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Campus: Huddleston Author(s): Charles, Pappas, Segleski, Stovall Date Created / Revised: 10-4-14 Six Weeks Period: 3rd Grade Level & Course: 6th Grade Math Timeline: 13 days Unit Title: Unit 6: Equivalent Expressions and One-Variable Equations Stated Objectives: TEK # and SE Lesson # 1 0f 1 (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace; (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution; (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems; (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; (E) create and use representations to organize, record, and communicate mathematical ideas; (F) analyze mathematical relationships to connect and communicate mathematical ideas; and (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. (7) Expressions, equations, and relationships. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to: (A) generate equivalent numerical expressions using order of operations, including whole number exponents and prime factorization; (B) distinguish between expressions and equations verbally, numerically, and algebraically; (C) determine if two expressions are equivalent using concrete models, pictorial models, and algebraic representations; and (D) generate equivalent expressions using the properties of operations: inverse, identity, commutative, associative, and distributive properties. (9) Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to represent situations. The student is expected to: (A) write one-variable, one-step equations and inequalities to represent constraints or conditions within problems; (B) represent solutions for one-variable, one-step equations and inequalities on number lines; and (C) write corresponding real-world problems given one-variable, one-step equations or inequalities. (10) Expressions, equations, and relationships. The student applies mathematical process standards to use equations and inequalities to solve problems. The student is expected to: (A) model and solve one-variable, one-step equations and inequalities that represent problems, including geometric concepts; and (B) determine if the given value(s) make(s) one-variable, one-step equations or inequalities true. See Instructional Focus Document (IFD) for TEK Specificity Key Understandings Misconceptions Key Vocabulary Numerical expressions can be represented in different forms while still having the same values. Concrete models, pictorial models, and algebraic representations can be used to determine if two expressions are equivalent. Properties of operations may be used to generate equivalent expressions. Real-world problems may be written when given an equation. Equations that represent problems may be solved using concrete, pictorial, and algebraic models. An equation remains true when the equation is evaluated with the solution of the equation. Some students may think that a constant term can be combined with a variable term (e.g., x + 5 = 6x). Some students may think variables are letters representing an object as opposed to representing a number or quantity of objects. Some students think of exponents as the multiplication of the base with the exponent (e.g. 4³ = 4(3)), rather than powers of the base (e.g., 4³ = (4)(4)(4)). Some students may think that the order of the variable and the constant is not important in subtraction expressions (e.g., x – 7 is not equal to 7 – x). Coefficient – a number that is multiplied by a variable(s) Constant – a fixed value that does not appear with a variable(s) Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other Exponent – in the expression xy, x is called the base and y is called the exponent. The exponent determines the number of times the base is multiplied by itself. Expression – a mathematical phrase, with no equal sign, that may contain a number(s), a variable(s), and/or an operator(s) Order of operations – the rules of which calculations are performed first when simplifying an expression Prime factorization – the process of decomposing a composite number as a unique product of prime factors Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b ≠ 0, which includes the subsets of integers, whole numbers, and counting (natural) numbers (e.g., -3, 0, 2, – , , etc.). The set of rational numbers is denoted by the symbol Q. Solution set – a set of all values of the variable(s) that satisfy the equation or inequality Variable – a letter or symbol that represents a number Suggested Day 5E Model Instructional Procedures Day 1 Engage Explain Explore Goal: Prime Factorization with Exponents Day 2/3 Engage Explain Explore Goal: Order of Operations (with Integers) Day 4 Explore Explain Goal: Writing Algebraic Expressions Materials, Resources, Notes (Engage, Explore, Explain, Extend/Elaborate, Evaluate) Pizzazz C-16 & C-17 Hopscotch Foldable Chalk Texas Go Math CSI – Order of Operations Sequence Cards Activity: Brain Pop Video – Prime Factorization Record Notes in Journal making sure to emphasize exponents Practice – Pizzazz C-16 & C-17 Record Notes in Journal – Hopscotch Foldable; emphasize that the “P” will represent more than just Parentheses as they go through later grades Practice the chant a couple of times inside with the motions “Parenthesis, Exponents, Multiplication & Division – from LEFT to RIGHT, LEFT to the RIGHT, Addition & Subtraction from the LEFT to the RIGHT, the LEFT to the RIGHT” Activity – Go outside and have students re-create the PEMDAS hopscotch; practice the chant and motions Practice 1 – Texas Go Math: Lesson 6.3 Guided and Independent Practice Practice 2 – CSI Around the Room for Order of Operations with Integers Record Notes in Journal; practice writing a couple as a whole class Activity – Use sequence cards to find the rule and write the rule as an expression Day 5 Engage Explore Explain Pizzazz B-76 & C-77 “I Have Who Has” – Algebraic Expressions Index Cards String/Yarn Measuring Up Goal: Writing Algebraic Equations Activity: Algebraic Equation Match; students will match graphs and tables to equations Algebraic Equation Match Measuring Up Goal: Evaluating Algebraic Expressions Record Notes in Journal – go over vocabulary related to expressions and how to evaluate algebraic expressions; emphasize when a number is next to a variable (or next to parentheses) that it means to multiply Activity – “I Have Who Has” Zip Line Race Practice – Pizzazz B-76 & C-77 Day 6 Engage Explore Explain Goal: Equivalent Algebraic Expressions Review Algebraic Expressions Activity: Each student will receive an index card necklace and will have to find another student in the class who has an expression that is equivalent to their necklace Practice – Measuring Up: Equivalent Numerical Expressions (pg. 142) Day 7/8 Engage Practice: Measuring Up – Writing Equations from Tables (pg. 130) Day 9/10 Engage Explore Explain Goal: Solving Addition and Subtraction Equations Activity – Use balance scales (borrow from science department) to have students explore what happens when adding and taking away objects to each side of the scales Balance Scales (science dept.) Pizzazz E-71 & E-72 Record Notes in Journal and practice a few as a whole class; emphasize that the equal sign is like a balance scale (when I move to the opposite side of the equation that I must use the opposite operation) Practice – Pizzazz E-71 & E-72 Day 11/12 Explore Explain Goal: Multiplication and Division Equations Record Notes in Journal and practice as a whole class; review all types of equations and expressions Activity – Around the Room (with a partner) Practice: Pizzazz E-73 & E-74 Around the Room Equations Day 13 Explore Explain Goal: Review Expressions and Equations Practice: Pizzazz B-77 & E-75 Algebraic Expressions and Equations and Word Problems Handout Accommodations for Special Populations Pizzazz B-77 & E-75 Algebraic Expressions and Equations and Word Problems Handout Accommodations for instruction will be provided as stated on each student’s (IEP) Individual Education Plan for special education, 504, at risk, and ESL/Bilingual.