Grade 6/7 Mathematics Course of Study – Sequence of Units
Term 1
Recommended
Length of Unit
Strand
Grade 6
Grade 7
3 weeks
Number Sense &
Numeration
3 weeks
Patterning &
Algebra
Data Management
Familiarize students to new textbooks.
Review to activate prior knowledge.
Operations with whole numbers,
decimal place value, composite and
prime numbers, order of operations
Geometric and number patterns
Familiarize students to new textbooks.
Review to activate prior knowledge
Whole numbers, decimals, factoring,
multiples, square roots,
order of operations, integers
Linear and number patterns, table of
values
Data Collection, graphing, interpreting,
mean
Suggested Cross-Strand Summative
Task(s)
Data Collection, graphing, interpreting,
central tendency
Suggested Cross-Strand Summative
Task(s)
1 week
2 weeks
0.5 week
Term 2
Recommended
Length of Unit
Strand
Grade 6
Grade 7
4 weeks
Number Sense &
Numeration
Measurement
Fraction, Decimal, Percent
Fractions, Decimals, Percent
Conversion of metric units, area of
parallelograms and triangles
Construction of angles and polygons,
Composite area, conversion of metric
units
Constructing lines, classifying triangles
and quadrilaterals, Congruency &
Similarity
Algebraic expressions and equations
2 weeks
2 weeks
Geometry & Spatial
Sense
3 weeks
Patterning &
Algebra
1 week
Simple algebraic expressions and
equations
Suggested Cross-Strand Summative
Task(s)
Suggested Cross-Strand Summative
Task(s)
Term 3
Recommended
Length of Unit
Strand
Grade 6
Grade 7
4 weeks
(combined
with P & A)
4 weeks
(combined
with NSN)
Number Sense &
Numeration
Operations with Decimals,
Rate and ratio
Rate and ratio
Patterning & Algebra
Table of Values, Graphing
Graphing proportional relationships
4 weeks
Measurement
Area of trapezoids
Surface Area and Volume of Right
Prisms
3 weeks
Geometry & Spatial
Sense
Building and sketching 3-D Surface
(G&S)
Surface Area and Volume of
Triangular and Rectangular Prisms
Transformational Geometry and
Cartesian Coordinate Plane (quadrant 1)
2 weeks
Data Management &
Probability
1 week
Experimental and Theoretical
Probability
Suggested Cross-Strand Summative
Task(s)
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Combined Grade 6 & Grade 7
Transformational Geometry and
Cartesian Coordinate Plane
(all 4 quadrants)
Experimental and Theoretical
Probability
Suggested Cross–Strand Summative
Task(s)
Page 29
Course of Study Sequence
Suggested
Timing
Term 1 – Number Sense & Numeration
Grade 6
Grade 7
Overall Expectations
3 weeks
6m8- read, represent, compare, and
order whole numbers to 1 000 000
6m9- solve problems involving the
multiplication and division of whole
numbers, using a variety of strategies
Nelson Grade 6
p. 36 – 47
Specific Expectations
6m13- read and print in words whole
numbers to one hundred thousand,
using meaningful contexts
6m16- solve problems that arise from
real-life situations and that relate to the
magnitude of whole numbers up to
1 000 000
p. 170 – 181
6m 24 – use estimation when solving
problems involving the addition and
subtraction of whole numbers, to help
judge the reasonableness of a solution
Overall Expectations
7m9-apply a variety of computational
strategies to solve problems involving
whole numbers
7m8-represent, compare, and order
numbers, including integers
7m9-demonstrate an understanding of
addition and subtraction of integers
Specific Expectations
7m21-solve multi-step problems arising from
real-life contexts and involving whole
numbers using a variety of tools and
strategies
7m22-use estimation when solving problems
involving operations with whole numbers, to
help judge the reasonableness of a solution
7m12- generate multiples and factors, using
a variety of tools and strategies
7m16-represent perfect squares and square
roots, using a variety of tools
6m18- use a variety of mental strategies
to solve addition, subtraction,
multiplication, and division problems
involving whole numbers
p. 184 – 195
p. 166 - 169
p. 196
6m19- solve problems involving the
multiplication and division of whole
numbers (four by four digit), using a
variety of tools and strategies
6m17- identify composite numbers and
prime numbers, and explain the
relationship between them (i.e., any
composite number can be factored into
prime factors)
6m 25 – explain the need for a standard
order for performing operations, by
investigating the impact that changing the
order has when performing a series of
operations
7m13-identify and compare integers found in
real-life contexts
7m14-represent and order integers, using a
variety of tools
7m26-add and subtract integers, using a
variety of tools
7m 23 – evaluate expressions that involve
whole numbers, including expressions that
contain brackets, using order of operations
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Combined Grade 6 & Grade 7
Page 30
Course of Study Sequence
Suggested
Timing
Term 1 – Patterning & Algebra
Grade 6
Grade 7
Overall Expectations
3 weeks
Overall Expectations
6m55- describe and represent
7m58- represent linear growth patterns
relationships in growing and shrinking
patterns (where the terms are whole
numbers)
(where the terms are whole numbers) using
concrete materials, graphs, and algebraic
expressions
7m59- model real-life linear relationships
graphically and algebraically
Nelson Grade 6
Specific Expectations
p. 2 -3
6m57- identify geometric patterns,
through investigation using concrete
materials or drawings, and represent them
numerically
p. 22 - 23
p. 4 – 6, 34
6m61- determine a term, given its term
number, by extending growing and
shrinking patterns that are generated by
adding or subtracting a constant, or
multiplying or dividing by a constant, to get
the next term
6m60- describe pattern rules (in words)
that generate patterns by adding or
subtracting a constant, or multiplying or
dividing by a constant to get the next term,
then distinguish such pattern rules from
pattern rules, given in words, that describe
the general term by referring to the term
number
Specific Expectations
7m60-represent linear growing patterns,
using a variety of tools and strategies
7m61- make predictions about linear growing
patterns, through investigation with concrete
materials
7m62-develop and represent the general
term of a linear growing pattern, using
algebraic expressions involving one operation
7m63-compare pattern rules that generate a
pattern by adding or subtracting a constant, or
multiplying or dividing by a constant, to get the
next term with pattern rules that use the term
number to describe the general term
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Combined Grade 6 & Grade 7
Course of Study Sequence
Page 31
Suggested
Timing
Grade 6
Term 1 – Data Management
Grade 7
Overall Expectations
2 weeks
6m67- collect and organize discrete or
continuous primary data and secondary
data and display the data using charts and
graphs, including continuous line graphs
6m68- read, describe, and interpret data, and
explain relationships between sets of data
Nelson Grade 6
p. 70
p. 77, 86, 87,
90 - 92
Specific Expectations
Specific Expectations
7m73 -collect data by conducting a survey or an
experiment to do with themselves, their
environment, issues in their school or community, or
content from another subject and record
observations or measurements
6m73- determine, through investigation, how
well a set of data represents a population, on
the basis of the method that was used to collect
the data
6m71- collect and organize discrete or
continuous primary data and secondary data
and display the data in charts, tables, and
graphs (including continuous line graphs) that
have appropriate titles, labels and scales (e.g.,
with appropriate scales) that suit the range and
distribution of the data, using a variety of tools
7m76-distinguish between a census and a
sample from a population
6m76- explain how different scales used on
graphs can influence conclusions drawn from
the data
p. 74- 76,
78 – 80,
88 - 89
7m71- make and evaluate convincing arguments,
based on the analysis of data
6m70-collect data by conducting a survey or
an experiment to do with themselves, their
environment, issues in their school or
community, or content from another subject,
and record observations or measurements
6m72- select an appropriate type of graph to
represent a set of data, graph the data using
technology, and justify the choice of graph
p. 84 - 85
Overall Expectations
7m70-collect and organize categorical, discrete,
or continuous primary data and secondary data
and display the data using charts and graphs,
including relative frequency tables and circle
graphs
6m75- compare, through investigation,
different graphical representations of the
same data
6m77- demonstrate an understanding of mean,
and use the mean to compare two sets of
related data, with and without the use of
technology
6m74- read, interpret, and draw conclusions
from primary data and from secondary data
presented in charts tables and graphs (including
continuous line graphs)
6m78- demonstrate, through investigation, an
understanding of how data from charts, tables,
and graphs can be used to make inferences
and convincing arguments
7m77-identify bias in data collection methods
7m74 -collect and organize categorical, discrete,
or continuous primary data and secondary data
and display the data in charts, tables, and graphs
(including relative frequency tables and circle
graphs) that have appropriate titles, labels
(appropriate units marked on the axes), and scales
(with appropriate increments) that suit the range and
distribution of the data, using a variety of tools
7m75-select an appropriate type of graph to
represent a set of data, graph the data using
technology, and justify the choice of graph
7m79-identify, through investigation, graphs that
represent data in misleading ways
7m80-determine, through investigation, the effect on
a measure of central tendency (mean, median,
mode) of adding or removing a value or values
7m78-read, interpret, and draw conclusions from
primary data and from secondary data presented in
charts, tables, and graphs (including relative
frequency tables and circle graphs)
7m81-identify and describe trends, based on the
distribution of the data presented in tables and
graphs, using informal language
7m82-make inferences and convincing arguments
that are based on the analysis of charts, tables, and
graphs
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Suggested
Combined Grade 6 & Grade 7
Course of Study Sequence
Term 2 – Number Sense & Numeration
Grade 6
Grade 7
Page 32
Timing
Overall Expectations
4 weeks
6m8- read, represent, compare, and
order decimal numbers to thousandths,
proper and improper fractions, and
mixed numbers
6m10-demonstrate an understanding of
relationships involving percent
Nelson Grade 6
Specific Expectations
p. 356 - 359
6m14- represent, compare, and order
fractional amounts with unlike
denominators, including proper and
improper fractions and mixed numbers,
using a variety of tools and using standard
fractional notation
Overall Expectations
7m8- represent, compare, and order
numbers
7m9- demonstrate an understanding of
addition and subtraction of fractions, and
apply a variety of computational strategies
to solve problems involving decimal
numbers
7m10- demonstrate an understanding of
proportional relationships using percent
Specific Expectations
7m11--represent, compare, and order
fractions, using a variety of tools
7m24-add and subtract fractions with simple
like and unlike denominators using a variety of
tools and algorithms
7m19-use a variety of mental strategies to
solve problems involving the addition and
subtraction of fractions
p. 56 – 57
p. 50 – 52
P. 268 – 269,
306 – 308
p. 274 - 277
6m11- represent, compare, and order
whole numbers and decimal numbers
from 0.001 to
1000 000, using a variety of tools
6m12- demonstrate an understanding of
place value in whole numbers and
decimal numbers from 0.001 to 1 000 000,
using a variety of tools and strategies
6m23- multiply and divide decimal
numbers by 10, 100, 1000, and 10 000
using mental strategies (use calculator to
develop the rule)
6m22- multiply whole numbers by 0.1,
0.01, and 0.001 using mental strategies
(use calculator to develop the rule)
7m25-demonstrate using concrete materials,
the relationship between the repeated addition
of fractions and the multiplication of that
fraction by a whole number
7m18-divide whole numbers by simple
fractions using concrete materials
7m11- represent, compare, and order
decimals to hundredths using a variety of tools
7m22- use estimation when solving problems
involving operations with decimals to help
judge the reasonableness of a solution
7m19-use a variety of mental strategies to
solve problems involving the addition and
subtraction of decimals
7m20-solve problems involving the
multiplication and division of decimal
numbers to thousandths by one-digit whole
numbers, using a variety of tools and strategies
7m18-divide whole numbers by decimal
numbers to hundredths, using concrete
materials
7m23-evaluate expressions that involve decimals,
including expressions that contain brackets, using
order of operations
7m21-solve multi-step problems arising from real-life
contexts and involving decimals, using a variety of
tools and strategies
SCDSB Grade 7, 8 and Combined Math Sept. Combined
2006
Grade 6 & Grade 7
Course of Study Sequence
Suggested
Timing
Term 2 – Number Sense & Numeration Continued
Grade 6
Grade 7
Page 33
Nelson Grade 6
Specific Expectations
p. 360 – 361
370 – 371
6m27 – determine and explain, through
investigation using concrete materials,
drawings, and calculators, the
relationships among fractions (i.e. with
denominators of 2, 4, 5, 10, 20, 25, 50, and
100), decimal numbers, and percents
p. 372 - 373
6m15- estimate quantities using
benchmarks of 10%, 25%, 50%, 75%,
and 100%
Specific Expectations
7m27-determine, through investigation, the
relationships among fractions, decimals,
percents and ratios
7m15- select and justify the most appropriate
representation of a quantity (i.e. fraction,
decimal, percent) for a given context
7m22-use estimation when solving problems
involving percents to help judge the
reasonableness of a solution
7m28-solve problems that involve
determining whole number percents, using
a variety of tools
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Suggested
Timing
Overall Expectations
3 weeks
Page 34
Combined Grade 6 & Grade 7
Course of Study Sequence
Term 2 – Measurement
Grade 6
6m29-estimate, measure and record
quantities, using the metric measurement
Grade 7
Overall Expectations
7m31- report on research into real-life
applications of area measurements
system
6m30-determine the relationships among
units and measurable attributes, including
the area of a parallelogram, and the area of
a triangle
Nelson Grade 6
p. 142 – 143
152 - 153
p. 144 – 145
146 - 147
p. 242
Specific Expectations
Specific Expectations
6m31- demonstrate an understanding of the
relationship between estimated and precise
measurements, and determine and justify
when each kind is appropriate
6m32 – estimate, measure, and record
length, area, and mass, using the metric
measurement system
6m33- select and justify the appropriate
metric unit (i.e., millimeter, centimeter,
decimeter, metre, decameter, kilometer) to
measure length or distance in a given reallife situation
7m35-solve problems that require
conversion between metric units of measure
6m34- solve problems requiring conversion
from larger to smaller metric units
6m35- construct a rectangle, a square, a
triangle and a parallelogram, using a variety
of tools
Review – area
6m36- determine, through investigation using
a variety of tools and strategies, the
relationship between the area of a rectangle
and the areas of parallelograms and
triangles, by decomposing and composing
p. 245 - 247
7m32- determine the relationships among
units and measurable attributes
Review - perimeter
7m36-solve problems that require
conversion between metric units of area
7m39-estimate and calculate the area of
composite two-dimensional shapes by
decomposing into shapes with known area
relationships
6m37- develop the formulas for the area of a
parallelogram [i.e., Area of parallelogram =
base x height] and the area of a triangle [i.e.,
Area of triangle = (basexheight ) ], using the area
2
p. 250 - 253
relationships among rectangles,
parallelograms, and triangles
6m38- solve problems involving the
estimation and calculation of the areas of
triangles and the areas of parallelograms
7m33-research and report on real-life
applications of area measurements
6m39- determine, using concrete materials,
the relationship between units used to
measure area (i.e., square centimeter, square
metre), and apply the relationship to solve
problems that involve conversions from
square metres to square centimetres
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 35
Combined Grade 6 & Grade 7
Course of Study Sequence
Suggested
Timing
Term 2 – Geometry and Spatial Sense
Grade 6
Grade 7
Overall Expectations
2 weeks
6m43- classify and construct polygons and
angles
Overall Expectations
7m43-construct related lines, and classify
triangles, and quadrilaterals
7m44- develop an understanding of
similarity, and distinguish similarity and
congruence
Nelson Grade 6
p. 210 - 211
Specific Expectations
Specific Expectations
6m48- measure and construct angles up to
7m46-construct related lines (i.e. parallel;
0
180 using a protractor, and classify them as
acute, right obtuse, or straight angles
0
0
perpendicular; intersecting at 30 , 45 , and
0
60 ), using angle properties and a variety of
tools and strategies
7m48-construct angle bisectors and
perpendicular bisectors, using a variety of
tools and strategies and represent equal
angles and equal lengths using mathematical
notation
7m47- sort and classify triangles and
quadrilaterals by geometric properties related
to symmetry, angles, and sides, through
investigation using a variety of tools and
strategies.
