1. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Addition and Subtraction of Fractions Part 1 Class 3 October 9, 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.

2. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Homework Discussion Discuss your response to last week’s homework as a table group. Read a quote you chose from the reading. Why was this an important idea? 2011

3. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Standards for Mathematical Practice

4. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013

5. Math Practices in Action Reflect back to last week’s activities for comparing and ordering. Choose two Standards for Mathematical Practice that were evident in that work. How were they evident? Be specific.

6. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 An Overview of the Fraction Standards

7. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Common Core State Standards for Fractions: Grades 1-6 As you read the fractions standards, Highlight the word Understand. Highlight the words visual model(s). As a table, discuss the fraction progressions that you found by examining these standards.

8. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Addition of Fractions

9. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Learning Intentions We are learning to  Develop “operation sense” related to addition of fractions.  Understand how estimation should be an integral part of fraction computation development.  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

10. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Big Ideas for Addition and Subtraction of Fractions Fraction addition and subtraction concepts build from and are dependent upon: –Foundational part-to-whole ideas –Equivalence ideas –Magnitude ideas Procedural fluency and conceptual understanding work together to deepen student understanding of fraction addition and subtraction.

11. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Launch: Building on What We Know Use a model to answer this question : There are some candies in a dish. 2/5 of the candies are chocolate. 3/10 of the candies are peppermint. Are there more chocolate or peppermint candies?

12. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Using Estimation Aunt Sally has a jar that holds one cup of liquid. Her salad dressing recipe calls for 2/3 cup of oil 1/8 cup of vinegar 1/2 cup of juice Is the jar large enough to hold all the oil, vinegar and juice?

13. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 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.

14. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Example of target # less than 1

15. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 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?

16. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 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.

17. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 NF Progression Document 1.Study the sections, diagrams, and margin notes on “Adding and Subtracting Fractions.” Read Grade 4, page 6. Read Grade 5, page 10. 2.Highlight important words and phrases, and note surprising ideas or questions raised. 3.In particular, note how the standard’s progression grows from grade 4 to grade 5 4.In your group, discuss highlighted key ideas and your questions about them. 4.17

18. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Learning Intentions We are learning to  Develop “operation sense” related to addition of fractions.  Understand how estimation should be an integral part of fraction computation development.  Read and interpret the cluster of CCSS standards related to addition/subtraction of fractions

19. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2012 - 2013 Success Criteria 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 an example for specific CCSS standards.