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WNCP Mathematics Curriculum
Continuum of Outcomes
Grade 2 to Grade 8
(Western Northern Canadian Protocol)
This document was created using outcomes from the WNCP Mathematics Curriculum and may be revised when Saskatchewan has completed Kindergarten to Grade 8 Curricula.
CONTACT _Con3CFB858E76 \c \s \l LJ DowellHantelmann
CONTACT _Con3CFB858E1 \c \s \l Regina Public Schools
October 9, 2008
Grades 23 Numbers (Counting) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade23456CountingSay the number sequence (to 100) by:
2s, 5s and 10s, forward and backward, using starting points that are multiples of 2, 5 and 10 respectively
10s using starting points from 1 to 9
2s starting from 1
Demonstrate if a number is even or odd
Describe order or relative position using ordinal numbers (up to tenth)
Say the number sequence (to 1000) forward and backward by:
5s, 10s or 100s, using any starting point
3s, using starting points that are multiples of 3
4s, using starting points that are multiples of 4
25s, using starting points that are multiples of 2
Grades 25 Numbers (Quantity, Place Value) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade234567Numbers to 100Numbers to 1000Numbers to 10 000Numbers to 1 000 000Quantity
Estimation
Place ValueRepresent and describe numbers to 100, concretely, pictorially and symbolically
Compare and order numbers to 100
Estimate quantities to 100 using referents
Illustrate, concretely and pictorially, the meaning of place value for numerals to 100Represent and describe numbers to 1000, concretely, pictorially and symbolically
Compare and order numbers to 1000
Estimate quantities less than 1000 using referents
Illustrate, concretely and pictorially, the meaning of place value for numerals to 1000Represent and describe whole numbers to 10 000, pictorially and symbolically
Compare and order numbers to 10 000
Represent and describe whole numbers to
1 000 000
Use estimation strategies, including:
frontend rounding
compensation
compatible numbers
in problemsolving contexts
Solve problems involving large numbers, using technology
Demonstrate an understanding of place value for numbers:
greater than one million
less than one thousandth
Grades 24 Numbers (Addition/Subtraction Whole Numbers) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade23456Addition and Subtraction Facts to 18Addition and Subtraction Facts to 18Basic Facts
(Addition, Subtraction)
Addition and Subtraction with Large Numbers
Addition and Subtraction with Large Numbers
Apply mental mathematics strategies to determine basic addition facts to 18 and related subtraction facts, such as:
using doubles
making 10
one more, one less
two more, two less
addition for subtraction
Demonstrate and explain the effect of adding zero to or subtracting zero from any number
Demonstrate an understanding of addition and subtraction (limited to 1 and 2digit numerals) with answers to 100 by:
using personal strategies for adding and subtracting with and without the support of manipulatives
creating and solving problems that involve addition and subtraction
explaining that the order in which numbers are added does not affect the sum
explaining that the order in which numbers are subtracted may affect the difference
Apply mental mathematics strategies and number properties to determine answers for basic addition facts to 18 and related subtraction facts, such as:
using doubles
making 10
using the commutative property
using the property of zero
thinking addition for subtraction
Describe and apply mental mathematics strategies for addition two 2digit numerals, such as:
adding from left to right
taking one addend to the nearest multiple of ten and then compensating
using doubles
Describe and apply mental mathematics strategies for subtracting two 2digit numerals, such as:
taking the subtrahend to the nearest multiple of ten and then compensating
thinking of addition
using doubles
Apply estimation strategies to predict sums and differences of two 2digit numerals in a problemsolving context
(Continued on page 5)
Grade 3
Demonstrate an understanding of addition and subtraction of numbers with answers to 1000 (limited to 1, 2 and 3digit numerals) concretely, pictorially and symbolically
by:
using personal strategies for adding and subtracting with and without the support of manipulatives
creating and solving problems in contexts that involve addition and subtraction of numbers
Demonstrate an understanding of addition and subtraction of numbers with answers to 10 000 (limited to 3 and 4digit numerals) by:
using personal strategies for addition and subtracting
estimating sums and differences
solving problems involving addition and subtraction
Grades 38 Numbers (Multiplication/Division Whole Numbers, Squares, Multiple, Factors, Order of Operations) (WNCP Outcome Continuum)
Grade345678Basic Facts
(Multiplication, Division)
Multiplication and Division with Large Numbers
Demonstrate an understanding of multiplication to 5 x 5 by:
