Alberta

Number

• Students analyze sets of real numbers.

  • Represent the elements of a set of numbers, including the empty set.

    • Sets, subsets and complements (9)

  • Describe a set of numbers as finite or infinite.

  • Justify whether a set of numbers is a subset of another.

  • Represent natural, integer, rational, and irrational number subsets of real numbers.

  • Identify the subsets to which a real number belongs.

• Students analyze exponent laws and powers of 10.

  • Investigate the role of parentheses in powers.

    • Powers with integer bases (9-I.2)
    • Powers with decimal and fractional bases (9-I.3)

  • Justify exponent laws, using repeated multiplication.

    • Powers with integer bases (9-I.2)
    • Powers with decimal and fractional bases (9-I.3)

  • Justify the zero exponent law.

  • Justify the negative exponent law.

    • Negative exponents (9-I.4)

  • Simplify expressions that include powers, using exponent laws limited to integer values for a, b, m, n.

    • Multiplication with exponents - integral bases (9-I.5)
    • Division with exponents - integral bases (9-I.6)
    • Multiplication and division with exponents - integral bases (9-I.7)
    • Power rule - integral bases (9-I.8)

  • Investigate the relationship between powers of 10 and place value.

    • Write powers of ten with exponents (9)

  • Express a power of 10 as a decimal number and as a fraction.

    • Evaluate powers of ten with negative exponents (9)

  • Express numbers of very large and very small magnitude, using scientific notation.

  • Convert between scientific notation and decimal numbers.

    • Convert between standard and scientific notation (9-J.1)

  • Discuss scientific notation in real-world situations.

Algebra

• Students interpret arithmetic operations, using single-variable polynomials.

  • Multiply monomials.

    • Multiply monomials (9-U.2)
    • Multiply monomials to find area (9-U.3)

  • Expand and simplify two polynomials with three terms or less.

    • Multiply two polynomials using algebra tiles (9)
    • Multiply two binomials (9)
    • Multiply two binomials: special cases (9)
    • Multiply polynomials (9)

  • Factor polynomial expressions involving common factors.

    • GCF of monomials (9)
    • Factor out a monomial (9)

  • Factor polynomials in the form x² + bx + c.

    • Factor quadratics with leading coefficient 1 (9)

  • Factor polynomial expressions, using difference of squares, limited to integer numbers.

    • Factor quadratics: differences of squares (9)

  • Justify the factors of a polynomial through expansion.

  • Determine when a polynomial is non-factorable.

• Students solve single-variable simple quadratic equations.

  • Determine the number of solutions for a quadratic equation in the form x² = a for values of a less than, greater than, and equal to 0.

  • Solve quadratic equations in the form x² = a, including in real-world situations.

  • Solve quadratic equations in the form x² + c = 0, where c is an integer.

• Students define solutions to single-variable linear inequalities.

  • Solve single-variable linear inequalities.

    • 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)
    • Solve two-step linear inequalities (9-O.8)

  • Determine whether a number is a solution to an inequality.

    • Identify solutions to inequalities (9-O.3)

  • Relate various representations of the solution set for an inequality.

    • Graph inequalities (9-O.1)
    • Write inequalities from graphs (9-O.2)

  • Represent the solution set for an inequality on the number line.

    • Graph solutions to one-step linear inequalities (9-O.7)
    • Graph solutions to two-step linear inequalities (9-O.9)

  • Represent the solution set for an inequality, using set-builder notation.

  • Solve problems by using inequalities, including in real-world situations.

Geometry

• Students analyze relationships between triangles.

  • Model congruent and similar triangles, using hands-on materials or a digital geometry environment.

  • Verify the three properties of triangle congruence.

    • SSS, SAS and ASA Theorems (9)

  • Justify the congruence of two triangles, using the properties of triangle congruence.

    • SSS, SAS and ASA Theorems (9)

  • Represent congruence of two triangles, using symbolic notation.

    • SSS, SAS and ASA Theorems (9)

  • Determine the three pairs of equal sides and three pairs of equal angles, given the congruence statement for two triangles.

    • Congruence statements and corresponding parts of triangles (9)

  • Justify triangle theorems, using hands-on materials or a digital geometry environment.

    • SSS Theorem in the coordinate plane (9)

  • Verify the properties of triangle similarity.

    • Triangle Proportionality Theorem (9)
    • Angle-angle criterion for similar triangles (9)

  • Justify the similarity of two triangles, using the properties of triangle similarity.

