the solution set is an open or a closed half-plane. M8A4f Determine the equation of a line given a graph, numerical information that defines the line or a context involving linear relationship. M8A4g Solve problems involving linear relationships. Unit 5 Framework Enduring Understandings Unit 5 Framework Essential Questions

Collecting and exploring data can sometimes help one discover What does data tell me? patterns in the way in which two quantities vary. How does change in one variable affect the other variable in a given Changes in varying quantities are often related by patterns, which once situation? discovered, can be used to predict outcomes and solve problems. Which tells me more about the relationship I am investigating – a table, Written descriptions, tables, graphs, and equations are useful in a graph or an equation? Why? representing and investigating relationships between varying quantities. What strategies can I use to help me understand and represent real Different descriptions (written descriptions, tables, graphs, and situations involving linear relationships? equations) of the relationship between varying quantities may have How can the properties of lines help me to understand graphing linear different strengths and weaknesses. functions? Linear functions may be used to represent and generalize real How is a linear inequality like a linear equation? How are they different? situations. Vocabulary Arithmetic sequence Constant function Literacy Function Line of best fit ELA8RC2 The student participates in discussions related to curricular Scatter plot Slope learning in all subject areas. Slope-intercept form ELA8RC3 The student acquires new vocabulary in each content area Unit 5 Assessment and uses it correctly. GPS Framework Unit 5 Linear Equations and Inequalities in Two ELA8RC4 The student establishes a context for information acquired by Variables, Culminating Task “Is the Data Linear?” pp. 41 – 43 of 43 reading across subject areas. Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 2

Georgia Performance Standards

Unit 5 Framework Enduring Understandings Unit 5 Framework Essential Questions

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 1 Warm-Up/Quick Practice Problem Solving Mental Math: Use the ‘triple, double, double’ strategy to multiply by 12 Solve routine problems and non-routine problems involving the Make a (for example, 16 feet = __ inches, think 16 x 3 = 48, 48 x 2 = 96 and 96 Table and Logical Reasoning strategies x 2 = 192) HM Course 3, “Problem-Solving Strategies,” pp. 819 and 821 Define relations using set notation Solve and graph inequalities in one variable on a number line Skill Mastery: Find fraction, decimal, and percent equivalents

Focus Lessons Ref # State Objectives Resources Materials Standards 3.1.1 M8A3d, e, f Review linear relationships and GPS Framework Unit 5 Linear Timer or clock with second hand linear equations Equations and Inequalities in Two Materials to gather data Variables, “Heartbeats,” pp. 9 - 11 Note: keep data for Week 4 Differentiated Task

3.1.2 M8A3d, e, f Understand the meaning of a GPS Framework Unit 5 Linear Copies of task linear equation Equations and Inequalities in Two Create a linear equation based on Variables, “Drain the Pool,” pp. 12 - 14 a context

3.1.3 Foundation for Understand the use of coordinate MIC Graphing Equations, “Where Student Activity Sheets 1 and 2— M8A4a, b systems to represent data There’s Smoke” Where’s the Fire? copies and transparency, pp. 65 – 66 Apply appropriate mathematical and Coordinates on a Screen, pp. 1 - Compass cards (MIC Looking At language to discuss coordinate 5 Angles, p. 96) systems Protractors

3.1.4 Foundation for Record data on a coordinate MIC Graphing Equations, “Where Student Activity Sheet 3 -- copies and M8A4a, b, e system using equations and There’s Smoke” Coordinates on a transparency, p. 67 inequalities Screen and Fire Regions, pp. 5 - 8 Centimeter rulers

3.1.5 See Variety of Instructional Tasks Variety of Instructional Tasks Homework

Weekly Focus: Identify a growth pattern as linear or nonlinear with “Water Lily” from MIC Ups and Downs, pp. 27 Weekly Focus: Identify – 28. (continue in week 2) proportional relationships

Maintenance: Review and apply the rules for computing with negative integers with “Negative Numbers” problems Maintenance: Solve 7 – 16 from MIC Revisiting Numbers, pp. 37 – 39. equations in one variable

Maintenance: Apply the concept of function with “Even More Secret Codes” from the GPS Framework Unit 4 Skill: Find fraction, decimal, Functional Relationships, pp. 77 - 90. and percent equivalents

Exploration: Investigate volume and surface area with “Reaching All Learners” and “Think and Discuss” from HM Course 3, p. 441.

Intervention:

Reflection with Closure How can I describe proportional relationships?

Journal How much data is needed before you can be sure the relationship is linear or proportional? Why is a grid system an efficient strategy to share information?

Evidence of Learning (Assessments) Weekly Focus: Selected MIC Graphing Equations Section A items Skill Mastery: Complete the chart. Fractions Decimals Percents 1 3/20 _____ 115% ____ 2.38 ______39% ____ 0.25 _____ Performance Assessments: Culminating Tasks:

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 2 Georgia Performance Standards

M8A4a Interpret slope as a rate of change. M8A4b Determine meaning of the slope and y-intercept in a given situation. M8A4c Graph equations in the form y = mx +b M8A4f Determine the equation of a line given a graph, numerical information that defines the line or a context involving linear relationship.

