Mathematics
Kto 7
Draft Learning Outcomes

Province of British Columbia
Ministry of Education

Table of Contents
Mathematics Overview
• The K to 12 Curriculum
• Mathematics 8 to 12
• Mathematics K to 7
Implementation Support
Learning Outcomes K to 7
• Number (Number Concepts)
• Number (Number Operations)
• Patterns and Relations (Patterns)
• Patterns and Relations (Variable and Equations)
• Shape and Space (Measurement)
• Shape and Space (Three-Dimensional Objects
and Two-Dimensional Shapes)
• Shape and Space (Transformations)
• Statistics and Probability (Data Analysis)
• Statistics and Probability (Chance and Uncertainty)

Mathematics Overview
The K to 12 Curriculum

Mathematics K to 7

The Mathematics K to 12 curriculum provides

The National Council of Teachers of Mathematics

students with the experiences and skills needed

(NCTM) Standards were used as a reference by

in the knowledge-based workplace, including

the developers of the Common Curriculum

probability and statistics, logic, measurement

Framework for K to 12 Mathematics. The

theory, and problem solving. The curriculum has

Kindergarten to Grade 7 learning outcomes have

been arranged according to the following four

been adapted from the Common Curriculum

curriculum organizers:

Framework to meet the needs of British

• Number
• Patterns and Relations
• Shape and Space

• Statistics and Probability
The Mathematics K to 12 curriculum reflects
that mathematics is a common human activity,

becoming more important in our increasingly
technological society. A greater proficiency in

mathematics will increase opportunities available

to the students of British Columbia.
The learning outcomes of the Mathematics

K to 12 curriculum were developed as part of the

Western Canadian Protocol for Collaboration in
Basic Education. They represent the combined
efforts and talents of British Columbia educators

and education partners and those of the
provinces of Alberta, Saskatchewan, and

Manitoba, as well as the Yukon Territory and

Northwest Territories. These learning outcomes
form the Common Curriculum Framework for

K to 12 Mathematics for Western Canada.

Columbians. There is an increased emphasis on

the applications of mathematics, problem solving
in real world contexts, and the use of technology
in learning and doing mathematics.

Opportunities to meet the prescribed learning

outcomes must be equally available to male and

female students. The Integrated Resource
Package (IRP), available in April 1995, will offer

gender-sensitive strategies to ensure that girls and
boys are equally attracted to mathematics.
The learning outcomes for Mathematics K to 7
are arranged according to four curriculum

organizers. In the Number organizer, the student

uses numbers to describe and represent quantities
in multiple ways. The student also develops
understanding of and proficiency in arithmetic
operations and uses calculations to solve

problems. The Patterns and Relations organizer
focuses on the use of patterns to allow students to
solve problems and describe the world around

them. In Grades 6 and 7 the concept of patterns is
expanded where the student represents algebraic

Mathematics 8 to 12
The Mathematics 8 to 12 curriculum will build

on the K to 7 curriculum. The curriculum is

intended to prepare students to meet the
challenges of a changing workplace by providing
them with the mathematical, problem solving,
and technological skills, depending upon their

personal, education, and career goals.

expressions in a variety of ways. In the Shape and

Space organizer the student uses measurement to
describe and compare real-world phenomena as

well as describing the characteristics and

relationships of three-dimensional objects and
two-dimensional shapes. In the Statistics and

Probability organizer, learning centres around
collecting and analyzing data to make predictions
and draw conclusions.

Implementation Support
The Ministry of Education will support the

teachers and districts commence

implementation of the Mathematics K to 7

implementation of the new curriculum in

curriculum in the following ways:

September 1995. Summer institutes are being
planned for July and August 1995 to permit

•

The Integrated Resource Package (IRP) for

school district personnel to continue

Mathematics K to 7 will be available in April

developing their implementation plans.

1995. The IRP will provide teachers with the
learning outcomes prescribed for each grade

level, suggested instructional and assessment
strategies, details of recommended learning
resources, methods of evaluation, and

illustrative examples.
•

Throughout the spring, the Ministry will
support regional forums and district school­

based workshops on the Mathematics K to 7
curriculum. These workshops will help

•
•

Full implementation is expected in 1996/97.
In addition, the Ministry will continue to

work with our education partners to support

the implementation process in a variety of
ways within available resources.