p. 224 - 225
6m46- sort and classify quadrilaterals by
geometric properties related to symmetry,
angles, and sides, through investigation using
a variety of tools and strategies
p. 222 – 223
6m47 – sort polygons according to the
number of lines of symmetry and the order
of rotational symmetry, through investigation
using a variety of tools
p. 218 - 221
6m49- construct polygons using a variety of
tools, given angle and side measurements
7m50-identify through investigation, the
minimum side and angle information (i.e.
side-side-side; side-angle-side; angle-sideangle) needed to describe a unique triangle
( to create congruent triangles).
7m53-distinguish between and compare
similar shapes and congruent shapes, using
a variety of tools and strategies
7m51-determine, through investigation using
a variety of tools, relationships among area,
perimeter, corresponding side lengths, and
corresponding angles of congruent shapes.
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 36
Combined Grade 6 & Grade 7
Course of Study Sequence
Suggested
Timing
Grade 6
Term 2 – Patterning & Algebra
Grade 7
Overall Expectations
3 weeks
Overall Expectations
7m58- represent linear growth patterns (where
6m56- use variables in simple algebraic
expressions and equations to describe
the terms are whole numbers) using concrete
materials, graphs, and algebraic expressions
relationships
7m59- model real-life linear relationships
graphically and algebraically, and solve simple
algebraic equations using a variety of
strategies, including inspection and guess and
check
Nelson Grade 6
Specific Expectations
p. 12 – 13,
20 – 21,
26 - 27
6m63- demonstrate an understanding of
different ways in which variables are used
7m66-translate phrases describing simple
mathematical relationships into algebraic
expressions using concrete materials
6m65- solve problems that use two or
three symbols or letters as variables to
represent different unknown quantities
7m67-evaluate algebraic expressions by
substituting natural numbers for the variables
6m64- identify, through investigation, the
quantities in an equation that vary and
those that remain constant
p. 24 - 25
6m66- determine the solution to a simple
equation with one variable of tools and
strategies
Specific Expectations
7m68 – make connections between evaluating
algebraic expressions and determine the term in a
pattern using the general term
7m69-solve linear equations of the form
ax = c or c = ax and ax + b = c or variations such
as b + ax = c and
c = bx + a (where a, b, and c are natural numbers)
by modeling with concrete materials, by
inspection, or by guess and check, with and
without the aid of a calculator
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Suggested
Timing
Combined Grade 6 & Grade 7
Course of Study Sequence
Term 3 – Number Sense & Numeration
Grade 6
Grade 7
Overall Expectations
4 weeks
(combined
with
patterning
and algebra)
6m9- solve problems involving the addition
and subtraction of decimal numbers to
thousandths, using a variety of strategies
6m10-demonstrate an understanding of
relationships involving ratio and unit rate
Nelson Grade 6
Specific Expectations
p. 362 – 365
374 - 375
Page 37
6m26- represent ratios found in real-life
contexts using concrete materials, drawings,
Overall Expectations
7m10 – demonstrate an understanding of
proportional relationships using ratio and
rate
Specific Expectations
7m29 -demonstrate an understanding of rate
as a comparison, or ratio, of two
p. 120 - 129
p. 270- 271,
283 – 286,
294 – 303,
310 - 311
Suggested
Timing
4 weeks
(combined
with number
sense and
numeration)
p. 14 - 16
and standard fractional notation
6m28- represent relationships using unit
rates
6m20-add and subtract decimal numbers to
thousandths, using concrete materials,
estimation, algorithms, and calculators
6m24- use estimation when solving
problems involving the addition and
subtraction of decimals, to help judge the
reasonableness of a solution
6m21 multiply and divide decimal numbers
to tenths by whole numbers, using concrete
materials, estimation, algorithms, and
calculators
measurements with different units
7m30-solve problems involving the
calculation of unit rates
Term 3 – Patterning & Algebra
Grade 6
Grade 7
Overall Expectations
6m55- describe and represent
relationships in growing and shrinking
patterns
Overall Expectations
7m59- model real-life linear relationships
graphically and algebraically
Specific Expectations
Specific Expectations
6m58- make table of values, for growing
patterns given pattern rules, in words, then
list the ordered pairs (with the first
coordinate representing the term number and
the second coordinate representing the term)
and plot the points in the first quadrant,
using a variety of tools
6m59- determine the term number of a given
term in a growing pattern that is represented
by a pattern rule in words, a table of values, or
a graph
7m64-model real-life relationships involving
constant rates where the initial condition
starts at 0, through investigation using tables
of values and graphs
7m65-model real-life relationships involving
constant rates using algebraic equations
with variables to represent the changing
quantities in the relationship
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 38
Combined Grade 6 & Grade 7
Course of Study Sequence
Suggested
Timing
Term 3 – Measurement
Grade 6
Overall Expectations
4 weeks
Nelson Grade 6
p. 322,
336 – 340
6m30- determine the relationships among
units and measurable attributes, including
the volume of a triangular prism
6m44 – sketch three-dimensional figures,
and construct three-dimensional figures
from drawings; (G&S)
Specific Expectations
6m50- build three-dimensional models
using connecting cubes, given isometric
Grade 7
Overall Expectations
7m32- determine the relationships among
units and measurable attributes, including
the volume of a right prism, and the area of
a trapezoid
Specific Expectations
7m37-determine, through investigation using
a variety of tools and strategies, the
p. 323,
334 - 335
p. 324 - 325
p. 326 - 327
p. 328
330 - 331
sketches or different views (i.e., top, side,
front) of the structure (G&S)
relationship for calculating the area of a
trapezoid, and generalize to develop the
formula
6m51- sketch, using a variety of tools,
isometric perspectives and different views
(i.e., top, side, front) of three-dimensional
figures built with interlocking cubes (G&S)
Area = (sum of lengths of parallel sides  height)  2
6m41- determine, through investigation using
a variety of tools and strategies, the surface
area of rectangular and triangular prisms
6m42- solve problems involving the
estimation and calculation of the surface
area of triangular and rectangular prisms
6m40- determine, through investigation using
a variety of tools and strategies, the
relationship between the height, the area of
the base, and the volume of a triangular
prism, and generalize to develop the formula
6m42-solve problems involving the
estimation and calculation of the volume of
triangular and rectangular prisms
6m32- estimate, measure, and record
capacity, and volume, using the metric
system
7m38-solve problems involving the
estimation and calculation of the area of a
trapezoid
7m49- investigate, using concrete materials,
the angles between the faces of a prism,
and identify right prisms
7m41--determine, through investigation using
a variety of tools, the surface area of right
prisms
7m42--solve problems that involve the
surface area of right prisms
7m40-determine, through investigation using
a variety of tools and strategies, the
relationship between the height, the area of
the base, and the volume of right prisms
with simple polygonal bases and generalize to
develop the formula
(i.e. Volume = area of base  height)
7m17-explain the relationship between
exponential notation and the measurement
of area and volume
7m42-solve problems that involve the volume
of right prisms and that require conversion
between metric measures of capacity and
volume (i.e. millilitres and cubic centimetres)
7m34-sketch different polygonal prisms that
share the same volume
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 39
Combined Grade 6 & Grade 7
Course of Study Sequence
Suggested
Timing
Term 3 – Geometry and Spatial Sense
Grade 6
Grade 7
Overall Expectations
3.5 weeks
Nelson Grade 6
p. 72 - 73
6m45- describe location in the first
quadrant of a coordinate system, and
rotate two-dimensional shapes
Specific Expectations
6m52- explain how a coordinate system
represents location, and plot points in the
first quadrant of a Cartesian plane
Overall Expectations
7m45- describe location in the four
quadrants of a coordinate system, dilatate
two-dimensional shapes, and apply
transformations to create and analyse
designs
Specific Expectations
7m54- plot points using all four quadrants of
the Cartesian coordinate plane
p. 416 - 425
6m54- create and analyse designs made by
reflecting, translating, and/or rotating a
shape, or shapes, by 90
0
or 180
0
6m53- identify, perform, and describe, through
investigation using a variety of tools,
0
0
rotations of 90 and 180 clockwise and
counterclockwise, with the centre of rotation
inside or outside the shape
p. 432 - 433
6m62- extend and create repeating patterns
that result from rotations, through
investigation using a variety of tools
7m56-create and analyse designs involving
translations, reflections, dilatations, and/or
simple rotations of two-dimensional shapes
using a variety of tools and strategies
7m55-identify, perform, and describe
dilatations (i.e. enlargements and reductions),
through investigation using a variety of tools
7m52-demonstrate an understanding that
enlarging or reducing two-dimensional
shapes creates similar shapes
7m 53 – distinguish between and compare
similar shapes and congruent shapes, using
a variety of tools and strategies (dilatations
create similar shapes that translations,
rotations, reflections generate congruent
shapes)
7m57-determine, through investigation using
a variety of tools, polygons or combinations of
polygons that tile a plane, and describe the
transformation(s) involved
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 40
Combined Grade 6 & Grade 7
Course of Study Sequence
Suggested
Timing
2 weeks
Nelson Grade 6
p. 392 - 393
Term 3 – Data Management & Probability
Grade 6
Grade 7
Overall Expectations
Overall Expectations
6m69- determine the theoretical probability
of an outcome in a probability experiment,
and us it to predict the frequency of the
outcome
7m72-compare experimental probabilities
with the theoretical probability of an
outcome involving two independent events
Specific Expectations
6m80- represent the probability of an event
(i.e., the likelihood that the event will occur),
using a value from the range of 0 (never
happens or impossible) to 1 (always happens
or certain)
Specific Expectations
7m83-research and report on real-world
applications of probabilities expressed in
fractions, decimal, and percent form
p. 390 – 391,
400 - 403
p. 394 - 396
6m79- express theoretical probability as a
ratio of the number of favourable outcomes to
the total number of possible outcomes, where
all outcomes are equally likely
6m81- predict the frequency of an outcome
of a simple probability experiment or game,
by calculating and using the theoretical
probability of that outcome
7m85-represent in a variety of ways all the
possible outcomes of a probability
experiment involving two independent
events (i.e. one event does not affect the
other event), and determine the theoretical
probability of a specific outcome involving
two independent events
7m86-perform a simple probability experiment
involving two independent events, and
compare the experimental probability with
the theoretical probability of a specific
outcome
7m84-make predictions about a population
when given a probability
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 41
Grade 7/8 Mathematics Course of Study – Sequence of Units
Term 1
Recommende
d Length of
Unit
Strand
1 week
3 weeks
Number Sense &
Numeration
3 weeks
Patterning &
Algebra
Data Management
2 weeks
0.5 week
Grade 7
Grade 8
Familiarize students to new textbooks.
Review to activate prior knowledge
Whole numbers, decimals, factoring,
multiples, square roots, order of
operations,
Integers
Linear and number patterns, table of
values
Familiarize students to new textbooks.