Unit 5 Framework Enduring Understandings Unit 5 Framework Essential Questions

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 2 Warm-Up/Quick Practice Problem Solving Mental Math: Use the 1/3,1/2, 1/2 strategy to divide by 12 (For example, Use simulations and tree diagrams to determine probability of compound 180 cookies are __dozen, think 180/3 = 60, 60/2 = 30 and 30/2 = 15, for events 15 dozen) MIC Great Predictions, “Free Meal” problems 1 – 8, pp. 40 – 42 Evaluate expressions with positive and negative integer exponents Note: Activity on page 41 can be assigned for Monday’s homework Determine probability of a compound event Skill Mastery: Find the two consecutive whole numbers in which a square root lies

Focus Lessons Ref # State Objectives Resources Materials Standards 3.2.6 M8A4a, b Identify points on a line, with and MIC Graphing Equations, “Directions Student Activity Sheet 4—copies and without using the coordinate grid as Pairs of Numbers” Directing transparency, p. 68 Explore the concept of slope Firefighters through #9, pp. 11 - 13 Graph paper

3.2.7 M8A4a, b Understand the relationship MIC Graphing Equations, “Directions Student work from previous lesson among all points on a straight line as Pairs of Numbers” Directing graphed on a coordinate grid Firefighters through #14, pp. 13 - 14 Develop the concept of slope

3.2.8 M8A4a, b Find the slope of a line MIC Graphing Equations, “Directions Student Activity Sheet 5—copies and Draw lines with a given slope as Pairs of Numbers” Up and Down transparency, p. 69 the Slope through #19, pp. 15 - 16 Rulers Graph paper

3.2.9 M8A4a, b, c, f Calculate points on a line MIC Graphing Equations, “Equation of No additional materials Write rules to describe how a Line” Directions and Steps through particular straight lines are drawn #6, pp. 21 - 22

3.2.10 See Variety of Instructional Tasks Variety of Instructional Tasks Homework

Weekly Focus: Identify a growth pattern as linear or nonlinear with “Water Lily” from MIC Ups and Downs, pp. 27 – Weekly Focus: Find slope of 28. a line

Maintenance: Review and apply the rules for computing with negative integers with “Negative Numbers” problems Maintenance: Determine 7 – 16 from MIC Revisiting Numbers, pp. 37 – 39. and continue arithmetic sequences Maintenance: Apply the concept of function with “Even More Secret Codes” from the GPS Framework Unit 4 Functional Relationships, pp. 77 - 90. Skill: Determine square roots

Exploration: Investigate volume and surface area with “Reaching All Learners” and “Think and Discuss” from HM Course 3, p. 441.

Intervention:

Reflection with Closure How can I remember which element in a real world situation will be represented as the ‘constant’?

Journal Explain why the slope of a line can be determined from any two points on that line. Explain the statement “slope is interpreted as a rate of change.”

Evidence of Learning (Assessments) Weekly Focus: Selected MIC Graphing Equations Section B items Skill Mastery: Squares and square roots Name the two consecutive integers the number falls between: 176 550 93 140 Performance Assessments: Culminating Tasks: Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 3

Georgia Performance Standards

Unit 5 Framework Enduring Understandings Unit 5 Framework Essential Questions

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 3 Warm-Up/Quick Practice Problem Solving Mental Math: Break up the dividend (Look for compatible factors and Solve routine problems and non-routine problems involving the Guess multiples; for example, 648  6 is 600  6 and 48  6) and Check and Make an Organized List strategies Determine possible outcomes of an event HM Course 3, “Problem-Solving Strategies,” pp. 816 and 823 Write large and small numbers using scientific notation Skill Mastery: Write the prime factorization using exponents

Focus Lessons Ref # State Objectives Resources Materials Standards 3.3.11 M8A4a, b, c, f, Understand equations of lines MIC Graphing Equations, “Equation of Graph paper g Relate equations of lines to graphs a Line” Directions and Steps through #5, pp. 21 - 22

3.3.12 M8A4a, b, c, f, Understand equations of lines MIC Graphing Equations, “Equation of Graph paper g Relate equations of lines to graphs a Line” Directions and Steps through #12, pp. 22 - 23

3.3.13 M8A4a, b, c, f, Understand equations of lines MIC Graphing Equations, “Equation of Graph paper g Relate equations of lines to graphs a Line” What’s the Angle? pp. 24 - 25 Protractors or compass cards Graph paper

3.3.14 M8A4a, b Understand positive and GPS Framework Unit 5 Linear Copies of task negative slope Equations and Inequalities in Two Graph paper Investigate slope of Variables, “Walk the Line” and “Right Optional: Graphing calculators perpendicular lines to the Point,” pp. 18 – 19 and 25 of 43

3.3.15 See Variety of Instructional Tasks Variety of Instructional Tasks Homework

Weekly Focus: Solve real world problems involving linear equations with “Life Science Link” from HM Course 3, p. Weekly Focus: Relate 642. equations, tables and graphs

Maintenance: Solve probability problems involving dependent events with “Ape Shapes” from MIC Great Maintenance: Evaluate Predictions, pp. 17 – 18. expressions with positive or negative exponents Maintenance: Apply knowledge of transformations with Hands On Lab “Combine Transformations” from HM Course 3, pp. 362 – 363. Skill: Write the prime factorization using exponents

Exploration: Explore exponential growth with “Aquatic Weeds” and “Double Trouble” from MIC Ups and Downs, pp. 29 – 31. (note: disregard questions 15b and 21a, regarding quadratic patterns)

Intervention:

Reflection with Closure What information from a line on a graph can I use to record that line’s equation accurately?

