Unit 3 Linear Equations Math 8
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1 Number of Days: 24 11/28/16 12/23/16 Unit Goals Stage 1 Unit Description: Students learn about linear equations in two variables. Students explore concepts of slope and intercepts as they write and graph linear equations in two variables. A study of linear equations will provide students with opportunities to model relationships between two quantities. Materials: graph paper*, calculators, Desmos website/app, AngLegs (* Paper tool available at LBUSD Instructional Tools Middle School Mathematical Tools) Standards for Mathematical Practice Transfer Goals SMP 1 Make sense of problems and persevere in solving Students will be able to independently use their learning to Make sense of never-before-seen problems and persevere in solving them. them. Construct viable arguments and critique the reasoning of others. SMP 2 Reason abstractly and Making Meaning quantitatively. UNDERSTANDINGS ESSENTIAL QUESTIONS SMP 3 Construct viable Students will understand that Students will keep considering arguments and critique the A linear equation of the form y = mx + b may Why is y = mx + b considered a linear equation? reasoning of others. SMP 4 Model with mathematics. How can similar triangles be used to explain why SMP 5 Use appropriate tools the slope is the same between any two points on a strategically. non-vertical line? SMP 6 Attend to precision. How can you use tables and graphs to represent SMP 7 Look for and make use of linear equations? structure. What is the relationship between the constant of SMP 8 Look for and express proportionality, the slope of the graph, and the unit regularity in repeated rate of a proportional relationship? reasoning. Standards for Mathematical Content Clusters Addressed [m] 8.EE.B Understand the connections between proportional relationships, lines, and linear equations. represent either a proportional ( b = 0 ) or nonproportional ( b 0 ) relationship depending on the value of b. Linear equations can be represented in different ways, such as algebraically, graphically, numerically in tables, or by verbal descriptions. The slope of a non-vertical line is the same between any two points along that line. In a proportional relationship between two quantities, the constant of proportionality, the slope of the graph, and the unit rate of the relationship are equal. KNOWLEDGE Students will know The definition of academic vocabulary words, such as linear equation, rate of change, slope, and slopeintercept form. A linear equation can be represented by y = mx + b and its graph is a straight line. The slope of a line is the change in y divided by the change in x. The graph of a proportional relationship is a straight line through the origin. Acquisition SKILLS Students will be skilled at and/or be able to Use slope-intercept form to graph or write linear equations. Find the slope of a line by using slope triangles or the slope formula. Graph proportional relationships and interpret the unit rate as the slope of the graph. Compare proportional relationships represented in different ways. LONG BEACH UNIFIED SCHOOL DISTRICT 1 Posted 11/3/16
2 Standards for Mathematical Practice SMP 1 Make sense of problems and persevere in solving them. SMP 2 Reason abstractly and quantitatively. SMP 3 Construct viable arguments and critique the reasoning of others. SMP 4 Model with mathematics. SMP 5 Use appropriate tools strategically. SMP 6 Attend to precision. SMP 7 Look for and make use of structure. SMP 8 Look for and express regularity in repeated reasoning. Assessed Grade Level Standards Standards for Mathematical Content [m] 8.EE.B Understand the connections between proportional relationships, lines, and linear equations. 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. Key: [m] = major clusters; [s] = supporting clusters; [a] = additional clusters LONG BEACH UNIFIED SCHOOL DISTRICT 2 Posted 11/3/16
3 Assessment Evidence Unit Assessment Evidence of Learning Stage 2 Claim 1: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Concepts and skills that may be assessed in Claim1: [m] 8.EE.B The student graphs proportional relationships. The student interprets the unit rate as the slope of the graph of a proportional relationship. The student compares two different proportional relationships represented in different formats. The student finds the equation y = mx or y = mx + b for a line. Claim 2: Students can solve a range of wellposed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies. Standard clusters that may be assessed in Claim 2: 8.EE.B Claim 3: The student can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others. Standard clusters that may be assessed in Claim 3: 8.EE.B Claim 4: The student can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Standard clusters that may be assessed in Claim 4: 8.EE.B Other Evidence Formative Assessment Opportunities Informal teacher observations Checking for understanding using active participation strategies Exit slips/summaries Modeling Lessons (SMP 4) s Formative Assessment Lessons (FAL) Quizzes / Chapter Tests Intranet Unit Assessment Resources Big Ideas Math Performance s SBAC Interim Assessment Blocks Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website M Mathematics Curriculum Documents LONG BEACH UNIFIED SCHOOL DISTRICT 3 Posted 11/3/16
