Middle School Instructional Practices Meeting 4: October 26, 2009 Strand 2: Patterns, Relationships, and Algebraic Thinking (Algebraic Reasoning) Key Skills: Solve problems using the order of operations Find the missing term in an algebraic sequence Generate multiple representations of functional relationships Solve problems involving equations or inequalities Resource Sample Activities HAPGs: Grade 6: Learning Focus 4.2 – Integers and Algebraic Relationships Grade 7: Learning Focus 4.1 – Algebraic Expression and Equations Learning Focus 4.2 – Developing Algebraic Reasoning Learning Focus 4.3 – Multiple Representations of Functions Grade 8: Learning Focus 3.1 – Patterns and Sequences Learning Focus 3.2 – Equivalence in Algebraic Expressions and Equations Learning Focus 3.3 – Solving Equations and Inequalities Grade 6: Number Equivalencies Task Cards, Integers and their Patterns, Find the Missing Term, Concrete Patterns, Create Your Own Pattern Grade 7: Order of Operations, High-Flying Expressions and Equations, Translating into Algebraic Terms, Modeling Algebraic Expressions and Equations Using Cups and Counters, Modeling Algebraic Expressions and Equations Using Algebra Tiles, Solving Addition & Subtraction Equations Concretely, Solving Multiplication Equations using Manipulatives, Solving Two-Step Equations Using Manipulatives, Developing an Algorithm using Function Machines, The Candy Jar Problem and its Function Machine, Visual and Arithmetic Sequences, Horizontal vs. Vertical Grade 8: Borders, Cutting a Pizza, Graphs of a Sequence, Guess My Rule, Pascal’s Triangle and the Fibonacci Sequence, The Rumor Problem, The Handshake Problem, Geometric Numbers, Algebraic Concentration Internet Activities: Engaging Mathematics: TEKS-Based Activities, Grade 7 Junior High Math Interactives: Patterns at LearnAlberta.ca, Function Machine at National Library of Virtual Manipulatives, Introduction to Functions and Patterns in Pascal’s Triangle at INTERACTIVATE, Exploring the Fibonacci Sequence and the Golden Ratio at NCTM website Illuminations, Math Spy Guys: Lesson 8: Summarizing/ Extending Patterns and Lesson 11: Balancing Equations, Neufeld Understanding Math 2008, “Understanding Algebra”, Discovering Math: Algebra (Grades 6-8) (see Resources column for a handout entitled How to Access Discovery Education), BrainPOP movies: Two-Step Equations and Equations with Variables Order of Operations, Activities 1 & 2, pp. 94 – 97 Patterns, pp. 116 – 117 Sequences, Activities 1 – 3, pp. 118 – 123 Technology and Sequences, Activities 1 & 2, pp. 126 – 129 Formulas, Activities 1 & 2, pp. 130 – 133 Expressions, pp. 134 – 135 Expressions and Equations, Activities 1 & 2, pp. 136 – 139 Multiple Representations, Activities 1 – 3, pp. 140 – 145 Equations with Models, Activities 1 – 5, pp. 146 – 156 Middle School Instructional Practices Meeting 4: October 26, 2009 Strand 2: Patterns, Relationships, and Algebraic Thinking (Algebraic Reasoning) Resource/Sample Activities Hands-On Standards, Grades 5 –6 Grade 5-6: Algebra Lesson 4 Order of Operations (Color Tiles), pp.106 – 107 Grade 5-6: Algebra Lesson 5 Expressions with a Variable (Color Tiles), pp.108 – 109 Grade 5-6: Algebra Lesson 6 Equations with a Variable (Cuisenaire Rods), pp.110 – 11 Grade 5-6: Algebra Lesson 7 Add & Subtract Equations (Cuisenaire Rods), pp.112 – 13 Grade 5-6: Algebra Lesson 8 Multiply & Divide Equations (Cuisenaire Rods), pp.114 – 15 Grade 5-6: Algebra Lesson 9 Patterns & Function Tales (Pattern Blocks), pp.116 – 17 Grade 5-6: Algebra Lesson 10 Intro. to Integers (Color Tiles), pp.118 – 19 Grade 5-6: Algebra Lesson 15 4-Quadrant Graphing (XY Coordinate Pegboard), pp.128 – 29 Grade 5-6: Algebra Lesson 16 Graphing Linear Eq. (XY Coordinate Pegboard), pp.130 – 31 Hands-On Standards, Grades 7 – 8 Grade 7-8: Algebra Lesson 1 Linear Functions (XY Coordinate Pegboard) pp. 80 – 81 Grade 7-8: Algebra Lesson 2 Variables (Algeblocks) pp. 82 – 83 Grade 7-8: Algebra Lesson 3 Combining Like Terms (Algeblocks) pp. 84 – 85 Grade 7-8: Algebra Lesson 4 Slope as Rate of Change (XY Coordinate Pegboard) pp. 86 – 87 Grade 7-8: Algebra Lesson 5 Lines in Slope-Intercept Form (XY Coordinate Pegboard) pp. 88– 89 Grade 7-8: Algebra Lesson 6 Prob. Solving with Rates of Change (XY Coordinate Pegboard) pp. 90 – 91 Grade 7-8: Algebra Lesson 7 Symbolic Algebra (XY Coordinate Pegboard) pp. 92 – 93 Grade 7-8: Algebra Lesson 8 Algebraic Equivalencies: Distributive Property (Algeblocks) pp. 94 – 95 Grade 7-8: Algebra Lesson 8 Algebraic Equivalencies: FOIL Method (Algeblocks) pp. 96 – 97 Grade 7-8: Algebra Lesson 9 Solving Linear Equations (Algeblocks) pp. 98 – 99 Grade 7-8: Algebra Lesson 10 Solving Nonlinear Equations (Color Tiles) pp. 100 – 101 Grade 7-8: Algebra Lesson 11 Solving Systems of Equations (Centimeter Cubes) pp. 102 – 103 Grade 7-8: Algebra Lesson 13 Problem Solving: Two-Step Linear Equations (Algeblocks) pp. 104 – 105 Grade 7-8: Algebra Lesson 14 Problem Solving: Multi-Step Nonlinear Equations (Color Tiles) pp. 106–7 Grade 7-8: Algebra Lesson 15 Linear Relationships (XY Coordinate Pegboard) pp. 108 – 109 Grade 7-8: Algebra Lesson 16 Writing Equations (XY Coordinate Pegboard) pp. 110 – 111