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# Sustaining Quality Curriculum

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1. Sustaining Quality Curriculum Grades 7 - 10

2. Curriculum The revised curriculum is coherent, focused on important mathematics, and well articulated across the grades.

3. Curriculum A coherent and well-articulated curriculum • effectively organizes and integrates important mathematical ideas; • challenges students to increasingly more sophisticated ideas; • focuses on concepts and skills that are critical to understanding important processes and relationships; • establishes explicit connections among concepts and skills; • has fewer but richer topics that support greater depth and understanding. ED Thoughts 2002

4. Improving Coherence Grades 1 - 8

5. Improving Coherence Grades 1 - 8

6. Improving Coherence Grades 1 - 8

7. Improving Coherence Grades 1 - 8

8. 2005 Draft Revision Improving Coherence Number of Expectations Grades 9 - 10

9. Revision -relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations (e.g., in solving equations, in measurement) Improving Coherence COURSE: GRADE 9 APPLIED and ACADEMIC

10. Revision -determine, through investigation using a variety of tools, (e.g., DGS, concrete materials), and describe the properties and, relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons (Sample Problem…. Improving Coherence across strands COURSE: GRADE 9 APPLIED and ACADEMIC

11. Cross Strand Example: Concept connection within a course (Grade 9 Applied and Academic) (1) Cut & fold several triangles to show a sum of 180 (2) Cut & “rearrange” several quads to show sum of 360 (3) “DRAW” diagonals of polygons to show # of triangle (4) charting of data “number of sides” versus “number of degrees” (5) Students then make a scatterplot and line of best fit - scatterplot with technology (6) build an algebraic model from the numerical data: D = 180(n – 2) OR from the graph rate of change is 180 initial value is 360  D = 180n – 360 (7) Apply: find the sum of the interior angles of a 20 sided polygon. OR -draw a triangle, quadrilateral, pentagon etc. using DGS -use the technology to find the sum of the interior angles of these shapes (use inductive reasoning)

12. Proposed Revision Within other expectations -identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b” In the process selecting tools -select and use a variety of concrete, visual, and electronic learning tools…to investigate mathematical ideas and to solve problems Improving Focus by combining expectations COURSE: GRADE 9 ACADEMIC (MPM1D)

13. Improving Focus on Important Mathematics Revision Removed (development of this concept can be incorporated into linear relationships if it is needed in solving a problem within that strand) COURSE: GRADE 10 APPLIED (MFM2P)

14. Improving Focus on Important Mathematics

15. Improving Focus on Important Mathematics

16. Revision -determine through investigation (e.g., using DGS, concrete materials), the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios (e.g., sinA=opposite/hypontenuse) Improving Focus on Important Mathematics COURSE: GRADE 10 Applied and Academic

17. Improving Focus on Important Mathematics Revision Grade 10 Applied -determine, through investigation, the relationship for finding the surface area of a pyramid (e.g., use the net of a square based pyramid to determine that the surface area is the area of the square base, plus the areas of the four congruent triangles) COURSE: GRADE 9 Applied to GRADE 10 Applied

18. Improving Focus on Important Mathematics Revision Grade 9 Applied: Linear relationships (understanding of, and applications of “real life” examples) Grade 10 Applied: Linear relationships are generalized as analytic geometry, spreading this concept over 2 years COURSE: GRADE 9 Applied to 10 Applied

19. Improving Focus On Important Mathematics

20. Improving Articulation Between The Grades

22. Curriculum Part A How much has been revised? Expert Grade Group Activity • Regroup by grade • Each grade group needs • revised curriculum • current curriculum • chart paper • marker • Your group’s task • Each group will provide a • “sense” of how much change has occurred for each grade; • general report on chart paper • verbal report.

23. Curriculum Part A How much has been revised? Expert Grade Group Activity • Be Sure To: • Focus on the Mathematics • Divide your strands amongst the members of your group. • Represent the amount of change using a scale from 1 – 10. • Identify the grade on the chart paper. • Share only the most significant changes for each strand.

