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

• Improve coherence and articulation across the grades

• The expectations need to focus on conceptual and procedural mathematics.

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

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

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

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

(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)

1999 Curriculum

-graph lines using a graphing calculator

COURSE: GRADE 9 ACADEMIC (MPM1D)

Proposed RevisionWithin 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

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.

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

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.

Curriculum Part A

How much has been revised? Expert Group Activity

Eight Groups Grade 7Grade 89 Applied9 Academic10 Applied10 Academic9 applied/9 academic comparisonAdministrator

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.

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.

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.

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’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.

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

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

GRADE 9 APPLIED

REVISION EXPECTED 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

GRADE 9 APPLIED

REVISION EXPECTED IMPACTNumeracy (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

GRADE 9 APPLIED: Transfer course

REVISION EXPECTED 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).

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

GRADE 10 APPLIED

REVISION EXPECTED 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

GRADE 10 APPLIED

REVISION EXPECTED 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)

GRADE 10 APPLIED

REVISION EXPECTED 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

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