Review to activate prior knowledge
Whole numbers, decimals, factoring,
exponents, powers, square roots, order
of operations, integers
Data Collection, graphing, interpreting,
central tendency
Suggested Cross-Strand Summative
Task(s)
Data Collection, graphing, interpreting,
central tendency
Suggested Cross-Strand Summative
Task(s)
Linear and number patterns,
Term 2
Recommended
Length of Unit
Strand
Grade 7
Grade 8
4 weeks
Number Sense &
Numeration
Measurement
Fractions, Decimals, Percent
Fractions, Decimals, Percent
Composite area, conversion of metric
units
Constructing lines, classifying triangles
and quadrilaterals, Congruency &
Similarity
Algebraic expressions and equations
Conversion of metric units,
Circumference and area of a circle
Constructing circles, angle
properties, similarity
Algebraic expressions and equations
Suggested Cross-Strand Summative
Task(s)
Suggested Cross-Strand Summative
Task(s)
2 weeks
2 weeks
Geometry & Spatial
Sense
3 weeks
Patterning & Algebra
1 week
Term 3
Recommende
d Length of
Unit
Strand
Grade 7
Grade 8
4 weeks
(with P & A)
4 weeks
(with NSN)
4 week
Number Sense &
Numeration
Patterning & Algebra
Rate and ratio
Rates and Proportions
Graphing proportional relationships
Solving equations
Linear Relationships
Surface Area & Volume of Cylinder
4 weeks
Geometry & Spatial
Sense
2 weeks
Data Management &
Probability
Measurement
Surface Area & Volume of Right
Prisms, Area of Trapezoids
Transformational Geometry and
Cartesian Coordinate Plane (all 4
quadrants)
Experimental and Theoretical
Probability
1 week
Suggested Cross–Strand Summative
Task(s)
SCDSB Grade 7, 8 and Combined Math Sept.Combined
2006
Grade 7 & Grade
8
Transformational Geometry and
Cartesian Coordinate Plane (all 4
quadrants)
Pythagorean Theorem
Theoretical and Experimental
Probability
Suggested Cross-Strand Summative
Task(s)
Page 42
Course of Study Sequence
Suggested
Timing
3 weeks
Term 1 – Number Sense & Numeration
Grade 7
Grade 8
Overall Expectations
Overall Expectations
7m8-represent, compare, and order numbers,
including integers
8m8-represent, compare, and order
equivalent representations of numbers,
including those involving positive exponents
7m9- demonstrate an understanding of
addition and subtraction of integers, and
apply a variety of computational strategies to
solve problems involving whole numbers
Specific Expectations
8m9-solve problems involving whole
numbers, and integers, using a variety of
computational strategies
Specific Expectations
7m21-solve multi-step problems arising from
real-life contexts and involving whole numbers
using a variety of tools and strategies
8m16-solve multi-step problems arising from
real-life contexts and involving whole numbers,
using a variety of tools and strategies
7m22-use estimation when solving problems
8m18-use estimation when solving problems
involving operations with whole numbers, to help
judge the reasonableness of a solution
involving operations with whole numbers to help
judge the reasonableness of a solution
7m12- generate multiples and factors, using a
variety of tools and strategies
8m15-determine common factors and
common multiples using the prime
factorization of numbers
8m11-express repeated multiplication using
exponential notation
7m16-represent perfect squares and square
roots, using a variety of tools
8m25-estimate, and verify using a calculator, the
positive square roots of whole numbers, and
distinguish between whole numbers that have
whole-number square roots (i.e. perfect square
numbers) and those that do not
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 43
Combined Grade 7 & Grade 8
Course of Study Sequence
Suggested
Timing
Term 1 – Number Sense & Numeration Continued
Grade 7
Grade 8
Specific Expectations
Specific Expectations
7m13-identify and compare integers found in
real-life contexts
7m14-represent and order integers, using a
variety of tools
7m26-add and subtract integers, using a
variety of tools
8m22-solve problems involving adding and
subtracting with integers using a variety of
tools
8m18-use estimation when solving problems
involving operations with integers to help judge
the reasonableness of a solution
8m21-represent the multiplication and
division of integers, using a variety of tools
8m18-use estimation when solving problems
involving operations with integers to help judge
the reasonableness of a solution
7m23-evaluate expressions that involve whole
numbers including expressions that contain
brackets, using order of operations
8m22-solve problems involving multiplication
and division with integers, using a variety of
tools
8m23-evaluate expressions that involve
integers including expressions that contain
brackets and exponents, using order of
operations
8m12- represent whole numbers in expanded
form using powers of ten
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 44
Combined Grade 7 & Grade 8
Course of Study Sequence
Suggested
Timing
Term 1 – Patterning and Algebra
Grade 7
Grade 8
Overall Expectations
3 weeks
7m58- represent linear growth patterns
(where the terms are whole numbers) using
concrete materials, graphs, and algebraic
expressions
7m59-model real-life linear relationships
graphically and algebraically,
Specific Expectations
Overall Expectations
8m54-represent linear growing patterns
(where the terms are whole numbers) using
graphs, algebraic expressions and equations
8m55-model linear relationships graphically
and algebraically,
Specific Expectations
8m59-describe different ways in which algebra
can be used in real-life situations
7m60- represent linear growing patterns,
using a variety of tools and strategies
7m61- make predictions about linear growing
patterns, through investigation with concrete
materials
8m60 – model linear relationships using table of
values, graphs, and equations
7m62- develop and represent the general term
of a linear growing pattern, using algebraic
expressions involving one operation
7m63- compare pattern rules that generate a
pattern by adding or subtracting a constant, or
multiplying or dividing by a constant, to get the
next term with pattern rules that use the term
number to describe the general term
8m56 – represent, through investigation with
concrete materials, the general term of a linear
pattern, using one or more algebraic
expressions
8m57-represent linear patterns graphically
(i.e. make a table of values that shows the term
number and the term, and plot the coordinates
on a graph), using a variety of tools
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 45
Combined Grade 7 & Grade 8
Course of Study Sequence
Term 1 – Data Management
Suggested
Timing
Grade 7
Overall Expectations
2 weeks
Grade 8
Overall Expectations
7m70- collect and organize categorical, discrete,
or continuous primary data and secondary data
and display the data using charts and graphs,
including relative frequency tables and circle
graphs
8m65-collect and organize categorical, discrete, or
continuous primary data and secondary data and
display the data using charts and graphs,
including frequency tables with intervals,
histograms, and scatter plots
7m71-make and evaluate convincing arguments,
based on the analysis of data
8m66- apply a variety of data management tools
and strategies to make convincing arguments
about data
Specific Expectations
Specific Expectations
7m73-collect data by conducting a survey or
an experiment to do with themselves, their
environment, issues in their school or
community, or content from another subject and
record observations or measurements
7m76-distinguish between a census and a
sample from a population
7m77- identify bias in data collection methods
8m68-collect data by conducting a survey or
an experiment to do with themselves, their
environment, issues in their school or
community, or content from another subject, and
record observations or measurements
8m72-explain the relationship between a
census, a representative sample, sample
size, and a population
7m74-collect and organize categorical,
discrete, or continuous primary data and
secondary data and display the data in charts,
tables, and graphs (including relative
frequency tables and circle graphs) that have
appropriate titles, labels (appropriate units
marked on the axes), and scales (with
appropriate increments) that suit the range and
distribution of the data, using a variety of tools
7m75-select an appropriate type of graph to
represent a set of data, graph the data using
technology, and justify the choice of graph
7m79-identify, through investigation, graphs
that represent data in misleading ways
7m80-determine, through investigation, the
effect on a measure of central tendency (mean,
median, mode) of adding or removing a value
or values
7m78-read, interpret, and draw conclusions
from primary data and from secondary data
presented in charts, tables, and graphs
(including relative frequency tables and circle
graphs)
7m81-identify and describe trends, based on
the distribution of the data presented in tables
and graphs, using informal language
7m82-make inferences and convincing
arguments that are based on the analysis of
charts, tables, and graphs
8m70-collect and organize categorical,
discrete, or continuous primary data and
secondary data, and display the data in
charts, tables, and graphs (including
histograms and scatter plots) that have
appropriate titles, labels (appropriate units
marked on the axes) and scales (with
appropriate increments) that suit the range and
distribution of the data, using a variety of tools
8m69-organize into intervals a set of data that
is spread over a broad range
8m71-select an appropriate type of graph to
represent a set of data, graph the data using
technology, and justify the choice of graph
8m75-demonstrate an understanding of the
appropriate uses of bar graphs and
histograms by comparing their characteristics
8m74-determine, through investigation the
appropriate measure of central tendency (i.e.
mean, median, or mode) needed to compare
sets of data
8m73-read, interpret, and draw conclusions
from primary data and from secondary data,
presented in charts, tables, and graphs
(including frequency tables with intervals,
histograms and scatter plots)
8m77-identify and describe trends, based on
the rate of change of data from tables and
graphs, using informal language
8m78-make inferences and convincing
arguments that are based on the analysis of
charts, tables, and graphs
Combined Grade 7 & Grade 8
Course of Study Sequence
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Suggested
Timing
Term 2 – Number Sense & Numeration
Grade 7
Grade 8
Overall Expectations
4 weeks
Page 46
7m8-represent, compare, and order numbers
7m9-demonstrate an understanding of
addition and subtraction of fractions, and
apply a variety of computational strategies to
solve problems involving decimal numbers
Overall Expectations
8m8-represent, compare, and order
equivalent representations of numbers
8m9-solve problems involving, decimal
numbers, and fractions using a variety of
computational strategies
7m10 – demonstrate an understanding of
proportional relationships using percent
Specific Expectations
7m11-represent, compare, and order
fractions, using a variety of tools
7m24-add and subtract fractions with simple
like and unlike denominators using a variety of
tools and algorithms
7m19-use a variety of mental strategies to
solve problems involving the addition and
subtraction of fractions
Specific Expectations
8m13-represent, compare, and order rational
numbers (i.e. positive and negative fractions)
8m20-solve problems involving addition,
subtraction with simple fractions
8m18-use estimation when solving problems
involving operations with fractions to help judge
the reasonableness of a solution
7m25-demonstrate using concrete materials, the
relationship between the repeated addition of
fractions and the multiplication of that fraction
by a whole number
8m19-represent the multiplication of
fractions, using a variety of tools and strategies
7m18-divide whole numbers by simple
fractions using concrete materials
8m20-solve problems involving multiplication
with simple fractions
8m19-represent the division of fractions using
a variety of tools and strategies
7m11-represent, compare, and order
decimals to hundredths using a variety of tools
8m20-solve problems involving division with
simple fractions
8m13-represent, compare, and order rational
numbers (i.e. decimals to thousandths)
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 47
Combined Grade 7 & Grade 8
Course of Study Sequence
Suggested
Timing
Term 2 – Number Sense & Numeration Continued
Grade 7
Grade 8
Specific Expectations
Specific Expectations
7m22-use estimation when solving problems
involving operations with decimals to help judge
the reasonableness of a solution
8m18-use estimation when solving problems
involving operations with decimals to help judge
the reasonableness of a solution
7m19-use a variety of mental strategies to
solve problems involving the addition and
subtraction of decimals
8m24-multiply and divide decimal numbers
by various powers of ten
7m20-solve problems involving the
multiplication and division of decimal
numbers to thousandths by one-digit whole
numbers, using a variety of tools and strategies
7m18-divide whole numbers by decimal
numbers to hundredths, using concrete materials
7m23-evaluate expressions that involve
decimals, including expressions that contain
brackets, using order of operations
7m21-solve multi-step problems arising from
real-life contexts and involving decimals, using a
variety of tools and strategies
7m27-determine, through investigation, the
relationships among fractions, decimals,
percents and ratios
8m14-translate between equivalent forms of a
number (i.e. fractions, decimals, percents)
7m15-select and justify the most appropriate
representation of a quantity (i.e. fraction,
decimal, percent) for a given context
7m22- use estimation when solving problems
involving percents to help judge the
reasonableness of a solution
8m18-use estimation when solving problems
involving percents to help judge the
reasonableness of a solution
7m28-solve problems that involve determining
whole number percents, using a variety of
tools
8m28-solve problems involving percent that
arise from real-life contexts
8m17-solve problems involving percents
expressed to one decimal place and wholenumber percents greater than 100
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 48
Combined Grade 7 & Grade 8
Course of Study Sequence
Term 2 – Measurement
Suggested
Timing
Grade 7
Overall Expectations
2 weeks
7m31- report on research into real-life
applications of area measurements
Grade 8
Overall Expectations
8m31-determine the relationships among
units and measurable attributes, including
the area of a circle
7m32 – determine the relationships among
units and measurable attributes
Specific Expectations
7m35-solve problems that require conversion
between metric units of measure
Specific Expectations
8m44- construct a circle, given its centre and radius,
or its centre and a point on the circle, or three points
on the circle (G&S)*
8m34- measure the circumference, radius,
and diameter of circular objects, using concrete
materials
Review – perimeter
Review – area
8m35-determine, through investigation using a
variety of tools and strategies, the relationships
7m36-solve problems that require conversion
between metric units of area (ie. Square
centimeters and square metres)
7m39-estimate and calculate the area of
composite two-dimensional shapes by
decomposing into shapes with known area
relationships
for calculating the circumference and the area
of a circle, and generalize to develop the
formulas [i.e. Circumference of a circle =  
diameter; Area of a circle =

2
 (radius) ]
8m33- solve problems that require
conversions involving metric units of area
(ie. Square centimeters and square metres)
8m36-solve problems involving the estimation
and calculation of the circumference and the
area of a circle
7m33-research and report on real-life
applications of area measurements
* (G&S) expectation is from Geometry and Spatial Sense strand
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 49
Combined Grade 7 & Grade 8
Course of Study Sequence
Suggested
Timing
Term 2 – Geometry and Spatial Sense
Grade 7
Grade 8
Overall Expectations
2 weeks
7m43-construct related lines, and classify
triangles, quadrilaterals
7m44-develop an understanding of similarity,
and distinguish similarity and congruence
Specific Expectations
7m46-construct related lines (i.e. parallel;
Overall Expectations
8m40-demonstrate an understanding of the
geometric properties of quadrilaterals and circles
and the application of geometric properties in the
real world;
8m41-develop geometric relationships
involving lines, triangles, and solve problems
involving lines and triangles;
Specific Expectations
8m45-investigate and describe applications of
geometric properties in the real world
0
0
perpendicular; intersecting at 30 , 45 , and
0
60 ), using angle properties and a variety of
tools and strategies
7m48-construct angle bisectors and
perpendicular bisectors, using a variety of
tools and strategies and represent equal angles
and equal lengths using mathematical notation
7m47-sort and classify triangles and
quadrilaterals by geometric properties related
to symmetry, angles, and sides, through
investigation using a variety of tools and
strategies.
