1. Implementing the CCSS 3 rd – 5 th Grade Kristin Frang, Mathematics Consultant

2. AGENDA  SMARTER Balanced Assessment Overview  Meaning of Fractions  Engaging Students in Math Talk  Operations with Fractions  CCSS Fraction Progressions  Next Steps

3. SMARTER Balanced Assessment Consortium (SBAC)

4. SMARTER Balanced Assessment Consortium PARCC vs. SBAC Computer Adaptive Features accessibility tools in alignment with UDL for all students Assessment in the last 12 weeks of school for grades 3 – 8 and 11 (formative assessments are being developed for grades 9 and 10 – stay tuned) Results within 2 – 3 weeks; retake option 2 performance tasks Practice/pilot items will be made available starting in the 2012- 2013 school year Background Information

6. “Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.” SBAC Assessment Claims “Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.” Concepts and Procedures Problem Solving “Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.” Communicating Reasoning “Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.” Data Analysis and Modeling (a/o Round 2 – released 12/9/11)

7. Maintain Focus and Coherence  The goal is coherence in curriculum, instruction, and learning  Standards are taken as atoms, but the power is in the bonds (Jason Zimba)  Think in chapters, not lessons (Phil Daro) Implementation Matters

8. What Went Wrong?

9. Big Ideas – Meaning of Fraction  Fractional parts are equal-size portions or equal shares of a whole or unit  Parts do not have to look the same  Unit can be object or a collection of things  Special names for the numbers that make up a fraction tell how many equal-size parts make up the whole (denominator) and how many of the fractional parts are being considered (numerator)  Denominator is divisor  Numerator is multiplier

10. 4 children want to share 5 candy bars so that everyone gets the same amount. How much can each child have?

11. Fair Sharing – 2 nd Grade 2.G.3 Partition circles and rectangles into two, three or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

12. 3 children want to share 5 candy bars so that everyone gets the same amount. How much can each child have?

13. 8 children want to share 6 cookies s so that everyone gets the same amount. How much can each child have?

14. Reasoning about Equal Size MP #3 Construct viable arguments and critique the reasoning of others MP #5 Use appropriate tools strategically A B

15. Meaning of a Fraction in 3 rd & 4 th Grade  Unit fraction is building blocks of fractions & every fraction is obtained by combining unit fractions Specifying the whole Explaining what is meant by “equal parts”  Multiple representations  Equivalence & Comparisons

16. Representing Fractions as Numbers Using a length unit, represent the following quantities 1 unit 1 / 5 8 / 3 2 1 / 6 © STEM 2012- Fractions & Measurement v1.0

17. Geoboards Make ½ on your geoboard in as many ways as you can and record on your dot paper.

18. Goals and Questions 18 Mathematical goals of the lesson are critical  Questions help advance a lesson towards its goal  Difficult to ask good questions in the abstract (i.e., in absence of goals)  No single right question in the pursuit of a goal  Certain types of questions are appropriate at different points in a lesson ©STEM @ MSU 2011 – Fall Facilitators’ Meeting - Midland, MI

19. Geoboard Lesson Annenberg

20. Questioning Framework - Boaler & Brodie  Take 10 minutes to use the transcript of the Geoboard lesson and the questioning framework to code the questions that the teacher asked  Talk with a neighbor and compare your codings

22. Equivalent Fractions  MP #7,8 Look for structure and generalize  Slicing Squares

24. Fraction Progression in CCSS Fraction Computation in 4 th & 5 th Grade  Meanings of operations on fractions same as meaning of operations on whole numbers Addition & Subtraction  Denominator indicates by what number the whole is divided  Numerator counts/tells how many of fractional pieces  Must have the same whole Multiplication  Denominator is a divisor Division  Partition/Fair-Sharing  Measurement/Repeated Subtraction

26. Each small cake takes ¾ of a cup of frosting. If Betty wants to make 24 small cakes, how much frosting will she need?

27. Multiple Groups

29. Multiplication Algorithm

30. CCSS Fraction Progression  Read Silently your grade level  Create a poster you will share with colleagues at other grade levels

31. Things Swimming Around In My Head  Chalk Talk  This is a silent way to reflect  Anyone may add to the chalk talk when they feel moved  You can comment on other people’s ideas simply by drawing a connecting line to the comment, circling other ideas, writing questions, or branching off for new ideas