Learning Outcomes

Number (Number Concepts)

Use numbers to describe quantities. Represent numbers in multiple ways. It is expected that students will:

Recognize, describe, and use
numbers from zero to 100 in a
variety of familiar settings
• orally count by ones, twos,
fives, and tens to 100
• estimate and count objects in a
set (zero to 50) and compare
estimates to the actual number

• recognize, build, compare, and
order sets of objects (zero to
50) using both comparative and
numerical terms
• read number words up to ten

• explore, represent, and
describe numbers up to 50 in a
variety of ways, including the
use of a calculator or computer
for numbers up to 100
• demonstrate and explain orally
an understanding of half

Develop a number sense for
whole numbers from zero to
1,000 and common fractions to
tenths

• estimate, then count an
increased number of objects in a
set, and compare the estimate
with the actual number
• skip count forwards and
backwards by twos, fives, tens,
25s, and 100s to 1,000 using
starting points that are
multiples; and skip count
forwards using random starting
points

Demonstrate a number sense for
whole numbers zero to 10,000 and
proper fractions
• estimate, then count the number
of objects in a set (zero to
1,000), and compare the
estimate with the actual number

• use skip counting (forwards and
backwards) to support
understanding of patterns in
multiplication and division
• compare and order numbers up
to 10,000

• read and write number words to
1,000

• recognize, build, compare, and
order sets that contain zero to
1,000 elements

• round numbers to nearest ten,
100, and 1,000

• round numbers to nearest tens
and 100s

• represent and describe numbers
to 10,000 in a variety of ways

• read and write number words
to 100, numerals to 1,000

• demonstrate concretely,
pictorially, and symbolically
place-value concepts to give
meaning to numbers up to
10,000

• use ordinal numbers to 100
• explore, represent, and describe
numbers to 1,000 in a variety of
ways, including the use of
calculators and computers
• demonstrate concretely and
pictorially place-value concepts
to give meaning to numbers
zero to 1,000

• demonstrate whether a number
is even or odd
• recognize and explain whether a
number is divisible by two, five,
or ten
• demonstrate and explain in a
variety of ways an understanding
of halves, thirds, fourths, fifths,
and tenths as part of a region or
a set

• sort numbers into categories
using one or more attributes

• demonstrate an understanding
of hundredths as part of a region
or set
• connect proper fractions to
decimal fractions (tenths and
hundredths) using manipulatives,
diagrams, and symbols

Demonstrate a number sense for
whole numbers, zero to 100,000,
and explore proper fractions and
decimal fractions

Develop a number sense for
decimal fractions and common
factions and explore number
sense for whole numbers

• demonstrate concretely and
pictorially an understanding of
place value from hundredths

» read and write numerals greater
than a million

• read and write numerals to a
million

• read and write number words
to 100,000
• use estimation strategies for
quantities up to 100,000

• recognize, model, and describe
multiples, factors, composites,
and primes
• compare and/or order whole
numbers

• use estimation strategies for
quantities up to a million

’ distinguish relationships
between multiples, factors,
composites, and primes
’ represent positive powers
concretely, pictorially, and
symbolically

1 use power, base, and exponent to
represent repeated multiplication
explain the meaning of integers
by extending counting numbers
to less than zero

Demonstrate a number sense for
decimal fractions and integers
(including whole numbers)
• recognize, model, identify, and
describe common multiples,
common factors, least common
multiples, greatest common
factors, and prime factorization
• write whole numbers as an
expanded numeral using powers
of ten and in scientific notation

• use divisibility rules to
determine whether a number is
divisible by two, three, four, five,
six, eight, nine, ten, eleven
• read and write numbers to any
number of decimal places

identify practical application of
integers

• recognize and illustrate that all
fractions and mixed numbers
can be represented in decimal
form (include terminating and
repeating decimals)

