List of Strands


Goals under Algebra
 Calculate unit rates and unit prices.

Classifying relations as linear or nonlinear by examining graphs, equations, or
tables.
 Compare two sets of data
using ratios.

Create, extend iterative patterns.

Describe how a change in one quantity results in a change in another quantity.

Describe how a change
in one variable affects the value of a related variable.

Develop fluency in the use of exponential notation.

Draw freehand sketches of graphs that model real phenomena and use such graphs to
predict and interpret events: Changes over time. Rates of change.
 Evaluate algebraic
expressions for a given value of the variable.

Evaluate numerical expressions using order of operations.

Explain the relationship between fractions and division.

Extend or find a missing element in a number pattern.

Extend or find a missing element in a pattern displayed in a table.
 Extend understanding
and use of equality and inequality symbols.

Find the distance between two points on a number line.

Find the missing number in the proportion using cross multiplication.
 Find the rule for a number pattern.

Find the rule for the pattern shown in a table.

Graph proportional relationships in the form y = kx and describe characteristics
of the graphs.

Identifies and plots ordered pairs in all four quadrants of the coordinate system.

Identify
and graph ordered pairs in Quadrant I on a coordinate plane.

Identify or graph solutions of inequalities on a number line.

Identify the reciprocal of a rational number.

Recognize and identify perfect squares and their square roots.

Represent and analyze simple functions using tables.

Represent patterns using verbal rules.

Select the better deal by finding and comparing the unit prices.

Simplify algebraic expressions by combining like terms.

Solve and explain twostep equations involving whole numbers using inverse operations.

Solve one step inequalities in
one variable.

Solve onestep linear equations in one variable.

Solve problems involving rates, average speed, distance, and time.
 Solve
problems involving scale factors, using ratio and proportion.
 Solve twostep
equations using inverse operations.

Translate verbal phrases to algebraic expressions.

Use parentheses to indicate which operation to perform first when writing expressions
containing more than two terms and different operations.

Use proportions to describe relationships and solve problems.

Use the algebraic terms appropriately: variable, coefficient, term, equation and
inequality.

Use variables in expressions describing geometric quantities.

Using charts and graphs, describe changes over time as increasing, decreasing, and
varying.

Write an expression using variables to represent unknown quantities.
 Write numbers using scientific
notation.

Write simple equations accurately to represent relationships.

Write simple inequalities accurately to represent relationships.
Goals under Basic Geometrical Ideas (2 D)

Identifying centre, radius, diameter, arc, sector, chord, segment, semicircle, circumference
of a circle.

Identifying point, line segment rays, angles open and closed figures.

Identifying sides, vertices, angles, diagonals, adjacent sides and opposite sides
of a quadrilateral.

Identifying vertices, sides, angles, interior and exterior, altitude and median
of a triangle.
Goals under Concept of Perimeter and Introduction
to Area
Goals under Data Analysis and Probability
 Appropriate representation
for a specific set of data.

Calculate basic probability of dependent events.

Calculate the probability of complementary events.

Calculate the range for a given set of data.

Compare different samples of a population with the data from the entire population
and identify a situation in which it makes sense to use a sample.
 Construct double bar graphs.

Construct line plots for the given set of data.

Construct stemandleaf plots.

Create a sample space for one or twostage events and represent it in the form of
a list, chart, picture, or tree diagram.

Describe an event as likely or unlikely and explain the degree of likelihood using
words such as certain, very likely, not likely, or impossible.

Describe the median for a set of data.

Describe the mode for a set of data.

Determine and justify the most appropriate graph to display a given set of data.

Determine experimental
probability of an event.

Determine probabilities of events: Multiplication rule for probabilities.

Determine the number of possible outcomes for simple events using a variety of methods
such as: organized lists or tree diagrams.

Determine theoretical and experimental probabilities and use them to make predictions
about events.

Determining the number of possible outcomes by using the fundamental counting principle
or other techniques

Develop fluency with permutations and combinations.

Develop the concept of sampling when collecting data from a population and decide
the best method to collect data for a particular question.

Explore vertexedge graphs and tree diagrams: Vertex, edge, neighboring/adjacent,
number of neighbors. Path, circuit.

Express probability using fractions, ratios, decimals, and percents.
 Find the mean of a set of data.

Find the probability of an event.

Find the probability of independent, and/or dependent events.

Find the theoretical probability of an event not occurring.

Find theoretical probability of a given event.

Formulate questions to collect, organize and display data.

Identify an appropriate sample to test a given hypothesis.

Identify and explain the misleading representations of data.

Identify data that represent sampling errors and explain why the sample might be
biased.
 Identify outliers of
a set of data.

