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Teaching to the Next Generation Sunshine State Standards August 17, 2010

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Next Generation Sunshine State Standards Eliminates: Mile wide, inch deep curriculum Constant repetition Emphasizes: Automatic Recall of basic facts Computational fluency Knowledge and skills with understanding

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Grade LevelOld GLE’s NGSSS K st nd rd th th th th th 9319

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Implementation Schedule for NGSSS Original FCAT (FT Items) New FCAT SF (2004) New Adoption K - 2nd 2007 Standards 3rd 2007 Standards w/ transitions 2007 Standards w/ transitions 2007 Standards 4th 1996 Standards 2007 Standards w/ transitions 2007 Standards 5th 1996 Standards 2007 Standards

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MA.3.A.2.1 Subje ct Grade Level Body of Knowled ge Big Idea/ Supporti ng Idea Benchma rk Coding Scheme for NGSSS MA.3.A.2.1

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Intent of the Standards The intent of the standards is to provide a “focused” curriculum. The intent of the standards is to provide a “focused” curriculum. How do we make sense of teaching deeply? How do we make sense of teaching deeply? Think of a swimming pool. Think of a swimming pool.

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Cognitive Complexity Low Complexity Relies heavily on the recall and recognition; computation Moderate Complexity Involves flexible thinking and usually multiple operations; problem solving High Complexity Requires more abstract reasoning, planning, analysis, judgment, and creative thought; multiple representations

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Topics not Chapters

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Four-Part Lesson Daily Spiral Review: Problem of Day Interactive Learning: Purpose, Prior Knowledge Visual Learning: Vocabulary, Instruction, Practice Close, Assess, Differentiate: Centers, HW

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Conceptual Understanding

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Old Instruction vs New Instruction

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NCTM Process Standards Problem Solving – –Developing perseverance – –Examples by grade level, Model drawing – –Teacher’s role Reasoning and Proof – –Mathematical conjectures – –Examples and counterexamples – –Examples by grade level

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NCTM Process Standards Communication – –Read, write, listen, think, and communicate/discuss – –Tool for understanding and explaining – –Increased use of math vocabulary – –Examples of rich problems by grade level

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NCTM Process Standards Connections – –Equivalence: fraction/decimal, cm/m – –Other content areas, science – –Real World contexts Representation – –Model Drawing

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Number Sense = 5

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The importance of developing number sense in a gradual sequence Activities that build upon one another for students to gain a better sense of number relationships Counting, which involves the skills of orally reciting numerals, matching and writing numerals to identify the quantity and understanding the concepts of more than, less than and equal to Participants will explore …

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Students Receive Information Students Apply Their Learning Active Learning Pyramid

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Instructional Strategies NCTM Math Process Standards: – –Problem Solving – –Representation – –Communication – –Connections - -Reasoning and Proof Cooperative learning, emergent literacy instruction, the use of manipulative materials, and think-pair-share will be highlighted

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Examining the Standards MA.K.A.1.1 Represent quantities with numbers up to 20, verbally, in writing, and with manipulatives. (Moderate)

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Examining the Standards MA.1.A.1.1 Model addition and subtraction situations using the concepts of “part- whole”, “adding to,” “taking away from”, “comparing,” and “missing addend”. (Moderate)

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Examining the Standards MA.2.A.2.1 Recall basic addition and related subtraction facts. (Low) MA.2.A.1.1 Identify relationships between the digits and their place values through the thousands, including counting by tens and hundreds. (Moderate)

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Write down the last two digits of the year you were born. (A) Divide that number by 4 and ignore any remainder. (B) Write down the day of the month you were born. (C) Which Day of the Week Were You Born? 26

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Sunday1Jan/Oct1 Monday2May2 Tuesday3August3 Wednesday4Feb/Mar/Nov4 Thursday5June5 Friday6Sept/Dec6 Saturday0Apr/July0 Find the number of the month you were born from the Month Table. (D) Add A + B + C + D 27

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Divide this total by seven and use the remainder to see which day you were born on from the table 28 Sunday1Jan/Oct1 Monday2May2 Tuesday3August3 Wednesday4Feb/Mar/Nov4 Thursday5June5 Friday6Sept/Dec6 Saturday0Apr/July0

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What are your thoughts about this activity? Were you amazed at the outcome? What would be the depth of knowledge for this activity? Justify your answer. Which Day of the Week Were You Born?