• demonstrate and describe
equivalent fractions

read and write numbers to
thousandths

• convert from terminating
decimals to fractions

• compare and/or order proper
and decimal fractions to
hundredths

demonstrate and explain the
meaning of improper fractions
and mixed numbers (positive),
concretely and pictorially

• convert from single-digit
repeating decimal numbers to
fractions using patterns

• represent and describe proper
fractions concretely, pictorially,
and symbolically

demonstrate and describe
equivalent mixed numbers and
improper fractions, concretely
and pictorially

compare and/or order improper
fractions, mixed numbers, and
decimal fractions to thousandths
demonstrate and explain the
meaning of ratio, concretely and
pictorially

demonstrate and explain the
meaning of percentage,
concretely and pictorially

• demonstrate concretely and
pictorially that the sum of
opposite integers is zero
• represent integers in a variety of
concrete, pictorial, and symbolic
ways

• compare and order integers

Number (Number Operations)
Demonstrate an understanding of and proficiency with calculations. Decide which arithmetic operation or
operations can be used to solve a problem and then solve the problem. It is expected that students will:

Demonstrate and use a variety of
methods to show the processes
of addition and subtraction on
one-digit whole numbers where
the maximum sum is 18

• demonstrate and orally
describe the process of
addition and subtraction of
whole numbers to 18 using
role play, manipulatives, and
diagrams (memorization is not
intended)

Use a variety of strategies to apply
a basic operation (=, -, x,+, /) on
whole numbers and use these
operations in solving problems
• demonstrate and describe the
process of addition and
subtraction of whole numbers
up to 1,000 with and without
regrouping using manipulatives,
diagrams, and symbols

• explore and demonstrate the
processes of multiplication and
division up to 50 using
manipulatives, diagrams, and
symbols

• recall addition and subtraction
facts to 18 and multiplication
facts to 25

Choose, use, and defend the
appropriate calculation strategy
or technology to solve problems

• calculate and justify the choice
of methods used to find sums,
differences, products, and
quotients using estimation
strategies, mental math
techniques, manipulatives,
algorithms, and calculators

• verify solutions to problems by
using inverse operations,
estimation, and calculators

Apply arithmetic operations on
whole numbers and illustrate their
use in solving problems

• demonstrate and describe the
process of addition and
subtraction of numbers up to
10,000 using manipulatives,
diagrams, and symbols
• demonstrate the process of
multiplication (three-digit by
one-digit) using manipulatives,
diagrams, and symbols
• demonstrate the process of
division (two-digit by one-digit)
using manipulatives, diagrams,
and symbols

• recall multiplication and division
facts to 81
• justify the choice of method for
multiplication and division
(estimation, calculator, mental
math, manipulatives, and
algorithms)
• verify solutions to multiplication
and division problems using
estimation and calculators

• verify solutions to multiplication
and division problems by using
the inverse operation

Demonstrate an understanding of
addition and subtraction of
decimals
• demonstrate an understanding
of addition and subtraction of
decimals fractions (tenths and
hundredths) using concrete and
pictorial representations

Apply arithmetic operations on
whole numbers and decimal
fractions and illustrate their use
in solving problems
• add and subtract decimal
fractions to hundredths
concretely, pictorially, and
symbolically

• estimate, mentally calculate, or
compute and verify the
product (three-digit by twodigit) and quotient (three-digit
by one-digit) of whole
numbers
• multiply and divide decimal
fractions to hundredths
concretely, pictorially, and
symbolically using single digit,
whole number multipliers, and
divisors

Apply the arithmetic operations
on whole numbers and decimals
in solving problems
• estimate the solutions to
calculations involving whole
numbers and decimal fractions

Apply the arithmetic operations of
decimal fractions and integers and
illustrate their use in solving
problems

• use patterns, manipulatives, and
diagrams to demonstrate the
concepts of multiplication and
division by decimal fraction
• use estimation strategies to
predict or assess the
reasonableness of calculations
• add, subtract, multiply, and
divide decimals (for more than
two-digit divisors or multipliers,
the use of technology is
expected)
• demonstrate an understanding
of order of operations using
paper and pencil and calculator
• add, subtract, multiply, and
divide integers concretely,
pictorially, and symbolically