4 1 day I will explore linear equations by participating in the Opening. OPENING TASK How Do I See The Pattern Growing? This Opening asks students to think about how they see a pattern growing. Give students time to work independently and then have them work with a partner. Next, facilitate a class discussion utilizing Talk Moves about how they see the pattern growing. This task is a gateway into the entire unit on linear equations. Conceptual Understanding: How Do I See The Pattern Growing? 4-5 I will investigate linear equations by Identifying solutions. Using a table of values to graph the relationship. Exploring the equations and graphs of vertical and horizontal lines. Using technology, such as graphing calculators or Desmos, to explore characteristics of the graphs. (SMP 5) o How can you recognize a linear equation? o What does the graph of a linear equation look like? o Explain why any solution point of a linear equation will lie on the graph of its line. (SMP 3) o Describe the graphs of x = a and y = b. Section 4.1 (Activity 1; STEM Video: Hurricanes! Procedural Skills and Fluency: Graphing Linear Equations Group Activity STEM Performance : Anatomy of a Hurricane LONG BEACH UNIFIED SCHOOL DISTRICT 4 Posted 11/3/16
5 I will explore the slope of a line by 4-5 Describing the different types of slopes (positive, negative, zero, and undefined). Using slope triangles to find the slope from a graph. Explaining that the slope is the same between any two distinct points on a non-vertical line in the coordinate plane using similar triangles. (SMP 3) Using the slope formula to find the slope from two points on the line. o Explain why you can use any two points on the line to find slope. (SMP 3) o How can you find the slope of a linear equation from a table? From a graph? Section 4.2 (Activities 1, 2, and 3; Conceptual Understanding: Point, Point, Slope Rise-Run Triangles Similar Triangles and Slope Interactive Activity Slope From Two Points Understanding Slope with Similar Triangles Video Procedural Skills and Fluency: Finding Slope: Solo-Team- Teach Slope PowerPoint Modeling: Baby Beats (SMP 4) 4-5 I will represent proportional relationships by Writing linear equations in the form y = mx. Interpreting the unit rate as equal to the slope of the graph and the constant of proportionality. Using tables, graphs, equations, and verbal descriptions to represent real-world proportional relationships. (SMP 2) Using tables, graphs, equations, and verbal descriptions to compare two different proportional relationships. o How can you use the unit rate to write an equation to represent a proportional relationship? o How is slope related to the unit rate and constant of proportionality in proportional relationships? Section 4.3 (Activities 1, 2, and 3; Examples 1 and 3) Desmos: Sugar, Sugar On Your Mark Activity Peaches and Plums Shelves Sore Throats Squares and Circles Stuffing Envelopes LONG BEACH UNIFIED SCHOOL DISTRICT 5 Posted 11/3/16
6 5-6 I will represent linear non-proportional relationships by Using patterns to build conceptual understanding of linear non-proportional relationships represented in tables, graphs, equations, and verbal descriptions. (SMP 2) Graphing linear equations in slope-intercept form using the slope and y-intercept. Determining the slope and y-intercept from analyzing an equation or graph. Writing an equation in slope-intercept form from a graph, a verbal description, or a table. (SMP 2) Deriving 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. Writing linear equations in the form y = mx + b and explaining that when b 0, the relationship between x and y is non-proportional. (SMP 3) o How can you determine the slope and the y-intercept of a linear equation from a graph? o How can you graph a line using the slope and y-intercept? o How do you write a linear equation in slopeintercept form to model a linear relationship given a graph, given a table, or a description? o Explain how you can identify a linear non-proportional relationship from a table, a graph, and an equation. (SMP 3) Section 4.4 (Activities 1 and 2; Section 4.6 (Activities 1 and 3; Conceptual Understanding: Linear Equation From a Table of Values mypd Course #3054: Building Conceptual Understanding of Functions Using Desmos The Pattern and Function Connection Book Which One Doesn t Belong? Linear Equations Writing Linear Functions Procedural Skills and Fluency: Cooperative Frames: Slope-Intercept Form Desmos Polygraph: Lines Gym Membership Plans Pig Pen School Lunch Performance Modeling: Styrofoam Cups (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 6 Posted 11/3/16
7 2-3 I will check my understanding of linear equations by participating in the FAL. FORMATIVE ASSESSMENT LESSON Defining Lines by Points, Slopes, and Equations (SMP 1, 2, 3, 5, 6, 7, 8) 1-2 I will prepare for the unit assessment on linear equations by Incorporating the Standards for Mathematical Practice (SMPs) along with the content standards to review the unit. Ch. 4 Study Help (p. 164) Ch. 4 Review (p ) Assembly Lines Performance 1 day Unit Assessment Synergy: Math 8 Unit 3 LONG BEACH UNIFIED SCHOOL DISTRICT 7 Posted 11/3/16
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