Journal What are some real world contexts that result in a graph showing a negative slope? How do the scales on the x-axis and y-axis affect the slope of the line? In which situations is the y-intercept 0? When does the line of an equation pass through (0, 0)?

Evidence of Learning (Assessments) Weekly Focus: Selected MIC Graphing Equations Section C items Skill Mastery: Write the prime factorization of each number using exponents. 45 168 92 51 Performance Assessments: Culminating Tasks:

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 4 Georgia Performance Standards

M8A3d Recognize functions in a variety of representations and a variety of contexts. M8A3e Identify relations and functions as linear or nonlinear. M8A3f Translate among verbal, tabular, graphic, or algebraic representations of functions. M8A4b Determine meaning of the slope and y-intercept in a given situation. M8A4c Graph equations in the form y = mx +b M8A4d Graph equations in the form ax + by = c M8A4f Determine the equation of a line given a graph, numerical information that defines the line or a context involving linear relationship. M8A4g Solve problems involving linear relationships. M8D4b Estimate and determine a line of best fit from a scatter plot.

Unit 5 Framework Enduring Understandings Unit 5 Framework Essential Questions

Arithmetic sequence ELA8RC2 The student participates in discussions related to curricular Constant function learning in all subject areas. Function Line of best fit ELA8RC3 The student acquires new vocabulary in each content area and Scatter plot uses it correctly. Slope Slope-intercept form ELA8RC4 The student establishes a context for information acquired by reading across subject areas. Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 4 Warm-Up/Quick Practice Problem Solving Mental Math: Break up the dividend Interpret graphs Evaluate expressions, including those containing absolute values Identify misleading representations of data Identify and continue arithmetic sequences MIC Insights into Data, “Different Impressions” problems 7-10 and Skill Mastery: Find percent of a number “Check Your Work” problems 1-2, pp. 26 – 28 and 30 - 31

Focus Lessons Ref # State Objectives Resources Materials Standards 3.4.16 M8A4b, c, d, f Graph a given linear equation GPS Framework Unit 5 Linear Copes of tasks Find the equation from given Equations and Inequalities in Two Optional: Graphing calculators information about the graph Variables, “Faster than a Graphing Calculator” and “Forget the Formula,” pp.15 – 17 of 43

3.4.17 M8A4f, g Explore alternate solutions to GPS Framework Unit 5 Linear Copies of task problems involving linear functions Equations and Inequalities in Two Variables, “Ring Size,” pp. 22 - 24 of 43

3.4.18 M8D4b Compare data on tables and scatter MIC Insights into Data, “Correlating Transparency of graph on page 45 M8A3d, e, f plots Data” Growing Babies through #7, pp. 44 - 47

3.4.19 M8D4b Understand linear correlation MIC Insights into Data, “Correlating Transparency of graphs on page 48 M8A3d, e Determine strength of linear Data” Growing Babies through #12, Optional: Transparency of Student correlation from a scatter plot pp. 44 - 47 Activity 2, p. 92

3.4.20 See Variety of Instructional Tasks Variety of Instructional Tasks Homework

Weekly Focus: Determine and justify a line of best fit with data gathered in Lesson 3.1.1 “Heartbeats” from GPS Weekly Focus: Determine Framework Unit 5 Linear Equations and Inequalities in Two Variables, pp. 10 - 12 equation from information on a graph; graph a line, given Maintenance: Solve probability problems involving dependent events with “Ape Shapes” from MIC Great the equation in the form of Predictions, pp. 17 – 18. y = mx +b

Maintenance: Apply knowledge of transformations with Hands On Lab “Combine Transformations” from HM Maintenance: Interpret data Course 3, pp. 362 – 363. from graphs

Skill: Find percent of a Exploration: Explore exponential growth with “Aquatic Weeds” and “Double Trouble” from MIC Ups and Downs, number pp. 29 – 31. (note: disregard questions 15b and 21a, regarding quadratic patterns)

Intervention:

Reflection with Closure Why can’t I just connect the points on a scatter plot—it looks just like a line graph?

Journal Why are scatter plots effective when gathering data and determining relationships? How many points should be plotted on a scatter plot to make accurate decisions about the relationship between the variables?

Evidence of Learning (Assessments) Weekly Focus: Selected MIC Insights into Data Section E items Skill Mastery: Percent of a number 18% of 92 48% of 48 120% of 90 200% of 25 Performance Assessments: Culminating Tasks:

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 5

Georgia Performance Standards M8A3d Recognize functions in a variety of representations and a variety of contexts. M8A3e Identify relations and functions as linear or nonlinear. M8A3f Translate among verbal, tabular, graphic, or algebraic representations of functions. M8A4e Graph the solution set of an inequality, identifying whether the solution set is an open or a closed half-plane. M8A4f Determine the equation of a line given a graph, numerical information that defines the line or a context involving linear relationship. M8A4g Solve problems involving linear relationships. M8D4b Estimate and determine a line of best fit from a scatter plot.

