Instructional Unit Plan Teacher: Grade Level: 8th Grade Mathematics Content Area(s): Mathematics Implementation Dates: MOVING STRAIGHT AHEAD Aug.8-Sept. 16, 2005 Unit Focus: Algebra Linear Relationships: Rates, Solving & Writing Equations, Patterns and Predictions, Drawing Tables & Graphs Vocabulary: Essential Terms Developed In Unit: Coefficient, coordinate pair, linear, linear relationship, point of intersection, rise, run, slope, y-intercept Terms Developed In Previous Units: independent/dependent variables, data, prediction, linear relationship, pattern, function, quantities, coordinate graph, x & y-axis (axes), rate, ratio, factors, equation, intersect, table, variable, inverse operations, intersection, graph, coordinate graph Concepts: o Recognize & represent the relationships among variables in a variety of ways o Identify variables & determine an appropriate range of values for independent/dependent variables o Collect data & use patterns in tables and graphs to make predictions (interpret data) o Recognize that linearity is associated w/ a constant rate of change b/w 2 variables o Find the slope & y-intercept of a linear equation & interpret the meaning of each o Write a linear equation w/ the slope & y-intercept Skills: o Basic operations using integers (mult. /div. Add/sub.) o Solve for a missing variable (use symbols to represent relationships b/w variables) o Graph data on a coordinate graph o Understand the meaning of parallel and intersecting lines o Compute and interpret ratios o Find rates of change b/w variables o Write equations/’rules’ based on a linear pattern Instructional Unit Plan Learning Activities – Description of the learning activities that will develop the knowledge and skills required by the performance standard: 1. Investigation 1-Predicting from Patterns o Problem 1.1b- Bouncing Balls Applications: 1-8 Extensions: 9 Math Reflections: 1 Big Math Idea-Summary: How do we identify, represent, and interpret linear relationships in tabular, graphical, and symbolic? 2. Investigation 2- Walking Rates o Problem: 2.1- Walking to the Yogurt Shop Connections: 14-17 o Problem 2.2- Changing the Walking Rate Applications: 1-5 / 7-9 o Problem 2.3- Walking for Charity Applications: 6 Connections 18-20 o Problem 2.4- Walking to Win Applications: 10-12 Assessment: Check-Up o Math Reflections: 1-5 o Big Math Idea- Summary: How do we write and interpret linear equations in y = mx + b form. 3. Investigation 3- Exploring Lines with a Graphing Calculator o Problem 3.1 Getting to the Point Connections: 24-26 o Problem 3.2 Graphing Lines Applications: 1-4 & 6 Connections: 18-21 Extensions: 28 & 29 o Problem 3.4 Planning a Skating Party Part 1 a. Applications: 5-8 b. Connections: 22-23 Part 2 a. Applications: 9-17 b. Assessment: Quiz A o Reflections: 1, 2, & 3 o Big Math Idea- Summary: How do we find and interpret the point of intersection of two lines? 4. Investigation 4- Solving Equations o Problem 4.1- Paying in Installments Applications: 1-8 Connections: 12 & 13 o Problem 4.2 - Using the Symbolic Method Applications: 9, Connections: 14 o Problem 4.3 - Analyzing Bones Applications: 10 Connections: 15 o Math Reflections: 1 o Big Math Idea: Summary What does the x and y intercepts mean in a equation Instructional Unit Plan 6. Investigation 5 – Exploring Slope o Problem 5.1 o ACE Questions: 14-16 o Connections: 17-20 o Extensions: 26 o Problem 5.2 o ACE Questions: 14-16 o Connections: 17-20 o Extensions: 26 o Big Math Idea-Summary How do find the slope of a line. How do we interpret slope as a ratio of vertical change to horizontal change. 7. Investigation 6 - Writing an Equation for a Line o Problems 6.1 o ACE Questions: 1-13 o Problem 6.2 o ACE Questions: 14-16 o Connections: 17-20 o Extensions: 26 o Problems 6.3 o Connections: 21-25 o Extensions: 27-30 o Big Idea: Summary o Identify x- and y-intercept from a graph or an equation. o District Assessment Description of the Assessments that will be used to provide evidence of student learning that targets the standards: Formative Assessment 1 Unit Test Check-Up Quiz Description of the rubrics or criteria that will be used to assess student performance: See Attachment Unit Resources: Tape CMP Books Graphing Calculators Balls Computers/ Excel Meter sticks Grid Paper Technology links: Chart Paper Microsoft Excel Markers/yarn Graphing Calculators Lab Sheets GMI website Transparencies ________________________________________________________________________ ________________________________________________________________________ New Mexico Content Standards, Benchmarks and Performances Addressed: Strand 1: Number and Operations Standard: Students will understand numerical concepts and mathematical operations 5-8 Benchmark 1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems Strand 2: Algebra Standard: Students will understand algebraic concepts and applications. 5-8 Benchmark 1: Understand patterns, relations, and functions Move between numerical, tabular, and graphical representations of linear relationships. Use variables to generalize patterns and information presented in tables, charts, and graphs: o Graph linear functions noting that the vertical change per unit of horizontal change (the slope of the graph) is always the same o Plot the values of quantities whose ratios are always the same, fit a line to the plot, and understand that the slope of the line equals the quantities 5-8 Benchmarks 2: Represent and analyze mathematical situations and structures using algebraic symbols. Demonstrate the difference between an equation and an expression. Graph solution sets of linear equations in two variables on the coordinate plane. Formulate and solve problems involving simple linear relationships, find percents of a given number, variable situations, and unknown quantities. Use symbols, variables, expressions, inequalities, equations, and simple systems of equations to represent problem situations that involve variables or unknown quantities.
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