Illustrate the use of ratios, rates,
percentages, and decimal numbers
in solving problems

• estimate and calculate
percentages
• distinguish between rate and
ratio
• explain and demonstrate the use
of proportion in solving
problems
• mentally convert among proper
fractions, decimal fractions, and
percents, to facilitate the
solution of problems

Patterns and Relations (Patterns)

Use patterns to describe the world around you and to solve problems. It is expected that students will:

Identify, create, and compare
patterns that arise from their
daily experiences

• identify, reproduce, extend,
create, and compare patterns
using actions, manipulatives,
diagrams, and spoken terms
• recognize patterns in the
environment

Investigate, establish, and
communicate rules for numerical
and non-numerical patterns that
arise from daily and mathematical
experiences, and use these rules
to make predictions

• identify, create, and describe
number and non-number
patterns

• translate patterns from one
mode to another using
manipulatives, diagrams, charts,
calculators, spoken and written
terms, and symbols
• explain the rule for a pattern
and make predictions based on
patterns using models and
objects

Investigate, establish, and
communicate rules for, and
predictions from, numerical and
non-numerical patterns

• identify and explain
mathematical relationships and
patterns through the use of
grids, tables, charts, or
calculators
• make and justify predictions,
using numerical and nonnumerical patterns

Construct, extend, and
summarize patterns, using rules,
charts, mental math, and
calculators

Use relationships to summarize,
generalize, and extend patterns

• develop charts to record and
reveal number patterns

• construct a visual
representation of a pattern to
clarify relationships and to
verify predictions

• describe how a pattern grows
using everyday language in
spoken and written form

• summarize a relationship using
everyday language in a spoken
or written form

• construct and expand patterns
in two and three dimensions,
concretely and pictorially

• create expressions and rules to
describe patterns and
relationships (e.g., area,
perimeter, volume)

• generate number patterns
from a problem-solving
context

• predict and justify pattern
extensions

• interpolate number values from
a given graph

♦ predict pattern relationships

Express patterns in terms of
variables and use expressions
containing variables to make
predictions
• create formulae for finding area,
perimeter, and volume

• predict and justify the nth value
of a number pattern

Patterns and Relations
(Variable and Equations)
Represent algebraic expressions in multiple ways. It is expected that students will:

Learning outcomes for Patterns
and Relations (Variable and
Equations) commence in Grade 6

Learning outcomes for Patterns
and Relations (Variable and
Equations) commence in Grade 6

Learning outcomes for Patterns
and Relations (Variable and
Equations) commence in Grade 6

Learning outcomes for Patterns
and Relations (Variable and
Equations) commence in Grade 6

Use informal and concrete
representations of equality and
operations on equality to solve
problems
• generalize a pattern by
substituting numbers into a
frame and compare the results
to the original pattern

Use variables and equations to
express, summarize, and apply
relationships as problem-solving
tools in a restricted range of
contexts

• generalize a pattern arising from
a problem-solving context using
an open number sentence with
appropriate variables

• demonstrate the meaning and
the preservation of equality
using objects, models, and
diagrams

• substitute number variables and
compare the results to concrete
models and tables

• graph ordered pairs in the first
quadrant, analyze results, and
generalize relations

• write expressions involving
variables using standard
mathematical conventions

• solve one-variable equations
with whole number coefficients
and solutions using informal
techniques

• analyze relations graphically to
discover how changes in one
quantity may affect another
• graph relations, analyze results,
and draw conclusions
• solve and verify simple linear
equations using a variety of
techniques
• use patterns and relations to
represent and solve problems by
translating everyday language
into mathematical symbols and
vice versa

• explain how to solve simple
problems with informal algebraic
methods

Shape and Space (Measurement)
Describe and compare real world phenomena using either direct or indirect measurement. It is expected that

students will:

Estimate, measure, and compare
using whole numbers and
nonstandard units of measure

Measure, estimate, and compare, using
whole numbers and nonstandard and
standard units of measure

Estimate, measure, and compare quanti­
ties, using decimal numbers and standard
units of measure

• classify, describe, and arrange
objects by using comparative
language to compare length,
size, area, weight, and volume

