2 Lesson 6: Using Equivalent Fractions to Add Fractions with Unlike Denominators Numerically Students will know… Adding and subtracting fractions with unlike denominators; the numerator tells the number of parts and the denominator tells the size of the parts Mixed numbers represent a whole number plus a fraction less than one Students will be able to… Use models to represent fractions and solve addition and subtraction problems with unlike denominators. Use benchmark fractions to reason about fractions. Identify the whole in a fraction context Write fractions in measures of a specific unit. Subtract mixed numbers and fractions with unlike denominators without regrouping Culminating Task: Cindy’s Cats 2 (Post-Assessment) Culminating Task: Cindy’s Cats 2 On-line Resources Text Resources Georgia Department of Education Illustrative Mathematics Inside Mathematics North Carolina Department of Public Instruction http://www.dpi.state.nc.us/acre/standards/common-coretools/# unmath Progressions for the Common Core State Standards in Mathematics Smarter Balanced Assessment Consortium Engage New York- Mathematics California Mathematics: Concepts, Skills, and Problem Solving: Grade 5. New York: McGraw-Hill,2009 Van de Walle, John, and LouAnn Lovin. Teaching Student-Centered Mathematics: Grades 3-5. Vol. 2., Pearson Publishers, 2006. McNamara, Julie, and Shaughnessy, Meghan, Beyond Pizzas and Pies, Scholastic, Inc 2010. Fosnot, Catherine Twomey, et al, Contexts for Learning mathematics, Investigating Fractions, Decimals, and Percents, Heinmann,2007. ETA Cuisenaire, The Super Source, Pattern Blocks,grades5-6,ETA Cuisenaire, 2007.
Solve application problems using addition and subtraction of fractions with unlike denominators (including mixed numbers) Post-Assessment- Cindy’s Cats 2 equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. A. Focus and Coherence Students will know… Adding and subtracting fractions with unlike denominators; the numerator tells the number of parts and the denominator tells the size of the parts Mixed numbers represent a whole number plus a fraction less than one Students will be able to… Use models to represent fractions and solve addition and subtraction problems with unlike denominators. Use benchmark fractions to reason about fractions. Identify the whole in a fraction context Write fractions in measures of a specific unit. Add and subtract mixed numbers and fractions with unlike denominators without regrouping B. Evidence of Math Practices What will students produce when they are making sense, persevering, attending to precision and/or modeling, in relation to the focus of the lesson? 1.Make sense of problems and persevere in solving them. Students plan their solution pathway as they read the problem, draw a representation to use as tool for reasoning, and write numerically to solve problems. 3. Construct viable arguments and critique the reasoning of others. Students explain their reasoning for fractions closest to 1 during the warm-up. Students justify their solutions to application problems both verbally and in writing.
Student prior knowledge: Definition of equivalency Students understand the relationship between mixed numbers and fractions less than 1 How to add and subtract fractions with like and unlike denominators. Which math concepts will this lesson lead to? Multiplication and division of fractions with like and unlike denominators. Ratios and proportional reasoning 4.Model with mathematics. Students choose a preferred model for solving fraction problems. 6. Attend to precision. Students accurately partition area models, and use numbers precisely to demonstrate addition and subtraction operations. Students explain their thinking using appropriate mathematical terms. Essential Question(s) How is equivalence maintained when adding or subtracting fractions with different sized parts? Formative Assessments Student explanations- verbal and written Problem solutions, strategies and models Anticipated Student Preconceptions/Misconceptions add or subtract the unlike denominator not knowing how to represent a whole Materials/Resources Sandwich Problem worksheet Cindy’s Cats 2 Post-Assessment C. Rigor: fluency, deep understanding, application and dual intensity What are the learning experiences that provide for rigor? What are the learning experiences that provide for evidence of the Math Practices? (Detailed Lesson Plan)
Pre-Assessment Name: _______________________ Date: _____________ Jim’s Trip to Disneyland Jim is planning a trip to Disneyland in Los Angeles, CA. He is leaving his house in Sacramento with a full take of gas. The chart below shows how much gas he will use along the way. Starting Point Destination Miles Tank of Gas Sacramento Fresno 172 miles 3/8 tank Fresno Bakersfield 97 miles 1/6 tank Bakersfield Los Angeles (Disneyland) 116 miles 1/4 tank Los Angeles (Disneyland) San Diego 134 miles ? How much gas will Jim have in the tank when he arrives in Fresno? Show your work. How much gas did he use to arrive at Disneyland? Show your work. Explain the difference in solving questions 1 and 2.