Download Science- Kindergarten

Area of Learning: Mathematics
Big Ideas
Grade 6

Mixed numbers and decimal numbers
represent quantities that can be
decomposed into parts and wholes.

Computational fluency and flexibility with
numbers extend to operations with whole
numbers and decimals.

Linear relations can be identified and
represented using expressions with
variables and line graphs and can be used
to form generalizations.

Properties of objects and shapes can be
described, measured, and compared using
volume, area, perimeter, and angles.

Data from the results of an experiment can
be used to predict the theoretical
probability of an event and to compare and
interpret.
Curricular Competencies
Reasoning and analyzing
 Use logic and patterns to solve
puzzles and play games
Elaborations
 numbers:
o Number: Number represents and describes quantity.
 Sample questions to support inquiry with students:
o In how many ways can you represent the number ___?
o What are the connections between fractions, mixed numbers, and decimal numbers?
o How are mixed numbers and decimal numbers alike? Different?
 fluency:
o Computational Fluency: Computational fluency develops from a strong sense of number.
 Sample questions to support inquiry with students:
o When we are working with decimal numbers, what is the relationship between addition and subtraction?
o When we are working with decimal numbers, what is the relationship between multiplication and division?
o When we are working with decimal numbers, what is the relationship between addition and multiplication?
o When we are working with decimal numbers, what is the relationship between subtraction and division?
 Linear relations:
o Patterning: We use patterns to represent identified regularities and to make generalizations.
 Sample questions to support inquiry with students:
o What is a linear relationship?
o How do linear expressions and line graphs represent linear relations?
o What factors can change or alter a linear relationship?
 Properties:
o Geometry and Measurement: We can describe, measure, and compare spatial relationships.
 Sample questions to support inquiry with students:
o How are the areas of triangles, parallelogram, and trapezoids interrelated?
o What factors are considered when selecting a viable referent in measurement?
 Data:
o Data and Probability: Analyzing data and chance enables us to compare and interpret.
 Sample questions to support inquiry with students:
o What is the relationship between theoretical and experimental probability?
o What informs our predictions?
o What factors would influence the theoretical probability of an experiment?
Elaborations
 logic and patterns:
o including coding
 reasoning and logic:
Content
Students are expected to know the
following:
 small to large numbers
Elaborations
 small to large numbers:
o place value from thousandths to
billions, operations with thousandths
1

Use reasoning and logic to
explore, analyze, and apply
mathematical ideas
 Estimate reasonably
 Demonstrate and apply mental
math strategies
 Use tools or technology to explore
and create patterns and
relationships, and test conjectures
 Model mathematics in
contextualized experiences
Understanding and solving
 Apply multiple strategies to solve
problems in both abstract and
contextualized situations
 Develop, demonstrate, and apply
mathematical understanding
through play, inquiry, and problem
solving
 Visualize to explore mathematical
concepts
 Engage in problem-solving
experiences that are connected to
place, story, cultural practices, and
perspectives relevant to local First
Peoples communities, the local
community, and other cultures
Communicating and representing
 Use mathematical vocabulary and
language to contribute to
mathematical discussions
 Explain and justify mathematical
ideas and decisions
 Communicate mathematical
thinking in many ways
 Represent mathematical ideas in
concrete, pictorial, and symbolic
forms
o





making connections, using
inductive and deductive
reasoning, predicting,
generalizing, drawing
conclusions through
experiences
Estimate reasonably:
o estimating using referents,
approximation, and
rounding strategies (e.g.,
the distance to the stop sign
is approximately 1 km, the
width of my finger is about
1 cm)
apply:
o extending whole-number
strategies to decimals
o working toward developing
fluent and flexible thinking
about number
Model:
o acting it out, using concrete
materials (e.g.,
manipulatives), drawing
pictures or diagrams,
building, programming
o http://www.nctm.org/Publi
cations/Teaching-ChildrenMathematics/Blog/Modelin
g-with-Mathematicsthrough-Three-Act-Tasks/
multiple strategies:
o includes familiar, personal,
and from other cultures
connected:
o in daily activities, local and
traditional practices, the
environment, popular
media and news events,


