7m50-identify through investigation, the
minimum side and angle information (i.e.
side-side-side; side-angle-side; angle-sideangle) needed to describe a unique triangle (to
create congruent triangles)
8m47-determine through investigation using a
variety of tools and strategies, the angle
relationships for intersecting lines and for
parallel lines and transversals, and the sum of
the angles of a triangle
8m48-solve angle-relationship problems
involving triangles, intersecting lines, and
parallel lines and transversals
8m43-sort and classify quadrilaterals by
geometric properties, including those based on
diagonals, through investigation using a variety
of tools
8m46-determine, through investigation using a
variety of tools, relationships among area,
perimeter, corresponding side lengths, and
corresponding angles of similar shapes
7m53-distinguish between and compare similar
shapes and congruent shapes, using a variety
of tools and strategies
7m51-determine, through investigation using a
variety of tools, relationships among area,
perimeter, corresponding side lengths, and
corresponding angles of congruent shapes
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 50
Combined Grade 7 & Grade 8
Course of Study Sequence
Suggested
Timing
Term 2 – Patterning and Algebra
Grade 7
Grade 8
Overall Expectations
3 weeks
7m58- represent linear growth patterns
(where the terms are whole numbers) using
concrete materials, graphs, and algebraic
expressions
7m59-model real-life linear relationships
graphically and algebraically, and solve
simple algebraic equations using a variety of
strategies, including inspection and guess
and check
Specific Expectations
Overall Expectations
8m54-represent linear growing patterns
(where the terms are whole numbers) using
graphs, algebraic expressions and equations
8m55-model linear relationships graphically
and algebraically, and solve and verify
algebraic equations, using a variety of
strategies, including inspection, guess and
check, and using a “balance” model
Specific Expectations
7m66-translate phrases describing simple
mathematical relationships into algebraic
expressions using concrete materials
7m67-evaluate algebraic expressions by
substituting natural numbers for the variables
7m68-make connections between evaluating
algebraic expressions and determine the
term in a pattern using the general term
7m69-solve linear equations of the form
ax = c or c = ax and ax + b = c or variations such
as b + ax = c and c = bx + a (where a, b, and c
are natural numbers) by modeling with concrete
materials, by inspection, or by guess and check,
with and without the aid of a calculator
8m61-translate statements describing
mathematical relationships into algebraic
expressions and equations
8m62-evaluate algebraic expressions with up
to three terms, by substituting fractions,
decimals, and integers for the variables
8m58-determine a term, given its term
number, in a linear pattern that is represented
by a graph or an algebraic equation
8m63-make connections between solving
equations and determining the term number in
a pattern, using the general term
8m64-solve and verify linear equations
involving a one-variable term and having
solutions that are integers, by using inspection,
guess and check, and a “balance” model
Combined Grade 7 & Grade 8
of Study Sequence
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Course
Suggested
Timing
Term 3 – Number Sense & Numeration
Grade 7
Grade 8
Overall Expectations
4 weeks
(combined
with P & A)
Page 51
7m10-demonstrate an understanding of
proportional relationships using percent,
ratio and rate
Specific Expectations
7m29-demonstrate an understanding of rate as
a comparison, or ratio, of two measurements
with different units
7m30-solve problems involving the calculation
of unit rates
Overall Expectations
8m10-solve problems by using proportional
reasoning in a variety of meaningful contexts
Specific Expectations
8m29-solve problems involving rates
8m27-solve problems involving proportions,
using concrete materials, drawings, and
variables.
Term 3 – Patterning and Algebra
Suggested
Timing
Grade 7
Overall Expectations
4 weeks
(combined
with Number
Sense and
Numeration)
7m59-model real-life linear relationships
graphically and algebraically
Specific Expectations
7m64-model real-life relationships involving
constant rates where the initial condition
starts at 0, through investigation using tables of
values and graphs
7m65-model real-life relationships involving
constant rates using algebraic equations with
variables to represent the changing quantities in
the relationship
Grade 8
Overall Expectations
8m55-model linear relationships graphically
and algebraically
Specific Expectations
8m60-model linear relationships using table
of values, graphs, and equations, through
investigation using a variety of tools
8m26-identify and describe real-life situations
involving two quantities that are directly
proportional
8m76-compare two attributes or
characteristics, using a scatter plot, and
determine whether or not the scatter plot
suggests a relationship
8m79-compare two attributes or
characteristics, using a variety of data
management tools and strategies
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Suggested
Timing
Combined Grade 7 & Grade 8
Course of Study Sequence
Term 3 – Measurement
Grade 7
Overall Expectations
4 weeks
Page 52
7m32-determine the relationships among
units and measurable attributes, including
the volume of a right prism and the area of a
trapezoid
Grade 8
Overall Expectations
8m30-research, describe, and report on
applications of volume and capacity
measurement
8m31-determine the relationships among
units and measurable attributes, including
the volume of a cylinder
Specific Expectations
7m37- determine, through investigation using a
variety of tools and strategies, the relationship
for calculating the area of a trapezoid, and
generalize to develop the formula
Area = (sum of lengths of parallel sides  height)  2
7m38- solve problems involving the estimation
and calculation of the area of a trapezoid
Specific Expectations
8m51-determine, through investigation using
concrete materials, the relationship between the
number of faces, edges, and vertices of a polyhedron
(i.e. number of faces + number of vertices =
number of edges + 2)
7m49 – investigate, using concrete materials,
the angles between the faces of a prism, and
identify right prisms
7m41-determine, through investigation using a
variety of tools, the surface area of right
prisms
7m42-solve problems that involve the surface
area of right prisms
7m40-determine, through investigation using a
variety of tools and strategies, the relationship
between the height, the area of the base, and
the volume of right prisms with simple polygonal
bases and generalize to develop the formula
(i.e. Volume = area of base  height)
8m38-determine through investigation using
concrete materials, the surface area of a
cylinder
8m39-solve problems involving the surface
area of cylinders using a variety of strategies
8m37-determine through investigation using a
variety of tools and strategies, the relationship
between the area of the base and height and
the volume of a cylinder, and generalize to
develop the formula
(i.e. Volume = area of base  height)
7m17-explain the relationship between
exponential notation and the measurement of
area and volume
7m42-solve problems that involve the volume
of right prisms and that require conversion
between metric measures of capacity and
volume (i.e. millilitres and cubic centimetres)
7m34-sketch different polygonal prisms that
share the same volume
8m39-solve problems involving the volume of
cylinders, using a variety of strategies
8m33-solve problems that require conversions
involving metric units of volume and capacity
(i.e. cubic centimetres and cubic metres;
millilitres and cubic centimetres)
8m32-research, describe, and report on
applications of volume and capacity
measurement
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 53
Combined Grade 7 & Grade 8
Course of Study Sequence
Suggested
Timing
Term 3 – Geometry and Spatial Sense
Grade 7
Grade 8
Overall Expectations
Overall Expectations
4 weeks
7m45-describe location in the four quadrants
of a coordinate system, dilatate twodimensional shapes, and apply
transformations to create and analyse
designs
Specific Expectations
8m42-represent transformations using the
Cartesian coordinate plane, and make
connections between transformations and
the real world
Specific Expectations
Review – plotting points in four quadrants
7m54-plot points using all four quadrants of
the Cartesian coordinate plane
7m56-create and analyse designs involving
translations, reflections, dilatations, and/or
simple rotations of two-dimensional shapes
using a variety of tools and strategies
8m53-identify through investigation, real-world
movements that are translations, reflections,
and rotations
7m55-identify, perform, and describe
dilatations (i.e. enlargements and reductions),
through investigation using a variety of tools
7m52-demonstrate an understanding that
enlarging or reducing two-dimensional shapes
creates similar shapes
8m52-graph the image of a point, or set of
points, on the Cartesian coordinate plane after
applying a transformation to the original point(s)
(i.e. translation; reflection in the x-axis, the yaxis, or the angle bisector of the axes that
passes through the first and third quadrants;
0
0
0
rotation of 90 , 180 , or 270 about the origin)
7m53-distinguish between and compare similar
shapes and congruent shapes, using a variety
of tools and strategies (dilatations create
similar shapes and that translations,
rotations, reflections generate congruent
shapes)
7m57-determine, through investigation using a
variety of tools, polygons or combinations of
polygons that tile a plane, and describe the
transformation(s) involved
8m49-determine the Pythagorean relationship,
through investigation using a variety of tools
and strategies
8m50-solve problems involving right triangles
geometrically, using the Pythagorean
relationship
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 54
Combined Grade 7 & Grade 8
Course of Study Sequence
Term 3 – Probability
Suggested
Timing
Grade 7
Grade 8
Overall Expectations
Overall Expectations
2 weeks
7m72-compare experimental probabilities
with the theoretical probability of an outcome
involving two independent events
Specific Expectations
8m67-use probability models to make
predictions about real-life events
Specific Expectations
7m83-research and report on real-world
applications of probabilities expressed in
fractions, decimal, and percent form
7m85-represent in a variety of ways all the
possible outcomes of a probability
experiment involving two independent events
(i.e. one event does not affect the other event),
and determine the theoretical probability of a
specific outcome involving two independent
8m80-compare, through investigation, the
theoretical probability of an event (i.e. the ratio
of the number of ways a favourable outcome can
occur compared to the total number of possible
outcomes) with experimental probability, and
explain why they might differ.
events
7m86-perform a simple probability
experiment involving two independent events,
and compare the experimental probability with
the theoretical probability of a specific
outcome
8m81-determine, through investigation, the
tendency of experimental probability to
approach theoretical probability as the
number of trials in an experiment increases,
using class-generated data and technologybased simulation models
7m84-make predictions about a population
when given a probability
8m82-identify the complementary event for a
given event, and calculate the theoretical
probability that a given event will not occur
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Grade 7 Mathematics Course of Study – Sequence of Units
Page 55
Term 1
Recommended
Length of Unit
Strand
1 week
Grade 7
Comments
Familiarize students to new textbooks.
Review to activate prior knowledge
Textbook Scavenger Hunt
Diagnostics
Exploration of manipulatives
Unit 1 and 4 of textbook
(also page 366-unit 10)
Unit 9
3 weeks
Number Sense &
Numeration
Whole numbers, decimals, factoring,
multiples, square roots,
order of operations, Integers
3 weeks
Patterning &
Algebra
Data Management
Linear patterns, table of values,
number patterns
Unit 10
Data Collection, graphing, interpreting,
central tendency
Suggested Cross-Strand Summative
Task(s)
Unit 5
2 weeks
0.5 week
See Summary of Tasks Pages of this
document
Term 2
Recommended
Length of Unit
Strand
Grade 7
Comments
4 weeks
Number Sense &
Numeration
Measurement
Fractions, Decimals, Percent
Unit 4, 8
Composite area, conversion of metric units
Unit 3, 6, 2
2 weeks
2 week
3 weeks
Geometry & Spatial
Sense
Patterning &
Algebra
1 week
Congruence & Similarity
Unit 7
Algebraic expressions and equations
Unit 10
Suggested Cross-Strand Summative
Task(s)
See Summary of Tasks Pages of this
document
Term 3
Recommended
Length of Unit
Strand
Grade 7
Comments
4 weeks
(combined
with P &A)
4 Weeks
(combined
with NSN)
4 weeks
Number Sense &
Numeration
Ratio and Rates
(conversion of metric units continued)
Unit 2
(ratios in scale drawings page 112-113)
Patterning & Algebra
Graphing Real-Life linear relationships modeling proportional relationships
Extend questions in Unit 2 to include
graphing of the relationships
Measurement
Surface Area & Volume of Right Prisms,
area of trapezoids
Transformational Geometry and Cartesian
Coordinate Plane (all 4 quadrants)
Theoretical and Experimental Probability
Unit 3, 6
Suggested Cross–Strand Summative
Task(s)
See Summary of Tasks Pages of this
document
3 weeks
2 weeks
Geometry & Spatial
Sense
Data Management &
Probability
1 week
Unit 7
Unit 11
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 56
Grade 7 Mathematics Course of Study – Suggested Summary Tasks
Term 1
Resource Option
Page/Unit
Reference
Strand(s)
Description
Comment
Math Makes Sense
7
Math Make Sense 7
Page 362-363
Number Sense
Page 212-213
Gage Mathematics
Assessment
Gage Mathematics
Assessment
Page 16 DMP701-8
Data Management
&Probability
Data Management
&Probability
Data Management
&Probability
Unit Problem: What
Time Is It?
Unit Problem: Organizing
a Winter Carnival
Winter Olympics
How Much Does A Pet
Cost?
Use of integers, operations
with integers
Collect, display, organize
and analyse data
Use of graphs to make
predictions
Investigation into yearly
costs of keeping a pet
Page 13
Term 2
Resource Option
Page/Unit
Reference
Strand(s)
Description
Comment
Math Make Sense 7
Page 320-321
Number Sense
Math Make Sense 7
Page 162-163
Number Sense
Impact Math
Page 22-56
Patterning and
Algebra
P&A
Unit Problem: At the
Shopping Mall
Unit Problem: Publishing
a Book
Patterns in Ancient
Cultures
Math Makes Sense
Page 432-433
Number Sense
Use of decimals, percent
and sales tax
Use of fractions, cost
calculation, decimals
Four activities that use
extension of patterns and
create equations to
represent situations
Use of probability,
Cross Strand
7
Math Makes
Sense
7
Page 242-243
Data Management
&Probability
Number Sense,
Patterning &Algebra,
Measurement
Investigation: A
Population Simulation
Designing a Patio
fractions, percent, analysis
of trends
Formulas for area used in
final task, use of various
2D geometric shapes
Planting Vegetables
Use of unit conversion and
area calculation
Tile Town
Use of area calculation,
price calculation
Patterns with Toothpicks
Table of Values, Prediction,
equation representation
Table of Values, Prediction,
equation representation
Table of Values, Prediction,
equation representation
Gage Mathematics
Assessment
Page 7
M702-6
Gage Mathematics
Assessment
Page 8
M703-3
Gage Mathematics
Assessment
Gage Mathematics
Assessment
Gage Mathematics
Assessment
Page 9
PA701-2
Number Sense,
Patterning &Algebra,
Measurement
Number Sense
Patterning &Algebra
Measurement
Patterning &Algebra
Page 10 PA701-5
Patterning &Algebra
Page 10 PA701-6
Patterning &Algebra
Patterns with Geometric
Figures
Patterns with Geometric
Figures
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 57
Grade 7 Mathematics Course of Study – Suggested Summary Tasks
Term 3
Resource Option
Page/Unit
Reference
Strand(s)
Description
Comment
Impact Math
Page 22-56
Measurement
Number Sense,
Patterning &Algebra,
Measurement
Gulliver ‘s Travels
Number Sense
Patterning &Algebra
Number Sense
Patterning &Algebra
Number Sense
Measurement
Number Sense
Measurement
Spaceship Earth
Four activities that involve
area calculation and basis
of formula for area of a
trapezoid
Use of volume calculations
Unit Problem: Fund
Raising
Unit Problem: Who’s the
Smartest
Unit Problem: Making
Food for a Bake Sale
Cross Strand
Investigation: Ratios in
Scale Drawings
Structure Construction
The 2$ Coin
Math Make Sense 7
3.1 – 5.2
Page 48-56 Number
Sense
Page 402-403
Math Make Sense 7
Page 72-73
Math Makes Sense
7
Page 110-111
Math Makes Sense
7
Page 112-113
Gage Mathematics
Assessment
Gage Mathematics
Assessment
Page 18 GSS701-4
Number Sense
Measurement
Geometry
Geometry
Page 6
Measurement
Impact Math
Use of table of values, real
life relationships, equations
Use of units of measure,
conversion and ratios
Use of units of measure,
surface area and volume
calculations
Use of Ratios, perimeter,
area, polygons
Building 3D figures
Calculating mass, volume
and value of various
amounts of money
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 58
Grade 7 Term 1 - Number Sense and Numeration
7m9 - apply a variety of computational strategies to solve problems involving whole numbers
7m8 - represent, compare, and order numbers, including integers
7m9 - demonstrate an understanding of addition and subtraction of integers
Textbook References/Other Resources
MMS = Math Makes Sense 7 Pearson (referenced as a primary source)
MMSCC = MMS Curriculum Companion
AA7 = Active Achievement Binder Grade 7
AA8 = Active Achievement Binder Grade 8
MP = Math Power (only referenced as a secondary source)
MB = Marilyn Burns ‘About Teaching Mathematics’
Examples
Sample Problems
Specific Expectations
Ministry Documents
TIPS4RM = Targeted Implementation and Planning Supports for Revised
Mathematics
TL = Think Literacy
IM = Impact Math
G7E = Grade 7 Exemplar
Learning
Tools
Timing
Textbook
References
Ministry
Documents
IM Number Sense
Activity 1 - 4
Overall
3 weeks
TL p. 29, 31, 32
7m21-solve multi-step problems
arising from real-life contexts and
involving whole numbers using a
variety of tools and strategies
7m22 – use estimation when
solving problems involving
operations with whole numbers, to
help judge the reasonableness of
a solution
7m12-generate multiples and
factors, using a variety of tools
and strategies
e.g. of strategies:
estimation, algorithms
calculators;
concrete
materials;
drawings;
MMS p. 6-13, 27
e.g. of strategies:
identify multiples on a hundreds chart;
create rectangles on a geoboard
Sample Problem: List all the
rectangles that have an area of 36
color tiles;
geoboards;
hundreds chart;
MMS p.14-18
geoboards;
grid paper;
linking cubes
MMS p.19-21
TIPS4RM Gr7 Unit 1 Day 1
AA7 p. 14-15
2
cm and have whole-number
dimensions.
