Students will be expected to demonstrate number sense.
9.N01 Students will be expected to 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 • solving problems involving powers
9.N01.01 Demonstrate the differences between the exponent and the base by building models of a given power, such as 23 and 32.
9.N01.02 Explain, using repeated multiplication, the difference between two given powers in which the exponent and base are interchanged.
9.N01.03 Express a given power as a repeated multiplication.
9.N01.04 Express a given repeated multiplication as a power.
9.N02 Students will be expected to demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents: (am)(an) = am+n; am ÷ an = am-n, m > n; (am)n = amn; (ab)m = ambm; (a/b)n = an/bn, b ≠ 0.
9.N02.01 Explain, using examples, the exponent laws of powers with integral bases (excluding base 0) and whole number exponents.
9.N02.03 Determine the sum of two given powers and record the process.
9.N02.04 Determine the difference of two given powers and record the process.
9.N02.05 Identify the error(s) in a given simplification of an expression involving powers.
9.N03 Students will be expected to demonstrate an understanding of rational numbers by comparing and ordering rational numbers and solving problems that involve arithmetic operations on rational numbers.
9.N03.01 Order a given set of rational numbers in fraction and decimal form by placing them on a number line.
Variables and Equations - Students will be expected to represent algebraic expressions in multiple ways.
9.PR03 Students will be expected to model and solve problems, where a, b, c, d, e, and f are rational numbers, using linear equations of the form: ax = b; x/a = c, 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); a/x = b, x ≠ 0
9.PR03.01 Solve the given linear equation, using concrete and pictorial representations, and record this process symbolically.
9.PR06 Students will be expected to model, record, and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially, and symbolically (limited to polynomials of degree less than or equal to 2).
9.PR06.01 Model addition of two given polynomial expressions, concretely and/or pictorially, and record the process symbolically.
9.PR06.06 Identify the error(s) in a given simplification of a given polynomial expression.
9.PR07 Students will be expected to model, record, and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially, and symbolically.
9.PR07.01 Model multiplication of a given polynomial expression by a given monomial, concretely or pictorially, and record the process symbolically.
9.PR07.04 Provide examples of equivalent polynomial expressions.
9.PR07.05 Identify the error(s) in a given simplification of a given polynomial expression.
Students will be expected to use direct and indirect measure to solve problems.
9.M01 Students will be expected to solve problems and justify the solution strategy, using the following circle properties: • 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 • a tangent to a circle is perpendicular to the radius at the point of tangency
9.M01.01 Demonstrate that:
9.M01.01.a the perpendicular from the centre of a circle to a chord bisects the chord
9.M01.03 Determine the measure of a given angle inscribed in a semicircle, using the circle properties.
9.M01.04 Explain the relationship among the centre of a circle, a chord, and the perpendicular bisector of the chord.
3-D Objects and 2-D Shapes - Students will be describe the characteristics of 3-D objects and 2-D shapes and analyze the relationships among them.
9.G01 Students will be expected to determine the surface area of composite 3-D objects to solve problems.
9.G01.01 Determine the area of overlap in a given composite 3-D object, and explain the effect on determining the surface area (limited to right cylinders, right rectangular prisms, and right triangular prisms).
9.G01.02 Determine the surface area of a given composite 3-D object (limited to right cylinders, right rectangular prisms, and right triangular prisms).
9.G01.03 Solve a given problem involving surface area.
Transformations - Students will be expected to describe and analyze position and motion of objects and shapes.
9.G02 Students will be expected to demonstrate an understanding of similarity of polygons.
9.G02.01 Determine if the polygons in a given presorted set are similar, and explain the reasoning.
9.G04.09 Draw, on a Cartesian plane, the translation image of a given shape using a given translation rule such as R2, U3, or →→, ↑↑↑; label each vertex and its corresponding ordered pair; and describe why the translation does not result in line or rotation symmetry.
9.SP02.05 Provide an example to demonstrate the significance of sample size in interpreting data.
9.SP03 Students will be expected to 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 • drawing conclusions to answer the question
9.SP03.01 Create a rubric to assess a project that includes the assessment of: • a question for investigation • the choice of a data collection method that includes social considerations • the selection of a population or a sample and the justification for the selection • the display of collected data • the conclusions to answer the question
9.SP03.02 Develop a project plan that describes: • a question for investigation • the method of data collection that includes social considerations • the method for selecting a population or a sample • the methods for display and analysis of data
9.SP03.03 Complete the project according to the plan, draw conclusions, and communicate findings to an audience.
9.SP03.04 Self-assess the completed project by applying the rubric.
9.SP04 Students will be expected to demonstrate an understanding of the role of probability in society.
9.SP04.01 Provide an example from print and electronic media where probability is used.
9.SP04.02 Identify the assumptions associated with a given probability, and explain the limitations of each assumption.
9.SP04.03 Explain how a single probability can be used to support opposing positions.
9.SP04.04 Explain, using examples, how decisions may be based on a combination of theoretical probability, experimental probability, and subjective judgment.