(thousandths to billions)
multiplication and division facts to
100 (developing computational
fluency)
order of operations with whole
numbers
factors and multiples — greatest
common factor and least common
multiple
improper fractions and mixed
numbers
introduction to ratios
whole-number percents and
percentage discounts
multiplication and division of
decimals
increasing and decreasing patterns,
using expressions, tables, and
graphs as functional relationships
one-step equations with wholenumber coefficients and solutions
perimeter of complex shapes
area of triangles, parallelograms,
and trapezoids
angle measurement and
classification
volume and capacity
triangles
combinations of transformations
line graphs
single-outcome probability, both
theoretical and experimental
financial literacy — simple
budgeting and consumer math
to billions
numbers used in science, medicine,
technology, and media
o compare, order, estimate
facts to 100:
o mental math strategies (e.g., the
double-double strategy to multiply 23
x 4)
order of operations:
o includes the use of brackets, but
excludes exponents
o quotients can be rational numbers
factors and multiples:
o prime and composite numbers,
divisibility rules, factor trees, prime
factor phrase (e.g., 300 = 22 x 3 x 52 )
o using graphic organizers (e.g., Venn
diagrams) to compare numbers for
common factors and common
multiples
improper fractions:
o using benchmarks, number line, and
common denominators to compare
and order, including whole numbers
o using pattern blocks, Cuisenaire Rods,
fraction strips, fraction circles, grids
o birchbark biting
ratios:
o comparing numbers, comparing
quantities, equivalent ratios
o part-to-part ratios and part-to-whole
ratios
o traditional Aboriginal language
speakers to English speakers or
French speakers, dual-language
speakers
percents:
o using base 10 blocks, geoboard, 10x10
grid to represent whole number
o






2
Connecting and reflecting
 Reflect on mathematical thinking
 Connect mathematical concepts to
each other and to other areas and
personal interests
 Use mathematical arguments to
support personal choices
 Incorporate First Peoples
worldviews and perspectives to
make connections to
mathematical concepts
cross-curricular integration
Patterns are important in
Aboriginal technology,
architecture, and art.
o Have students pose and
solve problems or ask
questions connected to
place, stories, and cultural
practices.
Explain and justify:
o using mathematical
arguments
Communicate:
o concretely, pictorially,
symbolically, and by using
spoken or written language
to express, describe,
explain, justify, and apply
mathematical ideas; may
use technology such as
screencasting apps, digital
photos
Reflect:
o sharing the mathematical
thinking of self and others,
including evaluating
strategies and solutions,
extending, and posing new
problems and questions
other areas and personal
interests:
o to develop a sense of how
mathematics helps us
understand ourselves and
the world around us (e.g.,
cross-discipline, daily
activities, local and
traditional practices, the
environment, popular
o




percents
finding missing part (whole or
percentage)
o 50% = 1/2 = 0.5 = 50:100
decimals:
o 0.125 x 3 or 7.2 ÷ 9
o using base 10 block array
o birchbark biting
patterns:
o limited to discrete points in the first
quadrant
o visual patterning (e.g., colour tiles)
o Take 3 add 2 each time, 2n + 1, and 1
more than twice a number all describe
the pattern 3, 5, 7, …
o graphing data on Aboriginal language
loss, effects of language intervention
one-step equations:
o preservation of equality (e.g., using a
balance, algebra tiles)
o 3x = 12, x + 5 = 11
perimeter
o A complex shape is a group of shapes
with no holes (e.g., use colour tiles,
pattern blocks, tangrams).
area:
o grid paper explorations
o deriving formulas
o making connections between area of
parallelogram and area of rectangle
o birchbark biting
angle:
o straight, acute, right, obtuse, reflex
o constructing and identifying; include
examples from local environment
o estimating using 45°, 90°, and 180° as
reference angles
o angles of polygons
o Small Number stories: Small Number
o






3



media and news events,
and social justice)
personal choices:
o including anticipating
consequences
Incorporate First Peoples:
o Invite local First Peoples
Elders and knowledge
keepers to share their
knowledge
make connections:
o Bishop’s cultural practices:
counting, measuring,
locating, designing,
playing,
explaining(http://www.csus
.edu/indiv/o/oreyd/ACP.ht
m_files/abishop.htm)
o First Nations Education
Steering Committee
(FNESC) Place-Based
Themes and Topics: family
and ancestry; travel and
navigation; games; land,
environment, and resource
management; community
profiles; art; nutrition;
dwellings
o Teaching Mathematics in a
First Nations Context,
FNESC
(http://www.fnesc.ca/k-7/)





and the Skateboard Park
(http://mathcatcher.irmacs.sfu.ca/stori
es)
volume and capacity:
o using cubes to build 3D objects and
determine their volume
o referents and relationships between
units (e.g., cm3, m3, mL, L)
o the number of coffee mugs that hold a
litre
o berry baskets, seaweed drying
triangles:
o scalene, isosceles, equilateral
o right, acute, obtuse
o classified regardless of orientation
transformations:
o plotting points on Cartesian plane
using whole-number ordered pairs
o translation(s), rotation(s), and/or
reflection(s) on a single 2D shape
o limited to first quadrant
o transforming, drawing, and describing
image
o Use shapes in First Peoples art to
integrate printmaking (e.g., Inuit,
Northwest coastal First Nations, frieze
work)
(http://mathcentral.uregina.ca/RR/data
base/RR.09.01/mcdonald1/).
line graphs:
o table of values, data set; creating and
interpreting a line graph from a given
set of data
o fish runs versus time
single-outcome probability:
o single-outcome probability events
(e.g., spin a spinner, roll a die, toss a
coin)
o listing all possible outcomes to
4
determine theoretical probability
comparing experimental results with
theoretical expectation
o Lahal bone game
financial literacy:
o informed decision making on saving
and purchasing
o How many weeks of allowance will it
take to buy a bicycle?
o

