Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Addition and Subtraction of Fractions Part 2 Class 8 June 29, 2011

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Learning Intentions We are learning to  Develop “operation sense” related to adding and subtracting 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

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Example of target # less than 1

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Addition Fraction Combinations: Debrief What did you understand about fractions that allowed you to make combinations? 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?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Connections to Standards 4.NF.3, 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 = /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 = 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. 3. Work as a group to cite three specific examples of how the previous activity made sense of this standard.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Don’t Forget Mixed Numbers The distance from Hank’s house to school is miles. His car broke down 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?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Connections to 4.NF.3c, 4.NF.3d 1.Read these standards, highlighting important words and phrases. 2. In your group, discuss highlighted key ideas in this standard and questions you may have. 3. Write an example on your slate for each standard.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 Looking at the Clusters of Content Standards Domain: Number and Operations: Fractions 1.Each person chooses one standard card from the envelope. 2. Prepare a summary of what this standard means and what students should know and be able to do. 3.Present your summary to the other teachers at your table, answering questions as necessary.

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 What did we see in our tasks today? What did you as students do to bring the standards alive? What did the facilitator as a teacher do to bring the standards alive? What else might you as teachers in your classroom do to bring the standards alive?

Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, Summer Institute 2011 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