1. K-2 Standards and Support Training Office of Standards and Learning Mary L. Ruzga mruzga@ed.sc.gov Summer 2015

2. Introductions Introduce yourself to your table mates Show of hands – How many Pre-K, K, 1 st, 2 nd, etc., Principal/Assistant, District Leader, other? have participated in Numeracy Leader training? have read the new standards? are comfortable with the new standards?

3. What will we do today: 1.Quick overview of format of the standards 2.Review the standards by engaging in activities which explain and demonstrate the need for possible new pedagogical techniques 3.Review and explore the K-2 portion of the Mathematics Support Document

4. Accessing the Standards and Resources www.ed.sc.gov

5. BASIC COURTESIES/REMINDERS Please turn off phones (emergency vibrate) Please refrain from texting, emailing, etc. No formal break – take care of personal needs Logistics (lunch, restrooms) Participate and respect those around you

6. Content Standards Process Standards Portrait of SC Graduate

7. Process Standards

8. Mathematical Process Standards 1.Make sense of problems and persevere in solving them. 2.Reason both contextually and abstractly. 3.Use critical thinking skills to justify mathematical reasoning and critique the reasoning of others. 4.Connect mathematical ideas and real-world situations through modeling. Source: South Carolina College- and Career-Ready Standards for Mathematics 2015

9. Mathematical Process Standards 5.Use a variety of mathematical tools effectively and strategically. 6.Communicate mathematically and approach mathematical situations with precision. 7.Identify and utilize structure and patterns. Source: South Carolina College- and Career-Ready Standards for Mathematics 2015

10. Content Standards

11. Format of Mathematics Content Standards K – 8 Grade Level Content Standards Source: South Carolina College- and Career-Ready Standards for Mathematics 2015

12. Format of Mathematics Content Standards K – 8 Grade Level Content Standards Source: South Carolina College- and Career-Ready Standards for Mathematics 2015

13. In grades K – 8: GradeLevel.KeyConcept.Standard Number (e.g., K.NS.1) or, if applicable, GradeLevel.KeyConcept.Standard NumberStandardLetter (e.g., K.NS.4a) Format of Math Content Standards Source: South Carolina College- and Career-Ready Standards for Mathematics 2015

14. Terms including - references content that must be mastered (See K.G.1) e.g. - references possible illustrative examples. (See 1.NSBT.2c) i.e. - references the only examples or terms that should be used. (See 2.MDA.3) Source: South Carolina College- and Career-Ready Standards for Mathematics 2015

15. Terms Fluently and fluency describe a student’s ability to compute with accuracy, flexibility, and efficiency (Kilpatrick, Swafford, & Findell, 2001). Real-world refers to authentic contexts through which students engage in mathematics and should serve as a stepping-stone for thinking about important mathematical concepts. Source: South Carolina College- and Career-Ready Standards for Mathematics 2015

16. Digging Into the K-2 Standards for Mathematics

17. K 1 st Grade 2 nd Grade 3 rd Grade 4 th Grade 5 th Grade Number Sense Number Sense and Base Ten Number Sense - Fractions Number Sense and Operations - Fractions Algebraic Thinking and Operations Geometry Measurement and Data Analysis Measurement and Data Analysis Measurement and Data Analysis Measurement and Data Analysis Measurement and Data Analysis Measurement and Data Analysis Progression of Key Concepts

19. Digging Into the Standards Look at the standards for Grades K-1. Discuss with your tablemates: If you count the standards and the a,b,c, etc. which Key Concept is the largest in each grade? Why do you think that is so?

20. Digging Into the Standards Look at the standards for Grade 2. Discuss with your tablemates: If you count the standards and the a,b,c, etc. which Key Concepts are the largest? Why do you think that is so and what is the relationship between those concepts?

21. Digging Into the Standards If grades K-1 have the largest amount of standards devoted to number sense where should the bulk of our teaching time for mathematics be spent? Two types of Number Sense: Pre-operational Operational Pre-operational mathematical development is one of the most important predictors to future mathematical success.