Unit 5 Framework Enduring Understandings Unit 5 Framework Essential Questions

Collecting and exploring data can sometimes help one discover What does data tell me? patterns in the way in which two quantities vary. How does change in one variable affect the other variable in a given Changes in varying quantities are often related by patterns, which situation? once discovered, can be used to predict outcomes and solve Which tells me more about the relationship I am investigating – a table, a problems. graph or an equation? Why? Written descriptions, tables, graphs, and equations are useful in What strategies can I use to help me understand and represent real representing and investigating relationships between varying situations involving linear relationships? quantities. How can the properties of lines help me to understand graphing linear Different descriptions (written descriptions, tables, graphs, and functions? equations) of the relationship between varying quantities may have How is a linear inequality like a linear equation? How are they different? different strengths and weaknesses. Linear functions may be used to represent and generalize real situations. Vocabulary Literacy Arithmetic sequence ELA8RC2 The student participates in discussions related to curricular Constant function learning in all subject areas. Function Line of best fit ELA8RC3 The student acquires new vocabulary in each content area and Scatter plot uses it correctly. Slope Slope-intercept form ELA8RC4 The student establishes a context for information acquired by reading across subject areas. Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 5 Warm-Up/Quick Practice Problem Solving Mental Math: Make compatibles in division (Decompose the dividend to Solve routine problems and non-routine problems involving the Guess and get multiples of the divisor; for example, 256  4 is the same as 240  4 Check and Logical Reasoning strategies and 16  4, for 60 + 4 as partial quotients) HM Course 3, “Problem-Solving Strategies,” pp. 816 and 821 All operations with fractions and mixed numbers Solve equations and inequalities in one variable Skill Mastery: Solve proportions

Focus Lessons Ref # State Objectives Resources Materials Standards 3.5.21 M8D4b Investigate scatter plots and lines MIC Insights into Data, “Lines that Student Activity Sheets 7-9 for each M8A3d, e of best fit Summarize Data” Egg Hunt through group, pp. 97 – 99 #8, pp. 53 - 55 Student Activity Sheet 10 for each student or pair of students, p. 100 Blank paper and graph paper Rulers 3.5.22 M8D4b Investigate scatter plots and lines MIC Insights into Data, “Lines that Student Activity Sheet 11 for each M8A3d, e of best fit Summarize Data” Egg Hunt through student or pair of students, p. 101 Interpret the y-intercept of a line of #15, pp. 56 - 58 Transparency of data on page 57 best fit in terms of the data Blank transparencies

3.5.23 M8A4e Graph the solution set of an GPS Framework Unit 5 Linear Scrap paper for students to participate inequality Equations and Inequalities in Two in the Left Hand/Right Hand Variables, “What Would that Graph experiment Look Like? pp. 35 – 37 of 43 Graph paper Optional: Graphing calculators

3.5.24 M8A4e Graph the solution set of an GPS Framework Unit 5 Linear Copies of task inequality Equations and Inequalities in Two Graph paper Variables, “Cholesterol – Good or Optional: Graphing calculators Bad?” pp. 38 – 39 of 43

3.5.25 See Variety of Instructional Tasks Variety of Instructional Tasks Homework

Weekly Focus: Solve a problem involving a line of best fit with “Mineral Samples” from GPS Framework Unit 5 Weekly Focus: Gather data Linear Equations and Inequalities in Two Variables, pp. 20 –21 of 43. for a scatter plot, refer to MIC Insights into Data, p. 58 Maintenance: Use a simulation to take a sample and interpret data gathered with “Fish Farmer Activity” and #1 - #3 from MIC Great Predictions, pp. 24 – 25. (Option: in week 2 of this activity, students can work with all data Maintenance: Solve multi- gathered in week 1 and answer #4 - #6.) step word problems

Maintenance: Create Venn diagrams with “Challenge 9-2” and problems 5, 10, and 13 –16 from HM Course 3, pp. Skill: Solve proportions 469 – 471.

Exploration: Explore the Golden Rectangle with “Challenge 5-2” from HM Course 3, p. 223. Extend with appropriate online sites.

Intervention:

Reflection with Closure Do I prefer to use tables or scatter plots to analyze data?

Journal Would there ever be situations when there is no line of best fit once the data is graphed on the scatter plot? Explain why or why not. How relevant is the y-intercept of a line of best fit on a scatter plot? What does that y-intercept signify? Why are some inequalities represented on a number line and others are graphed on the coordinate plane?

