Northwest Territories

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Skills available for Northwest Territories grade 9 math curriculum

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N Number

  • N.1 Develop number sense.

    • N.1.1 Demonstrate an understanding of powers with integral bases (excluding base 0) and whole number exponents by:

      • N.1.1.a representing repeated multiplication, using powers.

      • N.1.1.b using patterns to show that a power with an exponent of zero is equal to one.

      • N.1.1.c solving problems involving powers.

      • N.1.1.1 Demonstrate the differences between the exponent and the base by building models of a given power, such as 2³ and 3².

      • N.1.1.2 Explain, using repeated multiplication, the difference between two given powers in which the exponent and base are interchanged; e.g., 10³ and 3¹&sup0;.

      • N.1.1.3 Express a given power as a repeated multiplication.

      • N.1.1.4 Express a given repeated multiplication as a power.

      • N.1.1.5 Explain the role of parentheses in powers by evaluating a given set of powers; e.g., (–2)?, (–2?) and –2?.

      • N.1.1.6 Demonstrate, using patterns, that a&sup0; is equal to 1 for a given value of a (a ≠ 0).

      • N.1.1.7 Evaluate powers with integral bases (excluding base 0) and whole number exponents.

    • N.1.2 Demonstrate an understanding of operations on powers with integral bases (excluding base 0) and whole number exponents:

      • N.1.2.a (a to the m power) (a to the n power) = a to the m + n power.

      • N.1.2.b a to the m power / a to the n power = a to the m - n power, m > n.

      • N.1.2.c (a to the m power) to the n power = a to the mn power.

      • N.1.2.d (ab) to the m power = a to the m power x b to the m power.

      • N.1.2.e (a / b) to the n power = a to the n power / b to the n power, b ≠ 0.

      • N.1.2.1 Explain, using examples, the exponent laws of powers with integral bases (excluding base 0) and whole number exponents.

      • N.1.2.2 Evaluate a given expression by applying the exponent laws.

      • N.1.2.3 Determine the sum of two given powers, e.g., 5² + 5³, and record the process.

      • N.1.2.4 Determine the difference of two given powers, e.g., 4³ – 4², and record the process.

      • N.1.2.5 Identify the error(s) in a given simplification of an expression involving powers.

    • N.1.3 Demonstrate an understanding of rational numbers by:

    • N.1.4 Explain and apply the order of operations, including exponents, with and without technology.

    • N.1.5 Determine the square root of positive rational numbers that are perfect squares.

      • N.1.5.1 Determine whether or not a given rational number is a square number, and explain the reasoning.

      • N.1.5.2 Determine the square root of a given positive rational number that is a perfect square.

      • N.1.5.3 Identify the error made in a given calculation of a square root; e.g., is 3.2 the square root of 6.4?

      • N.1.5.4 Determine a positive rational number, given the square root of that positive rational number.

    • N.1.6 Determine an approximate square root of positive rational numbers that are non-perfect squares.

      • N.1.6.1 Estimate the square root of a given rational number that is not a perfect square, using the roots of perfect squares as benchmarks.

      • N.1.6.2 Determine an approximate square root of a given rational number that is not a perfect square, using technology; e.g., a calculator, a computer.

      • N.1.6.3 Explain why the square root of a given rational number as shown on a calculator may be an approximation.

      • N.1.6.4 Identify a number with a square root that is between two given numbers.

PR Patterns and Relations

SS Shape and Space

  • SS.1 Use direct and indirect measurement to solve problems.

    • SS.1.1 Solve problems and justify the solution strategy, using the following circle properties:

      • SS.1.1.a the perpendicular from the centre of a circle to a chord bisects the chord.

      • SS.1.1.b the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc.

      • SS.1.1.c the inscribed angles subtended by the same arc are congruent.

      • SS.1.1.d a tangent to a circle is perpendicular to the radius at the point of tangency.

      • SS.1.1.1 Provide an example that illustrates:

        • SS.1.1.1.a the perpendicular from the centre of a circle to a chord bisects the chord.

        • SS.1.1.1.b the measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc.

        • SS.1.1.1.c the inscribed angles subtended by the same arc are congruent.

        • SS.1.1.1.d a tangent to a circle is perpendicular to the radius at the point of tangency.

      • SS.1.1.2 Solve a given problem involving application of one or more of the circle properties.

      • SS.1.1.3 Determine the measure of a given angle inscribed in a semicircle, using the circle properties.

      • SS.1.1.4 Explain the relationship among the centre of a circle, a chord and the perpendicular bisector of the chord.

  • SS.2 Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

    • SS.2.2 Determine the surface area of composite 3-D objects to solve problems.

      • SS.2.2.1 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).

      • SS.2.2.2 Determine the surface area of a given composite 3-D object (limited to right cylinders, right rectangular prisms and right triangular prisms).

      • SS.2.2.3 Solve a given problem involving surface area.

    • SS.2.3 Demonstrate an understanding of similarity of polygons.

      • SS.2.3.1 Determine if the polygons in a given pre-sorted set are similar, and explain the reasoning.

      • SS.2.3.2 Draw a polygon similar to a given polygon, and explain why the two are similar.

      • SS.2.3.3 Solve a given problem, using the properties of similar polygons.

  • SS.3 Describe and analyze position and motion of objects and shapes.

