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:
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
Engaging Mathematics:
TEKS-Based Activities, Grade 7 / 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