7m16 –represent perfect squares
and square roots, using a variety
of tools
AA7 p. 19
Grade 7 Term 1 – Number Sense and Numeration Continued
SCDSB Grade 7, 8 and Combined Math Sept. 2006
TIPS4RM Gr7 Unit 1 Day 1
Page 59
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
Ministry
Documents
TIPS4RM Continuum and
Connections Integers
7m13-identify and compare
integers found in real-life
contexts
0
0
e.g. -10 C is much colder than +5 C
geoboard;
number cards;
number line;
thermometer;
two-colour
counters;
virtual
manipulatives;
7m14-represent and order
integers, using a variety of tools
7m26-add and subtract
integers, using a variety of tools
7m23-evaluate expressions that
involve whole numbers,
including expressions that contain
brackets, using order of
operations
MMS p.327-329
TIPS4RM Gr 7 Unit 2 Day 7
MMS p.330-336
TIPS4RM Gr7 Unit 2 Day 7-9
MMS p.337-355
TIPS4RM Gr7 Unit 2
Day 6, 15
Sample Problem:
2 + 3(4 + 5)
= 2 + 3(9)
= 2 + 27
= 29
calculators;
counters
MMS p. 366
AA7 p. 82-84
MP p. 38-39, 72-73
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Grade 7 Term 1- Patterning and Algebra
7m58 - represent linear growth patterns (where the terms are whole numbers)
Page 60
using concrete materials, graphs and algebraic expression
Specific Expectations
7m59 - model real-life linear relationships graphically and algebraically
Examples
Learning
Timing
Textbook
Sample Problems
Tools
References
Ministry
Documents
TIPS4RM Continuum and
Connections Patterning to
Algebraic Modelling
Overall
3 weeks
IM Patterning & Algebra
Activity 1,2
G7E "From Patterns to
Prediction"
7m60-represent linear growing
patterns, using a variety of tools
and strategies
7m61-make predictions about
linear growing patterns, through
investigation with concrete
materials
7m62-develop and represent the
general term of a linear growing
pattern, using algebraic
expressions involving one
operation
7m63-compare pattern rules that
generate a pattern by adding or
subtracting a constant, or
multiplying or dividing by a
constant, to get the next term with
pattern rules that use the term
number to describe the general
term
e.g. of strategies: make a table of
values using the term number and the
term; plot the coordinates on a graph;
write a pattern rule using words
e.g. the general term for the
sequence 4,5,6,7, … can be written
algebraically as n + 3, where n
represents the term number;
the general term for the sequence 5,
10, 20, … can be written algebraically
as 5n, where n represents the term
number
calculators;
concrete
materials;
drawings;
pattern blocks;
spreadsheets;
toothpicks
e.g. for 1,3,5,7,9, … the pattern rule is
“start at 1 and add 2 to each term to
get the next term”
e.g. for 1,3,5,7,9…the pattern rule is
“double the term number and subtract
1,” which can be written algebraically
as 2n –1
Sample Problem: For the pattern
1,3,5,7,9, .. investigate and compare
different ways of finding the 50th term.
calculators;
concrete
materials;
drawings;
pattern blocks;
spreadsheets;
toothpicks
MMS
p. 28-32
(extend questions to
ask for the general
term)
TIPS4RM Gr 7 Unit 2
Day 1 - 4
AA8 p. 146 Activity
#1 p. 148- concrete
part of Activity #4
AA7 p. 92-94
MMS p.368-377
TIPS4RM Gr 7 Unit 5
Day 1 - 4
IM Patterning & Algebra
p.16-17 (warm up activity)
Grade 7 Term 1 –Data Management
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 61
7m70 - collect and organize categorical, discrete, or continuous primary data and secondary data and
display the data using charts and graphs, including relative frequency tables and circle graphs
7m71 - make and evaluate convincing arguments, based on the analysis of data
Specific Expectations
Examples
Sample Problems
Learning
Tools
Teacher Note: This unit could
be completed in another subject
area.
7m73 -collect data by conducting a
survey or an experiment to do with
themselves, their environment, issues
in their school or community, or
content from another subject and
record observations or measurements
7m76-distinguish between a census
and a sample from a population
7m77-identify bias in data collection
methods
7m74- collect and organize
categorical, discrete or continuous
primary data and secondary data
and display the data in charts,
tables, and graphs (including relative
frequency tables and circle graphs)
that have appropriate titles, labels
(appropriate units marked on the
axes), and scales (with appropriate
increments) that suit the range and
distribution of the data, using a variety
of tools
7m75-select an appropriate type of
graph to represent a set of data,
graph the data using technology, and
justify the choice of graph
Timing
Textbook
References
Ministry
Documents
IM Data Management
Activity 1 - 4
Overall
2 weeks
Sample Problem: Conduct a survey
in your classroom in order to discover
which type of music students prefer.
e.g. use E-stat to find differences
between a sample and a census
Sample Problem: How reliable are
your results if you only sample girls to
determine the favourite type of book
read by students in your grade?
e.g. of data sources – electronic
data from websites such as E-Stat or
Census At Schools
e.g. Graph results of a student based
survey (i.e. favourite sports of grade 7
students) using a spreadsheet
program and select most appropriate
graph to represent data (i.e. line, bar
or circle graph)
MMS p. 169-171,
212-213
Internet;
TIPS4RM Gr7 Unit 1 Day 3
TIPS4RM Gr7 Unit 3 Day 1
MMS p. 172-183,
185 -197
204 -205
306-310
Fathom
grid paper;
GSP;
Internet;
spreadsheets;
Tinker Plots
TIPS4RM Gr7 Unit 3
Day 2 -10
AA7 p. 160-161,
167-169
e.g. line graphs that exaggerate
change by starting the vertical axis at
a point greater than zero
7m79-identify, through investigation,
graphs that represent data in
misleading ways
SCDSB Grade 7, 8 and Combined
Math Sept.
2006
Grade
7 Term
Specific Expectations
7m80-determine, through
investigation, the effect on a
measure of central tendency
1 –Data Management Continued
Examples
Sample Problems
e.g. changing the value of an outlier
may have significant effect on the
mean but no effect on the median
Learning
Tools
hundreds chart;
pentominoes
Timing
Page 62
Textbook
References
MMS p. 168, 198-201
MMSCC p.21-22
AA7 p. 170-172
Ministry
Documents
TIPS4RM Gr7 Unit 3
Day 11
(mean, median, mode) of adding
or removing a value or values
7m78-read, interpret, and draw
conclusions from primary data
and from secondary data
presented in charts, tables, and
graphs (including relative
frequency tables and circle
graphs)
7m81-identify and describe
trends, based on the distribution
of the data presented in tables
and graphs, using informal
language
Sample Problem: Use a set of data
whose distribution across its range
looks symmetrical, and change some
of the values so that the distribution
no longer looks symmetrical. Does
the change affect the median more
than the mean? Explain your
thinking.
e.g. of primary data: survey results,
measurements, observations
e.g. of secondary data:
temperature data or community data
in the newspaper, data from the
Internet about populations
MMS p.183, 188-192,
212-213
Internet;
newspaper;
AA7 p. 162-166
TL p. 62 - 68
TIPS4RM Gr7 Unit 3
Day 12, 13
Sample Problem: Use census
information to predict whether
Canada’s population is likely to
increase.
7m82-make inferences and
convincing arguments that are
based on the analysis of charts,
tables, and graphs
Grade 7 Term 2 – Number Sense and Numeration
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 63
7m8 – represent, compare, and order numbers
7m9 – demonstrate an understanding of addition and subtraction of fractions,
and apply a variety of computational strategies to solve problems involving decimal numbers
7m10 - demonstrate an understanding of proportional relationships using percent
Examples
Learning
Timing
Textbook
Ministry
Specific Expectations
Sample Problems
Tools
References
Documents
Overall
4 weeks
AA7 p. 69-75
TIPS4RM Continuum and
Connections Fractions
IM Number Sense
Activity 1 - 4
7m11- represent, compare and
order fractions using a variety of
tools
7m24-add and subtract fractions
with simple like and unlike
denominators using a variety of
tools and algorithms
e.g. when adding 3  1 , think about
4
what is needed to create a whole and
group (i.e. taking 1 from 1 and adding
4
7m19- use a variety of mental
strategies to solve problems
involving the addition and
subtraction of fractions
7m25-demonstrate using
concrete materials, the
relationship between the repeated
addition of fractions and the
multiplication of that fraction by
a whole number
7m18-divide whole numbers by
simple fractions using concrete
materials
2
2
it to 3 thus resulting with 1 1 )
4
4
TIPS4RM Gr7 Unit 7 Day 1
calculators;
Cuisenaire
rods;
drawings;
fraction circles;
fraction strips;
fraction tiles;
geoboards;
linking cubes;
number cards;
number line;
pattern blocks;
MMS p.120-139,
162-163
AA7 p. 41-44
e.g.
1 1 1
1
   3
2 2 2
2
e.g. divide 3 by
TIPS4RM Gr7 Unit 7
Day 2 - 7
MMS p.141-143
TIPS4RM Gr7 Unit 7 Day 8
1
using fraction
2
strips
7m11- represent, compare, and
order decimals to hundredths using a
variety of tools
MMS p.119
AA7 p. 55-56
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 64
Grade 7 Term 2 – Number Sense and Numeration Continued
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
Ministry
Documents
7m22- use estimation when solving
problems involving operations with
decimals to help judge the
reasonableness of a solution
7m19-use a variety of mental
strategies to solve problems involving
the addition and subtraction of
decimals
7m20-solve problems involving the
multiplication and division of
decimal numbers to thousandths
by one-digit whole numbers, using a
variety of tools and strategies
eg. How much will it cost to buy three
items costing $4.25 + $3.30 + $1.60?
Mental Strategy: 4 + 3 + 1 = 8
To make another dollar add .60 + .30 and
.10 from .25. Thus it will cost $9.15.
MMS p.118
e.g. of strategies: estimation, algorithms
MMS p. 145 –152
MMSCC p.9 – 12,
14 - 19
e.g. divide 4 by 0.8 using base ten
materials and estimation
7m18-divide whole numbers by
decimal numbers to hundredths,
using concrete materials
7m23-evaluate expressions that
involve decimals, including
expressions that contain brackets,
using order of operations
e.g. 14 - 2.3  5
= 14 – 11.5
= 2.5
e.g. of strategies:
estimation, algorithms
7m21-solve multi-step problems
arising from real-life contexts and
involving decimals, using a variety of
tools and strategies
7m27-determine, through
investigation, the relationships
among fractions, decimals,
percents and ratios
MMS p.153-155
MMSCC p. 13
e.g. use the TI-15 activity “Converting
Ratios, Fractions, Decimals and Percents”
e.g. “I would use a decimal for recording
the length or mass of an object, and a
fraction for part of an hour.”
decimal chart;
fraction circles;
geoboards;
MMS p.290-295
AA7 p. 57-58
TIPS4RM Gr7 Unit 7
Day 11
hundred chart
7m15-select and justify the most
appropriate representation of a
quantity (i.e. fraction, decimal,
percent) for a given context
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 65
Grade 7 Term 2 – Number Sense and Numeration Continued
Specific Expectations
7m22-use estimation when solving
problems involving percents to help
Examples
Sample Problems
e.g. approximate
5
27
to a
Learning
Tools
base ten
materials;
Timing
Textbook
References
MMS p.297-304,
311-313,
Ministry
Documents
judge the reasonableness of a solution
“friendly fraction” (i.e.
7m28-solve problems that involve
determining whole number percents,
using a variety of tools
make an easier conversion to
a percentage
Sample Problem: If there
are 5 blue marbles in a bag of
20 marbles, what percent of
the marbles are not blue?
