Moving Straight Ahead Unit Plan

							                                           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
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       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.