Mathematics Grade Level Content Expectations

1. Mathematics Grade Level Content Expectations Michigan Mathematics Leadership Academy Fall 2004

2. Overview • Background information • Review of GLCEs • Alignment to standards issues • Alignment to instructional materials • Instructional issues • State assessment

3. Background Information • Role of the MCTM • Survey • Report to SBE/MDE • Edited format • What the GLCEs Are and What They are Not • State assessment of what students should know and be able to do

4. Grade Level Format Strands Topics GLCEs Strand Format Strands Domains GLCEs Review the GLCEs

5. Strands in MI Mathematics GLCEs • Number and Operations • Algebra • Measurement • Geometry • Data and Probability Note about “secondary home”: Many expectations in Measurement and Number could be cross-listed in the Geometry and Algebra Strands

6. Mapping from the MCF Standards and Benchmarks to the GLCEs Algebra Geometry Measurement Data & Probability Number & Ops Algebra Data & Probability Patterns, Relationships, & Functions Geometry & Measurement Data Analysis & Statistics Number Sense & Numeration Numerical & Algebraic Operations & Analytical Thinking Probability & Discrete Mathematics

7. PSSM Number & Operations Algebra Geometry Measurement Data Analysis & Probability Michigan GLCEs Number & Operations Algebra Geometry Measurement Data & Probability Mapping to NCTM Principles and Standards

8. Grade LevelStructure • Preface -- main grade level ideas • Expectations listed by strand/topic: • Geometry • Topics: e.g. Grade 6: Understand the concept of congruence and basic transformations • Data and Probability • Topics: e.g. Grade 5: Find and interpret mean and mode • Algebra: • Topics: e.g. Grade 6: Understand the coordinate plane

9. Number and Operations Domains: • Meaning, notation, place value and comparisons (ME) • Number relationships and meaning of operations (MR) • Fluency with operations and estimation (FL)

10. Algebra Domains: • Patterns, relations, functions, and change (PA) • Representation (RP) • Formulas, expressions, equations and inequalities (FO)

11. Measurement Domains: • Units and systems of measurement (UN) • Techniques and formulas for measurement (TE) • Problem solving (PS)

12. Geometry Domains: • Geometric shapes, properties, and mathematical arguments (GS) • Location and spatial relationships (LO) • Spatial reasoning and geometric modeling (SR) • Transformation and symmetry (TR)

13. Data and Probability Domains: • Data representation (RE) • Analyzing data (AN) • Probability (PR)

14. Strand Structure, e.g.Measurement

15. GLCEs by Grade by Strand

17. Example from Number and Operations Strand N.MR.05.01: Understand the meaning of division of whole numbers, with and without remainders; relate division to fractions and repeated subtraction • Grade Level List TOPIC: Understand division of whole number. • Strand Matrix DOMAIN: Number relationships and meaning of operations.

18. Building up to MI GLCEs: MIGLCE: Grade 3, Number and Operation: Solve simple division problems involving remainders, viewing the remainder as the “number left over” (less than the divisor); e.g., 4 children per group, we have 25 children; there are 6 groups with 1 child left over; interpret based on problem context.

19. There are 93 students going to the circus. Five students can ride in each car. How many cars will be needed? Second graders’ solutions: From NCTM Principles and Standards, 2000, p. 87

20. Authors of Michigan’s GLCEs • Bill Schmidt MSU • Joan Ferrini-Mundy MSU • Glenda Lappan MSU • Jim Milgram Stanford U • Hung Hsi Wu U of Cal-Berkley • Paul Sally U of Chicago

21. Achieve States 1999: ILLINOIS, INDIANA, MARYLAND, MASSACHESETTS, MICHIGAN, NEW HAMSHIRE, NORTH CAROLINA, VERMONT, WASHINGTON, WISCONSIN 2000: OHIO 2001: CALIFORNIA, GEORGIA, OKLAHOMA

23. 58 - 26 56 - 28 Computing with Understanding

25. District Curriculum Guide • Content: What students should know and be able to do • Instruction: How to best engage students in learning content • Performance expectation: What we expect students to do – based upon incremental improvement • Assessment: A measure of meeting performance expectations

27. Addition • Combine two amounts • Add an amount to an amount

28. Subtraction • Take an amount from an amount • Compare two amounts

29. Multiplication • Repetitive addition • Product of two factors (area model)

30. Division • Repetitive Subtraction (quota) • Partition (area model)

31. Add to Compare Take Combine from Subtraction Addition Place Value and Operations Division Multiplication Product Quota or as an measure array Repetitive Partition addition

32. Problems 178 + 35 214 – 172 28 x 12 189 ÷ 7

33. 2002 Grade 4 Strands IV & V

34. Alignment to Standards Issues • National Assessment of Educational Progress (NAEP) • Third International Mathematics and Science Study (TIMSS) • Michigan Curriculum Framework Standards and Benchmarks (version 2.0)

35. Alignment to Instructional Materials Issues • Based on the structure of the program, not the order of the state expectations. • Alignment of GLCE to the point where we believe students should be expected to demonstrate the skill.

36. State & National Assessment • MEAP Data • NAEP • NCLB Percent Proficiency • MEAP categories

40. NCLB % Proficient Requirements

41. 2002 MEAP Grade 4

42. State Assessment • Items • Core and Extended Core • Future Core • Pilot items • Sample Items and Item Specifications • Vocabulary • Special Education and MI Access

43. MI-AccessSpecial Education Phase 1 (Moderate & Severe Cognitive Impairment) Phase 2.1 (Mild Cognitive Impairment) Phase 2.2 (Emotionally Impaired) Learning Disabled

44. MI Access • Extended GLCEs • Alternate Tests • Phase 1 • Phase 2.1 • Phase 2.2

45. MI Access • October 2005: Grades 3-8 • Extended GLCEs • Test format & administration differences

46. NEXT STEPS Contacts Resources PD Conferences

48. MDE Contacts MDE-MEAP • Ed Roeber roebere@michigan.gov • Mike Radke radkem@michigan.gov • Kyle Ward wardk2@michigan.gov MDE-Curriculum • Ruth Anne Hodges hodgesra@michigan.gov • Yvonne Caamal Canulcanuly@michigan.gov

49. Reports: Fall 2004 • Alignment to • MCF v2.0 • NAEP and TIMSS • Instructional Materials • State Assessment • Core, Extended Core Recommendations • Vocabulary

50. MI CLiMB – Next Generation • GLCEs • Instructional Sequence • Sample of Instruction • Sample of Assessment • “MEAP like” item