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FRAME THE LESSON Student Expectations Bundled in Lesson Noun=Underline Verb=Italicize 5th Grade TEACHER: Math LESSON DATE: Sept 21st Teaching Points & Activities Engage: Engage: 5.4 Algebraic Reasoning. The student applies mathematical process standards to CLASS: Explore: develop concepts of expressions and equations. Explore: Explain: Explain: Elaborate: M T W TH F Resources/Materials: Go Math Spiral Review # 19 Have a few toy bugs laying out on the table IF you have them. If you do not, have counters at each group. Using your Teacher Edition, use Lesson 7.3 o “Making Connections” o “Using the Digital Lesson” o “Learning Task” Have students watch the Go Math: On the Spot Tutor Video Go over page 303 together. Have students complete “Think, Pair, Share” o If you are unfamiliar with the concept, here is an article on it: http://www.readwritethink.org/professionaldevelopment/strategy-guides/using-think-pair-share-30626.html Have square tiles or counters at groups. Complete “Differentiated Instruction: Language Support” to work problems 1-4 on page 304. Have them represent what each expression is asking. Using your TE, use page 304 for “Share and Show” as well as the “Problem Solving” in order to delve into higher level questioning and facilitate group discussions. Have students finish page 304 cooperatively. Extension: “Enrich” o You will need to have square counters or tiles from your manipulative kit. Using Index Cards record word problems and have students use them as flash cards if they complete the assignment early Evaluate: Objective/Key Understanding: 5.4A: Identify prime and composite numbers. (1 WK) 5.4B: Represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity. (2WKS) 5.4E: Describe the meaning of parentheses and Stop & Check for Understanding—High Level Questions Any whole number greater than one can be decomposed into a unique set of prime factors. What determines whether a number is prime or composite? What is the relationship between prime and composite numbers and the rules of divisibility? Any whole number greater than one can be decomposed into a unique set of prime factors. What determines whether a number is prime or composite? brackets in a numeric expression. (2WKS) 5.4F: Simplify numerical expressions that do not involve exponents, including up to two levels of grouping. (2WKS) Closing Product/ Question/ Informal Assessment: A problem-solving model can be applied to critically reason through various problem situations in order to solve problems and analyze solutions. How can the information in a problem be analyzed to determine the question being asked and the relevant information provided and/or needed? What types of plans and/or strategies can be used to solve problems? How can solutions to problems be determined? How can solutions to problems be justified? How can the reasonableness of solutions and the problem solving process be evaluated? What is the relationship between prime and composite numbers and the rules of Small Group Purposeful Talk Question Stems: divisibility? Multi-step problems involving the four operations may be represented and solved with equations with a letter standing for the unknown quantity (whole numbers). How are equations used to represent the relationship between quantities in problem situations? What symbols can be used when representing problem situations with an equation? What is the process for writing and solving an equation from a problem situation? Vocabulary: Composite number, Counting (natural) numbers, Dividend, Divisor, Equation, Expression, Factor, Order of operations, Parentheses and brackets, Prime number, Product, Quotient, Whole numbers Critical Writing Prompt: Algebraic reasoning facilitates representing, generalizing, and formalizing patterns and relationships in everyday life. How can situations be identified and described algebraically? Rigor & Relevance: (Real World Connection) Organize and record your work for each of the following tasks. Using precise mathematical language, justify and explain each solution process. Mia and Thomás were discussing a famous number pattern called Fibonacci’s number sequence. The first ten numbers in the sequence are as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,… Rigor & Relevance: (Real World Connection) Analyze the problem situation(s) described below. Organize and record your work for each of the following tasks. Using precise mathematical language, justify and explain each solution process. Mia and Thomás were discussing a famous number pattern called Fibonacci’s number sequence. The first ten numbers in the sequence are as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,… Mia started to notice that some of the numbers were prime and some were composite. She told Thomás that there were 6 prime numbers and 4 composite numbers in the first ten numbers in the sequence. Thomás disagreed. a) Design a detailed plan that Thomás can use to identify the prime and composite numbers in the sequence using square tiles. b) Design a detailed plan Mia can use to identify the prime and composite numbers in the sequence using an organizational factor list. c) Analyze and explain the relationship between the two representations to identify the prime and composite numbers in the sequence and describe the advantages and disadvantages of both representations. d) Identify which numbers in the first ten numbers in Fibonacci’s sequence are prime or composite and explain if Thomás was correct to disagree with Mia’s statement. Spring Elementary School was collecting aluminum cans to recycle for money. Adolfo brought in 128 pounds of cans for each of the 9 months of school. Chris brought in one big bag containing 1,474 pounds. Laura brought in 1,863 pounds, but when she got to school, she realized that 237 pounds of the cans were actually steel cans and not aluminum. a) Write a numeric expression to determine the total number of pounds of aluminum cans brought in by Adolfo, Chris, and Laura. b) Describe the process that could be used to simplify the numeric expression representing total number of pounds of aluminum cans brought in by the three students. The teacher invited four parents to help take all of the aluminum cans brought in by Adolfo, Chris, and Laura to the recycling center. They divided all the aluminum cans evenly among the four vehicles. a) Using the numeric expression representing total number of pounds of aluminum cans brought in by the three students, write and solve an equation to determine, c, the number of pounds of aluminum cans each vehicle needed to carry. b) Explain the meaning of the grouping symbols used in the expression and why they are used.