Evidence of Learning (Assessments) Weekly Focus: Selected MIC Insights into Data Section E items Skill Mastery: Solve proportions 6.8 3.4 f 162 t 15 9.35 g     j 1.5 9 27 7.5 2.5 3 13.5 Performance Assessments: Culminating Tasks: Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 6

Georgia Performance Standards

M8A3d Recognize functions in a variety of representations and a variety of contexts. M8A3e Identify relations and functions as linear or nonlinear. M8A3f Translate among verbal, tabular, graphic, or algebraic representations of functions. M8A4a Interpret slope as a rate of change. M8A4b Determine meaning of the slope and y-intercept in a given situation. M8A4c Graph equations in the form y = mx +b M8A4d Graph equations in the form ax + by = c M8A4e Graph the solution set of an inequality, identifying whether the solution set is an open or a closed half-plane. M8A4f Determine the equation of a line given a graph, numerical information that defines the line or a context involving linear relationship. M8D4a Gather data that can be modeled with a linear function. M8D4b Estimate and determine a line of best fit from a scatter plot.

Unit 5 Framework Enduring Understandings Unit 5 Framework Essential Questions

Warm-Up/Quick Practice Problem Solving Mental Math: Make compatibles in division Solve problems involving patterns Find the third angle measurement in a triangle when given the first two MIC Patterns and Figures, “V and W Formations” and “Check Your angle measurements Work” pp. 5 -9 Evaluate expressions with positive and negative integer exponents Option: Continue work on “Crossing the River” task from Lesson 3.6.27 Skill Mastery: Multiply and divide decimals

Focus Lessons Ref # State Objectives Resources Materials Standards 3.6.26 M8D4a Record data to verify predictions GPS Framework Unit 5 Linear Ample supply of elastic bands M8D4b Graph results Equations and Inequalities in Two Measuring tapes Understand variables that might Variables, “Bungee Jump,” p. 40 of 43 Small toys (bean bags are affect results and predictions recommended in the task) Materials to record class data

3.6.27 M8A4d Contrast the standard form for the GPS Framework Unit 5 Linear Copies of the task equation of a line with slope form Equations and Inequalities in Two Access to manipulatives for the equation of a line Variables, “Crossing the River,” p. 31- 34 of 43

3.6.28 M8A3d, e, f Solve problems involving linear GPS Framework Unit 5 Linear Will vary depending on experiments M8A4a, b, c, d, relationships Equations and Inequalities in Two selected—see task, pp. 41 and 42 e, f, g Variables, Culminating Task “Is the Recording materials M8D4a Data Linear?” pp. 41 – 43 of 43

3.6.29 M8P2c Develop and evaluate GPS Framework Unit 5 Linear Student presentations of data gathered M8P3a, b mathematical arguments Equations and Inequalities in Two in previous lesson Communicate using appropriate Variables, Culminating Task “Is the mathematical language Data Linear?” pp. 41 – 43 of 43

3.6.30 See Variety of Instructional Tasks Variety of Instructional Tasks Homework

Weekly Focus: Model and record relationships algebraically and graphically with “Staircases” from GPS Weekly Focus: Solve Framework Unit 5 Linear Equations and Inequalities in Two Variables, pp. 26 - 29 of 43. problems involving linear equations in two variables Maintenance: Use a simulation to take a sample and interpret data gathered with “Fish Farmer Activity” and #1 - #3 from MIC Great Predictions, pp. 24 – 25. (Option: in week 2 of this activity, students can work with all data Maintenance: Interpret or gathered in week 1 and answer #4 - #6.) construct Venn diagrams

Maintenance: Create Venn diagrams with “Challenge 9-2” and problems 5, 10, and 13 –16 from HM Course 3, pp. Skill: Multiply and divide 469 – 471. decimals

Exploration: Explore the Golden Rectangle with “Challenge 5-2” from HM Course 3, p. 223. Extend with appropriate online sites.

Intervention:

Reflection with Closure What are some real world school situations that represent linear relationships I could record algebraically and graphically?

Journal How much data should be gathered in order to determine relationships and make predictions? Can every real world relationship be recorded algebraically?

Evidence of Learning (Assessments) Weekly Focus: Selected HM Course 3 Chapter 12 items Skill Mastery: Multiply and divide decimals 7.33 x 0.5 = 42.6 ÷ 0.3 = 16 x 0.25 = 237.6 ÷ 0.06 = Performance Assessments: Culminating Tasks: GPS Framework Unit 5 Linear Equations and Inequalities in Two Variables, Culminating Task “Is the Data Linear?” pp. 41 – 43 of 43