22. Meaning Attached to Counting... “Generally, children at midyear in kindergarten should have a fair understanding of counting, but children must construct this idea. It cannot be forced. Only the counting sequence is a rote process. The meaning attached to counting is the key conceptual idea on which all other number concepts are developed.” (Emphasis added) John A. Van de Walle

23. Digging Into the Standards What is meant by Pre-operational Number Sense? Compare: K.NS.1 and K.NS.2 to K.NS.3, K.NS.4 and K.NS.5 Discuss with your tablemates: How do the expectations in the first two standards differ from the expectations of the second three standards? Rote vs meaningful counting

24. Digging Into the Standards... Pre-Operational Number Sense (meaningful counting) Look at: K.NS.4a (cardinality) Counting Strategy 1, 2, 3, 4, 5 How many? K.NS.4b (conservation of number) Arrangement Strategy Count, spread out and re-count K.NS.4c (increasing/decreasing magnitude) One/two more/less K.NS.5 (one-to-one correspondence)

25. Digging Into the Standards Comparison of Quantities - Number Relationships Discuss with your tablemates: How do K.NS.7 and K.NS.8 differ from each other and how do both relate to K.NS.4c? All three deal with number relationships – how does one quantity relate to the other (increasing/decreasing magnitude).

26. Digging Into the Standards Comparison of Quantities Number Relationships versus Operations Think about: If comparisons are number relationships – how one quantity relates to the other – then is that counting or is it operations and as a teacher does it matter? Re-read K.NS.4c Let’s explore through an activity.

27. Is it counting or is it operations? Does it matter? K – Play “More/Less Than” with five frame Need: 5 frame; baggie of pink cards and paper clip; spinner on “Spinning More or Less”, “One More Than Recording Sheet”; and follow directions on recording sheet 1 st and 2 nd Grade – Play “Spinning More/Less” (Bingo) Need: one die, paper clip from baggie of pink cards; several two-color counters (one color for you; other for partner); “Spinning More/Less”, and follow directions on spinning sheet

28. Is it counting or is it operations? Does it matter? Talk with your tablemates: Which game would most likely support a counting solution strategy and which one an operational solution strategy? Read 1.ATO.5 Talk with your tablemates: How does counting relate to addition and subtraction?

29. Digging Into the Standards Read the following Standards: 1.NSBT.5 2.NSBT.2 2.NSBT.8 Then discuss with your tablemates: How does the K concept of counting “one more/less” relate to the above standards? If students are struggling with the above standards, what might you need to consider?

30. Extending Number Relationships to Multiples Understanding the increasing/decreasing principle (number relationships) is necessary in order to count and add by multiples. One ten and one more ten is? In addition to number relationships, students also need to have developed the concept of subitizing in order to count on or “add on”.

31. Digging Into the Standards Visualization “Sight Words/Numbers/Quantities” Look at KNS.6 Perceptual Subitizing Conceptual Subitizing Beginning of counting on... (Add)

32. Perceptual Subitizing – instantly seeing how many in a small set of 2-3 objects; recognizing a # without operational knowledge Conceptual Subitizing – similar to the ability to recognize a # without operational knowledge but with larger sets and recognizing the number as both a whole and as its composite parts

33. Digging Into the Standards Visualization “Sight Words/Numbers/Quantities” Look at KNS.6 Perceptual Subitizing Conceptual Subitizing Beginning of counting on – Play “What Number Do You See?”

34. Digging Into the Standards Read: K.ATO.4, 1.NSBT.2 - all parts 1.ATO.3, & 6, 2.NSBT.1 - all parts 2.ATO.2 Then discuss with your tablemates: How does the ability to perceptually and conceptually subitize relate to the above? If a student is struggling with the concepts in the above standards, what might you check for? How might the concept of subitizing be developed in relation to operations? (Play How Many are Hiding? )

35. Subitizing/Visualization Needed for Counting On and as Foundation for Operations... Play – “How Many are Hiding?” K – use 5 cubes; 1 st and 2 nd grade - use 10 cubes Need: Paper plate, cm cubes 1.Count out cubes; Partner A grab some of the cubes and hide under plate; ask Partner B – How many are hiding? How do you know? 2. Partner B states: I know ___ are hiding because ____ and ___ more equal 5/10. 3. Count to verify Partner B’s response 4. Exchange Roles and Repeat