• estimate, measure, record, compare
and order objects and containers
using nonstandard and standard unit

• construct specific lengths (mm)

• use comparative terms to
describe time and temperature
• relate relative sizes of
nonstandard units by
measuring the same object
with different units, and
recognize that different objects
may have the same mass

• select an appropriate
nonstandard unit to estimate,
measure, record, compare, and
order objects and containers
• estimate the number of
uniform objects and irregular
shapes that will cover a given
area and verify by covering and
counting
• compare and sequence events
according to the duration of
time (using nonstandard units),
time of day, days of the week,
and the seasons
• recognize and name the value
of pennies, nickels, and dimes

• use money as a form of
exchange
• create equivalent sets of coins
up to ten cents in value

• construct a shape, length, or object
using a specific nonstandard unit or
standard unit

• select the most appropriate standard
unit for measuring length (cm, m, km),
mass (g, kg), volume (L), and time
• describe relationships between
various standard units of measure
• relate the size of units to the number
of units needed when measuring
• recognize that the size and shape
of an object does not necessarily
determine its mass
• make connections among
manipulatives, diagrams, spoken
terms, and written symbols
• estimate and measure the passage
of time related to seconds, minutes
hours, days, weeks, months, and
years and relate the various
measures to each other
• read and write the date, including days
of the week, using abbreviations; name
the months of year in order
• read and write time to the nearest
minute using 12-hour notation on a
digital and analog clock

• select the most appropriate standard
unit (mm, cm, m, km) to measure
length
• describe relationship between mm, cm,
m and km
• estimate, measure, record, compare,
and order objects by length, height,
perimeter, and circumference using
standard units (mm, cm, m, km)
• estimate, measure, record, compare
and order shapes by area using
standard units (cm2, m2)
• construct a number of shapes given a
specific area (cm2)
• select the most appropriate standard
unit to measure area
• relate the size of units to the number of
the units needed in measuring the area
of an object with different units
• estimate, measure, record, compare,
and order the capacity of containers
using standard units (ml, L)
• relate the number of units to the size of
the units needed when measuring mass
• describe the relationship between
grams and kilograms
• solve problems involving mass using
grams and kilograms

• estimate, read, and record tempera­
ture to the nearest degree Celsius

• relate years, decades, centuries, and
millenniums

• relate temperature to real life situation'

• read and write time on a 24-hour clock

• identify and use coins and bills (to
$ 100) to estimate, count, record
collections, create equivalent sets,
and make change up to $ 10

• read and write time using a.m. and p.m.
• estimate, count, and record collections
of coins and bills up to $ 100

• make purchases and change up to $ 100
• read and write both money
notations (.89 and $0.89)

Use measurement concepts and
appropriate tools and results of
measurements to solve problems
in real life contexts

Be able to solve problems
involving perimeter, area, surface
area, volume, and angle
measurement

Solve problems involving the
properties of circles and their
connections with angles and time
zones

• recognize and explain the
meaning of length, width,
height, depth, thickness,
perimeter, and circumference

• convert between commonly
used SI units of length, mass,
and capacity

• measure the diameter, radius,
and circumference of circles and
generalize the relationships

• develop, verify, and use rules or
expressions for the perimeter
of polygons

• solve problems involving circles
(radius, diameter, and
circumference)

• develop, verify, and use rules or
expressions for the area of
rectangles

• explain how time zones are
determined

• solve problems involving mass
using grams, kilograms, and
tonnes
• evaluate the appropriateness
of units when selecting
different measuring tools
• estimate and measure the area
of irregular shapes by dividing
them into parts

• estimate and measure the
perimeter of irregular shapes
• estimate and measure the
effect of changing one or more
dimensions of a rectangle on
its perimeter or area
• relate perimeter and area of a
rectangle using manipulatives
and diagrams
• relate the units cm3 and ml

• estimate, measure, record, and
order containers by volume
using cm3
• construct objects of a specific
volume expressed in cm3