24. Curriculum Part A How much difference is there? Applied 9 vs Academic 9 Comparison Comparison Group Consider the 9 applied vs 9 academic revised courses. Comparison Group’stask Provide a sense of how these two courses compare. Consider the expectations themselves as well as the verbs used in similar expectations. Consider the level of abstraction involved in the expectations.

25. Curriculum Part A How much has been revised? Administrator’s Group Administrator’s Group Consider the sections of the introduction that pertain to administrators (e.g. principals, parents, teachers) Administrator’stask Compare the sections of the introduction and discuss any significant revisions, and how these will impact administrators. Also, strategize how teachers can best be supported throughout the implementation of the revisions.

26. Administrator’s Group Compare the sections of the introduction and discuss any significant revisions, and how these will impact administrators. Students Parents Teachers Principals Strategize how teachers can best Be supported throughout the implementation of the revisions.

27. Curriculum Part A How much has been revised? Expert Grade Group Activity • Be Sure To: • Focus on the Mathematics • Divide the strands amongst the members of your group. • Represent the amount of change using a scale from 1 – 10. • Identify the grade on the chart paper. • Share only the most significant changes for each strand.

28. Curriculum Part A Experts Report to Whole Group Expert Group Activity Your group’s visual report Each group will place their visual report on chart paper and place it on the wall for a lunch time “walk about”. Return to your home group Experts share with your group members a sense of the amount of change in the course/grade. (2 minutes each)

29. Revision • Analytic Geometry revised and moved to Grade 10 Applied • Operating with Exponents will be included in Grade 11,where it is applied • Surface Area included in Grade 10 Applied • Proportional reasoning substrand added Consideration of Appropriateness GRADE 9 APPLIED 30

30. WHAT HAS REMAINED THE SAME GRADE 9 APPLIED • The “big idea” of the course is relationships • Application and problem solving of “real life” situations • Investigation of concepts • Using a variety of tools (e.g., technology, concrete materials) to investigate and consolidate concepts

33. GRADE 9 APPLIED: Transfer course

34. WHAT HAS REMAINED THE SAME GRADE 10 APPLIED • Continuum of concept development in algebra, geometry, measurement (trigonometry) and mathematical relationships (introduction to quadratic relationships) • Application and problem solving of “real life” situations • Investigation of concepts • Using a variety of tools (e.g., technology, concrete materials) to investigate and consolidate concepts

38. We Learn… • 10% of what we read • 20% of what we hear • 30% of what we see • 50% of what we both hear and see • 70% of what is discussed with others • 80% of what we experience personally • 95% of what we teach to someone else William Glasser

39. Curriculum Part B Implementation Strategies Please remain in your expert group

40. Curriculum Part B A Closer Look – zooming in

41. Curriculum Part B Implementation considerations Interim adaptationsneed to occur when there are gaps in student learning for students coming from one grade, 1999/1997 curriculum, into the next grade, revised 2005 curriculum Curriculum changes occur when a new expectation has been added to the grade or when an expectation has been removed from the grade, or when a expectation has been significantly modified as a result of the revision.

42. Curriculum Part B Implementation considerations Interim adaptation, example 1 Grade 8 • graph images of points on the Cartesian coordinate plane after applying a transformation (translation; reflection in the x-axis or y-axis; rotation about the origin of 90°, 180°, or 270°) to the original points ;

43. Curriculum Part B Implementation considerations • Interim adaptation, example 2 • Grade 10 Applied • use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity

44. Curriculum Number Sense Grade 9 Applied Revised Curriculum 2005 Curriculum Changes: What expectations are new in this grade, and what expectations have been moved or removed Interim Adaptations: need to occur when there are gaps in student learning due to students coming from grade 8, 1997 curriculum into grade 9 revised curriculum 2005, Grade 9 Applied Curriculum 1999 Grade 8 Curriculum 1997

