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“Yeah, But How Do I Translate That to a Percentage?”
& Other Standards-Based Assessment FAQs
STA Convention ● May 6, 2022
Aaron Blake Denise
LO Em D P Ex LO Em D P Ex LO Em D P Ex
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
10 10 10
Chris Hunter

K-12 Numeracy Helping Teacher


Surrey Schools


email: hunter_c@surreyschools.ca


Twitter: @ChrisHunter36


blog: chrishunter.ca
chrishunter.ca/tag/standards-based/
Traditional


Students accumulate points
tied to events
e.g., “Quiz 2.3”
Compares students to each
other
Standards-Based
Students demonstrate
evidence in relation to
learning standards
e.g., “use ratios and rates to make
comparisons between quantities”
Compares student learning
against pro
fi
ciency levels
What letter grade or
percentage would you assign to
Aaron, Blake, and Denise?
FAQs
• Why change?
• Why reinvent the wheel?
• Assess what?
• How many learning standards?
• What do Emerging and Extending
mean?
• What does each pro
fi
ciency
level look like?
• How do I elicit evidence of
learning?
• How do I keep track of data?
• Yeah, but how do I translate
that to a percentage?
Menu Math
A. Two negative x-intercepts B. Vertex in quadrant II
C. Never enters quadrant III D. Vertex on the y-axis
E. Positive y-intercept F. No x-intercepts
G. Never enters quadrant I H. Has a minimum value
I. Horizontally stretched J.
Line of symmetry enters
quadrant IV
• Think about the following “design
speci
fi
cations” of quadratic functions

• You could build ten di
ff
erent quadratic
functions to satisfy these ten di
ff
erent
constraints

• Instead, build a set of as few quadratic
functions as possible to satisfy each
constraint at least once

• Write your functions in the form

y = a(x − p)2 + q
• Describe how and why you built each
function

• Be sure to identify which functions satisfy
which constraints
−Nat Banting
Which constraints
pair nicely?
Which constraints
cannot be paired?
Menu Math
A. Two negative x-intercepts B. Vertex in quadrant II
C. Never enters quadrant III D. Vertex on the y-axis
E. Positive y-intercept F. No x-intercepts
G. Never enters quadrant I H. Has a minimum value
I. Horizontally stretched J.
Line of symmetry enters
quadrant IV
−Nat Banting
Why change?
Tom Schimmer
“In this traditional system, experience has
trained students to play the game of
school. Schools dangle the carrot (the
academic grade) in front of their faces and
encourage students to chase it. With
these practices, schools have created a
culture of compliance.
Tom Schimmer
Becoming standards based is about
changing to a culture of learning.
‘Complete this assignment to get these
points’ changes to ‘Complete this
assignment to improve your learning.’ […]
Educators have trained learners to focus
on the academic grade; they can coach
them out of this assumption.”
Peter Liljedahl
“If you want to start valuing day-to-day
learning evidence or how students work
in groups, you’ll have to make a
paradigm shift.”
Point-Gathering Data-Gathering
more accurate
more fair
more relevant
no less objective
Peter Liljedahl
“Students start thinking about their learning
rather than their grades and, as they do so,
grading becomes a byproduct of learning
rather than the objective of learning.”
Why ?
Point-Gathering Data-Gathering
more accurate
more fair
more relevant
no less objective
Assess what?
Menu Math
A. Two negative x-intercepts B. Vertex in quadrant II
C. Never enters quadrant III D. Vertex on the y-axis
E. Positive y-intercept F. No x-intercepts
G. Never enters quadrant I H. Has a minimum value
I. Horizontally stretched J.
Line of symmetry enters
quadrant IV
• Think about the following “design
speci
fi
cations” of quadratic functions

• You could build ten di
ff
erent quadratic
functions to satisfy these ten di
ff
erent
constraints

• Instead, build a set of as few quadratic
functions as possible to satisfy each
constraint at least once

