Welcome to the Common Core Summer Institute for Fourth Grade! June 26 th - June 28 th

1. Welcome to the Common CoreSummer InstituteforFourth Grade! June 26th- June 28th Click Welcome Sign -Lexi and Shanna

2. Group Norms • Be engaged! You deserve the opportunity to learn and collaborate with colleagues. • Use our parking lot for questions, comments, and concerns.

3. This could happen to you if your not prepared for the CORE!

4. Numbers and Operations /Fractions Today we will look at the content standards from Numbers and Operations /Fractions. Our work today focuses on: *Highlighting the BIG IDEAS in the 4th grade content standards *Linking these BIG IDEAS with the Math Practice Standards *Examining how Investigations lessons fully support the Common Core State Standards for 4th grade

5. Task 2/3 of an apple is used to make an apple pie. We need to make 9 apple pies. How many apples do we need? Be sure to include an equation and visual representation to match your solution!

6. Task 2/3 of an apple is used to make an apple pie. We need to make 9 apple pies. How many apples do we need? Be sure to include an equation and visual representation to match your solution!

7. Fact: Fraction concepts are difficult • Fact: Our students (and many adults) struggle with fraction concepts. • Fact: What we have been doing isn’t working • Fact: The Common Core is grounded in research about how students come to understand fraction concepts.

8. We would like two volunteers to show how they solved this problem 2/3 of an apple is used to make an apple pie. We need to make 9 apple pies. How many apples do we need?

9. Fractions are a part of our everyday lives. Fraction work begins in 1st grade The foundation for a child’s conceptual understanding of fractions begins with partitioning and sharing. Students need practice partitioning unmarked regions

10. Pre-partitioned regions lead to a common misconception

11. In K-2 Common Core fraction work….

12. Partitioning K-2: Regions 3: Regions and Number lines 4:Strengthen Number lines, regions beginning to phase out 5: Number lines

13. Task • Directions for math tasks: • Please take 20 minutes to rotate around the room with your group to work on the following tasks. Please have a meaningful discussion of how each task connects with the Common Core and how you could implement these tasks in your classrooms. How can ½ be represented by 5 in one instance and 7 in another? In other words, ½ = 5 and ½ = 7 Why? List combinations of fractions that equal 1 whole Ex: ¾ + 1/8 + 1/8 =1 Lexi ate ¾ of her yogurt container. Shanna ate 3/8 of her yogurt container. They both ate the same amount of yogurt. Explain…

14. Task How can ½ be represented by 5 in one instance and 7 in another? In other words, ½ = 5 and ½ = 7 Why? List combinations of fractions that equal 1 whole Ex: ¾ + 1/8 + 1/8 =1 Lexi ate ¾ of her yogurt container. Shanna ate 3/8 of her yogurt container. They both ate the same amount of yogurt. Explain…

15. 15 Minute Break Please come back in a timely fashion! http://www.youtube.com/watch?v=6i5_EopdUGc

16. As a group, look through your Common Core State Standards: 4.NF.1 - 4.NF.7(pages 20-32 in Unpacking document) Locate the BIG IDEAS (main concepts, most important) and list them on your poster.

17. Let’s review some of the big ideas per by each standard. During our discussion did we cover the big ideas of standard 1? Standard - CC.4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n ×b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size.

18. Let’s review some of the big ideas per by each standard. During our discussion did we cover the big ideas of standard 2? Standard - CC.4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

19. Let’s review some of the big ideas per by each standard. • During our discussion did we cover the big ideas of standard 3? • Standard - CC.4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) • 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. • c. 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. • d. 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.

20. Let’s review some of the big ideas per by each standard. • During our discussion did we cover the big ideas of standard 4? • Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4). • Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) • Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

21. Let’s review some of the big ideas per by each standard. During our discussion did we cover the big ideas of standard 5? Standard - CC.4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.)