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Foundational Number Concepts Inclusion-If you ask a child to bring you 5 toy trucks and he brings you the fifth truck that he counts, he may not understand that all 5 trucks are included in the entire set of trucks. The fifth truck is only part of the set. One-to-One Correspondence -The matching of one number to one object. Children who call numbers at a faster or slower rate than they are able to point to, may not yet have mastered the skill.

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Conservation of Number -Children have acquired conservation of number when, for example, they recognize that a group of objects clustered tightly together still contains the same number of objects when spread over a larger area. Number Sense and Relationships - Just like learning to read, learning to count requires numerous opportunities for purposeful counting. Foundational Number Concepts

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Table Talk Activity: What do you know about five? The answer is 5, what is the question? Give Me Five!

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Sets of Five Write the number 1 on an index card Place the card on the table Place one counter above the card Write another number card that is one more than the first number Place the appropriate number of counters above that card Continue until you have sets of 1-5

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Developing “Five-ness” Read the article, “ Developing ‘Five-ness’ in Kindergarten” and highlight the meaningful points. Discuss highlighted points with table partners. Compare learning experiences identified in the article, with your past instructional strategies. How does the depth of knowledge in the ‘Five- ness” activities compare to the ‘Day of the Week” activity?

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Create a Picture Create a picture using up to 5 colors. Complete the sentence below and write it on the bottom of the picture. I used _______different colors in my picture.

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Five Frame

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Word Problems: Compare Sally has 4 apples. Jimmy has the same. How many apples does Jimmy have? Sally has 4 apples. She has 3 more than Jimmy. How many does Jimmy have now?

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Game Dot Cards 1-5 Shuffle the cards and give a set to each group. One person takes a card, the others find a card that is fewer or more than. Repeat so every one gets a turn.

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Marilyn Burns, 2005 The standard for mathematics should be the same as the standard for reading-bringing meaning to the printed symbols. In both situations, skills and understanding must go hand in hand. The challenge is how do we help students develop meaning and make sense of what they do?” Discuss Marilyn Burns’ purpose in the statement above.

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Why Connect Mathematics and Literature? Mathematics and literature bring order to the world around us Math and literature classify objects Math and literature emphasize problem solving skills Math and literature involve relationships and patterns Literacy, Libraries and Learning Literacy, Libraries and Learning 40

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Read the text aloud Draw a number line on chart paper sequenced from 0 to 10 Place the appropriate amount of sticky dots above the line to represent each counting number Count the number of sticky dots above each number Ten Black Dots by Donald Crews 41

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Make Ten Black Dots Book index cards black dots Materials number word numeral corresponding dots Instructions

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Create a foldable book similar to the one in the story Complete this on a separate sheet of paper – –We each needed _____ dots. – –I got my answer by _____. – –The entire class needed ____ dots. – –I know that because _______. What are the different ways that young learners will complete these tasks? Ten Black Dots Book

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Find a partner from another group Count the number of dots together Explain how your books are similar and different In what ways might you revise current instructional strategies to incorporate the in- depth understanding intended by the Next Generation Sunshine State Standards? Ten Black Dots Book

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one 1 two 2 three 3 four 4 five 5 six 6 seven 7 eight 8 nine 9 ten 10 Ten Black Dots

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Ten Frame Grid

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“Show Me” 10 Frame Activity Show me 4 objects on the 10 frame. How many counters are on the 10 frame? Show me 2 more, what is the number now? How many more to make 10? Show me seven. Show me 1 more, what is the number now? Show me 2 less, what is the number now? How many more to make 10? Using 2 ten frames, show me 13. Show me 5 more, what is the number now? Show me 6 less, what is the number now/ How can you make 20? How does the depth of knowledge in the “Show Me” activity compare to the “Five-ness” activity?