5 )
25
to
320 –321
calculators;
fraction circles;
geoboards;
MP p. 238-239,
242-247, 250
MB p. 250 Task 2 & 3
p. 251 Task 1
p. 252 Task 1 & 2
Grade 7 Term 2- Measurement
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 66
7m31 - report on research into real-life applications of area measurements
7m32 - determine the relationships among units and measurable attributes
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Overall
2 weeks
Textbook
References
Ministry
Documents
TIPS4RM Continuum and
Connections Perimeter,
Area
IM Measurement
Activities 1 - 4
7m35—solve problems that
require conversion between
metric units of measure
Review – perimeter
Review - area
7m36-solve problems that
require conversion between
metric units of area
7m39-estimate and calculate the
area of composite twodimensional shapes by
decomposing into shapes with
known area relationships
7m33—research and report on
real-life applications of area
measurements
e.g. millimetres and centimetres,
grams and kilograms, millilitres and
litres
i.e. square centimetres to square
metres
measuring cup;
measuring
tape;ruler;
e.g. of known area relationships rectangle, parallelogram, triangle
Sample Problem: Decompose a
pentagon into shapes with known
area relationships to find the area of
the pentagon.
e.g. building a skateboard; painting a
room
pattern blocks;
pentominoes;
tangrams
MMS p.44
MMS p216 - 224
TIPS4RM Gr7 Unit 4 Day 1
MMS p.234-237
TIPS4RM Gr7 Unit 4 Day 2
TL
MMS p. 231, 242
SCDSB Grade 7, 8 and Combined Math Sept. 2006
p. 44 - 49
TIPS4RM Gr7 Unit 4
Day 21-23
Page 67
Grade 7 Term 2 – Geometry and Spatial Sense
7m43 - construct related lines, and classify triangles, and quadrilaterals
7m44 – develop an understanding of similarity, and distinguish similarity and congruence
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
TL p. 28 - 30
Overall
2 weeks
7m46-construct related lines (i.e. parallel;
e.g. of strategy: paper folding
compass;
Ministry
Documents
MMSCC p.39 – 40,
TIPS4RM Gr7 Unit 6
GSP;
protractor;
straight edge;
Mira
48 - 50
AA7 p. 124 -129, 134
Day 1, 6, 7
e.g. of strategies: using
charts, using Venn diagrams
geoboards,
GSP
MMS p.250-254
MMSCC p. 46 -47,
58 -62
TIPS4RM Gr7 Unit 6
Day 2 - 4
e.g. “I can draw many triangles
if I’m only told the length of one
side, but there’s only one
triangle I can draw if you tell me
the lengths of all three sides.”
Sample problem: Do you
agree with the conjecture that
triangles with the same area
must be congruent? Justify
your reasoning.
geoboards;
GSP
perpendicular; intersecting at 30 0 , 45 0 , and
60 0 ), using angle properties and a variety of
tools and strategies
7m48-construct angle bisectors and
perpendicular bisectors, using a variety of tools
and strategies and represent equal angles and
equal lengths using mathematical notation
7m47- sort and classify triangles and
quadrilaterals by geometric properties related to
symmetry, angles, and sides, through
investigation using a variety of tools and
strategies.
7m50-identify through investigation, the
minimum side and angle information (i.e. sideside-side; side-angle-side; angle-side-angle)
needed to describe a unique triangle
7m53- distinguish between and compare similar
shapes and congruent shapes using a variety of
tools and strategies
7m51-determine, through investigation using a
variety of tools, relationships among area,
perimeter, corresponding side lengths, and
corresponding angles of congruent shapes
AA7 p. 130-132
MMS p.255-259
MMSCC p. 41 – 43
51 - 55
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 68
Grade 7 Term 2- Patterning and Algebra
7m58 - represent linear growth patterns (where the terms are whole numbers)
using concrete materials, graphs and algebraic expression
7m59 - model real-life linear relationships graphically and algebraically, and
solve simple algebraic equations using a variety of strategies, including inspection and guess and check
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Overall
3 weeks
Textbook
References
Ministry
Documents
TIPS4RM Continuum and
Connections Patterning to
Algebraic Modelling
TIPS4RM Continuum and
Connections Solving
Equations
7m66-translate phrases
describing simple mathematical
relationships into algebraic
expressions using concrete
materials
7m67-evaluate algebraic
expressions by substituting
natural numbers for the variables
7m68-make connections
between evaluating algebraic
expressions and determine the
term in a pattern using the
general term
7m69-solve linear equations of
the form ax = c or c = ax and ax +
b = c or variations such as
b + ax = c and c = bx + a (where
a, b, and c are natural numbers)
by modeling with concrete
materials, by inspection, or by
guess and check, with and without
the aid of a calculator
e.g. one more than three times a
number can be written algebraically
as 1 + 3x or 3x + 1
MMS p. 378-381,
387-389
algebra tiles;
counters;
pattern blocks
TIPS4RM Gr7 Unit 5 Day 1
AA7 p. 97-99
Sample Problem: Evaluate the
expression x+8 if x=3, 3+8=11
MMS p.383-386
p.38-39
e.g. for 3,5,7,9, … the general term is
the algebraic expression 2n + 1;
evaluating this expression when
n = 12 tells you that the 12th term is
2(12) + 1, which equals 25
AA7 p. 101
e.g. “I solved x + 7 = 15 by using
guess and check. First I tried 6 for x.
Since I knew that 6 plus 7 equals 13
and 13, is less than 15, then I knew
that x must be greater than 6.”
MMS p.390-394
algebra tiles;
TIPS4RM Gr7 Unit 5
Day 2,3
TIPS4RM Gr7 Unit 5
Day 5,6
AA7 p. 105
Grade 7 Term 3 – Number Sense and Numeration
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 69
7m10 - demonstrate an understanding of proportional relationships using ratio and rate
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Overall
4 weeks
(combined
with P & A)
Textbook
References
AA7 p. 69-75
Ministry
Documents
TIPS4RM Continuum and
Connections Proportional
Reasoning
IM Number Sense
Activity 1 - 4
7m29 -demonstrate an
understanding of rate as a
comparison, or ratio, of two
measurements with different
e.g. speed is a rate that compares
distance to time and that can be
expressed as kilometres per hour
Cuisenaire rods
MMS p. 45 – 65
units
7m30-solve problems involving
the calculation of unit rates
Sample problem: You go shopping
and notice that ‘s 25 kg of Ryan
Famous Potatoes cost $12.95, and 10
kg of Gillian’s Potatoes cost $5.78.
Which is the better buy? Justify your
answer.
MMS p.68, 72-73
calculators;
store sale
flyers;
Note: Extend rate problems to include a table of values and a graph to satisfy the patterning and algebra expectations.
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 70
Grade 7 Term 3 – Patterning and Algebra
7m59 – model real-life linear relationships graphically and algebraically
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Overall
4 weeks
(combined
with NSN)
Textbook
References
Ministry
Documents
7m64-model real-life
relationships involving constant
rates where the initial condition
starts at 0, through investigation
using tables of values and
graphs
7m65-model real-life
relationships involving constant
rates using algebraic equations
with variables to represent the
changing quantities in the
relationship
e.g. of relationships: speed, heart
rate, billing rate
Sample problem: Create a table of
values and graph the relationship
between distance and time for a car
traveling at a constant speed of 40
km/h. At that speed, how far would
the car travel in 3.5h? How many
hours would it take to travel 220 km?
e.g. of relationships: speed, heart
rate, billing rate
e.g. of an equation: the equation p =
4t represents the relationship
between the number of people that
can be seated (p) and the number of
tables (t), given that each table can
seat 4 people [4 people per table is
the constant rate].
calculators;
grid paper
Note: Extend rate
problems to include
a table of values and
a graph.
calculators;
grid paper
Note: Extend rate
problems to include
a table of values and
a graph.
SCDSB Grade 7, 8 and Combined Math Sept. 2006
TIPS4RM Gd 7 Unit 5 Day 4
Page 71
Grade 7 Term 3 – Measurement
7m32 - determine the relationships among units and measurable attributes, including the volume of a right prism
and the area of a trapezoid
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
TIPS4RM Continuum and
Connections Volume
Overall
4 weeks
7m37-determine, through
Sample Problem: Determine the
concrete
Ministry
Documents
MMS p. 226-230
G7E "Saving Space"
TIPS4RM Gr7 Unit 4
investigation using a variety of
tools and strategies, the
relationship for calculating the
area of a trapezoid, and
generalize to develop the
formula
Day 6-10
relationship between the area of a
parallelogram and the area of a
trapezoid by composing a
parallelogram from congruent
trapezoids.
materials;
grid paper;
GSP;
pattern blocks
Sample Problem: Use all methods to
find the area of a trapezoid. Use
strategies for finding area of a square,
rectangle, parallelogram to develop a
formula for area of a trapezoid.
Sample Problem: Identify the
perpendicular faces in a set of right
prisms.
Sample Problem: Investigate the
surface area of towers made from a
single column of connecting cubes,
and predict the surface area of a
tower that is 50 cubes high. Explain
your reasoning.
grid paper;
pattern blocks;
MMS p.232 - 233
TIPS4RM Gr7 Unit 4
Day 11
base ten
materials;
concrete
materials;
Conexions;
GSP;
linking cubes;
nets;
MMS p.97-100
MMSCC p. 27 -28,
34 - 37
TIPS4RM Gr7 Unit 4
Day 12-14, 17,18
Area = (sum of lengths of parallel sides 
height)  2
7m38-solve problems involving
the estimation and calculation of
the area of a trapezoid
7m49-investigate, using concrete
materials, the angles between the
faces of a prism, and identify right
prisms
7m41-determine, through
investigation using a variety of
tools, the surface area of right
prisms
7m42-solve problems that involve
the surface area of right prisms
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 72
Grade 7 Term 3 – Measurement Continued
Specific Expectations
Examples
Sample Problems
7m40-determine, through
investigation using a variety of
tools and strategies, the
relationship between the height,
the area of the base, and the
volume of right prisms with
simple polygonal bases
(parallelograms, trapezoids) and
generalize to develop the formula
(i.e. Volume = area of base 
e.g. of strategies: decomposing right
prism; stacking congruent layers of
concrete materials to form a right prism
Sample problem: Decompose right
prisms with simple polygonal bases into
triangular prisms and rectangular prisms.
For each prism, record the area of the
base, the height, and the volume on a
chart. Identify relationships.)
Sample Problem: Explain why area is
Learning
Tools
base ten
materials;
linking cubes;
Timing
Textbook
References
MMS p.101-103
MMSCC p. 25 -26,
29 - 33
Ministry
Documents
TIPS4RM Gr7 Unit 10
Day 1,4 - 8
height)
2
7m17-explain the relationship
between exponential notation and
the measurement of area and
volume
7m42-solve problems that involve
the volume of right prisms and
that require conversion between
metric measures of capacity and
volume (i.e. millilitres and cubic
centimetres)
7m34-sketch different polygonal
prisms that share the same
volume
expressed in square units [units ] and
volume is expressed in cubic units
3
[units ].
Sample Problem: An aquarium has a base in
the shape of a trapezoid. The aquarium is 75
cm high. the base is 50 cm long at the front,
75 cm long at the back, and 25 cm wide. Find
the capacity of the aquarium.
Sample Problem: The Neuman Company is
designing a new container for its marbles. The
MMS p.102-103
linking cubes
TIPS4RM Gr7 Unit 10
Day 9,10
3
container must have a volume of 200 cm .
Sketch three possible containers, and explain
which one you would recommend.
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 73
Grade 7 Term 3 – Geometry and Spatial Sense
7m45 - describe location in the four quadrants of a coordinate system,
dilatate two-dimensional shapes, and apply transformations to create and analyse designs
Specific Expectations
Examples
Learning
Timing
Textbook
Sample Problems
Tools
References
G7E "Geometer's Sketchpad"
Overall
3 weeks
7m54- plot points using all four
quadrants of the Cartesian
coordinate plane
e.g. Plot point A (2, 3) and reflect it
along the x and y axes
grid paper;
Ministry
Documents
IM Geometry and Spatial
Sense
Activities 1 - 4
AA7 p. 141-142
MMSCC p. 65 -71
TIPS4RM Gr7 Unit 8 Day 1
e.g. of strategies – paper folding
Sample Problem: Identify
transformations that may be observed
in architecture or in artwork [e.g. in
the art of M.C. Escher]
7m56-create and analyse designs
involving translations, reflections,
dilatations, and/or simple rotations
of two-dimensional shapes using a
variety of tools and strategies
7m55-identify, perform, and
describe dilatations (i.e.
enlargements and reductions),
through investigation using a variety of
tools
7m52-demonstrate an understanding
that enlarging or reducing twodimensional shapes creates similar
shapes
Sample Problem: Using grid paper
draw a 2cm by 2cm square. Suppose
this figure represents 25% of the
larger figure. Draw a figure that
would represent 100%.
7m53-distinguish between and
compare similar shapes and
congruent shapes, using a variety of
tools and strategies (dilatations
create similar shapes and that
translations, rotations, reflections
generate congruent shapes)
7m57-determine, through
investigation using a variety of tools,
polygons or combinations of
polygons that tile a plane, and
describe the transformation(s)
involved.
Sample Problem: A larger square
can be composed from four congruent
square pattern blocks. Identify
another pattern block you can use to
compose a larger shape that is similar
to the shape of the block.
MMS p. 261-265,
270-277
MMSCC p. 44 – 45,
56 - 57
concrete
materials;
drawings;
geoboards;
grid paper;
GSP;
Mira;
pattern blocks;
AA7 p. 135-136,
138-140
AA7 p. 137
MMS p. 266-269
SCDSB Grade 7, 8 and Combined Math Sept. 2006
TIPS4RM Gr7 Unit 8
Day 4-6
TIPS4RM Gr7 Unit 8 Day 7
TIPS4RM Gr7 Unit 8
Day 8 - 10
Page 74
Grade 7 Term 3 – Probability
7m72 - compare experimental probabilities with the theoretical probability
of an outcome involving two independent events
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Overall
2 weeks
7m83-research and report on
real-world applications of
probabilities expressed in
fractions, decimal, and percent
form
e.g. of applications – lotteries,
batting averages, weather forecasts,
elections
newspaper;
Statscan
Textbook
References
Ministry
Documents
7m85-represent in a variety of
ways all the possible outcomes
of a probability experiment
involving two independent
events (i.e. one event does not
affect the other event), and
determine the theoretical
probability of a specific outcome
involving two independent events.
e.g. of representations – tree
diagrams, tables, models, systematic
lists
7m86-perform a simple probability
experiment involving two
independent events, and
compare the experimental
probability with the theoretical
probability of a specific outcome
Sample Problem: Place 1 red
counter and 1 blue counter in an
opaque bag. Draw a counter, replace
it, shake the bag, and draw again.
Compare the theoretical and
experimental probabilities of drawing
a red counter 2 times in a row.
Sample Problem: The probability
that a bass fish is caught in Lake
Goodfish is 29%. Predict how many
bass will be caught in a fishing derby
there, if 500 fish are caught.
