Huntsville City 6-8 Math

1. Huntsville City 6-8 Math March 18, 2013 Jeanne Simpson AMSTI Math Specialist

2. Welcome • Name • School • Classes you teach • Your favorite math topic to teach

4. He who dares to teach must never cease to learn. John Cotton Dana

5. Five Fundamental Areas Required for Successful Implementation of CCSS

6. How do we teach?

7. A Shared Vision • Does each of us have a shared vision of what teaching and learning a mathematics lesson looks like? • Taking about 5 minutes, think of 3 or more components of a mathematics lesson you feel are important and should be found in a mathematics lesson. • Please do not share with your group, yet.

8. A Shared Vision • Draw a circle in the center of your chart paper. • Write your ideas anywhere on the chart paper provided to your group, just not in the circle. • Take about 5-7 minutes to discuss your ideas with your group. • Do your ideas reflect current research in mathematical education? • Do your ideas reflect the vision of the College- and Career-Ready standards?

9. A Shared Vision • Now, in your groups, write in the circle using 15 words or less, what your group decided are the components of a good mathematics lesson. • After 10 minutes, each group will share their thoughts.

10. How do we teach?

11. Standards for Mathematical Practice SMP1 - Make sense of problems and persevere in solving them SMP2 - Reason abstractly and quantitatively SMP3 - Construct viable arguments and critique the reasoning of others SMP4 - Model with mathematics SMP5 - Use appropriate tools strategically SMP6 - Attend to precision SMP7 - Look for and make use of structure SMP8 - Look for and express regularity in repeated reasoning

12. What Are The Practice Standards? • Capture the processes and proficiencies that we want our students to possess • Not just the knowledge and skills but how our students use the knowledge and skills • Describe habits of mind of the mathematically proficient student • Carry across all grade levels, K-12

13. Standards of Mathematical Practice • √ I already do this. • ! This sounds exciting! • ? I have questions.

14. High-Leverage Strategies • Problem solving • Demanding tasks • Student understanding • Discussion of alternative strategies • Extensive mathematics discussion • Effective questioning • Student conjectures • Multiple representations Name Strategy or SMP

15. What are we teaching?

16. Unpacking the Standards “To increase student achievement by ensuring educators understand specifically what the new standards mean a student must know, understand, and be able to do. (Unpacking) may also be used to facilitate discussion among teachers and curriculum staff and to encourage coherence…(Unpacking), along with on-going professional development is one of many resources used to understand and teach the CCSS.” -North Carolina Dept of Public Instruction Step 1: Target a standard Step 2: Chunk the Main Categories Step 3: Identify all standard components Step 4: Identify the Developmental Progression Step 5: Identify Key Vocabulary Step 6: Add Clarifying Information

17. Why are we Unpacking Standards? • To understand what the standards are asking students to know, understand, and be able to do • To make time for professional discussion about the standards • To build upon and use common terminology when discussing the implementation of the standards Unpacking is standards is not a substitute document for the Common Core Standards, it is a record of the conversation of those who are involved in the process of digging into the standards.

18. Step 1 – Target a Standard • What are you teaching this spring? • Find a group of 2-4 teachers who will explore that topic with you. • What standards are involved?

19. 2.G.3 Partition circles and rectangles into two, three, or four equal shares The final product…. Describe Recognize Partition circles and rectangles into four equal shares, using the word fourths, fourth of 2.G.3 Describe the whole as two halves, three thirds, four fourths 2.G.3 Recognize that equal shares of identical wholes need not have the same shape 2.G.3 Partition Partition circles and rectangles into three equal shares, using the word thirds, third of 2.G.3 Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Fourths Fourth of Identical whole Builds on 1.G.3 Needed for 3.G.2 Thirds Third of whole partition rectangle Halves Half of Partition a shape into fourths in different ways Pattern Blocks Fraction Bars/Circles 2/2 = one whole Equal shares circle

20. Step 2: Chunk the Main Categories Example 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. • All Standard(s) in the cluster(s) • Identify Key Verbs 2.G.3 Partition circles and rectangles into two, three, or four equal shares Describe Recognize Partition

21. lt blue Step 3: Identify all standard components Components from CCSS: • Analyze nouns and verbs What do students need to do? • Include bullets, examples, footnotes, etc. • Take standard apart according to the verbs to separate skills within the standard What do the students need to know?