• read and write SI notation for
recording date and time

• estimate, measure, and then
calculate the surface area of
right rectangular prisms (no
formula)
• discover, generalize, and use
rules for the volume of right
rectangular prisms
• determine the volume of an
object by measuring the
displacement of a liquid by that
object (cm3 or ml)
• recognize angles as being more
than 90 degrees, equal to 90
degrees, less than 90 degrees,
greater than 180 degrees
• estimate and measure angles
using a circular protractor
• draw and sketch an angle when
the degree measure is specified
• classify given angles as acute,
right, obtuse, straight, reflex
• identify and compare examples
of angles in the environment

• determine time in various
regions of the world
• research and report how
measurement instruments are
used in the community
• design and construct rectangles
given one or both of perimeter
and area (whole numbers)
• demonstrate and generalize that
many rectangles are possible for
a given perimeter or given area

Shape and Space (Three-Dimensional
Objects and Two-Dimensional Shapes)
Describe the characteristics of three-dimensional (3-D) objects and two-dimensional (2-D) shapes and analyze

the relationships among them. It is expected that students will:

Explore, sort and classify real
world and 3-D objects according
to their properties
• explore and describe real
world and 3-D objects using
descriptive attributes such as
big, little, like a box, like a can
• explore, identify, and classify
3-D objects in the environment
and according to their
properties
• construct 3-D objects using
materials such as plasticine,
blocks, and boxes

• identify and describe specific
2-D shapes such as circles,
squares, triangles, or rectangles
• construct and rearrange a
design using a set of 2-D
shapes
• compare, sort, classify, and
pattern 2-D shapes

Describe, classify, construct, and
relate 3-D objects and 2-D
shapes using common language
to describe properties

Describe, classify, construct, and
relate 3-D objects and 2-D
shapes, using mathematical
vocabulary to describe properties

• compare, contrast, sort, and
classify 2-D shapes and 3-D
objects using two or more
attributes

• design and construct nets for
pyramids and prisms

• identify, count, and describe
faces, vertices, edges, sides,
and angles for polygons and
solids

• describe and name 3-D objects
(cubes, spheres, cones,
cylinders, pyramids, and
prisms) and use appropriate
2-D names to describe faces
• describe and name pyramids
and prisms by the shape of the
base
• construct skeletons of a 3-D
object from a model and relate
skeletons (nets) to models
• demonstrate through
dismantling that a rectangular
solid has more than one net
• make identical, congruent 2-D
shapes
• construct and rearrange a
design using a set of 2-D
shapes
• recognize congruent (the
same) 3-D objects and 2-D
shapes in the environment
• explore the concepts of points,
lines, perpendicular lines,
parallel lines, and intersection
of 3-D objects

• relate nets to 3-D objects

• compare and contrast pyramids
and prisms to describe a
relationship
• identify and sort specific
quadrilaterals, such as squares,
rectangles, parallelograms, and
trapezoids
• classify angles in a variety of
orientations according to
whether they are right angle,
less than right angle, greater
than right angle
• recognize, draw, and name the
following: point, line, parallel
lines, and intersecting lines

Use the visualization of 2-D
shapes and 3-D objects to solve
problems related to spatial
relation
• construct, analyze, and classify
triangles according to the side
measurements
• build, represent, and describe
geometric objects and shapes
• classify and name polygons
according to the number of
sides (three, four, five, six,
eight)
• cover 2-D shapes with a set of
tangram pieces

Use visualization and symmetry
to solve problems involving
classification and sketching

• classify triangles according to
the measurement of their
angles
• sort quadrilaterals and regular
polygons according to number
of lines of symmetry
• recognize and appreciate
optical illusions
• reproduce a given geometric
drawing on grid paper
• sketch 3-D solids and skeletons
with or without grids

Link angle measures to the
properties of parallel lines

• measure and classify pairs of
angles, complementary, or
supplementary angles
• identify and name pairs of angles
pertaining to parallel lines and
transversals including:
• corresponding angles
• vertically opposite angles
• interior angles on the same
side of the transversal
• exterior angles on the small
side of the transversal
• interior alternate angles

• complete the drawing of a 3-D
object on grid paper given the
front face

• describe the relationships
between the pairs of angles
pertaining to parallel lines and
transversals