45. Expectations What’s New • What’s changed • Determine strategies for mental math and estimation (process expectation) • use a scientific calculator effectively for applications that arise throughout the course (process expectation) • judge the reasonableness of answers to problems (process expectation) • judge the reasonableness of answers produced by a calculator (process expectation) • evaluate numerical expressions involving natural-number exponents with rational number bases (implied) • Determine the meaning of negative exponents and of zero as an exponent... • Scientific notation…(2 expectations) • Exponent rules for multiplying, dividing and powers… • Illustrate equivalent ratios using a variety of tools (e.g., concrete materials, dynamic geometry software)(e.g., show that 4:6 represents the same ratio as 2:3 by showing that a ramp… • Represent directly proportional relationships with equivalent ratios, and proportions, arising from realistic situations • solve for the unknown value in a proportion… • make comparisons using unit rates Grade 9 Applied Number Sense and Algebra

46. Revised Curriculum 2005 Course: 9 applied Curriculum ActivityStrand: Number Sense and Algebra • New Expectations Illustrate equivalent ratios using a variety of tools (e.g., concrete materials, dynamic geometry software)(e.g., show that 4:6 represents the same ratio as 2:3 by showing that a ramp… • Represent directly proportional relationships with equivalent ratios, and proportions, arising from realistic situations • solve for the unknown value in a proportion… • make comparisons using unit rates • Removed Expectations *Determine strategies for mental math and estimation *use a scientific calculator effectively for applications that arise throughout the course *judge the reasonableness of answers to problems *judge the reasonableness of answers produced by a calculator (*process expectations) • evaluate numerical expressions involving natural-number exponents with rational number bases (implied) • Determine the meaning of negative exponents and of zero as an exponent... • Scientific notation…(2 expectations) • Exponent rules for multiplying, dividing and powers… Interim Adaptations Grade 8 Cur 1997 Grade 9 Cur 1999

47. Curriculum Patterning and Algebra Grade 8 Revised Curriculum 2005 Curriculum Changes: What expectations are new in this grade, and what expectations have been moved or removed Interim Adaptations: need to occur when there are gaps in student learning due to students coming from grade 8, 1997 curriculum into grade 9 revised curriculum 2005. Grade 8 Curriculum 1999 Grade 7 Curriculum 1997

48. Expectations What’s New What’s Changed -represent simple linear number patterns graphically -develop through investigation with concrete materials an algebraic expression for the general term of a linear number pattern -describe different ways algebra is used in real life situations -represent, through investigation, linear relationships using concrete materials, words, tables or values, graphs or equations. • investigate inequalities and test whether they are true or false by substituting whole number values for the variables (e.g., in 4x >= 18, find the whole number values for x) • present solutions to patterning problems and explain the thinking behind the solution process Grade 8 Patterning and Algebra

49. Revised Curriculum 2005 Grade: 8 Curriculum ActivityStrand: Patterning and Algebra Interim Adaptations New Expectations - represent simple linear number patterns graphically -develop through investigation with concrete materials an algebraic expression for the general term of a linear number pattern -describe different ways algebra is used in real life situations -represent, through investigation, linear relationships using concrete materials, words, tables or values, graphs or equations. Removed Expectations -investigate inequalities and test whether they are true or false by substituting whole number values for the variables (e.g., in 4x >= 18, find the whole number values for x) -present solutions to patterning problems and explain the thinking behind the solution process Grade 7 Curriculum 1999 Grade 8 Curriculum 1999

50. Grade 8 Patterning and Algebra Grade 9 Applied Number Sense and Algebra Interim Adaptations Divide the people at your table into two groups. One group should work on Grade 8 Patterning and Algebra and the other group should work on Grade 9 Applied Number Sense and Algebra to answer the question below: What adjustments (interim adaptations) are needed next year to ensure that students who met the 1997 curriculum expectations this year are supported as they work towards meeting the expectations from the revised 2005 curriculum next year?