    • Similarity rules for triangles (9)

  • Write a similarity statement for two similar triangles.

  • Determine the three pairs of equal angles and the three pairs of proportional sides, given the similarity statement for two triangles.

    • Side lengths and angle measures in similar triangles (9)

  • Solve problems involving triangles.

    • Midsegments of triangles (9)
    • Triangles and bisectors (9)
    • Solve problems involving corresponding parts of triangles (9)

Measurement

• Students analyze surface area and volume of right composite 3-D shapes.

  • Visualize and model the 2-D shapes that compose the surface of a composite 3-D shape, using 2-D models or a digital geometry environment.

  • Compare the surface area of a composite 3-D shape to the sum of the surface areas of the 3-D shapes from which it is composed.

  • Describe the effect of adding or removing one or more 3-D shapes on the surface area of a composite 3-D shape.

  • Calculate the surface area of composite 3-D shapes composed of prisms, pyramids, and cylinders.

  • Visualize and model a composite 3-D shape as a composition of multiple 3-D shapes, using 3-D models or a digital geometry environment.

  • Describe the effect of adding or removing one or more 3-D shapes on the volume of a composite 3-D shape.

  • Visualize the decomposition of a rectangular prism into rectangular pyramids, using 3-D models or a digital geometry environment.

  • Calculate the volume of composite 3-D shapes composed of prisms, pyramids, and cylinders, given the relevant formulas.

  • Solve problems involving surface area and volume of composite 3-D shapes.

  • Compare the surface areas of various rectangular prisms that have equal volumes, using cube structures or 2-D models.

  • Investigate the effect of decreasing the height and increasing the dimensions of the base on the volume of prisms, pyramids, and cylinders.

  • Solve problems involving surface area and volume in real-world situations.

Functions

• Students connect linear functions to real-world situations.

  • Express a linear function in function notation, given two points from the graph.

    • Slope-intercept form: write an equation from a table (9-S.9)

  • Express a linear function in function notation, given the slope and one point from the graph.

    • Slope-intercept form: write an equation from a table (9-S.9)

  • Interpret the meaning of x- and y-intercepts of linear functions within the context of real-world situations.

  • Express the domain and range of a linear function, using set-builder notation.

  • Relate various representations of a linear function.

    • Compare linear functions: graphs, tables and equations (9-S.14)

  • Evaluate a function in function notation, given an input value.

    • Evaluate a function (9-Q.6)

  • Determine the input value, given the output value of the function in function notation.

    • Find values using function graphs (9-Q.5)

  • Generate an arithmetic sequence, given a function.

    • Arithmetic sequences (9-L.2)
    • Write variable expressions for arithmetic sequences (9-L.5)

  • Predict input and output values of a linear function, using interpolation and extrapolation.

    • Interpret the graph of a function: word problems (9-Q.10)

  • Solve problems involving linear functions.

    • Write linear functions to solve word problems (9-S.12)

Statistics

• Students analyze distributions, using spread.

  • Determine the range, five-number summary, and interquartile range for a distribution.

    • Calculate mean, median, mode and range (9-Y.1)
    • Interpret charts to find mean, median, mode and range (9-Y.2)
    • Quartiles (9-Y.4)

  • Identify outliers in a distribution.

    • Identify an outlier (9)

  • Examine the effect of outliers on measures of central tendency and spread.

    • Identify an outlier and describe the effect of removing it (9)

  • Justify the inclusion or exclusion of an outlier from a data set.

  • Represent distributions, using box plots.

  • Interpret the spread of distributions represented by box plots.

    • Interpret box-and-whisker plots (9-P.5)

  • Compare the spread of distributions of two different samples of the same population, using box plots.

    • Interpret box-and-whisker plots (9-P.5)

Probability

• Students interpret probability of mutually exclusive and non-mutually exclusive events.

  • Calculate the probability of the intersection of two independent events.

    • Probability of independent events (9)

  • Determine whether two events are mutually exclusive.

  • Model sample spaces and events with Venn diagrams.

  • Calculate the probability of the union of two non-mutually exclusive events.

    • Probability of opposite, mutually exclusive and overlapping events (9)

  • Calculate the probability of the union of two mutually exclusive events.

    • Probability of opposite, mutually exclusive and overlapping events (9)

  • Identify complementary events.

  • Calculate the probability of an event, given the probability of its complement, and vice versa.

    • Probability of opposite, mutually exclusive and overlapping events (9)