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Welcome to the Common Core Summer Institute for Fourth Grade! June 26 th - June 28 th -Lexi and Shanna Click Welcome Sign

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

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

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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 4 th grade content standards *Linking these BIG IDEAS with the Math Practice Standards *Examining how Investigations lessons fully support the Common Core State Standards for 4 th grade

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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!

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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!

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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.

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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?

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

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Pre-partitioned regions lead to a common misconception

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In K-2 Common Core fraction work…. Students are … Partitioning (splitting) a region (circle, rectangle, square) into 2, 3 or 4 equal regions Communication about processes, content, vocabulary words. Students used to but are NOT …… Sharing sets equally Working with sets or multiple objects Writing fractions and fraction bars Learning “ numerator ” and “ denominator ”

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

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Task Lexi ate ¾ of her yogurt container. Shanna ate 3/8 of her yogurt container. They both ate the same amount of yogurt. Explain… 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 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.

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Task Lexi ate ¾ of her yogurt container. Shanna ate 3/8 of her yogurt container. They both ate the same amount of yogurt. Explain… 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

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

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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.

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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.

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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.)

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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.) 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. 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.

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Let’s review some of the big ideas per by each standard. During our discussion did we cover the big ideas of standard 4? a.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). b.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.) c.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?

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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.)

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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.)

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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.)

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Game Time! Tossing Fraction Tiles Concept addressed: 4.NF.3 A.Understand addition and subtraction 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. What does this mean and what does it look like?

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

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HOW IS YOUR MATH REASONING?

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MATH REASONING!

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Please solve the following problem

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MATH REASONING! Roles: 1 teacher 1 student

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Please solve the following problem

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MATH REASONING! Roles: 1 teacher 1 student

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Please solve the following problem

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MATH REASONING! Roles: 1 teacher 1 student

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

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

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

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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

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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.

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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

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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

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Egg Carton Time! (1)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? (2) 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? Number of Cartons Number of Eggs in a Carton Number of Eggs Equation (1) (2)

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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. 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? 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? 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?

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Task Solve the school carnival tasks at your table. Represent your solutions on a number line and model each with an equation. 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? 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? 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?

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

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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.)

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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?

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How does playing these games connect back to the standards? How can we enrich and or adjust this game to meet the needs of all learners, without jeopardizing their understanding of the standard(s) and MPs?

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1:1:1Exit Write down and share 1 thing you learned 1 idea you will use in your classroom 1 question you still have Tomorrow you will Report to Room __ alexis.picciano@cms.k12.nc.us shanna.rae@cms.k12.nc.us

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