• Write your functions in the form

y = a(x − p)2 + q
• Describe how and why you built each
function

• Be sure to identify which functions satisfy
which constraints
−Nat Banting
Which learning standards
did you “bump into” as you
solved the problem?
Pre-calculus 11
Learning Standards
Curricular Competencies Content
• analyze and apply mathematical
ideas using reason
• quadratic functions
• explain and justify mathematical
ideas and decisions
How many learning
standards?
What feels correct?
What doesn’t?
Operations with Fractions
add and subtract fractions
multiply and divide fractions
evaluate expressions with two
or more operations on fractions
solve contextual problems
involving fractions
Foundations of Mathematics and Pre-calculus 10
Learning Standard Delineated Learning Standards
systems of linear equations
Deconstruct this standard
into 2-4 subtopics, or
outcomes.
Foundations of Mathematics and Pre-calculus 10
Learning Standard Delineated Learning Standards
systems of linear equations
solve systems of linear equations
graphically
solve systems of linear equations
algebraically
model and solve contextual problems
involving systems of linear equations
What do Emerging
& Extending mean?
Source: Surrey Schools?
and social competence).
The Four-Point Provincial Proficiency Scale will be used to communicate student progress in
all areas of learning.
Proficiency
Scale
Emerging Developing Proficient Extending
The student
demonstrates an
initial understanding
of the concepts and
competencies
relevant to the
expected learning.
The student
demonstrates
a partial
understanding of
the concepts and
competencies
relevant to the
expected learning.
The student
demonstrates
a complete
understanding of
the concepts and
competencies
relevant to the
expected learning.
The student
demonstrates
a sophisticated
understanding of
the concepts and
competencies
relevant to the
expected learning.
At Grades 4-9, Boards will provide letter grades to parents upon request. A proficiency scale/letter
grade alignment table will be provided by the ministry.
Descriptive Feedback includes the strength-based written comments and/or documented
Source: BC Ministry of Education (as of the 2018/19 school year)
DRAFT K-9 Student Reporting Policy (2019) for Use in 2019/20 Pilot 2
and social competence).
The Four-Point Provincial Proficiency Scale will be used to communicate student progress in
all areas of learning.
Proficiency
Scale
Emerging Developing Proficient Extending
The student
demonstrates an
initial understanding
of the concepts and
competencies
relevant to the
expected learning.
The student
demonstrates
a partial
understanding of
the concepts and
competencies
relevant to the
expected learning.
The student
demonstrates
a complete
understanding of
the concepts and
competencies
relevant to the
expected learning.
The student
demonstrates
a sophisticated
understanding of
the concepts and
competencies
relevant to the
expected learning.
At Grades 4-9, Boards will provide letter grades to parents upon request. A proficiency scale/letter
grade alignment table will be provided by the ministry.
Descriptive Feedback includes the strength-based written comments and/or documented
conversations that describe individual student progress and identify specific goals to support
further student growth.
basic some good beyond initial partial complete sophisticated
with support independence depth
teach
What are some
implications?
What does
each pro
fi
ciency
level look like?
learning
standard
Extending


Pro
fi
cient


Developing


Emerging


Descriptive · Positive · Progressive & Additive
solve
systems of
linear
equations
graphically
Emerging


identify the
solution from a
graph or table

What is the solution
to the system
represented by the
graph?