    • SS.3.4 Draw and interpret scale diagrams of 2-D shapes.

      • SS.3.4.1 Identify an example of a scale diagram in print and electronic media, e.g., newspapers, the Internet, and interpret the scale factor.

      • SS.3.4.2 Draw a diagram to scale that represents an enlargement or a reduction of a given 2-D shape.

      • SS.3.4.3 Determine the scale factor for a given diagram drawn to scale.

      • SS.3.4.4 Determine if a given diagram is proportional to the original 2-D shape, and, if it is, state the scale factor.

      • SS.3.4.5 Solve a given problem that involves the properties of similar triangles.

    • SS.3.5 Demonstrate an understanding of line and rotation symmetry.

      • SS.3.5.1 Classify a given set of 2-D shapes or designs according to the number of lines of symmetry.

      • SS.3.5.2 Complete a 2-D shape or design, given one half of the shape or design and a line of symmetry.

      • SS.3.5.3 Determine if a given 2-D shape or design has rotation symmetry about the point at its centre, and, if it does, state the order and angle of rotation.

      • SS.3.5.4 Rotate a given 2-D shape about a vertex, and draw the resulting image.

      • SS.3.5.5 Identify a line of symmetry or the order and angle of rotation symmetry in a given tessellation.

      • SS.3.5.6 Identify the type of symmetry that arises from a given transformation on a Cartesian plane.

      • SS.3.5.7 Complete, concretely or pictorially, a given transformation of a 2-D shape on a Cartesian plane; record the coordinates; and describe the type of symmetry that results.

      • SS.3.5.8 Identify and describe the types of symmetry created in a given piece of artwork.

      • SS.3.5.9 Determine whether or not two given 2-D shapes on a Cartesian plane are related by either rotation or line symmetry.

      • SS.3.5.10 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.

      • SS.3.5.11 Create or provide a piece of artwork that demonstrates line and rotation symmetry, and identify the line(s) of symmetry and the order and angle of rotation.

SP Statistics and Probability

  • SP.1 Collect, display and analyze data to solve problems.

    • SP.1.1 Describe the effect of:

      • SP.1.1.a bias on the collection of data.

      • SP.1.1.b use of language on the collection of data.

      • SP.1.1.c ethics on the collection of data.

      • SP.1.1.d cost on the collection of data.

      • SP.1.1.e time and timing on the collection of data.

      • SP.1.1.f privacy on the collection of data.

      • SP.1.1.g cultural sensitivity on the collection of data.

      • SP.1.1.1 Analyze a given case study of data collection; and identify potential problems related to bias, use of language, ethics, cost, time and timing, privacy or cultural sensitivity.

      • SP.1.1.2 Provide examples to illustrate how bias, use of language, ethics, cost, time and timing, privacy or cultural sensitivity may influence data.

    • SP.1.2 Select and defend the choice of using either a population or a sample of a population to answer a question.

      • SP.1.2.1 Identify whether a given situation represents the use of a sample or a population.

      • SP.1.2.2 Provide an example of a situation in which a population may be used to answer a question, and justify the choice.

      • SP.1.2.3 Provide an example of a question where a limitation precludes the use of a population; and describe the limitation, e.g., too costly, not enough time, limited resources.

      • SP.1.2.4 Identify and critique a given example in which a generalization from a sample of a population may or may not be valid for the population.

      • SP.1.2.5 Provide an example to demonstrate the significance of sample size in interpreting data.

    • SP.1.3 Develop and implement a project plan for the collection, display and analysis of data by:

      • SP.1.3.a formulating a question for investigation.

      • SP.1.3.b choosing a data collection method that includes social considerations.

      • SP.1.3.c selecting a population or a sample.

      • SP.1.3.d collecting the data.

      • SP.1.3.e displaying the collected data in an appropriate manner.

      • SP.1.3.f drawing conclusions to answer the question.

      • SP.1.3.1 Create a rubric to assess a project that includes the assessment of:

        • SP.1.3.1.a a question for investigation.

        • SP.1.3.1.b the choice of a data collection method that includes social considerations.

        • SP.1.3.1.c the selection of a population or a sample and the justification for the selection.

        • SP.1.3.1.d the display of collected data.

        • SP.1.3.1.e the conclusions to answer the question.

      • SP.1.3.2 Develop a project plan that describes:

        • SP.1.3.2.a a question for investigation.

        • SP.1.3.2.b the method of data collection that includes social considerations.

        • SP.1.3.2.c the method for selecting a population or a sample.

        • SP.1.3.2.d the methods for display and analysis of data.

      • SP.1.3.3 Complete the project according to the plan, draw conclusions, and communicate findings to an audience.

      • SP.1.3.4 Self-assess the completed project by applying the rubric.

  • SP.2 Use experimental or theoretical probabilities to represent and solve problems involving uncertainty.

    • SP.2.4 Demonstrate an understanding of the role of probability in society.

      • SP.2.4.1 Provide an example from print and electronic media, e.g., newspapers, the Internet, where probability is used.

      • SP.2.4.2 Identify the assumptions associated with a given probability, and explain the limitations of each assumption.

      • SP.2.4.a Explain how a single probability can be used to support opposing positions.

      • SP.2.4.3 Explain, using examples, how decisions may be based on a combination of theoretical probability, experimental probability and subjective judgement.