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Weeks: 7- 9

Instructional Unit Plan Unit 6 Georgia Performance Standards M8G1a Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically. M8G1b Apply properties of angle pairs formed by parallel lines cut by a transversal. M8G1c Understand the properties of the ratio of segments of parallel lines cut by one or more transversals. M8G1d Understand the meaning of congruence: that all corresponding angle are congruent and all corresponding sides are congruent. M8G2a Apply properties of right triangles, including the Pythagorean theorem. M8G2b Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a right triangle. M8A1 Students will use algebra to represent, analyze, and solve problems. Unit 6 Framework Enduring Understandings Unit 6 Framework Essential Questions Parallel lines have the same slope and perpendicular lines have How can I be certain whether lines are parallel, perpendicular or skew opposite, reciprocal slopes. lines? When two lines intersect, vertical angles are congruent and adjacent Why do I always get a special angle relationship when any two lines angles are supplementary. intersect? When parallel lines are cut by a transversal, corresponding alternate When I draw a transversal through parallel lines, what are the special interior and alternate exterior angles are congruent. angle and segment relationships that occur? The length of segments formed by two non-parallel transversals cutting What information is necessary before I can conclude two figures are parallel lines is proportional to the distances of the parallel lines from congruent? the intersection of the transversals. How can my knowledge of constructing congruent triangles be used to Parallel lines can be constructed using the properties of parallel lines construct perpendicular and parallel lines? cut by a transversal. Can I find parallel lines that intersect? Why or why not? In Euclidean Geometry, there is exactly one line through a given point parallel to a second given line. Vocabulary Literacy Adjacent angles Alternate exterior/exterior angles Complementary angles Corresponding angles ELA8RC2 The student participates in discussions related to curricular Intersecting lines Perpendicular lines learning in all subject areas. Supplementary angles Reflection line Skew lines Same-side interior/exterior angles ELA8RC3 The student acquires new vocabulary in each content area Transversal Vertical angles Coincidental and uses it correctly. Congruent Equiangular Equilateral Linear pair Parallel lines ELA8RC4 The student establishes a context for information acquired by reading across subject areas. Unit 6 Assessment GPS Framework Unit 6 Parallel Lines and Congruence, Culminating Task “Surveying Constructions,” pp. 50 – 51 of 51

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 7

Georgia Performance Standards M8G1a Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically. M8G1b Apply properties of angle pairs formed by parallel lines cut by a transversal. M8G1c Understand the properties of the ratio of segments of parallel lines cut by one or more transversals. M8G1d Understand the meaning of congruence: that all corresponding angle are congruent and all corresponding sides are congruent. M8A1 Students will use algebra to represent, analyze, and solve problems.

Unit 6 Framework Enduring Understandings Unit 6 Framework Essential Questions

Parallel lines have the same slope and perpendicular lines have How can I be certain whether lines are parallel, perpendicular or skew opposite, reciprocal slopes. lines? When two lines intersect, vertical angles are congruent and adjacent Why do I always get a special angle relationship when any two lines angles are supplementary. intersect? When parallel lines are cut by a transversal, corresponding alternate When I draw a transversal through parallel lines, what are the special interior and alternate exterior angles are congruent. angle and segment relationships that occur? The length of segments formed by two non-parallel transversals cutting What information is necessary before I can conclude two figures are parallel lines is proportional to the distances of the parallel lines from congruent? the intersection of the transversals. How can my knowledge of constructing congruent triangles be used to Parallel lines can be constructed using the properties of parallel lines construct perpendicular and parallel lines? cut by a transversal. Can I find parallel lines that intersect? Why or why not? In Euclidean Geometry, there is exactly one line through a given point parallel to a second given line.

Vocabulary Literacy GPS Adjacent angles Alternate exterior/exterior angles Complementary angles Corresponding angles ELA8RC2 The student participates in discussions related to curricular Intersecting lines Perpendicular lines learning in all subject areas. Supplementary angles Reflection line Skew lines Same-side interior/exterior angles ELA8RC3 The student acquires new vocabulary in each content area Transversal Vertical angles and uses it correctly. Coincidental Congruent Equiangular Equilateral ELA8RC4 The student establishes a context for information acquired Linear pair Parallel lines by reading across subject areas.

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 7 Warm-Up/Quick Practice Problem Solving Mental Math: Divide by balancing (Multiply both the divisor and dividend Solve routine problems and non-routine problems involving the Make a by the same number to make ‘friendlier’ divisors; for example, with 3  Table and Work Backwards strategies 0.2 multiply both by 5 to get 15  1 ; for 120  50 multiply both by 2 for HM Course 3, “Problem-Solving Strategies,” pp. 819 and 817 240  100) Define relations using set notation Find square roots for perfect squares; find the two consecutive whole numbers in which a square root lies Skill Mastery: Apply order of operations

Focus Lessons Ref # State Objectives Resources Materials Standards 3.7.31 M8G1a Understand slope of sets of parallel MIC It’s All the Same, “Coordinate Graph paper or perpendicular lines Geometry” Parallel and Perpendicular, pp. 45 – 47 If technology is available, refer to websites noted on pages 7 and 15 of GPS Framework Unit 6 throughout the unit 3.7.32 M8G1a Review properties of parallel, GPS Framework Unit 6 Parallel Lines Copies of tasks perpendicular and intersecting and Congruence, “Constructions Straight edges lines and their related angle Revisited” Prerequisite Activities, pp. Protractors measurements 11 – 13 of 51 Compasses

3.7.33 M8G1a b c Introduce accurate GPS Framework Unit 6 Parallel Lines Copies of tasks M8A1 terminology to identify sets of and Congruence, “Constructions Straight edges lines and relative angle Revisited,” pp. 8 – 11 and 14 – 15 of Protractors positions 51 Compasses

3.7.34 M8G1a b c Apply properties of lines and GPS Framework Unit 6 Parallel Lines Copies of tasks M8A1 relative angle positions to solve and Congruence, “Lunch Line,” pp. 16 Access to straight edges and problems – 19 of 21 protractors