5
Area of Learning: Mathematics
Big Ideas

Decimals, fractions, and percents are
used to represent and describe parts
and wholes of numbers.

Computational fluency and
flexibility with numbers extend to
operations with integers and
decimals.

Linear relations can be represented in
many connected ways to identify
regularities and make generalizations.

The constant ratio between the
circumference and diameter of circles
can be used to describe, measure, and
compare spatial relationships.

Data from circle graphs can be used to
illustrate proportion and to compare and
interpret.
Grade 7
Elaborations
 numbers:
o Number: Number represents and describes quantity.
 Sample questions to support inquiry with students:
o In how many ways can you represent the number ___?
o What is the relationship between decimals, fractions, and percents?
o How can you prove equivalence?
o How are parts and wholes best represented in particular contexts?
 fluency:
o Computational Fluency: Computational fluency develops from a strong sense of number.
 Sample questions to support inquiry with students:
o When we are working with integers, what is the relationship between addition and subtraction?
o When we are working with integers, what is the relationship between multiplication and division?
o When we are working with integers, what is the relationship between addition and multiplication?
o When we are working with integers, what is the relationship between subtraction and division?
 Linear relations:
o Patterning: We use patterns to represent identified regularities and to make generalizations.
 Sample questions to support inquiry with students:
o What is a linear relationship?
o In how many ways can linear relationships be represented?
o How do linear relationships differ?
o What factors can change a linear relationship?
 spatial relationships:
o Geometry and Measurement: We can describe, measure, and compare spatial relationships.
 Sample questions to support inquiry with students:
o What is unique about the properties of circles?
o What is the relationship between diameter and circumference?
o What are the similarities and differences between the area and circumference of circles?
 Data:
o Data and Probability: Analyzing data and chance enables us to compare and interpret.
 Sample questions to support inquiry with students:
o How is a circle graph similar to and different from other types of visual representations of data?
o When would you choose to use a circle graph to represent data?
o How are circle graphs related to ratios, percents, decimals, and whole numbers?
o How would circle graphs be informative or misleading?
6
Curricular Competencies
Reasoning and analyzing
 Use logic and patterns to solve
puzzles and play games
 Use reasoning and logic to explore,
analyze, and apply mathematical
ideas
 Estimate reasonably
 Demonstrate and apply mental math
strategies
 Use tools or technology to explore
and create patterns and relationships,
and test conjectures
 Model mathematics in contextualized
experiences
Understanding and solving
 Apply multiple strategies to solve
problems in both abstract and
contextualized situations
 Develop, demonstrate, and apply
mathematical understanding through
play, inquiry, and problem solving
 Visualize to explore mathematical
concepts
 Engage in problem-solving
experiences that are connected to
place, story, cultural practices, and
perspectives relevant to local First
Peoples communities, the local
community, and other cultures
Communicating and representing
 Use mathematical vocabulary and
language to contribute to
mathematical discussions
 Explain and justify mathematical
ideas and decisions
 Communicate mathematical thinking
in many ways
Elaborations
 logic and patterns:
o including coding
 reasoning and logic:
o making connections, using
inductive and deductive
reasoning, predicting,
generalizing, drawing
conclusions through
experiences
 Estimate reasonably:
o estimating using referents,
approximation, and rounding
strategies (e.g., the distance to
the stop sign is approximately
1 km, the width of my finger
is about 1 cm)
 apply:
o extending whole-number
strategies to integers
o working toward developing
fluent and flexible thinking
about number
 Model:
o acting it out, using concrete
materials (e.g.,
manipulatives), drawing
pictures or diagrams,
building, programming
o http://www.nctm.org/Publicat
ions/Teaching-ChildrenMathematics/Blog/Modelingwith-Mathematics-throughThree-Act-Tasks/
 multiple strategies:
o includes familiar, personal,
and from other cultures
 connected:
o in daily activities, local and
Content
Students are expected to know the following:
 multiplication and division facts to 100
(extending computational fluency)
 operations with integers (addition,
subtraction, multiplication, division, and
order of operations)
 operations with decimals (addition,
subtraction, multiplication, division, and
order of operations)
 relationships between decimals, fractions,
ratios, and percents
 discrete linear relations, using
expressions, tables, and graphs
 two-step equations with whole-number
coefficients, constants, and solutions
 circumference and area of circles
 volume of rectangular prisms and cylinders
 Cartesian coordinates and graphing
 combinations of transformations
 circle graphs
 experimental probability with two
independent events
 financial literacy — financial percentage
Elaborations
 facts to 100:
o When multiplying 214 by 5, we can
multiply by 10, then divide by 2 to
get 1070.
 operations with integers:
o addition, subtraction,
multiplication, division, and order
of operations
o concretely, pictorially, symbolically
o order of operations includes the use
of brackets, excludes exponents
o using two-sided counters
o 9–(–4) = 13 because –4 is 13 away
from +9
o extending whole-number strategies
to decimals
 operations with decimals:
o includes the use of brackets, but
excludes exponents
 relationships:
o conversions, equivalency, and
terminating versus repeating
decimals, place value, and
benchmarks
o comparing and ordering decimals
and fractions using the number line
o ½ = 0.5 = 50% = 50:100
o shoreline cleanup
 discrete linear relations:
o four quadrants, limited to integral
coordinates
o 3n + 2; values increase by 3 starting
from y-intercept of 2
o deriving relation from the graph or
table of values
o Small Number stories: Small
Number and the Old Canoe, Small
Number Counts to 100
7

