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Topic: Equivalent Expressions COMMON CORE STATE STANDARDS • Domains Expressions and Equations, The Number System • Clusters Compute fluently with multi-digit numbers and find common factors and multiples; apply and extend previous understandings of arithmetic to algebraic expressions. • Standards for Mathematical Content 6.NS.B.4, 6.EE.A.2c, 6.EE.A.3, 6.EE.A.4 • Standards for Mathematical Practice All of the standards are addressed, with an emphasis on MP2, MP3, MP4, and MP5. For the full text of the Standards for Mathematical Practice, see the Unit pages of the Teacher Guide. DOMAIN Expressions and Equations 6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1−100 with a common factor as a multiple of a sum of two whole numbers with no common factor. 6.EE.A.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). 6.EE.A.3 Apply the properties of operations to generate equivalent expressions. 6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). Looking Back Looking Ahead Grade 6 Grade 5 5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. Grade 6 6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents. 6.EE.A.2a Write expressions that record operations with numbers and with letters standing for numbers. 6.EE.A.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. 6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Grade 7 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. – grade 6 • Teacher Guide Topic: Equivalent Expressions continued MATH BACKGROUND Students learned about properties of numerical expressions with parentheses in Grade 5, under the Operations and Algebraic Thinking domain of the Common Core State Standards. Students have also had extensive experience with the properties pertaining to 0 and 1. They will now learn how to apply the same properties to algebraic expressions. Seeing the full list of properties all in the same topic will help students distinguish one from the other and appropriately apply each one. The Greatest Common Factor lesson on is necessary to prepare students for The Distributive Property lesson. Because prime factorization is also a method for finding least common multiples, the topic also includes a lesson addressing that concept. ESSENTIAL QUESTION What are properties? Why are properties useful? FOCUS QUESTIONS The Focus Questions in this topic emphasize the usefulness of properties. Properties about 0 and 1 are special because of their usefulness as identities. Some lessons focus on using properties to rewrite expressions by reordering, regrouping, or factoring out a common factor. The Problem Solving lesson emphasizes that you can use properties to rewrite an expression, which may help you see a solution pathway or see a real-life problem situation in a new way. TOPIC PLANNING Topic: Equivalent Expressions Single Period Block Schedule Tools Readiness Lesson 1 day 1 2 day The Identity and Zero Properties 1 day 1 2 day Think-Write The Commutative Properties 1 day 1 2 day Integer Chips Place Value Blocks The Associative Properties 1 day 1 2 day Words to Expression Greatest Common Factor 1 day 1 2 day Venn Diagram The Distributive Property 1 day 1 2 day Area Models Words to Expression Least Common Multiple 1 day 1 2 day Venn Diagram Problem Solving 1 day 1 2 day Think/Write 1 day 1 2 day 1 day 1 2 day Topic Review Topic Assessment 10 days 5 days – grade 6 • Teacher Guide