Developing


determine the
solution given
equations in
slope-intercept
form

Solve graphically:




y = 2x − 5
y = −
1
4
x + 4
Pro
fi
cient


determine the
solution given
equations in
general form

Solve graphically:





determine the
number of
solutions

Analyze the system
to determine
whether it has one
solution, no
fi
2x + 5y + 25 = 0
4x − 2y + 14 = 0
Extending


create a system
given
constraints

Create a system so
that:


• the solution is
(-3, -1)


• one line has a
negative slope


• one line enters
the
fi
rst quadrant


Place the numbers
from 1 to 9 in the
boxes below so
that the system has
in
fi
nitely many
solutions:
solve
systems of
linear
equations
graphically
What is the solution
to the system
represented by the
graph?


form

Solve graphically:




y = 2x − 5
y = −
1
4
x + 4
Solve graphically:





determine the
number of
solutions

Analyze the system
to determine
whether it has one
solution, no
solution, or in
fi
nitely
many solutions:






2x + 5y + 25 = 0
4x − 2y + 14 = 0
y =
1
2
x − 4
3x − 6y − 12 = 0
Create a system so
that:


• the solution is
(-3, -1)


• one line has a
negative slope


• one line enters
the
fi
rst quadrant


Place the numbers
from 1 to 9 in the
boxes below so
that the system has
in
fi
nitely many
solutions:


x + y =


x + y =


(Each number can
be used only once.)
solve


systems of
linear
equations
algebraically
Emerging


verify the
solution by
substitution

Is (2, 5) a solution
to the system:




?


solve by
elimination
where
multiplication is
not necessary

Solve:




y = 3x − 1
x − 2y = 8
Pro
fi
cient


solve by
substitution
where neither
variable is
isolated in an
equation

Solve:






solve by
elimination
where
multiplication of
both equations
2x + 5y + 7 = 0
3x − y = − 2
Developing


solve by
substitution
where one
variable is
isolated in an
equation

Solve:






solve by
elimination
where
multiplication of
one equation is
x = 6 − 4y
2x − 3y = 1
Extending


select, apply,
and defend an
algebraic
approach 

Would you rather
solve the following
system by
elimination or
substitution?






Why?
4x − y − 3 = 0
6x − 2y − 5 = 0
solve


systems of
linear
equations
algebraically
Is (2, 5) a solution
to the system:




?


solve by
elimination
where
multiplication is
not necessary

Solve:





y = 3x − 1
x − 2y = 8
3x − 4y = 23
7x + 4y = 27
variable is
isolated in an
equation

Solve:






solve by
elimination
where
multiplication of
one equation is
necessary

Solve:




x = 6 − 4y
2x − 3y = 1
7x + 2y = − 1
3x − 4y = 19
variable is
isolated in an
equation

Solve:






solve by
elimination
where
multiplication of
both equations
is necessary

Solve:




2x + 5y + 7 = 0
3x − y = − 2
5x + 4y = 13
8x + 3y + 3 = 0
approach 

Would you rather
solve the following
system by
elimination or
substitution?






Why?
4x − y − 3 = 0
6x − 2y − 5 = 0
model and
solve
contextual
problems
involving
systems of
Emerging


interpret the
solution in
context given
a model

The heights of two
candles over time
can be modelled
by:






What is the
meaning, in
context, of the
solution (8, 4)?
h = 20 − 2t
h = 16 − 1.5t
Developing


model and
solve
combination
problems

Two t-shirts and
four hoodies sell for
$254. Four t-shirts
and
fi
ve hoodies
sell for $361. What
is the price of each
item?
Pro
fi
cient


model and
solve parts-
whole and
catch-up
problems

Tickets to a charity
hockey game cost
$12 for adults and
$8 for children. A
total of 150 tickets
were sold for
$1640. How many
of each type of
ticket were sold?


A gas vehicle has
an initial cost of
Extending


model and
solve mixture
problems

A scientist needs to
make 200 ml of a
42% alcohol
solution. They mix
30% alcohol and
50% alcohol
solutions. How
much of each
solution do they
need?
solve
contextual
problems
involving
systems of
linear
equations






What is the
meaning, in
context, of the
solution (8, 4)?
h = 20 − 2t
h = 16 − 1.5t
fi
sell for $361. What
is the price of each
item?
$12 for adults and
$8 for children. A
total of 150 tickets
were sold for
$1640. How many
of each type of
ticket were sold?