3.7.35 See Variety of Instructional Tasks Variety of Instructional Tasks Homework

Weekly Focus: Construct angles with Hands On Lab “Constructions” Think and Discuss and Try This from HM Weekly Focus: Model and Course 3, p. 335. define Unit 6 vocabulary If technology is available, refer to websites noted on pages 7 and 15 of GPS Framework Unit 6 throughout the unit Maintenance: Solve Maintenance: Graph and interpret lines of growth with “Gone Fishing” from MIC Insights into Data, p. 59. equations or inequalities in one variable Maintenance: Solve assorted measurement problems with “Physical Science Link” and “Home on the Range” from HM Course 3, pp. 398 and 445. Skill: Apply order of operations Exploration: Explore angle applications in real world contexts with “Ships Ahoy” and “Cars and Blind Spots” from MIC Looking at an Angle, pp. 6 - 7 and 9.

Intervention:

Reflection with Closure How does knowing these properties of lines and related angle positions make mathematicians more efficient in solving problems?

Journal Why is congruence so important in the study of geometry? Do transversals of parallel lines have to be straight lines? Why or why not? What is consistent among the angles of any two intersecting lines? Why?

Evidence of Learning (Assessments) Weekly Focus: Selected HM Course 3 Chapter 7 items Skill Mastery: Order of operations 4.2 + 62 – (8 + 12)2 = 137 – (3 x 45) + (25 ÷ 52) = (93 – 17) – (32 – 6) = 52 + 5 - 32 x 4 = Performance Assessments: Culminating Tasks:

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 8

Georgia Performance Standards M8G1a Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically. M8G1b Apply properties of angle pairs formed by parallel lines cut by a transversal. M8G1c Understand the properties of the ratio of segments of parallel lines cut by one or more transversals. M8G1d Understand the meaning of congruence: that all corresponding angle are congruent and all corresponding sides are congruent. M8G2a Apply properties of right triangles, including the Pythagorean theorem. M8G2b Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a right triangle. M8A1 Students will use algebra to represent, analyze, and solve problems.

Unit 6 Framework Enduring Understandings Unit 6 Framework Essential Questions

Vocabulary Literacy GPS

Adjacent angles Alternate exterior/exterior angles ELA8RC2 The student participates in discussions related to curricular Complementary angles Corresponding angles learning in all subject areas. Intersecting lines Perpendicular lines Supplementary angles Reflection line ELA8RC3 The student acquires new vocabulary in each content area Skew lines Same-side interior/exterior angles and uses it correctly. Transversal Vertical angles Coincidental Congruent ELA8RC4 The student establishes a context for information acquired Equiangular Equilateral by reading across subject areas. Linear pair Parallel lines

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 8 Warm-Up/Quick Practice Problem Solving Mental Math: Divide by balancing Interpret bar graphs and histograms Determine possible outcomes of an event MIC Insights into Data, “Using Data” problems 1-6, pp. 32 - 35 Write large and small numbers using scientific notation Skill Mastery: Order rational numbers

Focus Lessons Ref # State Objectives Resources Materials Standards 3.8.36 M8G1a b c d Apply properties of lines, angles GPS Framework Unit 6 Parallel Lines Copies of tasks M8A1 and congruence to solve problems and Congruence, “Window Pain” Part Access to straight edges and 1, pp. 20 – 24 of 51 protractors

3.8.37 M8G2a b Review and apply the Pythagorean MIC Looking at an Angle, “Reasoning No additional materials M8A1 theorem with Ratios” #3 - #5, pp. 47 - 49

3.8.38 M8G1a b c d Apply properties of lines, angles GPS Framework Unit 6 Parallel Lines Copies of tasks M8G2a b and congruence to solve problems and Congruence, “Building a House” Access to straight edges and M8A1 Prerequisite Activities, pp. 27 – 31 of protractors 51

3.8.39 M8G1a b c d Apply properties of lines, angles GPS Framework Unit 6 Parallel Lines Copies of tasks M8G2a b and congruence to solve problems and Congruence, “Building a House,” Many copies of “boards,” p. 33 of 51 M8A1 pp. 26 – 27 and 31 – 35 of 51 Access to straight edges and protractors

3.8.40 See Variety of Instructional Tasks Variety of Instructional Tasks Homework

Weekly Focus: Apply properties of lines, angles, and congruence to solve an area problem with “Window Pain” Weekly Focus: Solve Part 2 from GPS Framework Unit 6 Parallel Lines and Congruence, pp. 25 – 26 of 51. problems using the Pythagorean theorem Maintenance: Graph and interpret lines of growth with “Gone Fishing” from MIC Insights into Data, p. 59. Maintenance: Interpret data from graphs including Maintenance: Solve assorted measurement problems with “Physical Science Link” and “Home on the Range” from histograms and circle graphs HM Course 3, pp. 398 and 445. Skill: Order rational numbers Exploration: Explore angle applications in real world contexts with “Ships Ahoy” and “Cars and Blind Spots” from MIC Looking at an Angle, pp. 6 - 7 and 9.

