1. Mathematics Grades 3-5iEvolve Daniel J. Brahier (brahier@bgsu.edu) BGSU/St. Rose School Wednesday, 22 May 2013

2. Characteristics of the CCSS-Math • Fewer, clearer, and higher • Aligned with college and career expectations • Internationally benchmarked • Include rigorous content and application of higher-order skills • Evidence- and/or research-based • Build upon strengths and lessons of current state standards • Promote collaboration among states for instruction, resources, assessment, and professional development

3. So, what IS “mathematics”? • Something that you “know” • Something that you “do” • All of the above! Mathematics is a VERB – something you “do”

4. NCTM Process Standards (1989) • Problem Solving • Reasoning and Proof • Communication • Connections • Representation

5. Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

6. Student Responses Students rarely, if ever, answer a question “wrong.” Instead, they give a “correct” answer to a different question than we thought we were asking!

7. How do you “know” these? • 7 + 8 • 6 + 6 • 8 + 5

8. How do you “know” these? • 7 + 8 • 6 + 6 • 8 + 5

9. Knowing Basic Facts

10. How do you visualize 3 x 5? Which of these is/are most accurate? Which reveal misconceptions?

11. How do you find the answer? 160 x 50

12. What do you know about each? • 14.7 ÷ 1.05 • 126.68 ÷ 0.97 • 164 x 0.76 Where does the decimal go: 27.49 x 8.31 = 2284419

13. Butterfly Multiplication Why does this work???

14. Scientific and Engineering Practices (NSTA, 2012) • Asking questions and defining problems • Developing and using models • Planning and carrying out investigations • Analyzing and interpreting data • Using mathematics and computational thinking • Constructing explanations and designing solutions • Engaging in argument from evidence • Obtaining, evaluating, and communicating information

15. Practices of Math AND Science

16. Which is true about the Standards for Math Practice? • They are of equal importance. • They should be emphasized in an equitable manner at each grade level (similar time devoted to each). • They vary in importance at different grade levels.

17. Which is true about the Standards for Math Practice? • They are of equal importance. • They should be emphasized in an equitable manner at each grade level (similar time devoted to each). • They vary in importance at different grade levels.

18. An Old Joke • How do you kill a blue elephant? • With a blue elephant gun. • How do you kill a white elephant? • With a white elephant gun? • No, you first strangle the elephant until it turns blue and then use the blue elephant gun you already have!

19. Chinese Proverb Give me a fish and I eat for a day. Teach me to fish and I eat for a lifetime.

20. Practices Emphasis on the Mathematical Practices is equivalent to teaching our students “how to fish”!

22. Domains for Grades 3-5 • Operations and Algebraic Thinking • Number and Operations in Base Ten • Number and Operations – Fractions • Measurement and Data • Geometry

23. Big Ideas (“Critical Areas”) in Grade 3 • Understanding of multiplication and division strategies up to 100 • Understanding of fractions, particularly unit fractions (numerator = 1) • Understanding of rectangular arrays and area • Describing/Analyzing two-dimensional shapes

24. Big Ideas in Grade 4 • Understanding/Fluency with multi-digit multiplication and division with quotients having multiple digits • Fractions – equivalence, add/subtract with same denominator, multiply by whole numbers • Analyzing/Classifying geometric shapes based on parallel sides, symmetry, etc.

25. Big Ideas in Grade 5 • Understanding/Fluency with adding/subtracting fractions and general idea of multiplying/dividing fractions • Decimals, including fluency in decimal operations up to hundredths • Developing an understanding of volume in three-dimensional shapes

26. What Develops Conceptual Understanding?

27. Engage Students in Productive Struggle

28. Productive Struggle

29. Making Mathematical Relationships Explicit

30. The Next Generation Assessments

31. Prototype Item – Grade 4 (Part A)

32. Prototype Item – Grade 4 (Part B)

33. Prototype Item – Grade 4 (Part C)

35. Mathematics Grades 3-5iEvolve Daniel J. Brahier (brahier@bgsu.edu) BGSU/St. Rose School Wednesday, 22 May 2013