Represent mathematical ideas in
concrete, pictorial, and symbolic
forms
Connecting and reflecting
 Reflect on mathematical thinking
 Connect mathematical concepts to
each other and to other areas and
personal interests
 Use mathematical arguments to
support personal choices
 Incorporate First Peoples
worldviews and perspectives to
make connections to mathematical
concepts




traditional practices, the
environment, popular media
and news events, crosscurricular integration
o Patterns are important in
Aboriginal technology,
architecture, and art.
o Have students pose and solve
problems or ask questions
connected to place, stories,
and cultural practices.
Explain and justify:
o using mathematical
arguments
Communicate:
o concretely, pictorially,
symbolically, and by using
spoken or written language to
express, describe, explain,
justify and apply
mathematical ideas; may use
technology such as
screencasting apps, digital
photos
Reflect:
o sharing the mathematical
thinking of self and others,
including evaluating
strategies and solutions,
extending, and posing new
problems and questions
other areas and personal interests:
o to develop a sense of how
mathematics helps us
understand ourselves and the
world around us (e.g., crossdiscipline, daily activities,
local and traditional practices,
the environment, popular



(http://mathcatcher.irmacs.sfu.ca/st
ories)
two-step equations:
o solving and verifying 3x + 4 = 16
o modelling the preservation of
equality (e.g., using balance,
pictorial representation, algebra
tiles)
o spirit canoe trip pre-planning and
calculations
o Small Number stories: Small
Number and the Big Tree
(http://mathcatcher.irmacs.sfu.ca/st
ories)
circumference
o constructing circles given radius,
diameter, area, or circumference
o finding relationships between
radius, diameter, circumference,
and area to develop C = π x d
formula
o applying A = π x r x r formula to
find the area given radius or
diameter
o drummaking, dreamcatcher making,
stories of SpiderWoman (Dene,
Cree, Hopi, Tsimshian), basket
making, quill box making (Note:
Local protocols should be
considered when choosing an
activity.)
volume:
o volume = area of base x height
o bentwood boxes, wiigwaasabak and
mide-wiigwaas (birch bark scrolls)
o Exploring Math through Haida
Legends: Culturally Responsive
Mathematics
(http://www.haidanation.ca/Pages/l
8



media and news events, and
social justice)
personal choices:
o including anticipating
consequences
Incorporate First Peoples:
o Invite local First Peoples
Elders and knowledge
keepers to share their
knowledge
make connections:
o Bishop’s cultural practices:
counting, measuring,
locating, designing, playing,
explaining(http://www.csus.e
du/indiv/o/oreyd/ACP.htm_fil
es/abishop.htm)
o First Nations Education
Steering Committee (FNESC)
Place-Based Themes and
Topics: family and ancestry;
travel and navigation; games;
land, environment and
resource management;
community profiles; art;
nutrition; dwellings
o Teaching Mathematics in a
First Nations Context,
FNESC
(http://www.fnesc.ca/k-7/)





