Triton Faculty to Faculty Mathematics

1. Triton Faculty to FacultyMathematics Presented by: April Capuder (acapuder@sd81.org) Lincoln Middle School 8th Grade Mathematics Teacher and Curriculum Facilitator in Schiller Park Cynthia Harris (charri32@triton.edu) Triton College Mathematics Department Chair

2. What We’ll Be Doing Today • Engaging in several activities to dive deeply into the standards, with a focus on grades 6-8. • Using ratio and proportion “thinking tools” to solve problems • If time permits, Using vignettes to process the CCSS progressions Expressions and Equations (6-8) • Describing and providing resources for additional activities (or extensions to activities) for teacher teams. • Mathematics Common Core Standards & Triton Placement Statistics • Group activity for the Standards for Mathematical Practices • PARCC Assessments • Formative Assessment Lessons Resource aligned to CCSS

3. A FEW QUESTIONSABOUT YOU • ---- Please share ----- • How familiar are you with the Common Core Mathematics State Standards? • 1 2 3 4 5 • Not Familiar VERY familiar

4. The Common Core Standards

5. A Strong Foundation: The Common Core State Standards • Nearly every state in the nation is working individually and collectively to improve its academic standards and assessments to ensure students graduate with the knowledge and skills most demanded by college and careers • The Common Core State Standards in English language arts/literacy and mathematics were created by educators around the nation

6. *Minnesota adopted the CCSS in ELA/literacy only 46 States + DC Have Adopted the Common Core State Standards

7. Number of Topics Intended at Each Grade – Comparison to Previous Standards

8. CCSSM Congruence and NAEP Mathematics Performance States with past mathematics standards that were moresimilar to the CCSSM had statistically significantly higher NAEP 2009 performance.

9. Consistency With the CCSSM

10. Triton College Placement Statistics

11. Number of Students Taking the Placement Test

12. Number of Students Enrolling in the Prescribed Classes

13. Of all new students: 2.8% enter at college level through the placement test 20.6% enter at college level through a waiver 42.7% place into prealgebra (MAT 045) 22.2% place into beginning algebra and geometry (MAT 055) 4.7% place into intermediate algebra (MAT 085) 7% do not take the placement test

14. Topics from MAT 045

15. Thinking about Mathematics CCSS Mathematical Practices andRatios and Proportions

16. Begin with the Mathematical Practices Resource: http://commoncoretools.me/author/wgmccallum /

17. Activity:Unpacking the Standards for Mathematical Practice CCSSM, pages. 6-8 • READ the introductory paragraph on page 6. • Count by 8’s to form 8 groups • Read the corresponding Mathematical Practice. While reading, use the CLASSROOM as a lens to consider the teacher and student perspectives. • Discuss the key features and meaning of the Mathematical Practice. • What would it LOOK like, SOUND like and FEEL like in the classroom? • Make a poster toidentifyyour Mathematical Practice and its key features. Depict what it LOOKS like, SOUNDS like and FEEL like in the classroom. Be creative! • Each group presents its poster to the entire group.

18. Student Posters from Jordan School District in Utah Resource: http://elemmath.jordandistrict.org/mathematical-practices-by-standard/

19. Key Advances of the Common Core ANCHORED IN COLLEGE AND CAREER READINESS

20. The Common Core State Standards (CCSS) for Mathematics • Mathematical Domains Across Grade Level Bands CCSS, pages 10-57

21. Ratio and Proportion Activity • We are going to examine 3 tools highlighted in the CCSS to explore ratio a and rate reasoning to solve real-world and mathematical problems • “CCSS 6.RP.3 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.” • “CCSS 7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams & verbal descriptions of proportional relationships.” • Engage in solving a sampling of ratio and rate problems using as many of the tools as possible. • Share example work of the solutions and describe connections to the Mathematical Practices

22. Thinking Tools Resources supported in the CCSSM: • Ratio Tables • Double Number Lines • Tape Diagrams

23. Ratio Table A table of two (or more) quantities which are in equivalent ratios (i.e. a proportional relationship) 2 caterpillars eat 5 leaves. How many leaves for 30 caterpillars? GOAL: 30 Caterpillars + 2 + 5 x 3

24. Double Number Line Two number lines joined together to represent quantities in a proportional relationship (usually with different units) 20 ounces of soda costs $1.20 Find prices for at least 3 different sized cans.

