Northwest Territories

M Measurement

• M.1 Develop spatial sense through direct and indirect measurement.

  • M.1.1 Demonstrate an understanding of the limitations of measuring instruments, including:

    • M.1.1.a precision

    • M.1.1.b accuracy

    • M.1.1.c uncertainty

    • M.1.1.d tolerance

    • M.1.1.1 Explain why, in a given context, a certain degree of precision is required.

    • M.1.1.2 Explain why, in a given context, a certain degree of accuracy is required.

    • M.1.1.3 Explain, using examples, the difference between precision and accuracy.

    • M.1.1.4 Compare the degree of accuracy of two given instruments used to measure the same attribute.

    • M.1.1.5 Relate the degree of accuracy to the uncertainty of a given measure.

    • M.1.1.6 Analyze precision and accuracy in a contextual problem.

    • M.1.1.7 Calculate maximum and minimum values, using a given degree of tolerance in context.

    • M.1.1.8 Describe, using examples, the limitations of measuring instruments used in a specific trade or industry; e.g., tape measure versus Vernier caliper.

    • M.1.1.9 Solve a problem that involves precision, accuracy or tolerance.

G Geometry

• G.1 Develop spatial sense.

  • G.1.1 Solve problems by using the sine law and cosine law, excluding the ambiguous case.

    • G.1.1.1 Identify and describe the use of the sine law and cosine law in construction, industrial, commercial and artistic applications.

    • G.1.1.2 Solve a problem, using the sine law or cosine law, when a diagram is given.

      • Law of Sines (12-N.13)
      • Law of Cosines (12-N.14)

  • G.1.2 Solve problems that involve:

    • G.1.2.a triangles

    • G.1.2.b quadrilaterals

    • G.1.2.c regular polygons.

    • G.1.2.1 Describe and illustrate properties of triangles, including isosceles and equilateral.

      • Classify triangles (11-U.1)

    • G.1.2.2 Describe and illustrate properties of quadrilaterals in terms of angle measures, side lengths, diagonal lengths and angles of intersection.

      • Classify quadrilaterals (11-R.11)
      • Properties of parallelograms (11-R.12)

    • G.1.2.3 Describe and illustrate properties of regular polygons.

      • Polygon vocabulary (11-R.1)

    • G.1.2.4 Explain, using examples, why a given property does or does not apply to certain polygons.

    • G.1.2.5 Identify and explain an application of the properties of polygons in construction, industrial, commercial, domestic and artistic contexts.

    • G.1.2.6 Solve a contextual problem that involves the application of the properties of polygons.

  • G.1.3 Demonstrate an understanding of transformations on a 2-D shape or a 3-D object, including:

    • G.1.3.a translations

    • G.1.3.b rotations

    • G.1.3.c reflections

    • G.1.3.d dilations.

    • G.1.3.1 Identify a single transformation that was performed, given the original 2-D shape or 3-D object and its image.

    • G.1.3.2 Draw the image of a 2-D shape that results from a given single transformation.

      • Translations: graph the image (10-FF.1)
      • Reflections: graph the image (10-FF.4)
      • Rotations: graph the image (10-FF.7)

    • G.1.3.3 Draw the image of a 2-D shape that results from a given combination of successive transformations.

      • Compositions of congruence transformations: graph the image (10-FF.10)

    • G.1.3.4 Create, analyze and describe designs, using translations, rotations and reflections in all four quadrants of a coordinate grid.

      • Translations: find the coordinates (10-FF.2)
      • Translations: write the rule (10-FF.3)
      • Reflections: find the coordinates (10-FF.5)
      • Rotate polygons about a point (10-FF.6)
      • Rotations: find the coordinates (10-FF.8)
      • Congruence transformations: mixed review (10-FF.12)
      • Dilations: find the coordinates (10-FF.14)

    • G.1.3.5 Identify and describe applications of transformations in construction, industrial, commercial, domestic and artistic contexts.

    • G.1.3.6 Explain the relationship between reflections and lines or planes of symmetry.

    • G.1.3.7 Determine and explain whether a given image is a dilation of another given shape, using the concept of similarity.

    • G.1.3.8 Draw, with or without technology, a dilation image for a given 2-D shape or 3-D object, and explain how the original 2-D shape or 3-D object and its image are proportional.

      • Dilations: graph the image (10-FF.13)
      • Dilations: scale factor and classification (10-FF.15)

    • G.1.3.9 Solve a contextual problem that involves transformations.

N Number

• N.1 Develop number sense and critical thinking skills.

  • N.1.1 Analyze puzzles and games that involve logical reasoning, using problem-solving strategies.

    • N.1.1.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,

      • N.1.1.1.a guess and check

      • N.1.1.1.b look for a pattern

      • N.1.1.1.c make a systematic list

      • N.1.1.1.d draw or model

      • N.1.1.1.e eliminate possibilities

      • N.1.1.1.f simplify the original problem

      • N.1.1.1.g work backward

      • N.1.1.1.h develop alternative approaches.

    • N.1.1.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.

    • N.1.1.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.

  • N.1.2 Solve problems that involve the acquisition of a vehicle by:

    • N.1.2.a buying

    • N.1.2.b leasing

    • N.1.2.c leasing to buy.

    • N.1.2.1 Describe and explain various options for buying, leasing and leasing to buy a vehicle.

