Skill Descriptor: Describe numbers, ways of representing numbers, relationships among numbers, and number systems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Identify numbers with square roots that are between two benchmarks
• Identify rational numbers that are between two benchmark rational numbers
• Make approximations using the roots of perfect squares as benchmarks
• Determine square roots of rational numbers (that are perfect squares) using technology
• Determine square roots of positive rational numbers that are perfect squares
• Determine the corresponding positive rational numbers given square roots
• Order rational numbers in fraction and decimal form using number lines
• Identify errors in calculations of square roots
• Explain why square roots of rational numbers shown on calculators may be approximations

Skill Descriptor: Describe powers with integral bases and whole number exponents (excluding base 0).

Global Competencies: CM, CTPS

Achievement Indicators:

• Represent powers concretely, pictorially, or symbolically
• Record powers as repeated multiplication and vice-versa
• Evaluate powers with integral bases (excluding base 0) and whole number exponents
• Explain the difference between two powers where the exponent and base are interchanged
• Explain the role of parentheses in powers by evaluating a given set of powers
• Demonstrate the difference between the exponent and the base
• Demonstrate that a^0 is equal to 1 for a given value of a (a ≠ 0) using patterns

Skill Descriptor: Apply the order of operations, including exponents.

Global Competencies: CTPS

Achievement Indicators:

• Identify errors in applying the order of operations
• Solve expressions involving operations on rational numbers in fraction forms and decimal forms
• Apply the order of operations to solve problems

Skill Descriptor: Apply operations to powers (integral bases excluding base 0, and whole-number exponents).

Global Competencies: CM, CTPS

Achievement Indicators:

• Identify errors in simplifications of expressions involving powers
• Determine the sum or difference of powers
• Apply exponent laws to evaluate expressions
• Explain exponent laws of powers with integral bases (excluding base 0) and whole number exponents
• Solve exponent problems

Skill Descriptor: Compare and critique the presentation of data.

Global Competencies: CTPS, SGC

Achievement Indicators:

• Identify mathematical data examples of discrimination and racism in contemporary forms of media, including popular culture, movies, and literature
• Identify potential problems and describe limitations with data collection choices in case studies that use populations to answer questions
• Analyze how and why some perspectives get privileged over Wabanaki perspectives by examining power relations in data collection
• Analyze case studies involving data collection
• Critique generalizations made from samples of populations and determine if they are valid or not valid for the populations

Skill Descriptor: Create and interpret graphs to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Describe patterns found in graphs
• Identify attributes of histograms including title, labels for axes, and intervals
• Match equations with their corresponding graphs
• Create histograms from sets of data
• Graph linear relations, including horizontal and vertical lines
• Extrapolate graphs to determine unknown elements
• Extrapolate and interpolate approximate values of variables on graphs given the value of the other variable
• Explain why sets of data can be represented by histograms (continuous data) or bar graphs (discrete data)
• Interpret histograms to answer questions
• Analyze graphs to solve problems

Skill Descriptor: Describe theoretical, experimental, and subjective probability in society.

Global Competencies: CTPS

Achievement Indicators:

• Identify assumptions and limitations associated with probabilities
• Analyze examples where probability can be used to support opposing positions
• Analyze examples where probability is used in forms of media
• Analyze examples of decisions based on probability that may be a combination of theoretical probability, experimental probability, and subjective judgment

Skill Descriptor: Solve linear equations.

Global Competencies: CTPS

Achievement Indicators:

• Describe contexts for solving linear equations
• Represent problems using linear equations concretely, pictorially, or symbolically
• Record linear equations representing patterns in tables of values
• Record the process of solving linear equations
• Verify linear equations by substituting values from tables
• Verify solutions to linear equations by substituting rational numbers
• Justify solutions of linear equations
• Solve linear pattern problems using linear equations

Skill Descriptor: Solve linear inequalities (single variable with rational coefficients).

Global Competencies: CM, CTPS

Achievement Indicators:

• Translate problems into single variable linear inequalities using the symbols ≥, >, < or ≤
• Determine if rational numbers are possible solutions for linear inequalities
• Graph solutions of linear inequalities
• Verify solutions of linear inequalities by substitution
• Explain the algebraic process of solving linear inequalities and linear equations
• Explain and compare solutions of linear equations and linear inequalities
• Apply rules for adding, subtracting, multiplying, and dividing positive and negative numbers to solve inequalities
• Solve problems involving linear inequalities

Skill Descriptor: Describe polynomials (limited to polynomials of a degree less than or equal to 2).