representing and examining multiplication using equal grouping and arrays
creating and solving problems in context that involve multiplication
modelling multiplication using concrete and visual representations, and recording the process symbolically
relating multiplication to repeated addition
relating multiplication to division
Demonstrate an understanding of division (limited to division related to multiplication facts up to 5 x 5) by:
representing and explaining division using equal sharing and equal grouping
creating and solving problems in context that involve equal sharing and equal grouping
modelling equal sharing and equal grouping using concrete and visual representations, and recording the process symbolically
relating division to repeated subtraction
relating division to multiplication
Describe and apply mental mathematics strategies to determine basic multiplication facts to 9 x 9 and related division facts, such as:
skip counting from a known fact
using doubling or halving
using doubling or halving and adding or subtracting one more group
using patterns in the 9s facts
using repeated doubling
Explain the properties of 0 and 1 for multiplication and the property of 1 for division
(Continued on Page 7)
Grade 4
Demonstrate an understanding of multiplication (2 or 3digit by 1digit) to solve problems by:
using personal strategies for
multiplication with and without concrete materials
using arrays to represent multiplication
connecting concrete representations to symbolic representations
estimating products
Demonstrate an understanding of division (1digit divisor and up to 2digit dividend) to solve problems by:
using personal strategies for dividing with and without concrete materials
estimating quotients
relating division to multiplication
Apply mental mathematics strategies and number properties to determine answers for basic multiplication facts to 9 x 9 and related division facts, such as:
skip counting from a known fact
using doubling or halving
using patterns in the 9s facts
using repeated doubling or halving
Grade 5
Demonstrate an understanding of multiplication (2digit by 2digit) to solve problems
Apply mental mathematics strategies for multiplication, such as:
annexing then adding zero
halving and doubling
using the distributive property
Demonstrate, with and without concrete materials, an understanding of division (3digit by 1digit) and interpret remainders to solve problems
Grades 38 Numbers (Squares, Multiple, Factors, Order of Operations) (WNCP Outcome Continuum, 2008, CONTACT _Con3CFB858E76 \c \s \l LJ DowellHantelmann)
Grade345678Factors and Multiples
Divisibility Rules
Perfect Squares and Square Roots
Order of OperationsDemonstrate an understanding of factors and multiples by:
determining multiples and factors of numbers less than 100
identifying prime and composite numbers
solving problems involving multiples
Explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers)
Determine and explain why a number is divisible by 2, 3, 4, 5, 6, 8, 9 or 10, and why a number cannot be divided by 0
Demonstrate an understanding of perfect squares and square roots, concretely, pictorially and symbolically (limited to whole numbers)
Determine the approximate square root of numbers that are not perfect squares
Grades 38 Numbers (Fractions, Decimals, Percents, Ratios, Rates) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade345678Fractions
Decimals
Decimals
Percents
Ratios
Rates
Demonstrate an understanding of fractions by:
explaining that a fraction represents a part of a whole
describing situations in which fractions are used
comparing fractions of the same whole with like denominators
Grade 3
Demonstrate an understanding of fractions less than or equal to one by using concrete and pictorial representations to:
name and record fractions for the parts of a whole or a set
compare and order fractions
model and explain that for different wholes, two identical fractions may not represent the same quantity
provide examples of where fractions are used
Describe and represent decimals (tenths and hundredths) concretely, pictorially and symbolically
Relate decimals to fractions (to hundredths)
Grade 4
Demonstrate an understanding of addition and subtraction of decimals (limited to hundredths) by:
using compatible numbers
estimating sums and differences
using mental math strategies
to solve problemsDemonstrate an understanding of fractions by using concrete and pictorial representations to:
create sets of equivalent fractions
compare fractions with like and unlike denominators
Describe and represent decimals (tenths, hundredths, thousandths) concretely, pictorially and symbolically
Relate decimals to fractions (to thousandths)
Grade 5
Compare and order decimals (to thousandths), by using:
benchmarks
place value
equivalent decimals
Demonstrate an understanding of addition and subtraction of decimals (limited to thousandths)
Relate improper fractions to mixed numbers
