Revisiting MP2 What actions did you take in the last 2 weeks to be more conscious of MP2 Reason Abstractly and Quantitatively? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year

Division of Fractions: Balancing Conceptual and Procedural Knowledge November 27, 2012 Common Core Leadership in Mathematics2 (CCLM) Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year 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.

Trouble with Fractions? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year

Learning Intentions and Success Criteria We are learning to … apply and extend understandings of division to fractions that includes a focus on unit fractions in the context of real-world problems. We will be successful when we can… explain and provide examples of standard 5.NF.7 using visual models, contexts, and concept-based language to divide unit fractions by whole numbers and whole numbers divided by unit fractions. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year

Extending Meaning of Division to Fractions

3.OA.2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Building on What We Know Make up two problems for 56 ÷ 8, one where the group size is unknown and one where the number of groups is unknown.

Interpretations of Division Group Size Unknown I know the total number of objects. I know the number of groups/shares. How many objects are in each group/share? Example: I have 8 stickers. I am going to divide them equally between my friend and myself. How many stickers will we each get? 8 ÷ 2 = 4 *Partitive division, sharing model, dealing ou t. Number of Groups Unknown I know the total number of objects. I know the number of objects in each group/share. How many equal groups/shares can be made? Example: I have 8 stickers. I am going to stick 2 on each card. How many cards can I make? 8 ÷ 2 = 4 * Quotative division, measurement division, grouping, subtractive model.

Looking at Division Problems

Launch: Popcorn Party #1 Serving Size: 1/2 cup of popcorn How many servings can be made from: 1 cup of popcorn 2 cups of popcorn 3 1/2 cups of popcorn Have we done problems like this in the whole number world? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year

Explore: Popcorn Party #2 Serving Size: 1/3 cup of popcorn How many servings can be made from: 1 cup of popcorn 2 cups of popcorn 3 2/3 cups of popcorn Individually solve each problem using reasoning and models As a group, take turns and share your reasoning Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year

Explore #2: Juice Party Serving Size: 1/2 gallon of juice How can I divide that among: 2 friends 5 friends Individually solve each problem using reasoning and models As a group, take turns and share your reasoning Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year

Looking at the Standards

Standard 5NF 7c Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1 c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Standard 5NF 7a and 5NF 7b Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1 a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

MP2 Again “Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities.” What does it mean to “attend to the meaning of the quantities”? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year

Learning Intentions and Success Criteria We are learning to … apply and extend understandings of division to fractions that includes a focus on unit fractions in the context of real-world problems. We will be successful when we can… explain and provide examples of standard 5.NF.7 using visual models, contexts, and concept-based language to divide unit fractions by whole numbers and whole numbers divided by unit fractions. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year