22. Example 2.G.3 Partition circles and rectangles into two, three, or four equal shares Partition Describe Recognize Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Partition circles and rectangles into three equal shares, using the word thirds, third of 2.G.3 Partition circles and rectangles into four equal shares, using the word fourths, fourth of 2.G.3 Describe the whole as two halves, three thirds, four fourths 2.G.3 Recognize that equal shares of identical wholes need not have the same shape 2.G.3

23. Step 4: Identify the Developmental Progression Questions to consider when looking at the developmental progression of the standards… • How would you utilize these chunks (blue) for scaffolding toward mastery of the entire standard? • Where would you start when teaching this standard? • What is the chunk that demonstrates the highest level of thinking?

24. Vertical Alignment Using the progression document(s) from Ohio Department of Education and CCSS Writing Team: • Look to the grade level(s) below to see if the standard is introduced. • Look to the grade level(s) above to see if the standard is continued. Code each standard on the poster with: • builds on • introduced • needed for • or mastered and the grade level to which the standard aligns.

25. 2.G.3 Partition circles and rectangles into two, three, or four equal shares Partition Describe Recognize Recognize that equal shares of identical wholes need not have the same shape 2.G.3 Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Partition circles and rectangles into three equal shares, using the word thirds, third of 2.G.3 Partition circles and rectangles into four equal shares, using the word fourths, fourth of 2.G.3 Describe the whole as two halves, three thirds, four fourths 2.G.3 Introduced? Mastered? Needed for? Builds on? Builds on 1.G.3 Needed for 3.G.2

26. Step 5: Identify Key Vocabulary • Identify content vocabulary directly from the standard. • Identify additional vocabulary students will need to know to meet the standard. green

27. 2.G.3 Partition circles and rectangles into two, three, or four equal shares Describe Recognize Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Partition circles and rectangles into four equal shares, using the word fourths, fourth of 2.G.3 Describe the whole as two halves, three thirds, four fourths 2.G.3 Recognize that equal shares of identical wholes need not have the same shape 2.G.3 Partition Partition circles and rectangles into three equal shares, using the word thirds, third of 2.G.3 Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Fourths Fourth of Identical whole Builds on 1.G.3 Needed for 3.G.2 Thirds Third of whole partition rectangle Halves Half of Equal shares circle

28. Step 6: Add Clarifying Information • Kid-friendly language to add clarity • Clarifying pictures, words, or phrases • Definitions, examples • Symbols, formulas, pictures, etc. CAUTION: do not replace important vocabulary that is included in the standard. yellow

29. 2.G.3 Partition circles and rectangles into two, three, or four equal shares Describe Recognize Partition circles and rectangles into four equal shares, using the word fourths, fourth of 2.G.3 Describe the whole as two halves, three thirds, four fourths 2.G.3 Recognize that equal shares of identical wholes need not have the same shape 2.G.3 Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Partition Partition circles and rectangles into three equal shares, using the word thirds, third of 2.G.3 Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Fourths Fourth of Identical whole Builds on 1.G.3 Needed for 3.G.2 Thirds Third of whole partition rectangle Halves Half of Partition a shape into fourths in different ways Pattern Blocks Fraction Bars/Circles 2/2 = one whole Equal shares circle

30. Transfer Unwrapping to Chart

31. 2.G.3 Partition circles and rectangles into two, three, or four equal shares Main Idea of Standard Key Verbs Describe Recognize Partition circles and rectangles into four equal shares, using the word fourths, fourth of 2.G.3 Describe the whole as two halves, three thirds, four fourths 2.G.3 Recognize that equal shares of identical wholes need not have the same shape 2.G.3 Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Partition • Take standard apart according to the verbs to separate skills within the standard. • Use all components of standard. • Put in a logical sequence Partition circles and rectangles into three equal shares, using the word thirds, third of 2.G.3 Partition circles and rectangles into two equal shares, using the word halves, half of 2.G.3 Vertical alignment Fourths Fourth of Identical whole Vocabulary Builds on 1.G.3 Needed for 3.G.2 Thirds Third of whole partition rectangle Halves Half of Partition a shape into fourths in different ways Pattern Blocks Fraction Bars/Circles Clarifying information, student-friendly 2/2 = one whole Equal shares circle

