Addition and Subtraction of Fractions Part 2 Class 4 October 23, 2012 This material was developed for use by participants in the Common Core Leadership in Mathematics (CCLM^2) project through the University of Wisconsin-Milwaukee. Use by school district personnel to support learning of its teachers and staff is permitted provided appropriate acknowledgement of its source. Use by others is prohibited except by prior written permission.

Homework Discussion Read your partner’s homework reflections. Use a post-it note to comment on either: Reflection: Connect one of the grade 4 or grade 5 standards for operating on fractions to the content in this chapter. Using quotes from the chapter and examples of student work share ideas that are important as you implement a standards-based classroom. Repeat 2 more times.  2011

Further Exploration: Addition of Fractions

Learning Intentions We are learning to Use concrete models to explore and generalize about addition of fractions. Read and interpret the cluster of CCSS standards related to addition/subtraction of fractions. We will know we are successful when we can Justify our thinking when adding and subtracting fractions using concrete models and estimation strategies. Clearly explain and provide examples for specific CCSS standards.

Exploring Addition (Subtraction) of Fractions   Choose a target number from this set that is less than 1 or more than 1. Make a model of that number using your fraction strips to serve as a reference. Using your fraction strips find combinations to represent your target number. Start with combinations of 2 fractions, then 3, then 4, etc. Record your combinations. Also record any conjectures your group makes as you work on the task.  If you feel that you have explored all combinations for your first target number, pick a second one and do subtraction. Need task cards and recording sheet for combinations and conjectures

Example of target # less than 1

Addition Fraction Combinations: Debrief What patterns emerged as you made your combinations?   What ideas about addition of fractions surface as you engaged in these explorations? How did the fraction strip model support your thinking?

Connections to Standards 4.NF.3a, 4.NF.3b and 5.NF.1 1. Read these standards, highlighting important words and phrases. 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with 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.) 2. In your group, discuss highlighted key ideas in this standard and questions you may have about these standards. 3. Work as a group to cite three specific examples of how the previous activity made sense of these standards.

NF Progression Document Study the sections, diagrams, and margin notes on “Adding and Subtracting Fractions.” Read Grade 4, page 6. Read Grade 5, page 10. Highlight important words and phrases, and note surprising ideas or questions raised. In particular, note how the standard’s progression grows from grade 4 to grade 5 In your group, discuss highlighted key ideas and your questions about them.

Don’t Forget Mixed Numbers The distance from Hank’s house to school is 2 1/5 miles. His car broke down 3/5 of a mile from school. How far is Hank from his house? Estimate the answer- do not compute. Use a model to find the answer. Use at least two different strategies to find the answer. How does the model match this work?

Connections to 4.NF.3c, 4.NF.3d 4.NF.3c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4.NF.3d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. 1. Read and highlight important phrases and ideas in these standards. 2. In your group, discuss highlighted key ideas in this standard and questions you may have about the standards. 3. Write an example on your slate for each standard.

What Did We See in our Tasks Today? What connections can you make between your work as participants and the mathematical practices? Be specific. Put this on your slate and share at the table

Learning Intentions We are learning to Use concrete models to explore and generalize about addition of fractions. Read and interpret the cluster of CCSS standards related to addition/subtraction of fractions. We will know we are successful when we can Justify our thinking when adding and subtracting fractions using concrete models and estimation strategies. Clearly explain and provide examples for specific CCSS standards.