22. Let’s review some of the big ideas per by each standard. During our discussion did we cover the big ideas of standard 6? Standard - CC.4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

23. Let’s review some of the big ideas per by each standard. During our discussion did we cover the big ideas of standard 7? Standard - CC.4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons care valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

24. Game Time! Tossing Fraction Tiles Concept addressed: 4.NF.3 • Understand addition and subtraction fractions as joining and separating parts referring to the same whole. • Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. What does this mean and what does it look like?

25. Let’s refer to BOB(aka: The Back of the Book) • D Pages 151-156

26. HOW IS YOUR MATH REASONING?

27. MATH REASONING!

28. Please solve the following problem

29. MATH REASONING! Roles: 1 teacher 1 student

31. Please solve the following problem

32. MATH REASONING! Roles: 1 teacher 1 student

34. Please solve the following problem

35. MATH REASONING! Roles: 1 teacher 1 student

37. MATH REASONING! Now, let’s take a look at our CMS students and how they reason mathematically!

38. Time for Lunch http://www.youtube.com/watch?v=CoxNc-atJ14

39. Beyond Pizzas & PiesChapter 2 Can you relate? What did you notice? What do we need to change? Silently read and then turn and talk to a neighbor

40. New Common Core Lesson 3A.1 and 3A.2 • Multiplying a whole number by a fraction • Use visual models to solve word problems involving multiplication of a fraction and a whole number

41. Counting Around the Class: Let's count around the class by 1/4s. Say each number as a fraction, not a mixed number. Keep track of the fractions on the number line.

42. Pizza Pizza • Jake bought three kinds of pizza for a party. Each pizza was the same size. People were not very hungry, and at the end of the party there was ¾ of each pizza left. How much pizza was left in all? Write an equation and solve using a picture and a number line

43. Group work Please work on numbers 2-4 on page 44D. Be sure to include: • Equation • Number line representation • Picture representation • Story problem context for numbers 3 and 4

44. Egg Carton Time! • Eggs come in cartons of 12. Richard was making cakes for a party and used 2 cartons of eggs. How many eggs did he use? • Sabrina was making a cake for herself. She used ¼ of a carton of eggs. There are 12 eggs in each carton. How many eggs did she use?

45. Directions for math tasks: Please take 20 minutes to rotate around the room with your group to work on the following tasks. Please have a meaningful discussion of how each task connects with the Common Core and how you could implement these tasks in your classrooms. Glow sticks are a popular carnival prize. A box of glow sticks weighs ¼ of a pound. If I am carrying 7 pounds, how many boxes am I carrying? Amy is serving strawberry ice cream. Each scoop contains ¼ of a cup. By the end of her first shift, she has scooped out 4 servings. How much ice cream has she served? The water balloon both has ¾ of a gallon left. They need to fill 5 balloons. How much water should they use for each balloon?

46. Task Solve the school carnival tasks at your table. Represent your solutions on a number line and model each with an equation. Glow sticks are a popular carnival prize. A box of glow sticks weighs ¼ of a pound. If I am carrying 7 pounds, how many boxes am I carrying? Amy is serving strawberry ice cream. Each scoop contains ¼ of a cup. By the end of her first shift, she has scooped out 4 servings. How much ice cream has she served? The water balloon both has ¾ of a gallon left. They need to fill 5 balloons. How much water should they use for each balloon?

47. 15 Minute Break Please come back in a timely fashion! http://www.youtube.com/watch?v=D7QsgSpaoH8

48. Making Fraction Cards Use the list of “Fractions for Fraction Cards” from SAB page 27 (Page 72 in your Teacher’s Manual – Unit 6) to create fraction cards at your table. Work with 2 or 3 partners to create ALL fraction cards. You may use the square template at your table or create your own representations. After, play Capture Fractions with your group. (Directions are on the yellow sheet.)

49. Making Fraction Cards What did you learn as you made these? What learning would be taken away if these were handed to you already finished? What are some benefits of making mistakes?