7m84-make predictions about a
population when given a
probability
number cards;
number cubes;
spinner;
MMS p. 407- 423
Statscan
MMSCC p. 76
AA7 p. 173-181
Sample Problem: What is the
probability of rolling a 4 and spinning
red, when you roll a number cube and
spin a spinner that is equally divided
into four different colours?
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 75
Grade 8 Mathematics Course of Study – Sequence of Units
Term 1
Recommended
Length of Unit
Strand
1 week
3 weeks
3 weeks
2 weeks
Number Sense &
Numeration
Patterning &
Algebra
Data Management
0.5 week
Grade 8
Comments
Familiarize students to new textbooks.
Review to activate prior knowledge
Textbook Scavenger Hunt
Diagnostics
Whole numbers, decimals, factoring,
exponents, powers, square roots, order
of operations
Integers
Linear and number patterns
Units 1 and 8 of Text
Data Collection, graphing, interpreting,
central tendency
Suggested Cross-Strand Summative
Task(s)
Unit 5
Unit 9
Unit 1,10
See Summary of Tasks Pages of
this document
Term 2
Recommended
Length of Unit
Strand
Grade 8
Comments
4 weeks
Number Sense &
Numeration
Measurement
Fractions, Decimals, Percent
Unit 2, 4
Conversion of metric units,
Circumference and area of a circle
Constructing circles, angle properties,
similarity
Unit 6
2 weeks
2 weeks
3 weeks
Geometry & Spatial
Sense
Patterning &
Algebra
Algebraic expressions and solving
equations
Unit 6, 7,2
(cross strand invest – pg130)
Unit 5, 10
Term 3
Recommended
Length of Unit
Strand
Grade 8
Comments
4 weeks
(with P&A)
Number Sense &
Numeration
Rates and Proportions
Unit 2
4 weeks
(with NSN)
Patterning &
Algebra
Proportional relationships
Unit 10
4 weeks
4 weeks
Measurement
Geometry & Spatial
Sense
Unit 3, 6
Unit 9
2 weeks
Data Management &
Probability
Surface Area & Volume of Cylinders
Transformational Geometry and
Cartesian Coordinate Plane
(all 4 quadrants)
Pythagorean Theorem
Theoretical and Experimental
Probability
Suggested Cross–Strand Summative
Task(s)
1 week
Unit 8
Unit 11
See Summary of Tasks Pages of
this document
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Grade 8 Mathematics Course of Study – Summative Tasks
Page 76
Term 1
Resource Option
Page/Unit
Reference
Strand(s)
Description
Comment
Impact Math
Patterning &
Algebra
Math Makes Sense
8
Pages
60 -93
Patterning & Algebra,
Data Management
Where Should They Hold
the Fundraising Party?
Pages
2 –3
Number Sense,
Patterning & Algebra
Digital Roots
Investigating number
property through
patterning
Term 2
Resource Option
Page/Unit
Reference
Strand(s)
Description
Comment
Math Makes Sense
8
Pages 178 – 179
Number Sense
Measurement
Dividing a Square
Fractions, decimals, area
Math Makes Sense
8
Page 450
Patterning & Algebra
Number Sense
Choosing a Cell Phone
Plan
Graphing, expressions,
solving equations, decimals
Term 3
Resource Option
Page/Unit
Reference
Strand(s)
Description
Comment
Impact Math
Data Management
Impact Math
Geometry and
Spatial Sense
Math Makes Sense
8
Pages
60 - 93
Pages
60 - 93
Data Management
Probability (Is the
World Series Rigged?)
What is Shannon’s
Secret?
Probability with some data
management
Angle Relationships and
Pythagorean Theorem
Pages
130 - 131
Number Sense,
Patterning & Algebra,
Data Management
Golden Rectangles
Impact Math
Measurement
Pages
60 - 93
Math Makes Sense
8
Pages
482 - 483
Measurement,
Data Management,
Number Sense
Number Sense
Probability
The Ingenious Beverage
Can – Will We Ever Run
Out?
Integer Probability
Collection, organization,
analysis of data dealing
with the ratio of
rectangles
Exploring Volume of
cylinders
Geometry
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Investigation reinforcing
the integer skills through
probability
Page 77
Grade 8 Term 1- Number Sense & Numeration
8m8 - represent, compare and order equivalent representations of numbers
including those involving positive exponents
8m9 - solve problems involving whole numbers and integers, using a variety of computational strategies and integers
Textbook References/Other Resources
Ministry Documents
MMS = Math Makes Sense 8 Pearson
AA7 = Active Achievement Binder Grade 7
AA8 = Active Achievement Binder Grade 8
MP = Math Power
Specific Expectations
TIPS4RM = Targeted Implementation and Planning Supports for Revised
Mathematics
TL = Think Literacy
IM = Impact Math
G8E = Grade 8 Exemplar
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
Overall
3 weeks
8m16-solve multi-step problems arising
from real-life contexts and involving
whole numbers using a variety of tools
and strategies
8m18-use estimation when solving
problems involving operations with whole
numbers to help judge the
reasonableness of a solution
8m15-determine common factors and
common multiples using prime
factorization of numbers
8m11-express repeated multiplication
using exponential notation
8m25-estimate, and verify using a
calculator, the positive square roots of
whole numbers, and distinguish between
whole numbers that have whole-number
square roots (i.e. perfect square
numbers) and those that do not.
calculators;
concrete
materials;
drawings;
graphs
MMS p. 9 – 13
e.g. the prime factorization of 12
is 2  2  3; the prime factorization of
18 is 2  3  3; the greatest common
factor of 12 and 18 is 2  3 or 6; the
least common multiple of 12 and 18 is
2  2  3  3 or 2 2  3 2 or 36.
color tiles;
geoboards;
hundreds chart;
MMS p. 6 – 7, 14 – 18
Sample Problem: Explain why a
calculators;
geoboards;
grid paper;
MMS p.325 – 332
e.g. strategies:
estimation, algorithms
2
square with an area of 20 cm does
not have a whole-number side length.
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Ministry
Documents
IM Number Sense
Activity 1-4
TIPS4RM Gr8 Intro Unit
Day 2 - 5
AA8 p. 28 – 29
TL p.24
AA8 p. 24
TIPS4RM Gr8 Unit 3
Day 3, 4
AA8 p. 26 – 27
Page 78
Grade 8 Term 1 - Number Sense & Numeration Continued
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
Ministry
Documents
TIPS4RM Continuum and
Connections Integers
8m22-solve problems involving
adding and subtracting with
integers using a variety of tools
8m18-use estimation when
solving problems involving
operations with integers to help
judge the reasonableness of a
solution
8m21-represent the
multiplication and division of
integers, using a variety of tools
8m18- use estimation when
solving problems involving
operations with integers to help
judge the reasonableness of a
solution
8m22-solve problems involving
multiplication and division with
integers, using a variety of tools
8m23-evaluate expressions that
involve integers including
expressions that contain brackets
and exponents, using order of
operations
e.g. if black counters represent
positive amounts and red counters
represent negative amounts, you can
model 3  (2) as three groups of two
red counters
2
1
e.g. 347 = 3  10 + 4  10 + 7
integer tiles;
number cards;
numbered
cubes;
number lines;
geoboard;
two-colour
counters;
virtual
manipulatives;
MMS p. 364 - 379
AA8 p. 40 – 42
MMS p. 380 - 388
AA8 p. 43 – 47
base ten;
calculators;
centi-cubes;
MMS p. 390 – 392
MMS p. 19 – 23
TIPS4RM Gr8 Unit 3
Day 1
8m12-represent whole numbers in
expanded form using powers of ten
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 79
Grade 8 Term 1- Patterning & Algebra
8m54 - represent linear growing patterns (where the terms are whole numbers) using graphs,
algebraic expressions and equations
8m55 – model linear relationships graphically and algebraically
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
Overall
3 weeks
Ministry
Documents
IM Patterning & Algebra
Activities 1 - 4
TIPS4RM Continuum and
Connections Patterning to
Algebraic Modelling
8m59-describe different ways in
which algebra can be used in
real-life situations
e.g. the value of $5 bills and toonies placed
in an envelope for fund raising can be
represented by the equation
V = 5f + 2t
algebra tiles;
counters;
pattern blocks
e.g. Using toothpicks, I noticed that 1 square
needs 4 toothpicks, 2 connected squares
need 7 toothpicks, and 3 connected squares
need 10 toothpicks. I think that for n
connect squares I will need
drawings;
pattern blocks;
toothpicks;
8m60- model linear relationships
using table of values, graphs,
and equations
8m56-represent, through
investigation with concrete
materials, the general term of a
linear pattern, using one or more
algebraic expressions
8m57-represent linear patterns
graphically (i.e. make a table of
values that shows the term number
and the term, and plot the
coordinates on a graph), using a
variety of tools
calculators;
Fathom;
graph paper;
Tinkerplots
MMS p. 420 - 433
TIPS4RM Gr8 Unit 2
Day 1 - 6
Grade 8 Term 1 – Data Management
8m65 - collect and organize categorical, discrete, or continuous primary data and secondary data and display the data
using charts and graphs, including frequency tables with intervals, histograms, and scatter plots
8m66 - apply a variety of data management tools and strategies to make convincing arguments about data
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
IM Data Management
Activities 2 & 4
Overall
2 weeks
8m68-collect data by conducting a
survey or an experiment SCDSB
to do with
Grade 7, 8 and Combined Math Sept. 2006
themselves, their environment, issues in
e.g. “I think that in most cases a
their school or community, or content
larger sample size will be more
from another subject, and record
representative of the entire
observations or measurements;
population.”
8m72-explain the relationship between
a census, a representative sample,
sample size, and a population
8m70-collect and organize categorical,
e.g. data sources – electronic data
discrete, or continuous primary data
from websites such as E-Stat or
and secondary data, and display the
Census At Schools
data in charts, tables, and graphs
(including histograms and scatter plots)
e.g. the age of respondents to a
that have appropriate titles, labels
survey may range over 80 years
(appropriate units marked on the axes)
and may be organized into ten-year
and scales (with appropriate increments)
intervals
that suit the range and distribution of the
data, using a variety of tools
8m69-organize into intervals a set of
Sample Problem: How is a
data that is spread over a broad range
histogram similar to and different
8m71-select an appropriate type of
from a bar graph? Use examples to
graph to represent a set of data, graph
support your answer.
the data using technology, and justify the
choice of graph (ie. from types of graphs
already studied, including histograms and
scatter plots)
8m75-demonstrate an understanding of
the appropriate uses of bar graphs and
histograms by comparing their
characteristics
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Internet;
Ministry
Documents
MMS p. 187 – 193
Page 80
AA8 p. 175 – 176
computers;
Fathom;
grid paper:
Internet;
spreadsheets;
Tinkerplots
MMS p. 184 – 186,
205 – 209,
216 – 223
AA8 p. 170 – 174
Page 81
Grade 8 Term 1 – Data Management Continued
Specific Expectations
8m74-determine, through
investigation the appropriate
measure of central tendency (i.e.
mean, median, or mode) needed
to compare sets of data
8m73-read, interpret, and draw
conclusions from primary data
and from secondary data,
presented in charts, tables, and
graphs (including frequency tables
with intervals, histograms and
scatter plots)
8m77-identify and describe
trends, based on the rate of
change of data from tables and
graphs, using informal language
8m78-make inferences and
convincing arguments that are
based on the analysis of charts,
tables, and graphs
Examples
Sample Problems
Learning
Tools
e.g. in hockey compare heights or
masses of players on defence with
that of forwards
hundreds chart;
pentominoes;
e.g. primary data: survey results,
measurements, observations
e.g. secondary data: election data or
temperature data from the
newspaper, data from the Internet
about lifestyles
e.g. “The steep line going upward on
this graph represents rapid growth.
The steep line going downward on
this other graph represents rapid
decline.”
Sample Problem: Use data to make
a convincing argument that the
environment is becoming increasingly
polluted.
Internet;
newspaper;
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Timing
Textbook
References
Ministry
Documents
MMS p. 211 – 215
AA8
p. 177 – 179
MMS p. 194 – 204
TL p. 80, 84
Page 82
Grade 8 Term 2 - Number Sense & Numeration
8m8 - represent, compare and order equivalent representations of numbers
8m9 - solve problems involving decimal numbers, and fractions using a variety of computational strategies
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
Ministry
Documents
IM Number Sense &
Numeration
Activities 1 - 4
Overall
4 weeks
TIPS4RM Continuum and
Connections Fractions
MMS p. 135 – 138
8m13-represent, compare, and
order rational numbers (i.e.
positive and negative fractions)
number line;
8m20-solve problems involving
addition, subtraction with simple
fractions
calculators;
cuisenaire rods
drawings;
fraction circles;
fraction strips;
fraction tiles;
geoboards;
pattern blocks
MMS p. 139 – 147
graph paper;
linking cubes;
number cards;
number line;
pattern blocks
MMS p. 148 – 155
8m18- use estimation when
solving problems involving
operations with fractions to help
judge the reasonableness of a
solution
8m19-represent the
multiplication of fractions, using
a variety of tools and strategies
AA8 p. 54 – 56
e.g. use an area model to represent
1
1
multiplied by
4
3
8m20-solve problems involving
multiplication with simple
fractions
SCDSB Grade 7, 8 and Combined Math Sept. 2006
TIPS4RM Gr8 Unit 5
Day 1,2,11
AA8 p. 57 – 59
AA8
TIPS4RM Gr8 Unit 5
Day 3 - 7
p. 60 – 64
Grade 8 Term 2 - Number Sense & Numeration Continued
Page 83
Examples
Sample Problems
Specific Expectations
Learning
Tools
Timing
8m19-represent the division of
fractions using a variety of tools and
strategies
8m20-solve problems involving division
with simple fractions
8m13-represent, compare, and order
rational numbers (i.e. decimals to
thousandths)
8m18-use estimation when solving
problems involving operations with
decimals to help judge the
reasonableness of a solution
8m24-multiply and divide decimal
numbers by various powers of ten
8m14-translate between equivalent
forms of a number (i.e. fractions,
decimals, percents)
8m18-use estimation when solving
problems involving percents to help
judge the reasonableness of a solution
8m28-solve problems involving percent
that arise from real-life contexts
8m17-solve problems involving percents
expressed to one decimal place and
whole-number percents greater than 100
3
e.g. “To convert 230 000 cm to cubic
metres, I calculated in my head 230
6
3
000  10 to get 0.23 m .”