    • N.1.2.2 Solve, with or without technology, problems that involve the purchase, lease or lease to purchase of a vehicle.

    • N.1.2.3 Justify a decision related to buying, leasing or leasing to buy a vehicle, based on factors such as personal finances, intended use, maintenance, warranties, mileage and insurance.

  • N.1.3 Critique the viability of small business options by considering:

    • N.1.3.a expenses

    • N.1.3.b sales

    • N.1.3.c profit or loss.

    • N.1.3.1 Identify expenses in operating a small business, such as a hot dog stand.

    • N.1.3.2 Identify feasible small business options for a given community.

    • N.1.3.3 Generate options that might improve the profitability of a small business.

    • N.1.3.4 Determine the break-even point for a small business.

    • N.1.3.5 Explain factors, such as seasonal variations and hours of operation, that might impact the profitability of a small business.

A Algebra

• A.1 Develop algebraic reasoning.

  • A.1.1 Demonstrate an understanding of linear relations by:

    • A.1.1.a recognizing patterns and trends

    • A.1.1.b graphing

    • A.1.1.c creating tables of values

    • A.1.1.d writing equations

    • A.1.1.e interpolating and extrapolating

    • A.1.1.f solving problems.

    • A.1.1.1 Identify and describe the characteristics of a linear relation represented in a graph, table of values, number pattern or equation.

      • Find the slope of a linear function (12-A.3)
      • Linear functions over unit intervals (12-A.6)

    • A.1.1.2 Sort a set of graphs, tables of values, number patterns and/or equations into linear and nonlinear relations.

    • A.1.1.3 Write an equation for a given context, including direct or partial variation.

      • Write the equation of a linear function (12-A.5)

    • A.1.1.4 Create a table of values for a given equation of a linear relation.

    • A.1.1.5 Sketch the graph for a given table of values.

      • Graph a linear function (12-A.4)

    • A.1.1.6 Explain why the points should or should not be connected on the graph for a context.

    • A.1.1.7 Create, with or without technology, a graph to represent a data set, including scatterplots.

    • A.1.1.8 Describe the trends in the graph of a data set, including scatterplots.

    • A.1.1.9 Sort a set of scatterplots according to the trends represented (linear, nonlinear or no trend).

    • A.1.1.10 Solve a contextual problem that requires interpolation or extrapolation of information.

    • A.1.1.11 Relate slope and rate of change to linear relations.

    • A.1.1.12 Match given contexts with their corresponding graphs, and explain the reasoning.

    • A.1.1.13 Solve a contextual problem that involves the application of a formula for a linear relation.

S Statistics

• S.1 Develop statistical reasoning

  • S.1.1 Solve problems that involve measures of central tendency, including:

    • S.1.1.a mean

    • S.1.1.b median

    • S.1.1.c mode

    • S.1.1.d weighted mean

    • S.1.1.e trimmed mean.

    • S.1.1.1 Explain, using examples, the advantages and disadvantages of each measure of central tendency.

    • S.1.1.2 Determine the mean, median and mode for a set of data.

      • Mean, median, mode and range (10-HH.1)

    • S.1.1.3 Identify and correct errors in a calculation of a measure of central tendency.

    • S.1.1.4 Identify the outlier(s) in a set of data.

      • Identify an outlier (12-AA.3)

    • S.1.1.5 Explain the effect of outliers on mean, median and mode.

      • Identify an outlier and describe the effect of removing it (12-AA.4)

    • S.1.1.6 Calculate the trimmed mean for a set of data, and justify the removal of the outliers.

    • S.1.1.7 Explain, using examples such as course marks, why some data in a set would be given a greater weighting in determining the mean.

    • S.1.1.8 Calculate the mean of a set of numbers after allowing the data to have different weightings (weighted mean).

    • S.1.1.9 Explain, using examples from print and other media, how measures of central tendency and outliers are used to provide different interpretations of data.

    • S.1.1.10 Solve a contextual problem that involves measures of central tendency.

  • S.1.2 Analyze and describe percentiles.

    • S.1.2.1 Explain, using examples, percentile ranks in a context.

    • S.1.2.2 Explain decisions based on a given percentile rank.

    • S.1.2.3 Explain, using examples, the difference between percent and percentile rank.

    • S.1.2.4 Explain the relationship between median and percentile.

    • S.1.2.5 Solve a contextual problem that involves percentiles.

P Probability

• P.1 Develop critical thinking skills related to uncertainty.

  • P.1.1 Analyze and interpret problems that involve probability.

    • P.1.1.1 Describe and explain the applications of probability; e.g., medication, warranties, insurance, lotteries, weather prediction, 100-year flood, failure of a design, failure of a product, vehicle recalls, approximation of area.

    • P.1.1.2 Calculate the probability of an event based on a data set; e.g., determine the probability of a randomly chosen light bulb being defective.

    • P.1.1.3 Express a given probability as a fraction, decimal and percent and in a statement.

      • Calculate probabilities of events (12-Y.2)

    • P.1.1.4 Explain the difference between odds and probability.

    • P.1.1.5 Determine the probability of an event, given the odds for or against.

    • P.1.1.6 Explain, using examples, how decisions may be based on a combination of theoretical probability calculations, experimental results and subjective judgements.

    • P.1.1.7 Solve a contextual problem that involves a given probability.