Demonstrate an understanding of multiplication and division of decimals (1digit whole number multipliers and 1digit natural numbers divisors)
Demonstrate an understanding of percent (limited to whole numbers) concretely, pictorially and symbolically
Demonstrate an understanding of ratio, concretely, pictorially and symbolicallyCompare and order positive fractions, positive decimals (to thousandths) and whole numbers by using:
benchmarks
place value
equivalent fractions and/or decimals
Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences)
Demonstrate an understanding of the relationship between positive repeating decimals and positive fractions, and positive terminating decimals and positive fractions
Grade 7
Demonstrate an understanding of the addition, subtraction, multiplication and division of decimals (for more than 1digit divisors or 2digit multipliers, the use of technology is expected) to solve problems
Solve problems involving percents from 1% to 100%
Demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially and symbolically
(continued on page 10)
Grade 8
Demonstrate an understanding of percents greater than or equal to 0%
Demonstrate an understanding of ratio and rate
Solve problems that involve rates, ratios and proportional reasoning
Grades 68 Numbers (Integers) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade678IntegersDemonstrate an understanding of integers, concretely, pictorially and symbolicallyDemonstrate an understanding of addition and subtraction of integers, concretely, pictorially and symbolicallyDemonstrate an understanding of multiplication and division of integers, concretely, pictorially and symbolically
Grades 28 Patterns and Relations (Patterns) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade2345678PatternsDemonstrate an understanding of repeating patterns (35 elements) by: describing, extending, comparing, creating patterns using manipulatives, diagrams, sounds and actions
Demonstrate an understanding of increasing patterns by: describing, reproducing, extending, creating patterns using manipulatives, diagrams, sounds and actions (numbers to 100)Demonstrate an understanding of increasing/decreasing patterns by: describing, extending, comparing, creating patterns using manipulatives, diagrams, sounds and actions (numbers to 1000)Identify and describe patterns found in tables and charts, including a multiplication chart
Reproduce a pattern shown in a table or chart using concrete materials
Represent and describe patterns and relationships using charts and tables to solve problems
Identify and explain mathematical relationships using charts and diagrams to solve problemsDetermine the pattern rule to make predictions about subsequent elements
Demonstrate an understanding of the relationship within tables of values to solve problems
Represent and describe patterns and relationships using graphs and tablesDemonstrate an understanding of oral and written patterns and their equivalent linear relations
Create a table of values from a linear relation, graph the table of values, and analyze the graph to draw conclusions and solve problemsGraph and analyze twovariable linear relations
Grades 28 Patterns and Relations (Variables and Equations) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade2345678Variables and EquationsDemonstrate and explain the meaning of equality and inequality by using manipulatives and diagrams (0 to 100)
Record equalities and inequalities symbolically using the equal symbol or the not equal symbolSolve onestep addition and subtraction equations involving symbols representing an unknown numberExpress a given problem as an equation in which a symbol is used to represent an unknown number
Solve onestep equations involving a symbol to represent an unknown numberSolve problems involving singlevariable, onestep equations with whole number coefficients and whole number solutionsRepresent generalizations arising from number relationships using equations with letter variables
Demonstrate and explain the meaning of preservation of equality concretely, pictorially and symbolicallyDemonstrate an understanding of preservation of equality by:
modeling preservation of equality, concretely, pictorially and symbolically
applying preservation of equality to solve equations
Explain the difference between an expression and an equation
Evaluate an expression given the value of the variable(s)
Model and solve problems that can be represented by onestep linear equations of the form x + a = b, concretely, pictorially and symbolically, where a and b are integersModel and solve problems using linear equations of the form:
ax=b
EMBED Equation.3 = b, a`"0
ax+b=c
EMBED Equation.3 `"0
a(x+b)=c
concretely, pictorially and symbolically, where a, b and c are integers
Grades 28 Shape and Space (MeasurementTime) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade2345678TimeRelate days, weeks, months, years in a problemsolving context
