Overview of the K-5 CCSS focusing on Mathematical Practices

1. Overview of the K-5 CCSS focusing on Mathematical Practices Day-1 presented by Judith T. Brendel Math Supervisor, Pascack Valley Regional HS District jbrendel@pascack.k12.nj.us June 2012

2. THINGS we shouldn’t forget! ACTIVITY: Use the ruler on handout to measure a writing tool you have with you. What decisions did you make? : 1- What should I measure (shorter than the ruler)? 2- Should I use inches or centimeters? 3. Where should I start on the ruler? 4- Should I round up or down? How accurate do I need to be? What should I round to?

3. CCSS: Common CORE State standards NOT TO BE CONFUSED WITH CCC STANDARDS; NJ’s present Core-Curriculum Content Standards But, don’t throw away what you already have!

4. Let me know a little bit How familiar you are with the CCSS? • Closed fist – I know nothing. • 1 finger – I know they exist. • 5 fingers – I could be standing up here doing this presentation.

5. Our plan for these 2 days: Day-1 • Experience activities that model CCSS • Understand CCSS content, changes, focus per grade and expectations • Understand Math Practices • Resources, resources and more • Consider ‘your’ plan for day-2

6. Our plan for these 2 days: Day-2 • Select/modify activities for your class • Experience highly effective activities • Review/use sample curriculum guides • Review/use sample unit/lesson plans • Receive/research resources: activities, examples, online NCTM, ASCD, ….

7. WHAT’S NEW Measure standards that are rigorous, globally competitive, and consistent across the states. New Jersey’s choice The assessment consortium PARCC(Partnership for Assessment of Readiness for College and Careers) New assessments will replace current state NCLB tests (NJASK, HSPA) in 2014-2015.

8. What We’ve Learned during the past decades: • Absolutely, students must know the basics, but knowing basics not enough. • Students learning math with understandings is essential to enable students to solve problems. • Students learn math primarily by doing math rather than just by listening and memorizing.

9. What We’ve Learned during the past decades: • Absolutely, students must know the basics, but knowing basics not enough. • Students learning math with understandings is essential to enable students to solve problems. • Students learnmath primarily bydoing math rather than just by listening and memorizing.

10. What they’ve Learned during the past decades: • absolutely students must know the basics, but knowing basics not enough • students learning math w/understandings is essential to enable students to solve problems • students learn math primarily by doing math rather than just by listening and memorizing “IS” OVER “OF” WINDOWS doors WINDOWS doors YOU JUST MAKE A BOX! R x T = D .64 is POINT 64 When you multiply you always get a BIGGER number!

11. What we should do! Start with a problem (division w/one-digit divisors) Give to students and see what they do with it. Let them work in pairs. Let them talk about it. Paulo has 39 patches from states that he and his relatives have visited. He wants to arrange the patches on a board in 3 rows. How many patches will be in each row? (from Dr. Janet Caldwell)

12. Characteristics of the CCSS • Fewer and more rigorous • Aligned with college and career expectations • Internationally benchmarked • Rigorous content and applications of higher-order skills – rigor a depth, not complexity • Research-based • Common, coherent, fair and teachable

13. COMMON ADVANTAGES • FEWER standards means that teachers and students will have more time to focus on each knowledge & skill. • CLEAR standards means the parents, teachers and the general public will find it easier to understand the expectations for students • HIGHER standards means that all students will be fully prepared for the future, whether they choose to further their education or immediately enter the workforce. • COMMON standards means that schools can compare student test scores state-by-state or state to the national average.

14. TIMELINE * CCC database but Only CCSS questions CurriculumAssessments 2011-12 K-2New (none) 3-5, 6-8,11 NJASK, HSPA 2012-13 K-2, 6-8 (none), NJASK 3-5,HSNewNJASK*, HSPA* 2013-14 6-8 New NJASK*K-5, HS NJASK*, HSPA* 2014-15 K-11 NEW (PARCC) (This year’s 8th graders)

15. Big Things to Notice K-8 • Number is emphasized in K-5. • Algebra is imbedded in number until grade-6. • Less is expected in statistics and probability early; more at later grades. • Geometry is included in every grade but is limited in scope in K-8. • Length is included in grades 1-2; both other types of measurement are postponed until grade-3. • Some topics change grades from current NJ CCCs.