anguage/haida_legends/media/Less
ons/RavenLes4-9.pdf)
Cartesian coordinates:
o origin, four quadrants, integral
coordinates, connections to linear
relations, transformations
o overlaying coordinate plane on
medicine wheel, beading on
dreamcatcher, overlaying
coordinate plane on traditional
maps
transformations:
o four quadrants, integral coordinates
o translation(s), rotation(s), and/or
reflection(s) on a single 2D shape;
combination of successive
transformations of 2D shapes;
tessellations
o Aboriginal art, jewelry making,
birchbark biting
circle graphs:
o constructing, labelling, and
interpreting circle graphs
o translating percentages displayed in
a circle graph into quantities and
vice versa
o visual representations of tidepools
or tradional meals on plates
experimental probability:
o experimental probability, multiple
trials (e.g., toss two coins, roll two
dice, spin a spinner twice, or a
combination thereof)
o Puim, Hubbub
o dice games
(http://web.uvic.ca/~tpelton/fnmath/fn-dicegames.html)
financial literacy:
o financial percentage calculations
9
o
sales tax, tips, discount, sale price
10
Area of Learning: Mathematics
Big Ideas

Number represents, describes, and compares the
quantities of ratios, rates, and percents.

Computational fluency and flexibility extend to
operations with fractions.

Discrete linear relationships can be represented in
many connected ways and used to identify and make
generalizations.

The relationship between surface area and volume of
3D objects can be used to describe, measure, and
compare spatial relationships.

Analyzing data by determining averages is one way to
make sense of large data sets and enables us to compare
and interpret.
Curricular Competencies
Reasoning and analyzing
Grade 8
Elaborations
 numbers:
o Number: Number represents and describes quantity.
 Sample questions to support inquiry with students:
o How can two quantities be compared, represented, and communicated?
o How are decimals, fractions, ratios, and percents interrelated?
o How does ratio use in mechanics differ from ratio use in architecture?
 fluency:
o Computational Fluency: Computational fluency develops from a strong sense of number.
 Sample questions to support inquiry with students:
o When we are working with fractions, what is the relationship between addition and subtraction?
o When we are working with fractions, what is the relationship between multiplication and division?
o When we are working with fractions, what is the relationship between addition and multiplication?
o When we are working with fractions, what is the relationship between subtraction and division?
 Discrete linear relationships:
o Patterning: We use patterns to represent identified regularities and to make generalizations.
 Sample questions to support inquiry with students:
o What is a discrete linear relationship?
o How can discrete linear relationships be represented?
o What factors can change a discrete linear relationship?
 3D objects:
o Geometry and Measurement: We can describe, measure, and compare spatial relationships.
 Sample questions to support inquiry with students:
o What is the relationship between the surface area and volume of regular solids?
o How can surface area and volume of regular solids be determined?
o How are the surface area and volume of regular solids related?
o How does surface area compare with volume in patterning and cubes?
 data:
o Data and Probability: Analyzing data and chance enables us to compare and interpret.
 Sample questions to support inquiry with students:
o How does determining averages help us understand large data sets?
o What do central tendencies represent?
o How are central tendencies best used to describe a quality of a large data set?
Elaborations
 logic and patterns:
Content
Students are expected to know the
Elaborations
 perfect squares and cubes:
11

Use logic and patterns to solve
puzzles and play games
 Use reasoning and logic to
explore, analyze, and apply
mathematical ideas
 Estimate reasonably
 Demonstrate and apply mental
math strategies
 Use tools or technology to explore
and create patterns and
relationships, and test conjectures
 Model mathematics in
contextualized experiences
Understanding and solving
 Apply multiple strategies to solve
problems in both abstract and
contextualized situations
 Develop, demonstrate, and apply
mathematical understanding
through play, inquiry, and problem
solving
 Visualize to explore mathematical
concepts
 Engage in problem-solving
experiences that are connected to
place, story, cultural practices, and
perspectives relevant to local First
Peoples communities, the local
community, and other cultures
Communicating and representing
 Use mathematical vocabulary and
language to contribute to
mathematical discussions
 Explain and justify mathematical
ideas and decisions
 Communicate mathematical
thinking in many ways
 Represent mathematical ideas in





o including coding
reasoning and logic:
o making connections,
using inductive and
deductive reasoning,
predicting, generalizing,
drawing conclusions
through experiences
Estimate reasonably:
o estimating using
referents, approximation,
and rounding strategies
(e.g., the distance to the
stop sign is approximately
1 km, the width of my
finger is about 1 cm)
apply:
o extending whole-number
strategies to decimals and
fractions
o working toward
developing fluent and
flexible thinking of
number
Model:
o acting it out, using
concrete materials (e.g.,
manipulatives), drawing
pictures or diagrams,
building, programming
o http://www.nctm.org/Publ
ications/TeachingChildrenMathematics/Blog/Model
ing-with-Mathematicsthrough-Three-Act-Tasks/
multiple strategies:
o includes familiar,
personal, and from other
following:
 perfect squares and cubes
 square and cube roots
 percents less than 1 and greater
than 100 (decimal and fractional
percents)
 numerical proportional
reasoning (rates, ratio,
proportions, and percent)
 operations with fractions
(addition, subtraction,
multiplication, division, and order
of operations)
 discrete linear relations
(extended to larger numbers,
limited to integers)
 expressions- writing and
evaluating using substitution
 two-step equations with integer
coefficients, constants, and
solutions
 surface area and volume of
regular solids, including triangular
and other right prisms and
cylinders
 Pythagorean theorem
 construction, views, and nets of
3D objects
 central tendency
 theoretical probability with two
independent events
 financial literacy — best buys
o




