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Curriculum

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Title: Curriculum


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
Improving Coherence
Number of Expectations Grades 9 - 10
9
Improving Coherence
COURSE GRADE 9 APPLIED and ACADEMIC
10
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
Improving Focus by combining expectations
COURSE GRADE 9 ACADEMIC (MPM1D)
13
Improving Focus on Important Mathematics
COURSE GRADE 10 APPLIED (MFM2P)
14
Improving Focus on Important Mathematics
15
Improving Focus on Important Mathematics
16
Improving Focus on Important Mathematics
COURSE GRADE 10 Applied and Academic
17
Improving Focus on Important Mathematics
COURSE GRADE 9 Applied to GRADE 10 Applied
18
Improving Focus on Important Mathematics
COURSE GRADE 9 Applied to 10 Applied
19
Improving Focus On Important Mathematics
20
Improving Articulation Between The Grades
21
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
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 groups 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 Groups 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.

25
Curriculum Part A

How much has been revised? Administrators Group
Administrators Group Consider the sections of
the introduction that pertain to administrators
(e.g. principals, parents, teachers)
Administrators 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.

26
Administrators 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 groups 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
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

31
GRADE 9 APPLIED

32
GRADE 9 APPLIED

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

35
GRADE 10 APPLIED

36
GRADE 10 APPLIED

37
GRADE 10 APPLIED

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 adaptations need 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
Whats New
  • Whats 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 46 represents the same
    ratio as 23 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
Curriculum Activity Strand Number Sense
and Algebra
Revised Curriculum 2005 Course 9 applied
  • New Expectations Illustrate equivalent ratios
    using a variety of tools (e.g., concrete
    materials, dynamic geometry software)(e.g., show
    that 46 represents the same ratio as 23 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
Whats New
Whats 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 gt 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
Curriculum Activity Strand Patterning and
Algebra
Revised Curriculum 2005 Grade 8
  • 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 gt 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
Interim Adaptations
Grade 8 Patterning and Algebra
Grade 9 Applied Number Sense and Algebra
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?

51
Interim Adaptations
Grade 8 Patterning and Algebra Grade 9 Applied
Number Sense and Algebra
52
Curriculum Activity Strand______________
Revised Curriculum 2005 Course ____
  • Interim Adaptations

New Expectations Removed
Expectations
Grade ____ Curriculum 199_
Grade ___ Curriculum 199_
53
Curriculum Activity Strand______________
Revised Curriculum 2005 Grade ____
  • Interim Adaptations need to occur when there are
    gaps in student learning due to students coming
    from the 1999 curriculum into
  • the revised curriculum 2005

New Expectations Removed
Expectations
Grade ____ Curriculum 1999
Grade ___ Curriculum 1999
54
Curriculum Activity Strand______________
Your chance to work!
Revised Curriculum 2005 Course ____
55
Curriculum Activity Strand______________
Revised Curriculum 2005 Course ____
  • Interim Adaptations

New Expectations Removed
Expectations
Grade ____ Curriculum 199_
Grade ___ Curriculum 199_
56
Return to your Home Group
  • Report important changes/adaptations

57
Curriculum Connection
Consider the learning task. Can this task be used
to support curriculum expectations from each of
grades 7, 8, 9, and 10? Find the expectations,
and discuss what aspects of the task are most
appropriate for what grades. How else could this
task be used to support students in the course?
58
LOOKING FORWARD

PATHWAYS
59
PATHWAYS
60

PATHWAYS
We are continuing to work with the recommended
pathway, pathway A, that is scheduled to be
finalized by the end of this school year. We will
be consulting with the universities this month to
gather further information on adjustments to the
U mathematics courses arising from the direction
in Pathway A.
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