Sample Problem: Use a calculator to
help you generalize a rule for dividing
numbers by 1 000 000.
e.g.
3
4
= 0.75 = 75%
e.g. discount, sales tax, simple
interest
e.g. 12.5%, 115%
Sample Problem: The total cost of an
item with tax included [115%] is
$23.00. Use base ten materials to
determine the price before tax.
Textbook
References
Ministry
Documents
MMS p. 157 – 164
TIPS4RM Gr8 Unit 5
Day 8 - 10
base ten;
calculators;
decimal chart;
drawings;
geoboards;
number line;
AA8 p. 72 – 73
decimal chart;
fraction circles;
geoboards;
hundreds chart;
base ten;
calculators;
fraction circle;
geoboards;
MMS p. 165 - 168
SCDSB Grade 7, 8 and Combined Math Sept. 2006
MMS p. 169 – 171
AA8 p. 74 – 75
TIPS4RM Gr8 Unit 3
Day 2
AA8 p. 79 – 81
MMS p. 70 - 85
AA8 p. 82 – 85
Page 84
Grade 8 Term 2 - Measurement
8m31 - determine the relationships among units and measurable attributes, including the area of a circle
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
Ministry
Documents
IM Measurement
Activities 1 & 2
Overall
2 weeks
TIPS4RM Continuum and
Connections Perimeter,
Area
8m44-construct a circle, given its
centre and radius, or its centre
and a point on the circle, or three
points on the circle (G*S)
8m34-measure the
circumference, radius, and
diameter of circular objects, using
concrete materials
8m35-determine, through
investigation using a variety of
tools and strategies, the
relationships for calculating the
circumference and the area of a
circle, and generalize to develop
the formulas
[Circumference of a circle =
Area of a circle =


Sample Problem: Use string to
measure the circumferences of
different circular objects.
circular objects;
circle
geoboards;
compass;
measuring
tape;
string;
AA8 p. 137
TIPS4RM Gr8 Unit 3
Day 5
MMS p. 239 - 241
Sample Problem: Use string to
measure the circumferences and the
diameters of a variety of cylindrical
cans, and investigate the ratio of the
circumference to the diameter
TIPS4RM Gr8 Unit 3
Day 6,7
AA8 p 94 – 95
102 – 104
 diameter;
2
 (radius) ]
8m33- solve problems that require
conversions involving metric units
of area (i.e. square centimetres
and square metres)
8m36-solve problems involving
the estimation and calculation of
the circumference and the area
of a circle
MMS p. 242 - 251
SCDSB Grade 7, 8 and Combined Math Sept. 2006
TIPS4RM Gr8 Unit 3
Day 8 - 10
Page 85
Grade 8 Term 2 – Geometry & Spatial Sense
8m40 - demonstrate an understanding of the geometric properties of quadrilaterals and circles
and the application of geometric properties in the real world;
8m41 - develop geometric relationships involving lines, triangles,
and solve problems involving lines and triangles;
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
IM Geometry & Spatial
Sense
Activity 1, 4
TL p. 162
Overall
2 weeks
8m45-investigate and describe
applications of geometric
properties in the real world
e.g. properties of triangles,
quadrilaterals, and circles
8m47-determine through
investigation using a variety of
tools and strategies, the angle
relationships for intersecting
lines and for parallel lines and
transversals, and the sum of the
angles of a triangle
e.g. strategies: paper folding
geoboards;
GSP;
numbered
cubes;
concrete
materials;
GSP;
pattern blocks;
protractor
e.g. triangle – finding interior angles or
complementary angles
e.g. intersecting lines – finding
supplementary angles or opposite angles
e.g. transversals – finding alternate
angles or corresponding angles
Ministry
Documents
MMS p. 271 – 292
303 - 307
AA8 p. 128 – 131
8m48-solve angle-relationship
problems involving triangles,
intersecting lines, and parallel lines
and transversals
8m43-sort and classify
quadrilaterals by geometric
properties, including those based
on diagonals, through
investigation using a variety of
tools
Sample Problem: Which
quadrilaterals have diagonals that
bisect each other perpendicularly?
concrete
materials;
GSP
8m46-determine, through
investigation using a variety of tools,
relationships among area,
perimeter, corresponding side
lengths, and corresponding angles
of similar shapes
Sample Problem: Construct three similar
rectangles, using grid paper or a
geoboard, and compare the perimeters
and areas of the rectangles.
geoboards;
GSP
Grade
8 Term
SCDSB Grade 7, 8 and Combined
Math Sept.
2006
2 - Patterning & Algebra
AA8 p. 120 – 122
Page 86
8m54 - represent linear growing patterns (where the terms are whole numbers) using graphs,
algebraic expressions and equations
8m55 - model linear relationships graphically and algebraically, and solve and verify algebraic equations,
using a variety of strategies, including inspection, guess and check, and using a “balance” model
Examples
Sample Problems
Specific Expectations
Learning
Tools
Timing
Textbook
References
Overall
3 weeks
Ministry
Documents
IM Patterning & Algebra
Activities 1 - 4
TIPS4RM Continuum and
Connections Solving
Equations
8m61-translate statements
describing mathematical
relationships into algebraic
expressions and equations
8m62-evaluate algebraic
expressions with up to three terms,
by substituting fractions, decimals,
and integers for the variables
8m58-determine a term, given its
term number, in a linear pattern that
is represented by a graph or an
algebraic equation
e.g. for a collection of triangles, the total
number of sides is equal to three times the
number of triangles or
s = 3n
e.g. evaluate 3x + 4y = 2z, where
x = 1 , y = 0.6 and z = 3
8m64 –solve and verify linear
equations involving a one-variable
term and having solutions that are
integers, by using inspection,
guess and check, and a “balance”
model
8m63-make connections between
solving equations and determining
the term number in a pattern, using
the general term
Sample Problem: What is the value of
the variable in the equation
2x – 6 = -18?
algebra tiles;
e.g. for the pattern with the general term 2n
+ 1, solving the equation 2n + 1 = 17 tells
you the term number when the term is 17.
algebra tiles
MMS p. 419
2
AA8 p. 154
Sample Problem: Given the graph that
represents the pattern 1,3,5,7 … find the
10th term. Given the algebraic equation that
represents the pattern t = 2n – 1, find the
100th term.
SCDSB Grade 7, 8 and Combined Math Sept. 2006
AA8 p. 149
G8E p. 64, 65, 98 - 102
MMS p. 435 – 443
AA8 p. 155 – 156
MMS p. 440 – 443
AA8 p. 151 – 153
TL p. 154
Page 87
Grade 8 Term 3 - Number Sense & Numeration (NSN)
8m10 – solve problems by using proportional reasoning in a variety of meaningful contexts
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
TIPS4RM Continuum and
Connections
Proportional Reasoning
Overall
4 weeks
(with P&A)
8m29-solve problems involving
rates
8m27-solve problems involving
proportions, using concrete
materials, drawings, and
variables.
Sample Problem: A pack of 24 CDs
cost $7.99. A pack of 50 CDs costs
$10.45. What is the most economical
way to purchase 130 CDs?
Sample Problem: The ratio of stone
to sand in HardFast Concrete is
2 to 3. How much stone is needed if
15 bags of sand are used?
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Ministry
Documents
MMS p.65 – 68
TIPS4RM Gr8 Unit 8
Day 7,8
MMS p. 53 – 59
TIPS4RM Gr8 Unit 8
Day 2 - 4, 6
fraction circles;
Geoboards,
Page 88
Grade 8 Term 3 – Patterning and Algebra (P&A)
8m55 – model linear relationships graphically and algebraically, and solve and verify algebraic equations,
using a variety of strategies, including inspection, guess and check, and using a “balance model”
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
Ministry
Documents
Overall
4 weeks
(with NSN)
8m60-model linear relationships
using table of values, graphs,
and equations, through
investigation using a variety of
tools
8m26-identify and describe reallife situations involving two
quantities that are directly
proportional
8m76-compare two attributes or
characteristics, using a scatter plot,
and determine whether or not the
scatter plot suggests a relationship
8m79-compare two attributes or
characteristics, using a variety of
data management tools and
strategies (i.e. pose a relevant
question, then design an
experiment or survey, collect and
analyse the data, and draw
conclusions)
Sample Problem: Leah put $350 in a
bank certificate that pays 4% simple
interest each year. Make a table of
values to show how much the bank
certificate is worth after five years,
using base ten materials to help you.
Represent the relationship using an
equation.
e.g. the number of servings and the
quantities in a recipe, mass and
volume of a substance, circumference
and diameter of a circle
Sample Problem: Compare the
length and width of different-sized
leaves from a maple tree to determine
if maple leaves grow proportionally.
Collect, graph, and analyse data.
What generalizations can you make?
base ten;
grid paper
MMS p. 65 – 68,
TIPS4RM Gr8 Unit 8
Day 1,5
Grade 8 Term 3 - Measurement
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 89
8m30 – research, describe, and report on applications of volume and capacity measurement
8m31 – determine the relationships among units and measurable attributes including the volume of a cylinder
Examples
Learning
Timing
Textbook
Ministry
Specific Expectations
Sample Problems
Tools
References
Documents
Overall
4 weeks
IM Measurement
Activity 3
TIPS4RM Continuum and
Connections Volume
8m51-determine, through investigation
using concrete materials, the
relationship between the number of
faces, edges, and vertices of a
polyhedron (i.e. number of faces +
number of vertices = number of edges +
2)
8m38-determine through investigation
using concrete materials, the surface
area of a cylinder
Sample Problem: Use Polydrons
and/or paper nets to construct the five
Platonic solids [i.e. tetrahedron, cube,
octahedron, dodecahedron,
icosahedron] and compare the sum of
the numbers of faces and vertices to
the number of edges for each solid
Sample Problem: Use the label and
the plastic lid from a cylindrical
container to help determine its surface
area.
Conexions;
paper nets
concrete
materials;
paper towel roll
8m39-solve problems involving the
surface area of cylinders using a variety
of strategies
8m37-determine through investigation
using a variety of tools and strategies, the
relationship between the area of the
base and height and the volume of a
cylinder, and generalize to develop the
formula (Volume = area of base  height)
8m39-solve problems involving the
volume of cylinders, using a variety of
strategies
8m33-solve problems that require
conversions involving metric units of
volume and capacity (i.e. cubic
centimetres and cubic metres; millilitres
and cubic centimetres)
8m32-research, describe, and report on
applications of volume and capacity
measurement
MMS p. 258 - 260
TL p.152
AA8 p. 108 – 109
e.g. generalizing from the volume
relationship for right prisms, and
verifying using the capacity of thinwalled cylindrical containers
circular disks;
graduated
cylinder;
open topped
triangular prisms;
rulers;
Sample Problem: Compare the
volumes of the two cylinders that can
be created by taping the top and
bottom, or the other two sides, of a
standard sheet of paper.
Sample Problem: What is the
capacity of a cylindrical beaker with a
radius of 5 cm and a height of 15 cm?
e.g. cooking, closet space, aquarium
size
Sample Problem: Describe the
situations where volume and capacity
are used in your home.
SCDSB Grade 7, 8 and Combined
Sept. 2006
Grade Math
8 Term
3–
MMS p. 253 - 255
catalogues;
recipe cards;
tent
Geometry and Spatial Sense
8m42 – represent transformations using the Cartesian coordinate plane,
and make connections between transformations and the real world
Page 90
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
IM Geometry & Spatial
Sense Activity 2-4
Overall
4 weeks
Review – plotting points in four
quadrants
8m53-identify through
investigation, real-world
movements that are translations,
reflections, and rotations
8m52-graph the image of a
point, or set of points, on the
Cartesian coordinate plane after
applying a transformation to the
original point(s) (i.e. translation;
reflection in the x-axis, the y-axis,
or the angle bisector of the axes
that passes through the first and
Ministry
Documents
MMS p.393 - 397
MMS p. 398 – 407
geoboards;
grid paper;
GSP;
0
third quadrants; rotation of 90 ,
0
0
180 , or 270 about the origin)
8m49-determine the Pythagorean
relationship, through investigation
using a variety of tools and strategies
MMS p.337 – 343
geoboard;
GSP;
paper and
scissors;
square tiles
calculator;
GSP
8m50-solve problems involving right
triangles geometrically, using the
Pythagorean relationship
TIPS4RM Gr8 Unit 10
Day 1 - 3
G8E p. 12-14, 56 - 61
MMS p. 346 – 354
TIPS4RM Gr8 Unit 10
Day 4
AA8 p. 132 – 133
SCDSB Grade 7, 8 and Combined Math Sept. 2006
Page 91
Grade 8 Term 3 – Probability
8m67 – use probability models to make predictions about real-life events
Specific Expectations
Examples
Sample Problems
Learning
Tools
Timing
Textbook
References
Ministry
Documents
Overall
2 weeks
8m80-compare, through
investigation, the theoretical
probability of an event (i.e. the
ratio of the number of ways a
favourable outcome can occur
compared to the total number of
possible outcomes) with
experimental probability, and
explain why they might differ.
8m81-determine, through
investigation, the tendency of
experimental probability to
approach theoretical probability
as the number of trials in an
experiment increases, using
class-generated data and
technology-based simulation
models.
8m82-identify the complementary
event for a given event, and
calculate the theoretical
probability that a given event will
not occur.
Sample Problem: Toss a fair coin 10
times, record the results, and explain
why you might not get the predicted
result of 5 heads and 5 tails.
coins;
coloured
number cubes;
paper bag;
MMS p.456 - 465
Sample Problem: Compare the
theoretical probability of getting a 6
when tossing a number cube with the
experimental probabilities obtained
after tossing a number cube once, 10
times, 100 times and 1000 times.
integer tiles;
numbered
cubes;
MMS p. 467 - 470
Sample Problem: Bingo uses the
numbers from 1 to 75. If the numbers
are pulled at random, what is the
probability that the first number is a
multiple of 5? is not a multiple of 5?
SCDSB Grade 7, 8 and Combined Math Sept. 2006
IM Data Management &
Probability
Activities 1 - 4
G8E p. 104 -106,139-144
AA8 p. 200 – 201
TIPS4RM Gr8 Unit 6
Day 2 - 5
AA8 p. 212 – 214
MMS p. 471 - 473
TIPS4RM Gr8 Unit 6
Day 6
AA8 p. 210 – 211
Page 92