using colour tiles, pictures, or multi-link
cubes
o building the number or using prime
factorization
square and cube roots
o finding the cube root of 125
o finding the square root of 16/169
o estimating the square root of 30
percents:
o A worker’s salary increased 122% in three
years. If her salary is now $93,940, what
was it originally?
o What is ½% of 1 billion?
o The population of Vancouver increased by
3.25%. What is the population if it was
approximately 603,500 people last year?
o beading
proportional reasoning:
o two-term and three-term ratios, real-life
examples and problems
o A string is cut into three pieces whose
lengths form a ratio of 3:5:7. If the string
was 105 cm long, how long are the
pieces?
o creating a cedar drum box of proportions
that use ratios to create differences in
pitch and tone
o paddle making
fractions:
o includes the use of brackets, but excludes
exponents
o using pattern blocks or Cuisenaire Rods
o simplifying ½ ÷ 9/6 x (7 – 4/5)
o drumming and song: 1/2, 1/4, 1/8, whole
notes, dot bars, rests = one beat
o changing tempos of traditional songs
dependent on context of use
o proportional sharing of harvests based on
family size
12
concrete, pictorial, and symbolic
forms
Connecting and reflecting
 Reflect on mathematical thinking
 Connect mathematical concepts to
each other and to other areas and
personal interests
 Use mathematical arguments to
support personal choices
 Incorporate First Peoples
worldviews and perspectives to
make connections to
mathematical concepts





cultures
connected:
o in daily activities, local
and traditional practices,
the environment, popular
media and news events,
cross-curricular
integration
o Patterns are important in
Aboriginal technology,
architecture, and art.
o Have students pose and
solve problems or ask
questions connected to
place, stories, and cultural
practices.
Explain and justify:
o using mathematical
arguments
Communicate:
o concretely, pictorially,
symbolically, and by
using spoken or written
language to express,
describe, explain, justify,
and apply mathematical
ideas; may use
technology such as
screencasting apps, digital
photos
Reflect:
o sharing the mathematical
thinking of self and
others, including
evaluating strategies and
solutions, extending, and
posing new problems and
questions
other areas and personal






discrete linear relations:
o two-variable discrete linear relations
o expressions, table of values, and graphs
o scale values (e.g., tick marks on axis
represent 5 units instead of 1)
o four quadrants, integral coordinates
expressions:
o using an expression to describe a
relationship
o evaluating 0.5n – 3n + 25, if n = 14
two-step equations:
o solving and verifying 3x – 4 = –12
o modelling the preservation of equality
(e.g., using a balance, manipulatives,
algebra tiles, diagrams)
o spirit canoe journey calculations
surface area and volume:
o exploring strategies to determine the
surface area and volume of a regular solid
using objects, a net, 3D design software
o volume = area of the base x height
o surface area = sum of the areas of each
side
Pythagorean theorem:
o modelling the Pythagorean theorem
o finding a missing side of a right triangle
o deriving the Pythagorean theorem
o constructing canoe paths and landings
given current on a river (First Nations
Education Steering Committee)
o Aboriginal constellations and adaus
3D objects:
o top, front, and side views of 3D objects
o matching a given net to the 3D object it
represents
o drawing and interpreting top, front, and
side views of 3D objects
o constructing 3D objects with nets
o using design software to create 3D objects
13



interests:
o to develop a sense of how
mathematics helps us
understand ourselves and
the world around us (e.g.,
cross-discipline, daily
activities, local and
traditional practices, the
environment, popular
media and news events,
and social justice)
personal choices:
o including anticipating
consequences
Incorporate First Peoples:
o Invite local First Peoples
Elders and knowledge
keepers to share their
knowledge
make connections:
o Bishop’s cultural
practices: counting,
measuring, locating,
designing, playing,
explaining(http://www.cs
us.edu/indiv/o/oreyd/ACP
.htm_files/abishop.htm)
o First Nations Education
Steering Committee
(FNESC) Place-Based
Themes and Topics:
family and ancestry;
travel and navigation;
games; land,
environment, and
resource management;
community profiles; art;
nutrition; dwellings
o Teaching Mathematics in