16. GRADE-K focus The Common Core Standards emphasize that instructional time in Kindergarten should focus on two critical areas: • Representing and comparing whole numbers, initially with sets of objects; and • Describing shapes and space. https://sites.google.com/site/pvrsdportal/kindergarten-curriculum

17. Grade-K questions ? What about the calendar? What about patterns? What about telling time?

18. GRADE-1 focus instructional time should focus on four critical areas: • developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; • developing understanding of whole number relationships and place value, including grouping in tens and ones; • developing understanding of linear measurement and measuring lengths as iterating length units; and • reasoning about attributes of, and composing and decomposing geometric shapes.

19. Grade-1 What’s new?  New topics: what should I do? • Describe these shapes without talking about color. • Students need to know how to add 25 + 17. Ask kids what they’d do to find out how much 17 + 25 is. What do you think they might do?

20. GRADE-2 focus instructional time should focus on four critical areas: • Extending understanding of base-10 notation (multi-digits to 1,000) • Building fluency with addition and subtraction • Use standard units of measure (cm., inch; use ruler) • Describe and analyze shapes (sides, angles; compose, decompose; 2D and 3D) … building a foundation for area, volume, congruency, similarity, symmetry in later grades.

21. GRADE-3 focus instructional time should focus on four critical areas: • developing understanding of multiplication and division and strategies for multiplication and division within 100; • developing understanding of fractions, especially unit fractions (fractions with numerator 1); • developing understanding of the structure of rectangular arrays and of area; and • describing and analyzing two-dimensional shapes.

22. Grade-3 before/after NJASK? • Multiplication facts by memory (all of them for NJASK … Do these all year long.) • Fractions on number line (do after NJASK) • Equivalent fractions (do after NJASK) • Time (see new CCSS 3.MD.1.) see – symbol • Areas of rectilinear figures (like an ‘L’ shape w/right angles).

23. Left Out of Grade-3 • Decimals • Estimation • Congruence, symmetry, circles • Coordinate geometry, transformations • Patterns, functions • Probability, discrete math

24. What’s Different in Grade-3? • First time students use metric measuring • Ex. What might students do? 7 x 28 We need to do more mental math to help students gain number sense … working on pencil-paper procedures for computation will not help students gain good number sense. • Ex. Pose a problem. Jose has 3 boxes of 24 crayons, how many does he have in all.

25. FRACTIONS

26. Fractions Across Grades Grade-1 • taking squares/circles and dividing them up. Grade-2 • Know equal shares don’t need to be the same shape to be the same size Grade-3 • unit numerators • fractions on the number line

27. Grade-4 should focus on three critical areas: • developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; • developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; and • understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

28. What are we doing? GRADE-4 FRACTIONS, FACTIONS, fractions Don’t’ change till after NJASK Fill in gaps fall 2012 from grades K – 3 Add new topics: • number sentences w/variables (start using letters for unknowns) • factors and multiples

29. What’s omitted in grade-4? • Negative numbers • Estimation • Congruence, • Symmetry, • Transformations

30. Grade-4: Do AFTER NJASK • multiply 1 digit by 3 digits (425 x 6) • divide 4 digits by 1 digit ( 427 ÷ 3) • equivalent fractions (2/3 and 4/6) • decimal notation for fractions (2/5 = 0.40) • multiply fraction by whole number (2/3 x 6 ) Leave for next year: • Convert units to smaller ones (2 ft = 24 inches) • measure angles

31. Grade-5 Should focus on three critical areas: • developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); • extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and • developing understanding of volume.

32. Gr.5 – Fractions, Division, Decimals(This is going to be hard!) Fill in gaps fall 2012 from grades K-4 Add new topics • Whole number exponents for powers of 10 ( 321 = 3 x 102 + 2 x 101 + 1 or 100 ) • Multiply fractions and mixed numbers (½ x 4 ½ ) • Divide unit fractions and whole numbers (3 ÷ ½ ) • Converting little units into big 24” = ___ ft. • Line plot with fractional measures (a big group) • Volume

33. MULTIPLICATION and DIVISION

34. Multiplcation and Division Across Grades • Grade-2 Intro to multiplication briefly • Grade-3 When do you use it? (Understand and master facts) 1 digit x multiples of 10 4 x 60 = 240 • Grade-4 Use multiplication to compare (twice as big, three times a big) and 1 digit mult. up to 4 digits, 2 digits x 2 digits, 2 digits x 3 digits • Grade-5 Fluent with multiplication • Grade-6 Fluent with division

35. NEW ASSESSMENTS

36. New Assessments (PARCC) K-2 ASSESSMENTS Will not be done electronically May be optional for districts GRADES 3-8, 11 Will have all/part electronically Results back to teachers in a few weeks Technology-Availability Survey to districts fall 2011 to collect data about each school.