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Make a “Ten Bead” Bracelet

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How are the process standards of problem solving, representation, communication, reasoning and proof, and connections addressed in the previous activities? How will allowing students to think for themselves impact their computational fluency? Debriefing: 49

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Looking back at the benchmarks discussed, what background knowledge must children know in order to meet the requirements of this standard? How might you utilize manipulatives to support conceptual depth and understanding? Debriefing: 50

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Debriefing: How will you assess students’ understanding of the benchmark, MA.K.A.1.1? What other benchmarks in grades K-2, are related to this benchmark? In what ways might you revise current instructional strategies to incorporate the in- depth understanding intended by the Next Generation Sunshine State Standards?

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Addition and Subtraction Strategies Participants will explore … – –The use of invented strategies to solve multi- digit addition and subtraction problems – –The use of Base 10 blocks, partial sums, and differences to solve multi-digit addition problems – –The empty number line as a method to focus on place value when solving subtraction problems

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Invented Strategies Overview These strategies are personal and flexible for the students Students will solve the same problem in different ways that make sense to them “There is mounting evidence that children both in and out of school can construct methods for adding and subtracting multi-digit numbers without explicit instruction.” (Carpenter, et al., 1998, p. 4)

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The Standard Algorithm You’re not allowed to use it today

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Problem 1 The two scout troops went on a field trip. There were 46 girl scouts and 38 boy scouts. How many scouts went on the trip? – –Van de Walle, 2007, p. 223

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Problem 2 Sam had 46 baseball cards. He went to a card show and got some more cards for his collection. Now he has 73 cards. How many cards did Sam buy at the card show? – –Van de Walle, 2007, p. 223

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Problem 3 There were 84 children on the playground. The 37 second-grade students came in first. How many children were still outside? – –Van de Walle, 2007 p. 225

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Problem 4 Tommy was on page 67 of his book. Then he read 58 more pages. How many pages did Tommy read in all? – –Van de Walle, 2007, p. 222

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What do you think? What are the advantages of using invented strategies? What are the disadvantages of using invented strategies? What depth of knowledge does this activity lead to?

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Getting Students to Invent Their Own Strategies Utilize word problems -Notice the wording involved in the previous problems Allow plenty of time Listen to different strategies Have students explain their methods Record verbal explanations for others to model Pose problems to be solved mentally

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Transitioning to “New” Standard Algorithms Using Base -10 Blocks for Addition – –For each problem, one person of the pair should be the “doer” and the other person the “recorder.” – –Keep a “written record” to translate what you do with the blocks into a paper-and- pencil algorithm.

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Base-10 Blocks as a Model Problem 1: Problem 2: Problem 3:

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Partial Sums = (30 + 2) + (20 + 9) = (2 + 9) + (30 +20) = = 61

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Partial Sums: Focus on Place Value = (30 + 2) + (20 + 9) = (2 + 9) + ( ) = = 61

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Partial Sums

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Using Base-10 Blocks for Subtraction Using Base-10 blocks and place-value charts to develop the traditional algorithm for subtraction. Problem 1: 73 – 26 Problem 2: 60 – 32

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Partial Differences – 26 = (70 + 3) – (20 + 6) = ( ) – (20 + 6)= (60 – 20) + (13 – 6)= =

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Jigsaw Strategy: The Empty Number Line Divide into dyads Read your half of the article (5 min.) Highlight important ideas When ready, share your ideas with your partner What was surprising or interesting within your group discussion?

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Developing Two-Digit Subtraction Using the Empty Number Line Be ready to describe the child’s strategy to your partner What depth of knowledge is exhibited in this strategy? Video Link: p?viewkey=05f243646d6f1e199f0b p?viewkey=05f243646d6f1e199f0b

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Examine the Big Ideas related to the Base-10 Number system across Grades K - 2. – –How is the content across the grade levels related? How does the content progress to a deeper level of understanding? – –How does the content prepare students for more advanced mathematics? – –How do the prior activities support children to get to the depth of knowledge identified by the State (Moderate – DOK2)? Studying the Standards 70

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How might you use the strategies/methods discussed today in your classroom? What do you expect your students to find challenging about invented and standard methods for addition and subtraction? What misconceptions might students hold about addition and subtraction that you will need to address? What can I do tomorrow morning? Teaching the Content 71

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