Two key suggestions that came from the various focus groups across Ontario were:

1. Two key suggestions that came from the various focus groups across Ontario were:

2. Improve coherence and articulation across the grades • The expectations need to focus on conceptual and procedural mathematics.

3. 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. 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

7. 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)

8. 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)

9. Improving Focus on Important Mathematics

10. 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

11. Improving Articulation Between The Grades

12. Curriculum Part A How much has been revised? Expert Group Activity Eight Groups Grade 7 Grade 8 9 Applied 9 Academic 10 Applied 10 Academic 9 applied/9 academic comparison Administrator

13. 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.

14. 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.

15. 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.

16. 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.

17. 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

18. 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

19. GRADE 9 APPLIED

20. GRADE 9 APPLIED

21. GRADE 9 APPLIED: Transfer course

22. 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

23. GRADE 10 APPLIED

24. GRADE 10 APPLIED

25. GRADE 10 APPLIED

26. As a whole group, discuss how these changes will effect your planning and your students next year. What are the key issues???????