from nets
o bentwood boxes, lidded baskets, packs
central tendency:
o mean, median, and mode
theoretical probability:
o with two independent events: sample
space (e.g., using tree diagram, table,
graphic organizer)
o rolling a 5 on a fair die and flipping a
head on a fair coin is 1/6 x ½ = 1/12
o deciding whether a spinner in a game is
fair
financial literacy:
o coupons, proportions, unit price, products
and services
o proportional reasoning strategies (e.g.,
unit rate, equivalent fractions given prices
and quantities)
14
a First Nations Context,
FNESC
(http://www.fnesc.ca/reso
urces/math-first-peoples/)
15
Area of Learning: Mathematics
Big Ideas
 The principles and processes underlying operations with
numbers apply equally to algebraic situations and can be
described and analyzed.

Computational fluency and flexibility with numbers
extend to operations with rational numbers.

Continuous linear relationships can be identified and
represented in many connected ways to identify
regularities and make generalizations.

Similar shapes have proportional relationships that
can be described, measured, and compared.

Analyzing the validity, reliability, and representation
of data enables us to compare and interpret.
Grade 9
Elaborations
 numbers:
o Number: Number represents and describes quantity. (Algebraic reasoning enables us to describe and
analyze mathematical relationships.)
 Sample questions to support inquiry with students:
o How does understanding equivalence help us solve algebraic equations?
o How are the operations with polynomials connected to the process of solving equations?
o What patterns are formed when we implement the operations with polynomials?
o How can we analyze bias and reliability of studies in the media?
 fluency:
o Computational Fluency: Computational fluency develops from a strong sense of number.
 Sample questions to support inquiry with students:
o When we are working with rational numbers, what is the relationship between addition and subtraction?
o When we are working with rational numbers, what is the relationship between multiplication and division?
o When we are working with rational numbers, what is the relationship between addition and multiplication?
o When we are working with rational numbers, what is the relationship between subtraction and division?
 Continuous linear relationships:
o Patterning: We use patterns to represent identified regularities and to make generalizations.
 Sample questions to support inquiry with students:
o What is a continuous linear relationship?
o How can continuous linear relationships be represented?
o How do linear relationships help us to make predictions?
o What factors can change a continuous linear relationship?
o How are different graphs and relationships used in a variety of careers?
 proportional relationships:
o Geometry and Measurement: We can describe, measure, and compare spatial relationships. (Proportional
reasoning enables us to make sense of multiplicative relationships.)
 Sample questions to support inquiry with students:
o How are similar shapes related?
o What characteristics make shapes similar?
o What role do similar shapes play in construction and engineering of structures?
 data:
o Data and Probability: Analyzing data and chance enables us to compare and interpret.
 Sample questions to support inquiry with students:
o What makes data valid and reliable?
16
o
o
Curricular Competencies
Reasoning and analyzing
 Use logic and patterns to solve
puzzles and play games
 Use reasoning and logic to
explore, analyze, and apply
mathematical ideas
 Estimate reasonably
 Demonstrate and apply mental
math strategies
 Use tools or technology to explore
and create patterns and
relationships, and test conjectures
 Model mathematics in
contextualized experiences
Understanding and solving
 Apply multiple strategies to solve
problems in both abstract and
contextualized situations
 Develop, demonstrate, and apply
mathematical understanding
through play, inquiry, and problem
solving
 Visualize to explore mathematical
concepts
 Engage in problem-solving
experiences that are connected to
place, story, cultural practices, and
perspectives relevant to local First
Peoples communities, the local
community, and other cultures
Communicating and representing
 Use mathematical vocabulary and
language to contribute to
mathematical discussions
What is the difference between valid data and reliable data?
What factors influence the validity and reliablity of data?
Elaborations
 logic and patterns:
o including coding
 reasoning and logic:
o making connections, using
inductive and deductive
reasoning, predicting,
generalizing, drawing
conclusions through
experiences
 Estimate reasonably:
o estimating using referents,
approximation, and
rounding strategies (e.g.,
the distance to the stop
sign is approximately 1
km, the width of my finger
is about 1 cm)
 apply:
o extending whole-number
strategies to rational
numbers and algebraic
expressions
o working toward
developing fluent and
flexible thinking of number
 Model:
o acting it out, using
concrete materials (e.g.,
manipulatives), drawing
pictures or diagrams,
building, programming
o http://www.nctm.org/Publi
cations/Teaching-ChildrenMathematics/Blog/Modeli
ng-with-Mathematics-
Content
Students are expected to know the
following:
 operations with rational numbers
(addition, subtraction, multiplication,
division, and order of operations)
 exponents and exponent laws with
whole-number exponents
 operations with polynomials, of
degree less than or equal to 2
 two-variable linear relations, using
graphing, interpolation, and
extrapolation
 multi-step one-variable linear
equations
 spatial proportional reasoning
 statistics in society
 financial literacy — simple budgets
and transactions
Elaborations
 operations:
o includes brackets and exponents
o simplifying (-3/4) ÷ 1/5 + ((-1/3) x (-5/2))
o simplifying 1 – 2 x (4/5)2
o paddle making
 exponents:
o includes variable bases
o 27 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128; n4 = n
xnxnxn
o exponent laws (e.g., 60 = 1; m1 = m; n5 x
n3 = n8; y7/y3 = y4; (5n)3 = 53 x n3 =
125n3; (m/n)5 = m5/n5; and (32)4 = 38)
o limited to whole-number exponents and
whole-number exponent outcomes when
simplified
o (–3)2 does not equal –32
o 3x(x – 4) = 3x2 – 12x
 polynomials:
o variables, degree, number of terms, and
coefficients, including the constant term
o (x2 + 2x – 4) + (2x2 – 3x – 4)
o (5x – 7) – (2x + 3)
o 2n(n + 7)
o (15k2 -10k) ÷ (5k)
o using algebra tiles
 two-variable linear relations:
o two-variable continuous linear relations;
includes rational coordinates
o horizontal and vertical lines
o graphing relation and analyzing
o interpolating and extrapolating
approximate values
o spirit canoe journey predictions and daily
checks
 multi-step:
17