Identify situation with independent or dependent events in an experiment, simulation,
or situation.

Illustrate and apply the concept of complementary events.

Interpret and construct Venn diagrams to sort and describe data.

Interpret data from double bar graphs.

Interpret data from line graphs.

Interpret data from line plots.

Interpret data in stemandleaf plots.

Know that probability of certain event is 1 and of impossible event is 0.

List the possible combinations
of two elements chosen from a given set.

Organize and display data in bar graphs.

Organize and display data in histogram.

Organize and display data in line graphs.

Organize and display data to make circle graphs.

Read and interpret histograms.

Read, construct and interpret circle graphs.

Read, interpret and draw conclusions from a bar graph.

Record data in a frequency table.

Represent and interpret data using frequency distribution tables.
 Solve
contextual problems represented by vertexedge graphs.

Understand when the probability of an event is 0 or 1.

Use data to estimate the probability of future events.

Use observations about differences in data to make justifiable inferences.

Use tree diagrams, tables, and organized lists to compute probabilities for simple
compound events.

Use vertexedge graphs and algorithmic thinking to represent and find solutions
to practical problems: Finding the shortest network connecting specified sites.
Goals under Data Handling
Goals under Geometry
 Apply the angle sum theorem
to find the missing angle in a triangle.

Apply the Exterior Angle Theorem of triangles.

Classify angles as acute, obtuse, right, or straight.

Classify triangles as right, acute or obtuse.

Classify triangles as scalene, isosceles, or equilateral.

Compare and contrast cylinders and cones.

Compare and contrast right prisms and pyramids.

Describe the effect of performing transformations on figures using coordinate grid.

Describe the transformation used to move a polygon from one location to another
location in a coordinate plane.

Determine and use lines of symmetry.

Determine relationships among the radius, diameter, center and circumference of
a circle.

Determine the area of irregular shapes using strategies and procedures of combining
and dividing shapes.

Effects on perimeter and area of a 2 dimensional shape when the dimensions are
changed.

Estimate and justify estimates of area of irregular shapes.

Estimate angles using referents.

Find the area of a sector in a circles using radian measure.

Identifies and distinguishes among point, ray, line, line segment, and angle.

Identify a threedimensional
object from its net.

Identify and/or describe properties of cubes, pyramids, spheres, prisms, cones and
cylinders.

Identify basic shapes to demonstrate lines that illustrate intersection, parallelism,
and perpendicularity.

Identify, describe, and predict results of reflections of two dimensional shapes.

Identify, describe, and predict results of rotations of two dimensional shapes.

Identify, describe, and predict results of translations of two dimensional shapes.

Identify,
describe, compare, and classify polygons by number of sides.

Identify/classify/compare quadrilaterals according to sides and angles.

Interpret
and sketch front, back, top, bottom and side views of solid figures.

Model, sketch, draw, and label complementary angles, supplementary angles, vertical
angles, and adjacent angles.

Plot points on a coordinate graph in quadrant 1.

Represent threedimensional figures using nets made up of rectangles and triangles.

Solve problems involving scale drawings, maps, and indirect measurement.

State
the missing coordinate of a given figure in the coordinate grid using geometric
properties.

Understand that the sum of angles of any quadrilateral is 360 degrees and use this
information to solve problems.

Use a protractor to measure angles.

Use multiple classification criteria to classify triangles.
Goals under Introduction to Algebra
Goals under Knowing our Numbers
Goals under Measurement

Application problems involving the volume of fundamental solid figures.

Apply the
angle sum theorem to solve the problems involving triangles.

Calculate unit rates and unit prices.

Classify angles as right, obtuse, acute, or straight.

Classify triangles as right, acute or obtuse.

Classifying angles as right, acute, and obtuse angles.

Compare and convert units of measure for length within the U.S. Customary system
and the metric system.

Compare and convert units of measure for volume within the U.S. Customary system
and the metric system.

Compare and convert units of measure for weight/mass within the U.S. Customary system
and the metric system.

Compare and estimate angles using referents.

Compute surface area of cylinders using formulae.

Construct nets for prisms and pyramids.

Convert units within Customary system.

Convert units within metric system.

Count the distance between two points on a horizontal or vertical line and compare
the lengths of the paths on a grid.

Determine relationships among the radius, diameter, center and circumference of
a circle.

Determine the area of irregular shapes using strategies and procedures of combining
and dividing shapes.

Determine the perimeter of irregular shapes using strategies and procedures of combining
and subdividing the shapes.

Determine the sum of the measures of interior angles of quadrilaterals.

Determine the volume of rectangular prisms by counting cubes and develop the formula.