25. Tape Diagrams From the CCSSM Glossary: “A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model. “

26. Two fifths of the boys in the class are on a trip. If there are 40 boys in the class, how many went on the trip? 40 8 8 8 8 8 16 Boys

27. Two fifths of the boys in the class are on a trip. If there are 40 boys on the trip, how many are in the class? 40 20 20 20 20 20 100 Boys

28. The recipe calls for 5 parts ginger ale to 2 parts orange juice. If I want to make 28 quarts, how many cups of each are needed? 4 4 4 4 4 4 4

29. Using the Bar Model with Per Cents Margie spent $360 for a coat on sale for 20% off. Nancy wants to buy the same coat. Unfortunately, it is no longer on sale. How much will Nancy pay for the coat? $450 - 20%

30. Choose one problem and solve it in as many ways as you can. (ratio table, double number line, tape diagram, algebraic methods, scale factors,...) • Problem A: If 2 pounds of beans costs $5, how much will 15 pounds of beans cost? • Problem B: If 75% of the budget is $1200, what is the full budget? • Problem C: To make Perfect Purple paint mix 1/2 cup blue paint with 1/3 cup red paint. If you want to make 20 cups of Perfect Purple, how many cups of each color do you need? • Problem D*: There are 25% more seventh graders than sixth graders in the after-school club. If there are 135 6th and 7th graders altogether in the club, how many are 6th graders? • Problem E*: Yellow and blue paint were mixed in a ratio of 5 to 3 to make green paint. After 14 liters of blue paint were added, the amounts of yellow and blue paint in the mixture was equal. How much green paint was in the mixture at first? * HS

32. Problem A

33. Problem B

34. Problem C

35. Problem D

36. Problem E

37. Connecting to the Common Core What Standards for Mathematical Practice did we just engage in? What about Content?

38. Learning Progressions

39. PARCC Assessments

40. What’s Next?Common Assessments • Common Core State Standards are critical, but it is just the first step • Common assessments aligned to the Common Core will help ensure the new standards truly reach every classroom

41. Partnership for Assessment of Readiness for College and Careers (PARCC)

42. K-12 and Postsecondary Roles in PARCC K-12 Educators & Education Leaders • Educators will be involved throughout the development of the PARCC assessments and related instructional and reporting tools to help ensure the system provides the information and resources educators most need Postsecondary Faculty & Leaders • Nearly 750 institutions and systems covering hundreds of campuses across PARCC states have committed to help develop the high school assessments and set the college-ready cut score that will indicate a student is ready for credit-bearing courses

43. The PARCC Goals • Create high-quality assessments • Build a pathway to college and career readiness for all students • Support educators in the classroom • Develop 21st century, technology-based assessments • Advance accountability at all levels • Build an assessment that is sustainable and affordable

44. Timeline Through First PARCC Administration in 2014-2015 PARCC Tools & Resources Partnership Resource Center launched Professional development modules released K-2 Formative Tools Released Diagnostic assessments released College-ready tools released Summative PARCC Assessments (2014-15 SY) Winter 2015 Spring 2015 Fall 2014 Spring 2013 Summer 2013 Fall 2013 Winter 2014 Spring 2014 Summer 2014 Pilot/field testing begins Expanded field testing of diagnostic assessment Expanded field testing Optional Diagnostic and Midyear PARCC Assessments Standard Setting in Summer 2015 PARCC Assessment Implementation

45. We will fully implement the Common Core State Standards in 2014-2015 We will take the new national test with Common Core Standards in Spring of 2015

46. PARCC Assessment PrototypeRatio and Proportion - Gasoline Consumption Part A http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html

47. PARCC Assessment PrototypeRatio and Proportion - Gasoline Consumption Part B http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html

48. PARCC Assessment PrototypeRatio and Proportion - Gasoline Consumption Part C http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html

49. Continuing to Think about Mathematics CCSS – Vignette Study

50. Activity – Discussing Vignettes • Based on actual dialogues heard between students in various coaching experiences as well as research. • Highlights big teaching dilemmas in a particular content area. • More accessible than reading a research article or full length Progression documents