A gas vehicle has
an initial cost of
$31 000 and an
operating cost of
$1500 per year. An
electric vehicle has
an initial cost of
$43 000 and an
operating cost of
$500 per year. How
many years will it
take for the total
cost of both
vehicles to be
same?
50% alcohol
solutions. How
much of each
solution do they
need?
How do I elicit
evidence of
learning?
EVIDENCE


OF STUDENT


LEARNING
Products
Observations
Conversations
learning
standard
Emerging Developing Pro
fi
cient Extending
learning
standard
Emerging Developing Pro
fi
cient Extending
10p + 6q + 38 = 0
−10p + 25q + 55 = 0
31q + 93 = 0
q = − 3
31q = − 93
5p + 3q + 19 = 0
2p − 5q − 11 = 0
①
②
chrishunter.ca/2020/11/23/principles-of-math-videos/
vs.
How do I keep
track of data?
Name
Learning Outcome
1 2 3 4 5 6 7 8 9 10
Aaron Ex P Ex P P P P Ex P P
Blake D Em Ex P P Em D Ex P D
Denise D Em P D P D Em D D Em
…
Name
Learning Outcome
1 2 3 4 5 6 7 8 9 10
Aaron Ex P Ex P P P P Ex P P
Blake D Em Ex P P Em D Ex P D
Denise D Em P D P D Em D D Em
…
D P P Ex Ex → Ex
Peter Liljedahl
“The fact that she didn’t know how to do
something in the beginning is expected–she
is learning, not learned, and she shouldn’t
be punished for her early-not-knowing.”
How do I
translate that to a
percentage?
80
descriptor
79 80 81
descriptor
descriptor descriptor
B
73 74 75 76 77 78 79 80 81 82 83 84 85
descriptor
descriptor descriptor
descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor
9
Letter Grades and Percentages
Letter grades are used in Grades 10-12 to indicate a student’s level of performance in relation
to the Learning Standards. The process for Letter grade symbols and corresponding
percentages and definitions are set out in the Provincial Letter Grades Order.
Letter
Grade
Percentage
Range
Definition
A 86 - 100
The student demonstrates excellent or outstanding performance in relation to the
learning outcomes for the course or subject and grade.
B 73 – 85
The student demonstrates very good performance in relation to the learning outcomes
for the course or subject and grade
C+ 67 – 72
The student demonstrates good performance in relation to the learning outcomes for the
course or subject and grade.
C 60 – 66
The student demonstrates satisfactory performance in relation to the expected learning
outcomes for the course or subject and grade.
C- 50 – 59
The student demonstrates minimally acceptable performance in relation to the learning
outcomes for the course or subject and grade.
At the end of the school year or at the completion of a course, teachers assign a letter grade to
indicate each student’s overall progress in the area of learning or course. Due to the cumulative
nature of learning, the final term work may be more heavily weighted as it indicates more
F 0 – 49
The student has not demonstrated, or is not demonstrating, minimally acceptable
performance in relation to the learning outcomes for the course or subject and grade.
Letter

Grade
Percentage
Range
De
fi
nition
Hi-B 82 – 85
The student demonstrates pretty, pretty, pretty,
pretty good performance in relation to the learning
outcomes for the course or subject and grade.
Mid-B 77 – 81
The student demonstrates pretty, pretty, pretty good
performance in relation to the learning outcomes for
the course or subject and grade.
Lo-B 73 – 76
The student demonstrates pretty, pretty good
performance in relation to the learning outcomes for
the course or subject and grade.
C- C C+ B A
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99100
F
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
descriptor
Aaron Blake Denise
LO Em D P Ex LO Em D P Ex LO Em D P Ex
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
10 10 10
(7 × 3) + (3 × 4)
10 × 4
=
33
40
= 83 %
(2 × 1) + (3 × 2) + (3 × 3) + (2 × 4)
10 × 4
=
25
40
= 63 %
(3 × 1) + (5 × 2) + (2 × 3)
10 × 4
=
19
40
= 48 %
1-2-3-4
Aaron Blake Denise
LO Em D P Ex LO Em D P Ex LO Em D P Ex
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
10 10 10
(7 × 4) + (3 × 5)
10 × 5
=
43
50
= 86 %
(2 × 2) + (3 × 3) + (3 × 4) + (2 × 5)
10 × 5
=
35
50
= 70 %
(3 × 2) + (5 × 3) + (2 × 4)
10 × 5
=
29
50
= 58 %
2-3-4-5
What letter grade or
percentage would you assign to
Aaron, Blake, and Denise?
"Yeah But How Do I Translate That to a Percentage?" -- STA Convention 2022.pdf