37. New Assessments (PARCC) Whatever is in the CCSS for each grade-level K-8 may be assessed. Quarterly assessments are being considered Detailed results to be received by teacher w/in a few weeks. These will all be ‘secured’ tests (Districts will have testing ‘windows’ instead of same date for all districts and schools.)

38. New Assessments The Dream ! Whatever is in the CCSS for each grade-level K-8 may be assessed. Quarterly assessments are being considered Computer adaptive assessments Four-week testing windows Computer score-able constructed response items Item banks for Formative, Benchmark AND Summative assessments Student, class, school, district, state and nation results three days after the window closes

39. CCSS COMMON CORE STATE STANDARDS

40. Grade K-8, 9-12 math is divided into categories K to 8 High School Grade Conceptual Category Domain Domain Cluster Cluster Standards Standards

41. K-8 math is divided into 4 DOMAINS OA Operations & Algebraic Thinking NB Number & Operations in Base 10 NBF Number & Operations - Fractions MD Measurement and Data G Geometry

42. What does it look like? Grade-3 DOMAIN:Operations & Algebraic thinking CLUSTER: 3.OARepresent and solve problems involving multiplication and division. Standard 3.0A.1Interpret products of whole numbers, e.g. interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. Standard 3.0A.2Interpret whole-number quotients Standard 3.0A.3Use x and ÷ within 100 … Standard 3.0A.4Determine the unknown .. 8 x ? = 48 5 = ÷ 3, 6 x 6 =

43. What does it look like? Grade-4 DOMAIN:Operations & Algebraic thinking CLUSTER: 4.OAUse the four operations with whole numbers to solve problems Standard 4.0A.1Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 … Represent verbal statements of multiplicative comparisons as mutiplication equations. Standard 4.0A.2Multiply or divide to solve word... Standard 3.0A.3Solve multi-step word problems … whole numbers … four operations … Assess the reasonableness of answers.

44. What does it look like? Grade-5 DOMAIN:Operations & Algebraic thinking CLUSTER: 5.OAWrite and interpret numerical expressions. Standard 5.0A.1Use parenthesis, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. (new to gr. 5) Standard 5.0A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

45. Easy to remember! • 4.0A • 3.MD • 5.G • 2.NBT • 4.NF Operations & Algebraic Thinking Measurement and Data Number & Operations Base 10 Number & Operations Fractions

46. AN OVERVIEW WHAT has been added? What has been moved?

47. Grade- 1 (add/remove?) ADD: Move symbols = < > from gr.-3 to gr. 1 1.NBT.3 ADD: Zero as the identity element (e.g. 7 + 0 = 7) Zero as an additive identity element is not explicitly articulated in the CCSS at any grade. 1.OA.3 ADD: Calculator (use of a calculator is explicitly included only in the CCSS for Mathematical Practice. 1.NBT.4) ADD: Weight (lb., gram, kilogram), Capacity (pint, quart, liter), Temperature (degrees Celsius, degrees Fahrenheit) ADD: Data generated from chance devices 1.MD.4 ADD: Use simple shapes to make designs, patterns, …

48. Grade- 2 (add/remove) • ADD: Determine whether a whole number is ODD or EVEN from grade-3 to 2.OA.3 • ADD: Compare two 3-Digit numbers based on meanings of hundreds tens and ones digits using > < = symbols to record comparisons 2.NB.4 REMOVE • Move actual using of symbols > < = for first time to grade-1.NBT.3

49. Grade- 3 (add/remove) • ADD: Fluently multiply and divide within 100, … 3.0A.7 • ADD: Move memorize the multiplication table from grade-4 to grade-3. By end of grade-3, know from memory all products of two one-digit numbers. REMOVE • Move determining whether a whole number is odd or even from grade-3 to grade-2.A.3 • Move actual using of symbols > < = from grade-3 to grade-1.NBT.3

50. Grade- 4 (add/remove) • ADD: Move from grade-5: Find all factor pairs of whole numbers in the range. Recognize 1-100. 4.OA.4 • ADD: Move from grade-5: Recognizeangles as geometric shapes when … understand concept of angle measurement. 4.MD.5 • ADD: Move from grade-5: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 4.MD.6 Move memorize the multiplication table from grade-4 to grade-3. By end of grade-3, know from memory all products of two one-digit numbers.