Explain and justify mathematical
ideas and decisions
 Communicate mathematical
thinking in many ways
 Represent mathematical ideas in
concrete, pictorial, and symbolic
forms
Connecting and reflecting
 Reflect on mathematical thinking
 Connect mathematical concepts to
each other and to other areas and
personal interests
 Use mathematical arguments to
support personal choices
 Incorporate First Peoples
worldviews and perspectives to
make connections to
mathematical concepts






through-Three-Act-Tasks/
multiple strategies:
o includes familiar, personal,
and from other cultures
connected:
o in daily activities, local and
traditional practices, the
environment, popular
media and news events,
cross-curricular integration
o Patterns are important in
Aboriginal technology,
architecture, and art.
o Have students pose and
solve problems or ask
questions connected to
place, stories, and cultural
practices.
Explain and justify:
o using mathematical
arguments
Communicate:
o concretely, pictorially,
symbolically, and by using
spoken or written language
to express, describe,
explain, justify and apply
mathematical ideas; may
use technology such as
screencasting apps, digital
photos
Reflect:
o sharing the mathematical
thinking of self and others,
including evaluating
strategies and solutions,
extending, and posing new
problems and questions
other areas and personal
o



includes distribution, variables on both
sides of the equation, and collecting like
terms
o includes rational coefficients, constants,
and solutions
o solving and verifying 1 + 2x = 3 – 2/3(x +
6)
o solving symbolically and pictorially
proportional reasoning:
o scale diagrams, similar triangles and
polygons, linear unit conversions
o limited to metric units
o drawing a diagram to scale that represents
an enlargement or reduction of a given
2D shape
o solving a scale diagram problem by
applying the properties of similar
triangles, including measurements
o integration of scale for Aboriginal mural
work, use of traditional design in current
Aboriginal fashion design, use of similar
triangles to create longhouses/models
statistics:
o population versus sample, bias, ethics,
sampling techniques, misleading stats
o analyzing a given set of data (and/or its
representation) and identifying potential
problems related to bias, use of language,
ethics, cost, time and timing, privacy, or
cultural sensitivity
o using First Peoples data on water quality,
Statistics Canada data on income, health,
housing, population
financial literacy
o banking, simple interest, savings, planned
purchases
o creating a budget/plan to host a First
Peoples event
18



interests:
o to develop a sense of how
mathematics helps us
understand ourselves and
the world around us (e.g.,
cross-discipline, daily
activities, local and
traditional practices, the
environment, popular
media and news events,
and social justice)
personal choices:
o including anticipating
consequences
Incorporate First Peoples:
o Invite local First Peoples
Elders and knowledge
keepers to share their
knowledge
make connections:
o Bishop’s cultural practices:
counting, measuring,
locating, designing,
playing,
explaining(http://www.csu
s.edu/indiv/o/oreyd/ACP.ht
m_files/abishop.htm)
o First Nations Education
Steering Committee
(FNESC) Place-Based
Themes and Topics: family
and ancestry; travel and
navigation; games; land,
environment, and resource
management; community
profiles; art; nutrition;
dwellings
o Teaching Mathematics in a
First Nations Context,
19
FNESC
(http://www.fnesc.ca/resou
rces/math-first-peoples/)
20