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"Yeah But How Do I Translate That to a Percentage?" -- STA Convention 2022.pdf

  • 1. “Yeah, But How Do I Translate That to a Percentage?” & Other Standards-Based Assessment FAQs STA Convention ● May 6, 2022 Aaron Blake Denise LO Em D P Ex LO Em D P Ex LO Em D P Ex 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10
  • 2.
  • 3. Chris Hunter
 K-12 Numeracy Helping Teacher Surrey Schools email: hunter_c@surreyschools.ca 
 Twitter: @ChrisHunter36 blog: chrishunter.ca chrishunter.ca/tag/standards-based/
  • 4. Traditional Students accumulate points tied to events e.g., “Quiz 2.3” Compares students to each other Standards-Based Students demonstrate evidence in relation to learning standards e.g., “use ratios and rates to make comparisons between quantities” Compares student learning against pro fi ciency levels
  • 5. What letter grade or percentage would you assign to Aaron, Blake, and Denise?
  • 6. FAQs • Why change? • Why reinvent the wheel? • Assess what? • How many learning standards? • What do Emerging and Extending mean? • What does each pro fi ciency level look like? • How do I elicit evidence of learning? • How do I keep track of data? • Yeah, but how do I translate that to a percentage?
  • 7. Menu Math A. Two negative x-intercepts B. Vertex in quadrant II C. Never enters quadrant III D. Vertex on the y-axis E. Positive y-intercept F. No x-intercepts G. Never enters quadrant I H. Has a minimum value I. Horizontally stretched J. Line of symmetry enters quadrant IV • Think about the following “design speci fi cations” of quadratic functions • You could build ten di ff erent quadratic functions to satisfy these ten di ff erent constraints • Instead, build a set of as few quadratic functions as possible to satisfy each constraint at least once • Write your functions in the form
 y = a(x − p)2 + q • Describe how and why you built each function • Be sure to identify which functions satisfy which constraints −Nat Banting Which constraints pair nicely? Which constraints cannot be paired?
  • 8. Menu Math A. Two negative x-intercepts B. Vertex in quadrant II C. Never enters quadrant III D. Vertex on the y-axis E. Positive y-intercept F. No x-intercepts G. Never enters quadrant I H. Has a minimum value I. Horizontally stretched J. Line of symmetry enters quadrant IV −Nat Banting
  • 10.
  • 11. Tom Schimmer “In this traditional system, experience has trained students to play the game of school. Schools dangle the carrot (the academic grade) in front of their faces and encourage students to chase it. With these practices, schools have created a culture of compliance.
  • 12. Tom Schimmer Becoming standards based is about changing to a culture of learning. ‘Complete this assignment to get these points’ changes to ‘Complete this assignment to improve your learning.’ […] Educators have trained learners to focus on the academic grade; they can coach them out of this assumption.”
  • 13.
  • 14. Peter Liljedahl “If you want to start valuing day-to-day learning evidence or how students work in groups, you’ll have to make a paradigm shift.”
  • 15. Point-Gathering Data-Gathering more accurate more fair more relevant no less objective
  • 16. Peter Liljedahl “Students start thinking about their learning rather than their grades and, as they do so, grading becomes a byproduct of learning rather than the objective of learning.”
  • 17. Why ?
  • 18.
  • 19. Point-Gathering Data-Gathering more accurate more fair more relevant no less objective
  • 21. Menu Math A. Two negative x-intercepts B. Vertex in quadrant II C. Never enters quadrant III D. Vertex on the y-axis E. Positive y-intercept F. No x-intercepts G. Never enters quadrant I H. Has a minimum value I. Horizontally stretched J. Line of symmetry enters quadrant IV • Think about the following “design speci fi cations” of quadratic functions • You could build ten di ff erent quadratic functions to satisfy these ten di ff erent constraints • Instead, build a set of as few quadratic functions as possible to satisfy each constraint at least once • Write your functions in the form