Passage of time (minutes, hours, days, weeks, months, years) using nonstandard and standard units
Relate seconds to a minute, minutes to an hour, days to a month in a problem solving context
Telling time (digital and analog clocks, including 24 hour clocks)
Calendar dates in a variety of formats
Grades 28 Shape and Space (Measurement) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade2345678Length, width, height, mass (weight), volume, capacity
Relate the size of a unit of measure to the number of units (limited to nonstandard units) used to measure length and mass (weight)
Compare and order objects (length, height, distance around and mass) using nonstandard units and make statements of comparison
Measure length to nearest nonstandard unit by:
using multiple copies of a unit
using a single copy of a unit (iteration process)
Demonstrate that changing the orientation of an object does not alter the measurements of its attributesDemonstrate an understanding of measuring length (width, height using cm and m) and mass (using g, kg) by:
selecting and justifying referents for units (cm/m) (g/kg)
modelling and describing the
relationship between the units (cm/m) (g/kg)
estimating length or mass using referents
measuring and recording length, width, height and mass
Demonstrate an understanding of measuring length (mm), volume (cm, m) and capacity (mL, L) by:
selecting and justifying referents for the units (mm, cm, m, mL, L)
Length: modelling and describing the relationship between mm and cm units, and between mm and m units
Volume: estimating volume by using referents for (cm, m)
measuring and recording volume (cm, m)
constructing rectangular prisms for a given volume
Capacity: describing the relationship between mL and L
selecting and justifying referents for mL or L units
estimating capacity by using referents for mL or L
measuring and recording capacity (mL or L)
Develop and apply a formula for determining the volume of right rectangular prisms
Determine and apply formulas for determining the volume of right prisms and right cylinders
Grades 28 Shape and Space (MeasurementPerimeter, Area, Surface Area, Constructing Nets)
(WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade2345678Perimeter
Area
Surface Area
Constructing NetsCompare and order objects (distance around) using nonstandard units and make statements of comparison
Demonstrate an understanding of perimeter of regular and irregular shapes by:
estimating perimeter using referents for centimetre or metre
measuring and recording perimeter (cm, m)
constructing different shapes for a given perimeter (cm, m) to demonstrate that many shapes are possible for a perimeterDemonstrate an understanding of area of regular and irregular 2D shapes by:
recognizing that area is measured in square units
selecting and justifying referents for the units cm/m
estimating area by using referents for cm/m
determining and recording area (cm/m)
constructing different rectangles for a given area (cm/m) in order to demonstrate that many different rectangles may have the same area
Design and construct different rectangles given either perimeter or area, or both (whole numbers) and draw conclusions
Develop and apply a formula for determining the:
perimeter of polygons
area of rectangles
Develop and apply a formula for determining the area of
triangles
parallelograms
circles
Determine the surface area of:
right rectangular prisms
right triangular prisms
right cylinders
to solve problems
Draw and construct nets for 3D objects
Grades 28 Shape and Space (MeasurementAngles, Circles) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade2345678Angles
Circles
Demonstrate an understanding of angles by:
identifying examples of angles in the environment
classifying angles according to their measure
estimating the measure of angles using 45, 90,
180 as reference angles
determining angle measures in degrees
drawing and labeling angles when the measure is specified
Demonstrate that the sum of interior angles is:
180 in a triangle
360 in a quadrilateral
Demonstrate an understanding of circles by:
describing the relationships among radius, diameter and circumference of circles
relating circumference to pi
determining the sum of the central angles
constructing circles with a given radius or diameter
solving problems involving the radii, diameters and circumferences of circles
Grades 28 Shape and Space (Pythagorean Theorem) (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade2345678Pythagorean
TheoremDevelop and apply the Pythagorean theorem to solve problems
Grades 28 Shape and Space (3D Objects and 2D Shapes) (WNCP Outcomes Continuum, 2008, LJ DowellHantelmann)
Grade23456783D Objects
2D ShapesSort 2D shapes and 3D objects using two attributes and explain the sorting rule
Describe, compare and construct 3D objects, including: cubes, spheres, cones, cylinders, pyramids
Describe, compare and construct 2D shapes, including: triangles, squares, rectangles, circles
Identify 2D shapes as parts of 3D objects in the environment