32. Effective Instructional Tasks • Engage students with challenging tasks that involve active meaning making • Help students connect new learning with prior knowledgeand address preconceptions and misconceptions • Engage students in socially constructing knowledge through talk,activity, and interaction around meaningful problems • Provide students timely feedbackso they can revise their work, thinking, and understandings Common Core Mathematics in a PLC at Work: Grades 6-8, p. 58

33. Lesson/Unit Planning • What tasks can help your students learn this standard? • acos2010.wikispaces.com • Huntsville City 6-8 • Websites • CMP Units

34. Critical Areas of Focus “These (Mathematical) practices are intended to underlie all instruction in mathematics, but if one focuses only on the standard statements very little direct evidence of them can be found. Also, the first page at each grade (K-8) identifies a series of ‘Critical Areas’ that are to be used as the broad ideas on which to plan all instruction around at that grade…A focus on the standards statements will find no reference to these and will miss a large part of the instructional impact intended with the new Standards.” -Kansas Department of Education

35. 6th Grade Focus Areas Ratios and Proportional Relationships Connect to whole number multiplication and division Applying to problems Standards 1-3 Number Systems Dividing fractions Negative numbers Coordinate plane Standards 4-11 Expressions and Equations Variables and expressions Solve one-step equations Standards 12-20 Statistics Understanding different measures of center Standards 25-29 Geometry – Standards 21-24

36. 7th Grade Focus Areas Ratios and Proportional Reasoning Applying to problems Graphing and slope Standards 1-3 Number Systems, Expressions and Equations Standards 4-10 Geometry Scale drawings, constructions, area, surface area, and volume Standards 11-16 Statistics Drawing inferences about populations based on samples Standards 17-20 Probability – Standards 21-24

37. 8th Grade Focus Areas Expressions and Equations Represent, analyze, and solve a variety of problems Linear equations, systems of equations, linear functions, slope, bivariate data Standards 7-10, 25-28 Functions Define, evaluate, compare Use to model relationships Standards 11-15 Geometry Transformations, similar triangles, angles formed by parallel lines, Pythagorean theorem, volume Standards 16-24 Other Irrational numbers, radical, integer exponents Standards 1-6

38. Power Standards • ENDURANCE – something a student will need to know for a longer period of time • LEVERAGE – something that is taught and used in more than one curricular area • READINESS – something that is a prerequisite skill for future learning

39. How do we know if they learned?

42. The PLC Teaching-Assessing-Learning Cycle

43. Step One Collaborative teams identify learning targets and design common unit tasks and assessment instruments.

44. Questioning Whiteboards Step Two Teachers implement formative assessment classroom strategies. Traffic Lights Diagnostic Interviews Clickers

45. Step Three Students take action on in-class formative assessment feedback.

46. Step Four Students use assessment instruments from step one for motivation, reflection, and action.

47. Step Five Collaborative teams use ongoing assessment feedback to improve instruction.

48. Common Formative Assessments Are… Are not… • Created by collaborative teams of teachers • Unit-by-unit • Given in time to adjust instruction • District benchmark tests • Summative • Always graded

49. Common Formative Assessments • Decide what to assess • Decide how to assess • Develop the assessment plan • Determine the timeline • Write the assessment • Review the assessment before administration • Set proficiency criteria and decide how to gather the data

50. 1. Decide what to assess • Which learning targets are most likely to cause certain students difficulty? • Which targets are prerequisite skills for information to come later in this unit? • Which targets are absolutely necessary for students to know? • What level of thinking do we expect from our students for each learning target?