1. Welcome Back! 5 th Grade Planning *Please make a fraction kit while we wait for everyone to arrive.* December 2, 2014 8:00 – 10:45 am

2. Survey Results: Focus for Today

3. Survey Results: Current Curriculum

4. Guiding Questions for Today What are the 5 th grade CC content standards for multiplying and dividing fractions? How does the SBAC assess understanding of these standards? What experiences does Math Expressions offer? How might we integrate Math Expressions and the PUSD Units to enhance student understanding? Is there a lesson we would like to co-teach?

5. Let’s use the Canvas Page! What do we want to put on the page? How might we make it a tool for collaboration?

10. How will students be held accountable on the SBAC?

11. SBAC Practice Item ¼ m How many squares with a side length of 1/4 m are needed to tile this rectangle? 5NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Lessons 4, 6

12. SBACish Practice Item 12/100 m 5/100 m If you covered this rectangle completely with stickers with a side length of 1/100, how many stickers will cover the whole shape? 5NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Lessons 4, 6

13. SBACish Practice Item What is the area of this rectangle? 1/3 in 1/4 in 5NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Lessons 4, 6

14. SBACish Practice Item Lucy is making a bracelets. She has 3 feet of string. Each bracelet requires 1/4 feet of string. Write an equation to find the number of bracelets she can make. Calculate how many bracelets she can make. 5.NF.7c 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? Lessons 10-14

15. Models Offered in Math Expressions TE pages 187BB – 187HH How do these models compare to those detailed in the CC Progressions and on the SBAC practice items? Are there any gaps we need to fill? Give yourself a brief tour of chapter 3. What do you notice? What is the overall instructional style offered in the book: teacher shows – students practice; students explore – teacher asks questions…?

16. A Perspective on Textbooks: An argument for professional decision making (Phil Daro) Each lesson is written for 5 different teacher “types” or perspectives. A lesson was never intended to be taught in its entirety. Publishers anticipate you will use what fits into your perspective. You know more than the publisher. Trust yourself to make informed curriculum decisions.

17. PUSD Unit of Study ME Chapter 3, Multiply and Divide Fractions Pathway: My Connect Math Central Units of Study 5 th Grade Unit 3 Give yourself a brief tour of the unit.

18. How can we connect our understanding of multiplying whole numbers to multiplying fractions?

19. Jobs Standards Tracker – What standard/s is/are addressed in each lesson? Note-Takeron GoogleDocs – What ideas and adjustments did we discuss? Time Keeper Task Master Other areas of focus/expertise: Homework – What would be appropriate homework for each lesson? Differentiation – How might we differentiate the lesson?

20. ME Unit 3: Multiplication and Division with Fractions Big Idea 1: Multiplication with Fractions Lesson 1: Basic Multiplication Concepts Lesson 2: Multiplication with Non-Unit Fractions Lesson 3: Multiplication with Fractional Solutions Lesson 4: Multiply a Fraction by a Fraction Lesson 5: Multiplication Strategies Lesson 6: Multiply Mixed Numbers

21. The District Instructional Leaders replaced Lesson 1 with an investigation. (This might be a good lesson to co-teach.)

22. Statements to Explore Whole Numbers (Always true, Never True, Sometimes True) Fractions (Always true, Never True, Sometimes True) 1. Multiplication is the same as repeated addition. 2. Times means “groups of.” 3. A multiplication problem can be shown as a rectangle. 4. You can reverse the order of the factors and the product stays the same. 5.You can break numbers apart to make multiplying easier. 6. When you multiply two numbers, the product is larger than the factors.

23. Lesson 2 Since the DILs left it as is in ME... – As a critical connoisseur of curriculum, what are your thoughts?

24. Lesson 3 Let’s discuss... Will the students be ready to work with a new model (area model) at this point? If so... How might we make the rectangle area model more understandable? How might we modify Farm Fractions to make it more of a problem solving experience? If not... What additional modeling experiences will they need with the number line? How might the commutative property support students when looking at the number line experience on TE 205 (student book 74) How might working with fraction strips enhance student access to multiplying a fraction by a whole number? What additional number talks might help students find patterns and relationships?

25. Lesson 4 How might the use of fraction strips enhance the experience in Activity 1? How might the “Reflect and Generalize” problems be usable as a number talk? How might we use fraction strips to solve problems similar to those in Activity 2 and guide students toward a generalization about multiplying a fraction by a fraction?