 y = a(x − p)2 + q • Describe how and why you built each function • Be sure to identify which functions satisfy which constraints −Nat Banting Which learning standards did you “bump into” as you solved the problem?
  • 22. Pre-calculus 11 Learning Standards Curricular Competencies Content • analyze and apply mathematical ideas using reason • quadratic functions • explain and justify mathematical ideas and decisions
  • 25. Operations with Fractions add and subtract fractions multiply and divide fractions evaluate expressions with two or more operations on fractions solve contextual problems involving fractions
  • 26. Foundations of Mathematics and Pre-calculus 10 Learning Standard Delineated Learning Standards systems of linear equations Deconstruct this standard into 2-4 subtopics, or outcomes.
  • 27. Foundations of Mathematics and Pre-calculus 10 Learning Standard Delineated Learning Standards systems of linear equations solve systems of linear equations graphically solve systems of linear equations algebraically model and solve contextual problems involving systems of linear equations
  • 28. What do Emerging & Extending mean?
  • 30. and social competence). The Four-Point Provincial Proficiency Scale will be used to communicate student progress in all areas of learning. Proficiency Scale Emerging Developing Proficient Extending The student demonstrates an initial understanding of the concepts and competencies relevant to the expected learning. The student demonstrates a partial understanding of the concepts and competencies relevant to the expected learning. The student demonstrates a complete understanding of the concepts and competencies relevant to the expected learning. The student demonstrates a sophisticated understanding of the concepts and competencies relevant to the expected learning. At Grades 4-9, Boards will provide letter grades to parents upon request. A proficiency scale/letter grade alignment table will be provided by the ministry. Descriptive Feedback includes the strength-based written comments and/or documented Source: BC Ministry of Education (as of the 2018/19 school year)
  • 31. DRAFT K-9 Student Reporting Policy (2019) for Use in 2019/20 Pilot 2 and social competence). The Four-Point Provincial Proficiency Scale will be used to communicate student progress in all areas of learning. Proficiency Scale Emerging Developing Proficient Extending The student demonstrates an initial understanding of the concepts and competencies relevant to the expected learning. The student demonstrates a partial understanding of the concepts and competencies relevant to the expected learning. The student demonstrates a complete understanding of the concepts and competencies relevant to the expected learning. The student demonstrates a sophisticated understanding of the concepts and competencies relevant to the expected learning. At Grades 4-9, Boards will provide letter grades to parents upon request. A proficiency scale/letter grade alignment table will be provided by the ministry. Descriptive Feedback includes the strength-based written comments and/or documented conversations that describe individual student progress and identify specific goals to support further student growth. basic some good beyond initial partial complete sophisticated with support independence depth teach What are some implications?
  • 34. solve systems of linear equations graphically Emerging identify the solution from a graph or table What is the solution to the system represented by the graph? Developing determine the solution given equations in slope-intercept form Solve graphically: y = 2x − 5 y = − 1 4 x + 4 Pro fi cient determine the solution given equations in general form Solve graphically: 