Draw,
label, and classify angles, quadrilaterals, and triangles based on their properties.

Estimate and
justify estimates of area of irregular shapes.

Estimate the perimeter of irregular figures.

Estimate the surface areas of simple geometric solids.

Estimate the volumes of simple geometric solids.

Estimates capacity/volume of familiar object.

Estimates lengths of familiar objects.

Estimates weight/mass of familiar object.

Find area of circles.
 Find
area of parallelograms.

Find surface areas of right rectangular prisms and cubes.

Find the area of rectangles.
 Find
the area of squares.
 Find the area
of trapezoids.
 Find the area of
triangles.
 Find the circumference
of a circle.
 Find the
perimeter of parallelograms.

Find the perimeter of rectangles.

Find the perimeter of squares.

Find the perimeter of trapezoids.

Find the perimeter of triangles.

Find the surface area of right rectangular prisms by constructing nets.

Find the volume of a right rectangular prisms and Cubes.

Find the volume of cylinders.

Identify and describe the diameter, radius, chord, and circumference of a circle.

Identify angle and side properties of triangles and quadrilaterals: sum of the interior
angles of any triangle is 180 degrees.

Identify equivalent customary units of capacity.

Identify equivalent metric units of capacity.

Identify, measure, describe, classify, and construct various angles.
 Interpret
and sketch front, back, top, bottom and side views of solid figures.
 Knows the
precision of different measuring instruments.

Measure angles using a protractor.

Measure length to the nearest half, fourth, eighth, and sixteenth of an inch.

Real world problems involving one elapsed time, counting forward and backward.

Recognize
pi as the ratio between the circumference and diameter of any circle.
 Select
and use units of appropriate size and type to measure length, perimeter, area and
volume.

Select appropriate standard units and tools to measure length, area, volume, weight,
time, and the size of angles.

Solve problems involving elapsed time.

Solve problems involving scale drawings, maps, and indirect measurement.

Solve problems involving the circumference of a circle when given the diameter or
radius.

Solve problems involving the perimeter of polygons.

Solve realworld problems involving elapsed time.

Use a scale to find a distance on a map or a length on a scale drawing.

Use
appropriate customary measurement tools for length, capacity and mass.

Use estimation to justify reasonableness of a volume of a rectangular prism.
Goals under Negative Numbers and Integers
Goals under Number and Operations
 Add fractions with like and
unlike denominators.
 Add integers.

Add mixed fraction with
like and unlike denominators.

Add rational numbers.

Apply the relationship between squares and square roots.

Calculate given percentages of quantities and solve problems involving discounts
at sales, interest earned, and tips.

Compare and order fractions greater than or equal to zero.

Compare and order negative rational numbers.

Compare and order rational numbers.

Compare and order whole numbers using the appropriate symbol.

Compare and/or order integers.

Compare rational numbers using symbols.

Compare, and order decimal numbers to thousandths

Convert improper fractions to mixed numbers, and mixed numbers to improper fractions.

Convert standard
notation to scientific notation, and vice versa.

Create equivalent fractions, given a fraction.

Define absolute value and determine its effect on a number or expression.

Define and identify
the zero property of multiplication.

Demonstrate an understanding of place value to billions.

Demonstrate an understanding of positive integer exponents, in particular, when
used in powers of ten.

Demonstrate an understanding of the concepts of prime and composite numbers.

Demonstrate
computational fluency with addition of decimals.

Demonstrate computational fluency with division of decimals.

Demonstrate computational fluency with multiplication of decimals.
 Demonstrate
computational fluency with subtraction of decimals.

Determine the greatest common factor of a set of whole numbers.

Determine the least common multiple of a set of whole numbers.

Determine the square root of perfect squares and mentally approximate other square
roots by identifying the two whole numbers between which they fall.
 Develop fluency in the
use of exponential notation.
 Divide
fractions
 Divide integers.

Divide mixed numbers

Divide positive and negative rational numbers.

Divide up to a fourdigit dividend by a oneor twodigit divisor including decimals.

Estimate and justify the results of addition of positive rational numbers.

Estimate and justify the results of subtraction of positive rational numbers.

Estimate products of whole
numbers.

Estimating differences of whole numbers by using appropriate strategies such as
rounding, frontend estimation, and compatible numbers.

Estimating quotients of whole numbers by using appropriate strategies such as rounding,
frontend estimation, and compatible numbers.

Estimating sums of whole numbers by using appropriate strategies such as rounding,
frontend estimation, and compatible numbers.

Explain the placement of square roots on a number line.

Explain the relationship between fractions and division.