Global Competencies: CTPS

Achievement Indicators:

• Describe contexts for first-degree polynomial expressions
• Identify the variables, degree, number of terms, and coefficients (including the constant term) of simplified polynomial expressions
• Match equivalent polynomial expressions in simplified form
• Represent polynomial expressions concretely, pictorially, or symbolically
• Record expressions for models of polynomials

Skill Descriptor: Apply operations to polynomial expressions (limited to polynomials of a degree less than or equal to 2).

Global Competencies: CTPS

Achievement Indicators:

• Identify like and unlike terms
• Identify or provide examples of equivalent polynomial expressions pictorially or symbolically
• Identify errors in simplification of polynomial expressions
• Represent the addition and subtraction of polynomial expressions concretely, pictorially, or symbolically
• Represent multiplication and division of polynomial expressions by monomials concretely, pictorially, or symbolically
• Apply personal strategies for the addition, subtraction, multiplication and division of polynomial expressions

Skill Descriptor: Estimate and measure using personal referents and measurement tools.

Global Competencies: CM, CTPS

Achievement Indicators:

• Identify faces of cylinders and prisms
• Determine the area of overlap of composite or concrete 3D right cylinders, right rectangular prisms, and right triangular prisms
• Determine surface area of composite or concrete 3D right cylinders, right rectangular prisms, and right triangular prisms
• Apply strategies for determining the surface area of right cylinders, right rectangular and right triangular prisms
• Explain the relationship between area of 2D shapes and surface area of composite or concrete 3D objects
• Explain the effect of overlap on determining the surface area of composite or concrete 3D right cylinders, right rectangular prisms, and right triangular prisms

Skill Descriptor: Apply properties of circles to solve problems.

Global Competencies: CM, CTPS

Achievement Indicators:

• Determine the measure of angles inscribed in semicircles
• Demonstrate that perpendicular lines from the centre of circles to chords, bisect the chord
• Demonstrate that measures of central angles are equal to twice the measure of the inscribed angle subtended by the same arc
• Demonstrate that inscribed angles subtended by the same arc are congruent
• Demonstrate that tangents to a circle are perpendicular to the radius at the point of tangency
• Explain relationships between centres of circles, chords, and perpendicular bisectors of chords

Skill Descriptor: Describe polygons and 3D objects.

Global Competencies: CM, CTPS, ICE

Achievement Indicators:

• Describe composite and concrete 3D objects including top, front, and side views
• Compare views of composite 3D objects to the views of concrete 3D objects
• Create composite or concrete 3D objects given top, front, and side views
• Create top, front, and side views that result from rotations around the vertical axis (limited to multiples of 90 degrees)
• Create polygons that are similar to given polygons
• Predict top, front and side views that would result from described rotations around the vertical axis and (limited to multiples of 90 degrees)
• Explain why sets of polygons are not similar
• Explain the relationship between corresponding sides of similar polygons
• Explain why right triangles with shared acute angles are similar
• Solve problems that involve similarity of polygons

Skill Descriptor: Describe line and rotational symmetry.

Global Competencies: CTPS

Achievement Indicators:

• Describe types of symmetry, line, rotational symmetry, order, and angle of rotation in examples of art
• Describe types of symmetry that result from transformations of 2D shapes
• Describe the order and angle of rotation of 2D shapes or designs with rotational symmetry
• Identify lines of symmetry or the order and angle of rotational symmetry in tessellations
• Classify 2D shapes or designs according to the number of lines of symmetry
• Compare 2D shapes by determining rotational or line symmetry
• Determine if 2D shapes or designs have rotational symmetry about the centre point of the shape or design
• Record coordinates and complete 2D shapes or designs given one half of the shape or design and a line of symmetry
• Record coordinates and complete transformations of 2D shapes
• Rotate 2D shapes about a vertex
• Apply translation rules to translate images of shapes and label vertexes and corresponding ordered pairs
• Explain why translations do not result in line or rotational symmetry

Skill Descriptor: Solve scale diagram problems involving 2D shapes by using properties of similar triangles.

Global Competencies: CTPS

Achievement Indicators:

• Provide examples of scale diagrams in forms of media
• Enlarge and reduce 2D shapes
• Determine scale factors for diagrams drawn to scale
• Determine if diagrams are proportional to original 2D shapes
• Determine the scale factor of proportional scale diagrams of 2D shapes
• Interpret scale factors of scale diagrams