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Teaching to the Next Generation SSS (2007)

Teaching to the Next Generation SSS (2007). Elementary Pre-School Inservice August 17, 2010. Next Generation Sunshine State Standards . Eliminates: Mile wide, inch deep curriculum Constant repetition Emphasizes: Automatic Recall of basic facts Computational fluency

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Teaching to the Next Generation SSS (2007)

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  1. Teaching to the Next Generation SSS(2007) Elementary Pre-School Inservice August 17, 2010

  2. 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

  3. Comparison of Standards

  4. Coding Scheme for NGSSS MA.3.A.2.1

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

  6. What is Rigor?

  7. What Rigor is Not a measure of the quantity of content to be covered. a special program or curriculum for select students. about severity or hardship. only about higher-order thinking.

  8. Rigor Rigor is quality instruction that focuses on the depth of the learning not the breadth. It’s not more work; it’s meaningful, respectful work that requires the student to think deeply and critically to accomplish the assigned tasked. Eric Bergholm, Hillsborough County Public Schools, Florida

  9. What are the NCTM Process Standards? • Problem Solving • Reasoning and Proof • Connections • Communication • Representation 11

  10. NCTM Process Standards Problem Solving Developing perseverance and critical thinking Teacher’s Role: Allowing students to struggle Is multiplying by four the same as doubling and then doubling again. Does it always work? Why?

  11. COUNT THE SQUARES!

  12. How many are in the figure? 71

  13. Reasoning and Proof Mathematical conjectures Examples and counterexamples Connections Math: fraction/decimal, cm/m Other content areas, science Real-world contexts NCTM Process Standards

  14. NCTM Process Standards Communication Read, write, listen, think, and communicate/discuss Tool for understanding and explaining thinking Increased use of math vocabulary

  15. NCTM Process Standards Representation Useful tools for building understanding Tables, describe in words, draw a picture, write an equation Concrete-Representational-Abstract Model Diagram Example of Model Diagram from enVisionMATH

  16. Topics not Chapters

  17. Resources with enVisionMATH Daily Review WB Problem of the Day Interactive Learning Quick Check WB Center Activities Reteaching WB Practice WB Enrichment Interactive Stories (K-2) Letters Home Interactive Recording Sheets Vocabulary Cards Assessments

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

  19. Conceptual Understanding

  20. Conceptual Understanding

  21. Conceptual Understanding

  22. Old Instruction vs New Instruction

  23. Old Instruction vs New Instruction

  24. Focus on Fractions!

  25. Teaching for Depth • Fractions as a window into depth • Using sharing situations to introduce fractions • Representing fractions with flexible wholes • Estimating fraction sums and differences • Adding and subtracting fractions through stories

  26. NGSSS: Fractions (3rd) MA.3.A.2.1Represent fractions, including fractions greater than one, using area, set and linear models. MA.3.A.2.2 Describe how the size of the fractional part is related to the number of equal sized pieces in the whole. MA.3.A.2.3 Compare and order fractions, including fractions greater than one, using strategies and models. MA.3.A.2.4Use models to represent equivalent fractions, including fractions greater than one, and identify representations of equivalence. 30

  27. MA.4.A.2.3Generate equivalent fractions and simplify fractions. MA.4.A.2.4 Compare and order decimals, and estimate fraction and decimal amounts in real-world problems. NGSSS: Fractions (4th)

  28. MA.5.A.2.1 Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value or properties. MA.5.A.2.2 Add and subtract fractions and decimals fluently, and verify the reasonableness of the results, including in problem situations. MA.5.A.2.3 Make reasonable estimates of fraction and decimal sums and differences, and use techniques for rounding. NGSSS: Fractions (5th)

  29. Perspective… When asked to compare 4/5 and 2/3, a student said… “I know that 4/5 is greater than 2/3.” How would you respond? Hopefully you would ask the student how he or she knew.

  30. Perspective… The student said… I made both fractions using manipulatives. I knew that 4/5 was bigger because 4/5 has 4 pieces and 2/3 only has 2 pieces and since 4 is greater than 2 then 4/5 is greater than 2/3. We have a Problem!

  31. QUIZ: Which Fraction is Greater? • 3/7 and 5/8 • 4/7 and 4/9 • 9/10 and 5/4 • 3/8 and 5/8 • 6/7 and 8/9

  32. Think about this… Alex and Jessica are racing their bicycles. Alex is 3/7 of the way to the finish line and Jessica is 2/3 of the way to the finish line. Which racer is closer to the finish line? How do you know?

  33. Think about this… Marc and Larry each bought the same type of energy bar. Marc has 1/8 of his energy bar left, Larry has 1/10 of his energy bar left. Who has more energy bar left? How do you know?

  34. Think about this… Riley and Paige each bought a small pizza. Riley ate 5/6 of her pizza, and Paige ate 7/8 of her pizza. Who ate more pizza? How do you know?

  35. Let’s Talk About Why! • 3/7 and 5/8 • 4/7 and 4/9 • 9/10 and 5/4 • 3/8 and 5/8 • 6/7 and 8/9

  36. A new perspective… At what grade level would you ask a student to compare 22/23 and 26/27? According to the intent of the new standards, this question is appropriate for a student in Grade 3.

  37. Why Fractions? Because sometimes they’re the only way to get your fair share… This is particularly important when it comes to and . And the doorbell rang…

  38. Share 2 cookies among 4 people.

  39. Share 4 cookies among 3 people.

  40. Share 4 cookies among 5 people.

  41. Sharing Cookies Teaching Children Mathematics, March 2007

  42. Share 3 candy bars among 6 people.

  43. Share 3 candy bars among 6 people. How much of a candy bar will each person need to give the newcomer if a 7th person comes along?

  44. The whole is important… Consider telling the “whole” story with pattern blocks. Use the yellow hexagon as the whole. What fraction is represented by 5 green triangles?

  45. The whole is important… Consider telling the “whole” story with pattern blocks. Use the yellow hexagon as the whole. What fraction is represented by 1 blue rhombus?

  46. The whole is important… Now use 2 yellow hexagons as the whole. What fraction is represented by 4 blue rhombuses?

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