• determine experimentally the
minimum information needed
to draw/identify a given 2-D
shape

• use mathematical reasoning to
determine the measures of
angles in a diagram
• perform calculations with angle
measures
• construct angle bisectors and
perpendicular bisectors
• explain in more than one way
why the sum of the measures of
the angles of a triangle is 180
degrees

Shape and Space (Transformations)

Perform, analyze, and create transformations. It is expected that students will:

Describe verbally the relative
position of both 3-D objects and
2-D shapes

• use directional terms such as
over, under, beside, near, far,
left, and right to describe the
relative position of objects and
shapes
• match size and shape of figures
by superimposing one on top
of the other
• identify and fit pieces of puzzles
or shapes that go together
(part to whole relationships)

• explore and describe reflection
in mirrors

Use positional language,
numbers, and directional words
to describe relative positions of
objects in one dimension and to
communicate motion in real
world contexts

• communicate and apply
positional language and
cardinal directions (relating to
compasses and maps) in
written, verbal, or numerical
form

• graph whole number points on
a horizontal or a vertical
number line
• trace a path on a line using
oral or written instructions

• make congruent shapes and
symmetrical 2-D shapes by
folds and reflections

Use number and direction words
to describe the relative positions
of objects in two dimensions,
using real world contexts
• communicate and apply terms
of directions to maps (north,
south, east, and west)
• place an object on a grid using
columns and rows
• describe the position of an
object on a grid using columns
and rows
• trace a path on a grid or map
using oral or written
instructions and vice versa
• create and verify symmetrical
2-D shapes by drawing lines of
symmetry

Describe motion in terms of a
slide, a flip, or a turn

• recognize motion as a slide
(translation), turn (rotation),
or a flip (reflection)
• recognize tessellations created
with regular and irregular
shapes in the environment

• locate planes of symmetry by
cutting solids
• use co-ordinates to describe
the position of objects in two
dimensions

• plot whole number ordered
number pairs in the first
quadrant with intervals of one,
two, five, and ten
• identify a point in the first
quadrant using ordered pairs

• cover a surface using one or
more tessellating shapes
• create and identify
tessellations using regular
polygons

• identify regular polygons that
can tessellate a plane

Create patterns and designs that
incorporate symmetry,
translations, tessellation, and
reflections

Create and analyze patterns and
designs using congruence,
symmetry, translation, rotation,
and reflection

• create, analyze, and describe
designs using translations
(slides) and reflections (flips)

• create, analyze, and describe
designs using rotation (turns),
reflections (flips), and
translations (slides)

• draw designs using ordered
pairs in the first quadrant of
the co-ordinate grid, together
with slide and flip images

• use informal concepts of
congruence to describe images
after rotations (turns),
reflections (flips), and
translations (slides)
• draw designs using ordered pairs
in all four quadrants of the co­
ordinate grid, together with
slide and flip images

• connect reflections with lines
and planes of symmetry

Statistics and Probability (Data Analysis)

Collect, display, and analyze data to make predictions about a population. It is expected that students will:

Collect, organize, and analyze
with assistance, data based on
first-hand information
• collect first-hand information
by counting objects, conducting
surveys, measuring, and
performing simple experiments
• sort objects to one attribute
chosen by teacher or student
• construct a pictograph using
one-to-one correspondence

• compare data using appropriate
language including quantitative
terms
• pose oral questions in relation
to the data gathered

Collect data based on first- and
second-hand information, display
results in more than one way,
interpret data, and make
predictions
• formulate questions and
categories for data collection
and actively collect first-hand
information

• use a variety of methods to
collect and record data,
including measuring devices,
printed resources, and tallies

Collect first- and second-hand
data, assess and validate the data
collection process, and graph the
data
• select an appropriate sample or
population and organize the
collection of data
• manipulate data to create an
interval graph/table for display
purposes
• construct a bar graph and
pictograph using many-to-one
correspondence and justify the
choice of intervals and
correspondence used

• sort and organize data by one
or more attributes and by
using graphic organizers such
as lists and charts

