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Mathematics in the Era of Common Core State Standards

Mathematics in the Era of Common Core State Standards. Focusing on California Mathematics Framework Train the Trainer Sessions May 13, 2014 Hilary Dito & Pam Tyson. Workshop Goals.

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Mathematics in the Era of Common Core State Standards

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  1. Mathematics in the Era of Common Core State Standards Focusing on California Mathematics Framework Train the Trainer Sessions May 13, 2014 Hilary Dito & Pam Tyson

  2. Workshop Goals • To examine the Common Core State Standards through the lens of the CA Mathematics Framework at a specific grade level • To understand the major focus of a grade level • To explore how the Mathematics Framework supports learning for all students

  3. http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp

  4. Content Domains Grades K - 12

  5. Standards Page(s) Domain Standard Cluster Refer to pages 58-62 of the Grade Six chapter of the Framework

  6. Three Shifts

  7. Focus “Instruction should focus deeply on only those concepts that are emphasized in the standards so that students can gain strong foundational conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom.” CDE Mathematics Framework, Overview Chapter, page 2

  8. Focus “Instruction should focus deeply on only those concepts that are emphasized in the standards so that students can gain strong foundational conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom.” CDE Mathematics Framework, Overview Chapter, page 2

  9. K-8 Areas To Understand Deeply

  10. Focus • Read pages 1-3 of the Grade Six chapter of the Framework • What are the implications for classroom instruction? • Share one insight with a partner

  11. Focus WHAT STUDENTS LEARN IN GRADE SIX

  12. Focus

  13. 6th Grade Mathematics

  14. 6th Grade Mathematics– from PARCC Framework Turn to the Content Standards Pages in the framework chapter (Grade 6: pages 58-62) • Highlight the Major Clusters green • Highlight the Supporting Clusters blue • Highlight the Additional Clusters yellow How do the supporting clusters and the additional clusters reinforce the major clusters?

  15. 6th Grade Mathematics – from PARCC Framework

  16. Compare the Cluster-Level Emphasis of other grades • Read the cluster-level emphasis for • 3rd Grade • 11th Grade How do the supporting clusters and the additional clusters reinforce the major clusters? How does • grade 3 support the work in grade 6? • grade 6 support the work in grade 11?

  17. 3rd Grade Mathematics – from PARCC Framework

  18. 11th Grade Mathematics –from SBAC Assessment Blueprint* * Note: PARCC and SBAC have similar priority clusters for grades K-8. High school standards have slight variances in major, supporting and additional clusters

  19. NOT YOUR MOTHER’S ALGEBRA 1 These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step.” - CCSS (2010, p.5)

  20. Coherence “Some of the connections in the standards knit topics together at a single grade level. Most connections are vertical, as the standards support a progression of increasing knowledge, skill, and sophistication across the grades.” CDE Mathematics Framework, Overview Chapter, page 3

  21. Coherence “Some of the connections in the standards knit topics together at a single grade level. Most connections are vertical, as the standards support a progression of increasing knowledge, skill, and sophistication across the grades.” CDE Mathematics Framework, Overview Chapter, page 3

  22. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (6.RP.2 ▲) Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. (6.RP.3a,b ▲) a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Recognize and represent proportional relationships between quantities. (7.RP.2 ▲) Understand the connections between proportional relationships, lines, and linear equations. (8.EE.5 ▲) 6.RP.2 ▲ 6.RP. 3a,b▲ 7.RP.2▲ 8.EE.5▲ & Coherence: a learning trajectory

  23. 6.RP.3a. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Can you solve this problem using 2 different mathematical methods? Can you solve this problem using 3 different mathematical methods? Share your solutions

  24. A Tape Diagram expresses a ratio by representing parts with pieces of tape

  25. A Tape Diagram expresses a ratio by representing parts with pieces of tape

  26. A Double Number Line diagram sets up two number lines with zeroes connected

  27. “Representing ratios in various ways can help students see the additive and multiplicative structure of rations (MP.7)” “In standard 6.RP.3.a p, students create tables of equivalent ratios and represent the resulting data on a coordinate grid. Eventually, students see this additive and multiplicative structure in the graphs of ratios, which will be useful later when studying slopes and linear functions. (See also Standard 6.EE.9 p)” Mathematics Framework, Grade Six, page 12

  28. A look at the Framework Read the section on Ratios and Proportional Reasoning (pages 9-20) • How do the examples build on the three shifts (focus, coherence and rigor)? • How are the Standards for Mathematical Practices integrated into the Content Standards? • How does the framework support instruction in the classroom, especially in regard to the major work of a grade-level?

  29. Reflecting on our work with the Mathematics Framework, • How will the framework guide your instructional planning? • What are your next steps to gain understanding in regards to implementing CCSS?

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