 determine the number of solutions Analyze the system to determine whether it has one solution, no fi 2x + 5y + 25 = 0 4x − 2y + 14 = 0 Extending create a system given constraints Create a system so that: • the solution is (-3, -1) • one line has a negative slope • one line enters the fi rst quadrant Place the numbers from 1 to 9 in the boxes below so that the system has in fi nitely many solutions:
  • 35. solve systems of linear equations graphically What is the solution to the system represented by the graph? form Solve graphically: y = 2x − 5 y = − 1 4 x + 4 Solve graphically: 
 determine the number of solutions Analyze the system to determine whether it has one solution, no solution, or in fi nitely many solutions: 2x + 5y + 25 = 0 4x − 2y + 14 = 0 y = 1 2 x − 4 3x − 6y − 12 = 0 Create a system so that: • the solution is (-3, -1) • one line has a negative slope • one line enters the fi rst quadrant Place the numbers from 1 to 9 in the boxes below so that the system has in fi nitely many solutions: x + y = x + y = (Each number can be used only once.)
  • 36. solve 
 systems of linear equations algebraically Emerging verify the solution by substitution Is (2, 5) a solution to the system: ? solve by elimination where multiplication is not necessary Solve: y = 3x − 1 x − 2y = 8 Pro fi cient solve by substitution where neither variable is isolated in an equation Solve: solve by elimination where multiplication of both equations 2x + 5y + 7 = 0 3x − y = − 2 Developing solve by substitution where one variable is isolated in an equation Solve: solve by elimination where multiplication of one equation is x = 6 − 4y 2x − 3y = 1 Extending select, apply, and defend an algebraic approach Would you rather solve the following system by elimination or substitution? Why? 4x − y − 3 = 0 6x − 2y − 5 = 0
  • 37. solve 
 systems of linear equations algebraically Is (2, 5) a solution to the system: ? solve by elimination where multiplication is not necessary Solve: y = 3x − 1 x − 2y = 8 3x − 4y = 23 7x + 4y = 27 variable is isolated in an equation Solve: solve by elimination where multiplication of one equation is necessary Solve: x = 6 − 4y 2x − 3y = 1 7x + 2y = − 1 3x − 4y = 19 variable is isolated in an equation Solve: solve by elimination where multiplication of both equations is necessary Solve: 2x + 5y + 7 = 0 3x − y = − 2 5x + 4y = 13 8x + 3y + 3 = 0 approach Would you rather solve the following system by elimination or substitution? Why? 4x − y − 3 = 0 6x − 2y − 5 = 0
  • 38. model and solve contextual problems involving systems of Emerging interpret the solution in context given a model The heights of two candles over time can be modelled by: What is the meaning, in context, of the solution (8, 4)? h = 20 − 2t h = 16 − 1.5t Developing model and solve combination problems Two t-shirts and four hoodies sell for $254. Four t-shirts and fi ve hoodies sell for $361. What is the price of each item? Pro fi cient model and solve parts- whole and catch-up problems Tickets to a charity hockey game cost $12 for adults and $8 for children. A total of 150 tickets were sold for $1640. How many of each type of ticket were sold? A gas vehicle has an initial cost of Extending model and solve mixture problems A scientist needs to make 200 ml of a 42% alcohol solution. They mix 30% alcohol and 50% alcohol solutions. How much of each solution do they need?
  • 39. solve contextual problems involving systems of linear equations What is the meaning, in context, of the solution (8, 4)? h = 20 − 2t h = 16 − 1.5t fi sell for $361. What is the price of each item? $12 for adults and $8 for children. A total of 150 tickets were sold for $1640. How many of each type of ticket were sold? A gas vehicle has an initial cost of $31 000 and an operating cost of $1500 per year. An electric vehicle has an initial cost of $43 000 and an operating cost of $500 per year. How many years will it take for the total cost of both vehicles to be same? 50% alcohol solutions. How much of each solution do they need?