36. Subitizing/Visualization Needed for Counting On and as Foundation for Operations... “How Many are Hiding?” Handouts Continuum of Understanding Stages of Counting by Multiples

37. Read K.ATO.2 1.ATO.1 2.ATO.1 Addition is a Joining/Part-Part Whole action Parts of the Whole, Separation, Comparison

38. Digging Into the Standards Operations: K.ATO.1 and 2

39. Digging Into the Standards – “Start Unknown” 1.ATO.4 Understand subtraction as an unknown addend problem. Sandra had some pennies. George gave her 4 more. Now Sandra has 12 pennies. How many pennies did Sandra have to begin with? (Join: Initial Unknown/ Add to: Start Unknown) _____ + 4 = 12 Semantic Form of the equation 12 – 4 = _____ Computational Form What might we do in our classrooms to help students come to see the two forms as equivalent?

40. Once you know students can subitize and count on, focus on the operations – Subtraction as Think Addition and vice versa. How would the game, “How Many are Hiding” relate to 1.ATO.4 if students were required to write the number sentences? How many are hiding and how do you know? I know 7 are hiding because 10 – 3 (amount showing) = 7 (amount hiding) You are right, 7 are hiding because 3 + 7 = 10 3. Count to verify number sentences 4. Exchange Roles and Repeat 5. Results can re recorded in a variety of forms.

41. 18 7 3 8 11 24 35 Number Bonds Funnel Machine

42. 24 4 10 38 31 7 Number Machine Another design for Number Bonds

43. Digging Into the Standards The tendency in the US is to have children solve a lot of problems in a class period and focus on the correct answer rather than focusing in-depth on one or two well-chosen problems at a time, the relationship between the structures of the problems and the variety of approaches to the solutions. John A. Van De Walle

44. Digging Into the Standards 1.ATO.3 vs 2.ATO.4 Read the above two standards then discuss with your tablemates: How do the student expectations in these two standards differ? Equal Groups concrete objects Size of each group (4) Lesson 2 Handout Number of groups (3) 4 + 4 + 4 = 12 Handout x 2

45. Important Considerations at each Grade K-2 Rote Counting Meaningful Counting Cardinality (last number spoken) Conservation of Number (arrangement) Increasing/decreasing Magnitude Principle (one/two more/less) (number relationships) One-to-One Correspondence Subitizing (visualization) Comparisons (quantity relationships) Check for student solution strategies in order to determine: Is it counting or is it operations? This determines how to move the student forward in understanding.

46. Support Document Support Document Overview

47. Mathematics Support Document Overview  “Overview” http://ed.sc.gov/agency/ccr/Standards- Learning/Mathematics.cfm o Mathematics Edmo Group

48. Mathematics Support Document Review Process:  Work by grade levels – YOUR DECISON o Move into Grade Alike Groups o Open browser  http://maryruzga.weebly.com http://maryruzga.weebly.com  Not hyperlinked at this time  Grade Levels Review/explore  Share out one activity/lesson/resource

49. SCDE Mathematics Team: https://edmo.do/j/snmcix https://edmo.do/j/snmcix 1. Create an account. (If you have an account, log in.) 2. Enter URL above. 3. Different Grade Band “Folders” Joining Mathematics Edmodo Group

50. Office of Standards and Learning: https://edmo.do/j/fu7i2y https://edmo.do/j/fu7i2y 1. Create an account. (If you have an account, log in.) 2. Enter URL above. Joining Office Edmodo Group

51. Mathematics Support Document Feedback and Certificate of Participation  https://scde.formstack.com/forms/summer_p lo_evaluation_form_copy_1_copy https://scde.formstack.com/forms/summer_p lo_evaluation_form_copy_1_copy  See Yellow Handout for link or the QR code

52. Geometry Handout My Contact Information Mary L. Ruzga mruzga@ed.sc.gov Thank you for spending time with me today.