Intervention:

Reflection with Closure Are there any real world applications for these concepts beyond construction and architecture?

Journal Why is there only one line through a given point parallel to a second given line? How many transversals can be drawn through a set of parallel lines? Why is it useful to know if two lines are perpendicular?

Evidence of Learning (Assessments) Weekly Focus: Selected HM Course 3 Chapter 7 items Skill Mastery: Order rational numbers 2 8 -9.5 23  -0.63 4.1 3 3 Performance Assessments: Culminating Tasks: Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 9

Georgia Performance Standards

M8G1a Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically. M8G1b Apply properties of angle pairs formed by parallel lines cut by a transversal. M8G1c Understand the properties of the ratio of segments of parallel lines cut by one or more transversals. M8G1d Understand the meaning of congruence: that all corresponding angle are congruent and all corresponding sides are congruent. M8G2a Apply properties of right triangles, including the Pythagorean theorem. M8G2b Recognize and interpret the Pythagorean theorem as a statement about areas of squares on the sides of a right triangle. M8A1 Students will use algebra to represent, analyze, and solve problems.

Unit 6 Framework Enduring Understandings Unit 6 Framework Essential Questions

Vocabulary Literacy GPS ELA8RC2 The student participates in discussions related to curricular Adjacent angles Alternate exterior/exterior angles learning in all subject areas. Complementary angles Corresponding angles Intersecting lines Perpendicular lines ELA8RC3 The student acquires new vocabulary in each content area Supplementary angles Reflection line and uses it correctly. Skew lines Same-side interior/exterior angles ELA8RC4 The student establishes a context for information acquired Transversal Vertical angles by reading across subject areas. Coincidental Congruent Equiangular Equilateral Linear pair Parallel lines

Atlanta Public Schools Teaching Plans Eighth Grade Quarter: 3 Week: 9 Warm-Up/Quick Practice Problem Solving Mental Math: Convert decimals to percents and percents to decimals. Solve routine problems and non-routine problems involving the Logical Include percents greater than 100 and less than 1. Reasoning and Make a Table strategies Evaluate expressions, including those containing absolute values HM Course 3, “Problem-Solving Strategies,” pp. 821 and 819 Identify and continue arithmetic sequences Skill Mastery: Find percent of a number

Focus Lessons Ref# State Objectives Resources Materials Standards 3.9.41 M8G1a b c d Apply properties of lines, angles GPS Framework Unit 6 Parallel Lines Copies of tasks M8G2a b and congruence to solve problems and Congruence, “Shelving Day 1,” Access to sample paper ‘bricks,” M8A1 pp. 36 – 40 of 51 straight edges, and protractors

3.9.42 M8G1a b c d Apply properties of lines, angles GPS Framework Unit 6 Parallel Lines Student work from previous lesson M8G2a b and congruence to solve problems and Congruence, “Shelving Day 1,” Access to sample paper ‘bricks,” M8A1 pp. 36 – 40 of 51 straight edges, and protractors

3.9.43 M8G1a b c d Apply properties of lines, angles GPS Framework Unit 6 Parallel Lines Copies of tasks M8A1 and congruence to solve problems and Congruence, “Shelving Day 2,” Access to straight edges and pp. 41 – 48 of 51 protractors

3.9.44 M8G1a b c d Apply geometric properties to GPS Framework Unit 6 Parallel Lines Copies of task M8A1 construct a scaled drawing and Congruence, Culminating Task Access to geometry and measurement M8P2c Develop and evaluate “Surveying Constructions,” pp. 50 – 51 tools mathematical arguments of 51 M8P3a, b Completed tasks to present Communicate using appropriate mathematical language 3.9.45 See Variety of Instructional Tasks Variety of Instructional Tasks Homework

Weekly Focus: Design roads that are parallel and perpendicular to each other with “Coordinate Geometry” Roads Weekly Focus: Continue to be Crossed from MIC It’s All the Same, p. 48. work on “Shelving Day 1,” “Shelving Day 2,” and Maintenance: Graph and interpret data on a scatter plot with “Check Your Work” #2 - #3 from MIC Insights into “Surveying Construction” Data, pp. 62 - 63. tasks

Maintenance: Solve multi- Maintenance: Review properties of geometric figures with “Polygon Rummy” from HM Course 3, p. 374. step word problems

Exploration: Explore informal strategies to solve systems of equations. Refer to supplemental HM Course 3 Skill: Find percent of a materials. number

Intervention:

Reflection with Closure What can I use to help me remember all the vocabulary related to this work with angles and lines?

Journal How do these related angle measurements connect with our work with circles? Why is it reasonable that alternate exterior angles or alternate interior angles are congruent? How do these geometry concepts relate to algebra?

Evidence of Learning (Assessments) Weekly Focus: Selected HM Course 3 Chapter 7 items Skill Mastery: Percent of a number 13% of 70 125% of 300 75% of 60 250% of 45 Performance Assessments: Culminating Tasks: GPS Framework Unit 6 Parallel Lines and Congruence, Culminating Task “Surveying Constructions,” pp. 50 – 51 of 51