Describe 3D objects according to the shape of the faces, and the number of edges and vertices
Sort regular and irregular polygons, including: triangles, quadrilaterals, pentagons, hexagons, octagons according to the number of sidesDescribe and construct rectangular and triangular prisms
Describe and provide examples of edges and faces of 3D objects and sides of 2D shapes that are: parallel, intersecting, perpendicular, vertical, horizontal
Identify and sort quadrilaterals, including: rectangles, squares, trapezoids, parallelograms, rhombuses according to their attributesConstruct and compare triangles in different orientations
including: scalene, isosceles, equilateral, right,
obtuse,
acute
Describe and compare the sides and angles of regular and irregular polygonsPerform geometric constructions, including:
perpendicular line segments,
parallel line segments,
perpendicular bisectors,
angle bisectorsDraw and interpret top, front and side views of 3D objects composed of right rectangular prisms
Grades 48 Shape and Space (Transformations, Symmetry) (WNCP Outcomes Continuum, 2008, LJ DowellHantelmann)
Grades45678Transformations
SymmetryDemonstrate an understanding of line symmetry by:
identifying and creating symmetrical 2D shapes
drawing one or more lines of symmetry in a 2D shapePerform a single transformation (translation, rotation or reflection) of a 2D shape, (with and without technology) and draw and describe the image
Identify a single transformation including a translation, a rotation and a reflection of 2D shapesPerform a combination of translation(s), rotation(s), and/or reflection(s) on a single 2D shape, (with and without technology), and draw and describe the image
Perform a combination of successive transformations of 2D shapes to create a design, and identify and describe the transformations
Identify and plot points in the first quadrant of a Cartesian plane using whole number ordered pairs
Perform and describe single transformations of a 2D shape in first quadrant of Cartesian plane (limited to whole number vertices)
Identify and plot points in the four quadrants of a Cartesian plane using integral ordered pairs
Perform and describe transformations (translations, rotations or reflections) of a 2D shape in all four quadrants of a Cartesian plane (limited to integral number vertices)
Demonstrate an understanding of tessellation by:
explaining the properties of shapes that make tessellating possible
creating tessellations
identifying tessellations in the environment
Grades 28 Statistics (WNCP Outcome Continuum, 2008, LJ DowellHantelmann)
Grade2345678Collect Data Gather and record data about self and others to answer questionsCollect firsthand data and organize it using:
tally marks
line plots
charts
lists
to answer questionsDifferentiate between firsthand and secondhand dataSelect, justify and use appropriate methods of collecting data, including:
questionnaires
experiments
databases
electronic media
Demonstrate an understanding of central tendency and range by:
determining the measures of central tendency (mean, median, mode) and range;
determining the most appropriate measures of central tendency to report findings
Graph DataConstruct and interpret concrete graphs and pictographs to solve problemConstruct, label and interpret bar graphs to solve problemsDemonstrate an understanding of manytoone correspondence
Construct and interpret pictographs and bar graphs involving manytoone correspondence to draw conclusions
Construct and interpret double bar graphs to draw conclusionsCreate, label and interpret line graphs to draw conclusionsConstruct, label and interpret circle graphs to solve problemsAnalyze DataGraph collected data and analyze the graph to solve problemsDetermine the effect on the mean, median and mode when an outlier is included in a data set
Critique ways in which data is presented
Probability (Continuum of WNCP Outcomes, 2008, LJ DowellHantelmann)
Grade5678Describe the likelihood of a single outcome occurring using words, such as:
impossible, possible, certain
Compare the likelihood of two possible outcomes occurring using words, such as: less likely, equally likely, more likelyDemonstrate an understanding of probability by:
identifying all possible outcomes of a probability experiment
differentiating between experimental and theoretical probability experiment
determining the theoretical/experimental probability of outcomes in a probability experiment
comparing experimental results with the theoretical probability for an experimentExpress probabilities as ratios, fractions and percents
Identify the sample space (36 or fewer elements combined) for a probability experiment involving two independent events
Conduct a probability experiment to compare the theoretical probability (tree diagram, table or other graphic organizer) and experimental probability of two independent eventsSolve problems involving the probability of independent events
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