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 1997 CURRICULUM NUMBER SENSE AND NUMERATION SPRING 2005 DRAFT NUMBER SENSE AND NUMERATION Understanding Number Computations Applications Counting Quantity Relationships Operational Relationships Proportional Relationships Grades 1 - 8

5. 1997 CURRICULUM PATTERNING AND ALGEBRA SPRING 2005 DRAFT PATTERNING AND ALGEBRA No sub headings for Grades 1 – 6 Modelling Linear Equations Patterns and Relationships Expressions and Equality (Gr. 1-4) Variables, Expressions and Equations (Gr. 5-8) Improving Coherence Grades 1 - 8

6. 1999 Curriculum No reference to radicals COURSE: GRADE 9 APPLIED and ACADEMIC 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

7. (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. (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 (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 Cross Strand Example: Concept connection within a course (Grade 9 Applied and Academic) 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. 1999 Curriculum -graph lines using a graphing calculator COURSE: GRADE 9 ACADEMIC (MPM1D) 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

9. Improving Focus on Important Mathematics 1997 CURRICULUM Grade 7 SPRING 2005 DRAFT Grade 7 develop the formula for finding the area of a trapezoid; determine, through investigation, the relationship for calculating the area of a trapezoid, generalizing to develop the formula, using a variety of tools (e.g. concrete materials, dynamic geometry software) and strategies. Sample problem: Determine the relationship between the area of a parallelogram and the area of trapezoid by composing a parallelogram from congruent trapezoids.

10. 1999 Curriculum -define the formulas for the sine, the cosine, and the tangent of angles, using the ratios of sides in right triangles COURSE: GRADE 10 Applied and Academic 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

11. Improving Articulation Between The Grades 1997 CURRICULUM Grade 7 SPRING 2005 DRAFT Grade 5 develop the formula for finding the volume of a rectangular prism (area of base) x (height) using concrete materials; understand the relationship between the dimensions and the volume of a rectangular prism; develop, through investigation, the relationship between the height, the area of the base and the volume of a rectangular prism, (i.e. Volume = Area of Base x Height), using stacked congruent rectangular layers of concrete materials. Sample Problem: Create a variety of rectangular prisms using multi-link cubes, record the areas of the base, the heights and the volume measurements on a chart and identify relationships.

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’s task 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 Consider the sections of the introduction that pertain to administrators (e.g. principals, parents, teachers) Administrator’s task 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. MFM1P 1999  Analytic Geometry  Operating with Exponents  Surface Area of 3D figures Consideration of Appropriateness 30 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 GRADE 9 APPLIED

18. WHAT HAS REMAINED THE SAME  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 GRADE 9 APPLIED

19. REVISIONEXPECTED IMPACT OF REVISION Proportional Reasoning substrand added Analytic Geometry is removed and manipulation of some algebraic skills moved to Grade 10 and 11, incorporated as required Ratio and proportion incorporated as a substrand, to strengthen their understanding of this important concept Algebraic concepts are introduced at more appropriate times, and as needed for other course content, thus greater success expected

20. GRADE 9 APPLIED REVISIONEXPECTED IMPACT Numeracy (manipulation) skills are incorporated into substrands as required (e.g., rational numbers and integers are in the substrand “Manipulating Expressions and Solving Equations”) Measurement and Geometry focuses on optimization of 2D shapes, and on the volume of 3D figures The number of expectations has been reduced Numeracy skills are intended to be introduced in context, giving “meaning” to the skill, thus greater success expected. Surface area of 3D figures is in grade 10 applied (developmental continuum) More time is available to investigate concepts and consolidate skills

21. GRADE 9 APPLIED: Transfer course REVISIONEXPECTED IMPACT OF REVISION Some concepts and skills presently in grade 9 applied are now moved into other grades, if /when required. A transfer course (1/2 credit) will be developed for students wishing to move into Grade 10 Academic. “Transfer courses are designed to adequately prepare students to meet the expectations of a different type of course” (OSS, p.17).

22. WHAT HAS REMAINED THE SAME  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 GRADE 10 APPLIED

23. REVISIONEXPECTED IMPACT OF REVISION Linear relations are generalized as analytic geometry Piecewise linear functions is removed Manipulation of some algebraic skills has been moved to Grade 11, incorporated as required Developmental continuum of linear relationships that was developed in grade 9 applied, piecewise only as an application if needed Algebra as required for the course content, thus more success expected

24. GRADE 10 APPLIED REVISIONEXPECTED IMPACT OF REVISION Quadratic Relations strand focuses on graphical interpretation, and is assisted with technology, less algebra is required than presently Measurement focuses on surface area of 3D figures, trigonometry, and an introduction of the imperial system of measurement More success due to the manipulatives and technology support suggested in the expectations Developmental continuum (measurement, including the introduction of imperial measurement, proportional reasoning)

25. GRADE 10 APPLIED REVISIONEXPECTED IMPACT OF REVISION Some concepts and skills presently in grade 10 applied are now moved into other grades, if and when required. Less focus on algebraic skills with respect to quadratic relationships, thus more success expected

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