• evaluate the process by which
the data was collected

• identify attributes and rules in
pre-sorted sets

• solve logic problems with a
prepared matrix

• display data in more than one
way, including concrete graphs,
pictographs, bar graphs, and
rank ordering
• discuss data, communicate
conclusions, and make
predictions and inferences to
solve similar problems
• generate new questions from
displayed data
• obtain new information by
performing arithmetic
operations on the data

Develop and implement a plan
for the collection, display, and
analysis of data gathered from
appropriate samples

Develop and implement a plan for
the collection, display, and analysis
of data gathered from appropriate
samples

Develop and implement a plan for
the collection, display, and analysis
of the data using measures of
variability and central tendency

• identify a question to generate
appropriate data, and predict
results

• formulate a key question from
a problem-solving context

• formulate questions which
explore whether or not a
relationship exists in a real
world context

• distinguish between a total
population and a sample
• use a variety of methods to
collect and record data
• create classifications and
ranges for grouping data

• display data by hand or by
computer in a variety of ways,
including:
• frequency diagrams
• line plots
• broken-line graphs

• evaluate the graphic
presentation of the data to
ensure clear representation of
the results
• discuss the reasonableness of
data and results

• make inferences to generate a
conclusion regarding the data

• identify appropriate data
sources (first-hand, second­
hand, combination)
• select and justify appropriate
methods of collecting data
(designing and using structured
questionnaires, experiments,
observations, and electronic
networks)

• select and justify the choice of
an appropriate sample of
population to be used to
answer a question
• discuss how data collected are
affected by the nature of the
sample, the method of
collection, the sample size, and
biases

• display data by hand or by
computer in a variety of ways
including:
• histograms
• double bar graphs
• stem and leaf plots
• read and interpret graphs that
are provided
• describe the general
distribution of data
• smallest and largest value
• frequency, which occurs
most often/least often
• value in the middle
• patterns
• analyze sets of data to make
comparisons and test
predictions

• select and justify appropriate
methods of collecting data
(designing and using
questionnaires, interviews,
experiments, and research)
• display data by hand or by
computer in a variety of ways,
including circle graphs

• read and interpret graphs that
are provided
• determine measures of central
tendency for a set of data
• mode
• median
• mean
• determine measures of the
distribution of a set of data
• range
• extremes, gaps, and
clusters
• quartiles
• interpolate from data to make
predictions

Statistics and Probability
(Chance and Uncertainty)
Use experimental or theoretical probability to represent and solve problems involving uncertainty. It is expected

that students will:

Describe concepts of chance and
chance events using ordinary
vocabulary

Use simple experiments designed
by others to illustrate and
explain probability and chance

• predict the chance of an event
happening using the terms
never, sometimes, always

• describe the likeliness of an
outcome using terms such as
likely, unlikely, fair chance,
probable, expected
• conduct a probability
experiment, choose an
appropriate recording method,
and make conclusions and
predictions from the results

Conduct simple probability
experiments to explain outcomes
• identify an outcome as possible,
impossible, certain, uncertain
• compare outcomes as equally
likely, more likely, less likely
• design and conduct experiments
to answer his or her own
questions

Predict outcomes, conduct
experiments, and communicate
the probability of single events

Use numbers to communicate
the probability of single events
from experiments and models

• list all possible outcomes of an
event

• distinguish between
experimental and theoretical
probability of single events

• explain events using the
vocabulary of probability
• best/worst
• probable/improbable
• never/less likely/equally
• likely/more likely/always

• conduct probability
experiments and explain the
results using the vocabulary of
probability
• conduct probability
experiments to demonstrate
that results are not influenced
by factors such as the age,
experience, or skills of the
participant

• using various polyhedrons
make the connection between
the number of faces and the
probability of a single event
• calculate theoretical probability
using numbers between zero
and one
• demonstrate that different
outcomes may occur when
repeating the same experiment
• compare experimental results
with theoretical results

Create and solve problems using
probability
• use a table to identify all
possible outcomes of two
independent events
• use a given simulation method
to solve probability problems,
e.g., Monte Carlo method
• create and solve problems using
the definition of probability as
favourable outcomes over total
outcomes

Province of British Columbia

Ministry of Education

Printed on recycled paper