26. Additional Experience Recommended by the District Instructional Leaders Might be a good lesson to co-teach.

27. Lesson 5 What is the focus standard in this lesson? Which parts of this lesson can we weave together into a cohesive opportunity for thinking deeply about mathematics? What parts can we leave out? Activity 1: Think about Simplification How might we turn this into an experience where students “uncover” these methods before we label them? – Unit Fraction Method – Multiply and then Simplify Method – Simplify and then Multiply Method Activity 2: Solve Multiplication Problems – How might we turn this into an opportunity for students to make decisions about how they are multiplying and simplifying the problems?

28. Lesson 6: Multiply and Divide Mixed Numbers What is the key standard in this lesson? What makes sense to use from the book and from the PUSD unit to give students a powerful mathematical experience? How else might we engage students in the mathematics so they can construct understanding?

29. ME Unit 3: Multiplication and Division with Fractions Big Idea 2: Multiplication Links Lesson 7: Relate Fraction Operations Lesson 8: Solve Real World Problems Lesson 9: Make Generalizations

30. Lesson 7: Relate Fraction Operations The DILs recommend skipping this lesson. Differentiation Intervention (Activity Card 3-7, TE p. 241): Predict and Verify... Quite an interesting investigation. Might be worth exploring. The Challenge activity is also fairly interesting and definitely challenging.

31. Lesson 8: Fraction Word Problems What is the key standard in this lesson? How might having students write word problems support their thinking? How might a problem sort (greater than ___, less than ___) support their thinking? How might using a visualization, representation, and sense- making protocol support their thinking? How might the Trail Mix problem provide a rich context for thinking about operations with fractions in-context? Look at the Differentiation Challenge Level (TE 253)

32. The Trail Mix Problem How much of each ingredient will you need to feed the exact number of students in your class? Trail Mix Trail mix is a healthy snack food. It got its name from hikers and backpackers who ate it on their journeys. You will need: ½ cup raisins ¾ cup peanuts 2/3 cup granola ½ cup dried fruit 2 tablespoons sunflower seeds ¼ cup M&Ms Combine ingredients in bowl. Mix well. Scoop into baggies for a snack on the go. Serves 6

33. Lesson 9: Make Generalizations What is the key standard in this lesson? How might we turn this into a rich math experience? (Could we design a game?) What number talk would lay a foundation for thinking about scale factors?

34. ME Unit 3: Multiplication and Division with Fractions Big Idea 3: Division with Fractions Lesson 10: When Dividing is also Multiplying Lesson 11: Solve Division Problems Lesson 12: Distinguish Multiplication from Division

35. Lesson 10: When Dividing Is Also Multiplying What if we paralleled our introduction to multiplication by doing the same investigation with division... – In Lessons for Multiplying and Dividing Fractions by Marilyn Burns: Chapter 8, Introducing Division of Fractions, p. 75

36. Division Statement Whole Numbers (Always true, Never True, Sometimes True) Fractions (Always true, Never True, Sometimes True) 1. You can solve a division problem by subtracting. 2. To divide two numbers, a ÷ b, you can think, “How many bs are in a?” 3. You can check a division problem by multiplying. 4. The division sign (÷) means “into groups of.” 5. The quotient tells “how many groups” there are. 6. You can break the dividend apart to making dividing easier.

37. Division Statement Whole Numbers (Always true, Never True, Sometimes True) Fractions (Always true, Never True, Sometimes True) 7. Remainders can be represented as whole numbers or fractions. 8. If you divide a number by itself, the answer is one. 9. If you divide a number by one, the answer is the number itself. 10. You can reverse the order of the dividend and the divisor, and the quotient stays the same.

38. Back to Lesson 10 What is the key standard? What parts of the lesson support that standard? How can we modify the lesson so it is engaging and allows students to construct conceptual understanding? How might fraction strips help? How might Division Patterns (p. 84) and The Quotient Stays the Same (p. 97) support the key ideas in this lesson? (Multiplying and Dividing Fractions by Marilyn Burns)

39. Lesson 11: Solve Division Problems Activity 1: The “describe a situation” problems are interesting. How might we make them even more interactive? (Perhaps have a student write a situation and another student has to figure out the problem that goes with it... Kind of like a riddle.) Activity 2: How might we make this page of problems more interesting? (Use the “less is more” principle)

40. Lessons 12 - 14 What are the important elements of each lesson according to the content standards? What is important to teach and what can be cut? How might we make the lessons more interactive and meaningful?