New Brunswick

9.N Number

• Develop number sense

  • 9.N1 Demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents by: representing repeated multiplication using powers; using patterns to show that a power with an exponent of zero is equal to one; and solving problems involving powers.

    • Understanding exponents (9-I.1)
    • Exponents with integer bases (9-I.2)

  • 9.N2 Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents.

    • Multiplication with exponents - integral bases (9-I.5)
    • Power rule - integral bases (9-I.8)
    • Evaluate expressions using properties of exponents (9-I.13)

  • 9.N3 Demonstrate an understanding of rational numbers by: comparing and ordering rational numbers and solving problems that involve arithmetic operations on rational numbers.

    • Compare rational numbers (9-A.2)
    • Put rational numbers in order (9-A.3)
    • Add and subtract rational numbers (9-B.4)
    • Add and subtract rational numbers: word problems (9-B.5)
    • Multiply and divide rational numbers (9-B.6)
    • Multiply and divide rational numbers: word problems (9-B.7)

  • 9.N4 Explain and apply the order of operations, including exponents, with and without technology.

    • Evaluate numerical expressions involving integers (9-B.2)
    • Evaluate numerical expressions involving rational numbers (9-B.8)

  • 9.N5 Determine the square root of positive rational numbers that are perfect squares.

    • Square roots of perfect squares (9-A.6)
    • Square roots of fractions and decimals (9-A.7)

  • 9.N6 Determine an approximate square root of positive rational numbers that are non-perfect squares.

    • Estimate square roots (9-A.8)

9.PR Patterns & Relations

• Use patterns to describe the world and solve problems

  • 9.PR1 Generalize a pattern arising from a problem-solving context using linear equations and verify by substitution.

    • Write direct variation equations (9-R.4)
    • Write and solve direct variation equations (9-R.5)
    • Slope-intercept form: write an equation from a word problem (9-S.10)
    • Write linear functions to solve word problems (9-S.12)

  • 9.PR.2 Graph linear relations, analyze the graph and interpolate or extrapolate to solve problems.

    • Interpret the graph of a function: word problems (9-Q.10)
    • Graph a proportional relationship (9-R.3)
    • Slope-intercept form: graph an equation (9-S.6)
    • Complete a table and graph a linear function (9-S.13)

• Represent algebraic expressions in multiple ways

  • 9.PR3 Model and solve problems using linear equations of the form: ax = b; x/a = b, a ≠ 0; ax + b =c; x/a + b = c, a ≠ 0; ax = b + cx; a(x + b) = c; ax + b = cx + d; a(bx + c) = d(ex + f); and a/x = b, x ≠ 0 where a, b, c, d, e and f are rational numbers.

    • Model and solve equations using algebra tiles (9-N.1)
    • Write and solve equations that represent diagrams (9-N.2)
    • Solve one-step linear equations (9-N.3)
    • Solve two-step linear equations (9-N.4)
    • Solve advanced linear equations (9-N.5)
    • Solve equations with variables on both sides (9-N.6)
    • Solve equations: complete the solution (9-N.7)
    • Solve linear equations: word problems (9-N.10)
    • Solve linear equations: mixed review (9-N.11)

  • 9.PR4 Explain and illustrate strategies to solve single variable linear inequalities with rational coefficients within a problem-solving context.

    • Graph inequalities (9-O.1)
    • Write inequalities from graphs (9-O.2)
    • Identify solutions to inequalities (9-O.3)
    • Solve one-step linear inequalities: addition and subtraction (9-O.4)
    • Solve one-step linear inequalities: multiplication and division (9-O.5)
    • Solve one-step linear inequalities (9-O.6)
    • Graph solutions to one-step linear inequalities (9-O.7)
    • Solve two-step linear inequalities (9-O.8)
    • Graph solutions to two-step linear inequalities (9-O.9)
    • Solve advanced linear inequalities (9-O.10)
    • Graph solutions to advanced linear inequalities (9-O.11)

  • 9.PR5 Demonstrate an understanding of polynomials (limited to polynomials of degree less than or equal to 2).

    • Polynomial vocabulary (9-V.1)
    • Model polynomials with algebra tiles (9-V.2)

  • 9.PR6 Model, record and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially and symbolically (limited to polynomials of degree 1 or 2).

    • Add and subtract polynomials using algebra tiles (9-V.3)
    • Add polynomials to find perimeter (9-V.5)

  • 9.PR7 Model, record and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree 1 or 2) by monomials, concretely, pictorially and symbolically.

    • Multiply a polynomial by a monomial (9-V.6)
    • Multiply polynomials to find area (9-V.7)
    • Divide a polynomial by a monomial (9-V.8)

9.SS Shape & Space

• Use direct and indirect measurement to solve problems

  • 9.SS1 Solve problems and justify the solution strategy using circle properties including: the perpendicular from the centre of a circle to a chord bisects the chord; the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc; the inscribed angles subtended by the same arc are congruent; and a tangent to a circle is perpendicular to the radius at the point of tangency.

    • Central angles (9-F.4)
    • Arcs and chords (9-F.8)
    • Tangent lines (9-F.9)
    • Inscribed angles (9-F.11)

• Describe 3-D objects and 2-D shapes, and analyze the relationships

  • 9.SS2 Determine the surface area of composite 3-D objects to solve problems.

  • 9.SS3 Demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons.

    • Similar figures: side lengths and angle measures (9-E.17)

• Describe and analyze position and motion of objects and shapes

  • 9.SS4 Draw and interpret scale diagrams of 2-D shapes.

    • Scale drawings: word problems (9-C.7)
    • Similar triangles and indirect measurement (9-E.18)
    • Area and perimeter of similar figures (9-E.19)
    • Dilations and scale factors (9-E.26)

  • 9.SS5 Demonstrate an understanding of line and rotational symmetry.

    • Symmetry (9-E.5)
    • Count lines of symmetry (9-E.6)
    • Draw lines of symmetry (9-E.7)

9.SP Statistics & Probability

• Collect, display and analyze data to solve problems

  • 9.SP1 Describe the effect of the following on data collection: bias; use of language; ethics; cost; time and timing; privacy; and cultural sensitivity.

    • Identify biased samples (9-Y.5)

  • 9.SP2 Select and defend the choice of using either a population or a sample of a population to answer a question.

  • 9.SP3 Construct, label, and interpret histograms to solve problems.

    • Interpret bar graphs, line graphs and histograms (9-P.1)
    • Create bar graphs, line graphs and histograms (9-P.2)

  • 9.SP4 Develop and implement a project plan for the collection, display and analysis of data by: formulating a question for investigation; choosing a data collection method that includes social considerations; selecting a population or a sample; collecting the data; displaying the collected data in an appropriate manner; and drawing conclusions to answer the question.

• Use experimental or theoretical probabilities to solve problems

  • 9.SP5 Demonstrate an understanding of the role of probability in society.

    • Theoretical probability (9-X.1)
    • Experimental probability (9-X.2)
    • Probability of independent and dependent events (9-X.5)