Find and position integers, fractions, mixed numbers, and decimals on the number
line.
 Find the factors of
whole numbers.
 Find the
multiples of whole numbers.

Find the prime factorization of whole numbers.

Identify and demonstrate inverse operations of addition, subtraction, multiplication,
and division.

Identify and describe the characteristics of even and odd integers.

Identify and determine common equivalent fractions, mixed numbers, decimals, and
percents.
 Identify
and locate decimals on a number line.

Identify common factors of a set of whole numbers.

Identify common multiples of a set of whole numbers.

Identify the place values of decimals.

Identify, interpret and use ratios in different contexts.

Inverse relationship between multiplication and division of fractions.
 Locate integers on a number line

Model addition and
subtraction of decimal in a variety of ways.

Model addition of integers.

Model multiplication and division of decimal in a variety of ways.
 Model subtraction of integers.

Multiply commonly used
fractions using area models.

Multiply decimals up to four decimal places by up to fourdigit whole number.

Multiply fractions.

Multiply integers.
 Multiply
mixed numbers.
 Multiply
rational numbers.
 Order
and compare percents.
 Read and write
decimals.
 Read
and write numbers using scientific notation.

Read, write decimals using pictures

Read, write, recognize, and model percents.

Reads, writes, and identifies fractions and mixed numbers with denominators including
2, 3, 4, 5, 6, 8, 10, 12, 20, 25, 100, and 1000.

Recall basic multiplication facts and corresponding division facts.
 Recognize
that a quotient may be larger than the dividend when the divisor is a fraction.

Represent
fractions as terminating or repeating decimals.

Represent rational numbers as fractions or terminating decimals when possible, and
translate between these representations.

Select and use appropriate operations addition, subtraction, multiplication, division,
and positive integer exponents to solve problems with rational numbers.

Simplify expressions,
without exponents, using the order of operations

Simplify fractions.

Solve applied problems involving division of whole numbers.

Solve applied problems involving multiplication of whole numbers.
 Solve multi step problems
involving decimals.

Solve one step problems involving decimals.

Solve problems involving decimals multiplication, in which the multiplier is a decimal.

Solve problems involving decimals multiplication, in which the multiplier is a whole
number.
 Solve
problems involving decimals.

Solve problems involving division of decimals, in which the divisor is a whole number
or decimal.

Solve problems involving fractions.

Solve problems involving multiplication of positive fractions with whole numbers.

Solve problems involving
percents.

Solve problems involving proportions.

Solve problems involving rates.

Solve problems involving scale drawings.

Solve problems using rational numbers with square roots of perfect squares.

Solve
realworld problems involving addition of whole numbers.

Solve realworld problems involving subtraction of whole numbers.
 Subtract fraction with
like and unlike denominators.

Subtract integers.

Subtract mixed fraction with like and unlike denominators.

Subtract rational numbers.

Understand and apply the basic concept of negative numbers.

Understand integer division as the inverse of integer multiplication.
 Understand
integer subtraction as the inverse of integer addition.

Use appropriate techniques to estimate, determine, and then justify the reasonableness
of solutions to problems involving whole numbers

Use estimation to solve problems product and quotient with decimals.
 Use estimation
to solve problems sum and difference with decimals.

Use estimation to solve problems with fractions.

Use exponential notation to represent repeated multiplication of whole numbers.

Use integers to represent
reallife situations.

Use inverse operations to solve problems and check solutions involving calculations
with integers.

Use repeated multiplication notation to represent exponential notation of whole
numbers.

Use rounding with decimals to solve realworld and mathematical problems.

Use the inverse operations of addition and subtraction to solve problems and check
solutions involving adding and subtracting fractions and mixed numbers.

Use the order of operations, including the use of exponents, decimals and rational
numbers, to simplify numerical expressions.

Uses divisibility rules.

Using models, divide commonly used fractions.

Write a Decimal in expanded form.

Write a whole number to 999,999 in expanded form using exponents.
 Write whole numbers
in exponential form and viceversa.
Goals under Playing with Numbers
Goals under Ratio and Proportion
Goals under Understanding Elementary Shapes (2D
and 3D)

Classifying acute, obtuse, right, straight, reflex, complete and zero angles.

Classifying elements of 3D figures.

Classifying trapezium, parallelogram, rectangle, square, rhombus and polygon.

Classifying triangles based
on sides and angles.
 Identifying
3D shapes.

Identifying intersecting, perpendicular and parallel lines.

Identifying nets for cube, cuboids, cylinders, cones and tetrahedrons.
 Identifying regulars
as well as non regular polygons.

Measure the angles through protractor.

Measuring right, straight angle in terms of revolutions.
Goals under Whole Numbers