  • 40.
  • 41. How do I elicit evidence of learning?
  • 43.
  • 44. learning standard Emerging Developing Pro fi cient Extending learning standard Emerging Developing Pro fi cient Extending
  • 45. 10p + 6q + 38 = 0 −10p + 25q + 55 = 0 31q + 93 = 0 q = − 3 31q = − 93 5p + 3q + 19 = 0 2p − 5q − 11 = 0 ① ②
  • 47. vs.
  • 48. How do I keep track of data?
  • 49. Name Learning Outcome 1 2 3 4 5 6 7 8 9 10 Aaron Ex P Ex P P P P Ex P P Blake D Em Ex P P Em D Ex P D Denise D Em P D P D Em D D Em …
  • 50. Name Learning Outcome 1 2 3 4 5 6 7 8 9 10 Aaron Ex P Ex P P P P Ex P P Blake D Em Ex P P Em D Ex P D Denise D Em P D P D Em D D Em … D P P Ex Ex → Ex
  • 51.
  • 52. Peter Liljedahl “The fact that she didn’t know how to do something in the beginning is expected–she is learning, not learned, and she shouldn’t be punished for her early-not-knowing.”
  • 53. How do I translate that to a percentage?
  • 56. B 73 74 75 76 77 78 79 80 81 82 83 84 85 descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor
  • 57.
  • 58. 9 Letter Grades and Percentages Letter grades are used in Grades 10-12 to indicate a student’s level of performance in relation to the Learning Standards. The process for Letter grade symbols and corresponding percentages and definitions are set out in the Provincial Letter Grades Order. Letter Grade Percentage Range Definition A 86 - 100 The student demonstrates excellent or outstanding performance in relation to the learning outcomes for the course or subject and grade. B 73 – 85 The student demonstrates very good performance in relation to the learning outcomes for the course or subject and grade C+ 67 – 72 The student demonstrates good performance in relation to the learning outcomes for the course or subject and grade. C 60 – 66 The student demonstrates satisfactory performance in relation to the expected learning outcomes for the course or subject and grade. C- 50 – 59 The student demonstrates minimally acceptable performance in relation to the learning outcomes for the course or subject and grade. At the end of the school year or at the completion of a course, teachers assign a letter grade to indicate each student’s overall progress in the area of learning or course. Due to the cumulative nature of learning, the final term work may be more heavily weighted as it indicates more F 0 – 49 The student has not demonstrated, or is not demonstrating, minimally acceptable performance in relation to the learning outcomes for the course or subject and grade.
  • 59. Letter
 Grade Percentage Range De fi nition Hi-B 82 – 85 The student demonstrates pretty, pretty, pretty, pretty good performance in relation to the learning outcomes for the course or subject and grade. Mid-B 77 – 81 The student demonstrates pretty, pretty, pretty good performance in relation to the learning outcomes for the course or subject and grade. Lo-B 73 – 76 The student demonstrates pretty, pretty good performance in relation to the learning outcomes for the course or subject and grade.
  • 60. C- C C+ B A 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99100 F descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor descriptor
  • 61. Aaron Blake Denise LO Em D P Ex LO Em D P Ex LO Em D P Ex 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 (7 × 3) + (3 × 4) 10 × 4 = 33 40 = 83 % (2 × 1) + (3 × 2) + (3 × 3) + (2 × 4) 10 × 4 = 25 40 = 63 % (3 × 1) + (5 × 2) + (2 × 3) 10 × 4 = 19 40 = 48 % 1-2-3-4
  • 62. Aaron Blake Denise LO Em D P Ex LO Em D P Ex LO Em D P Ex 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 (7 × 4) + (3 × 5) 10 × 5 = 43 50 = 86 % (2 × 2) + (3 × 3) + (3 × 4) + (2 × 5) 10 × 5 = 35 50 = 70 % (3 × 2) + (5 × 3) + (2 × 4) 10 × 5 = 29 50 = 58 % 2-3-4-5
  • 63. What letter grade or percentage would you assign to Aaron, Blake, and Denise?