Northwest Territories

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Skills available for Northwest Territories grade 10 math curriculum

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M Measurement

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

    • M.1.1 Demonstrate an understanding of the Système International (SI) by:

      • M.1.1.a describing the relationships of the units for length, area, volume, capacity, mass and temperature

      • M.1.1.b applying strategies to convert SI units to imperial units.

      • M.1.1.1 Explain how the SI system was developed, and explain its relationship to base ten.

      • M.1.1.2 Identify the base units of measurement in the SI system, and determine the relationship among the related units of each type of measurement.

      • M.1.1.3 Identify contexts that involve the SI system.

      • M.1.1.4 Match the prefixes used for SI units of measurement with the powers of ten.

      • M.1.1.5 Explain, using examples, how and why decimals are used in the SI system.

      • M.1.1.6 Provide an approximate measurement in SI units for a measurement given in imperial units; e.g., 1 inch is approximately 2.5 cm.

      • M.1.1.7 Write a given linear measurement expressed in one SI unit in another SI unit.

      • M.1.1.8 Convert a given measurement from SI to imperial units by using proportional reasoning (including formulas); e.g., Celsius to Fahrenheit, centimetres to inches.

    • M.1.2 Demonstrate an understanding of the imperial system by:

      • M.1.2.a describing the relationships of the units for length, area, volume, capacity, mass and temperature

      • M.1.2.b comparing the American and British imperial units for capacity

      • M.1.2.c applying strategies to convert imperial units to SI units.

      • M.1.2.1 Explain how the imperial system was developed.

      • M.1.2.2 Identify commonly used units in the imperial system, and determine the relationships among the related units.

      • M.1.2.3 Identify contexts that involve the imperial system.

      • M.1.2.4 Explain, using examples, how and why fractions are used in the imperial system.

      • M.1.2.5 Compare the American and British imperial measurement systems; e.g., gallons, bushels, tons.

      • M.1.2.6 Provide an approximate measure in imperial units for a measurement given in SI units; e.g., 1 litre is approximately ¼ US gallon.

      • M.1.2.7 Write a given linear measurement expressed in one imperial unit in another imperial unit.

      • M.1.2.8 Convert a given measure from imperial to SI units by using proportional reasoning (including formulas); e.g., Fahrenheit to Celsius, inches to centimetres.

    • M.1.3 Solve and verify problems that involve SI and imperial linear measurements, including decimal and fractional measurements.

      • M.1.3.1 Identify a referent for a given common SI or imperial unit of linear measurement.

      • M.1.3.2 Estimate a linear measurement, using a referent.

      • M.1.3.3 Measure inside diameters, outside diameters, lengths, widths of various given objects, and distances, using various measuring instruments.

      • M.1.3.4 Estimate the dimensions of a given regular 3-D object or 2-D shape, using a referent; e.g., the height of the desk is about three rulers long, so the desk is approximately three feet high.

      • M.1.3.5 Solve a linear measurement problem including perimeter, circumference, and length + width + height (used in shipping and air travel).

      • M.1.3.6 Determine the operation that should be used to solve a linear measurement problem.

      • M.1.3.7 Provide an example of a situation in which a fractional linear measurement would be divided by a fraction.

      • M.1.3.8 Determine, using a variety of strategies, the midpoint of a linear measurement such as length, width, height, depth, diagonal and diameter of a 3-D object, and explain the strategies.

      • M.1.3.9 Determine if a solution to a problem that involves linear measurement is reasonable.

    • M.1.4 Solve problems that involve SI and imperial area measurements of regular, composite and irregular 2-D shapes and 3-D objects, including decimal and fractional measurements, and verify the solutions.

      • M.1.4.1 Identify and compare referents for area measurements in SI and imperial units.

      • M.1.4.2 Estimate an area measurement, using a referent.

      • M.1.4.3 Identify a situation where a given SI or imperial area unit would be used.

      • M.1.4.4 Estimate the area of a given regular, composite or irregular 2-D shape, using an SI square grid and an imperial square grid.

      • M.1.4.5 Solve a contextual problem that involves the area of a regular, a composite or an irregular 2-D shape.

      • M.1.4.6 Write a given area measurement expressed in one SI unit squared in another SI unit squared.

      • M.1.4.7 Write a given area measurement expressed in one imperial unit squared in another imperial unit squared.

      • M.1.4.8 Solve a problem, using formulas for determining the areas of regular, composite and irregular 2-D shapes, including circles.

      • M.1.4.9 Solve a problem that involves determining the surface area of 3-D objects, including right cylinders and cones.

      • M.1.4.10 Explain, using examples, the effect of changing the measurement of one or more dimensions on area and perimeter of rectangles.

      • M.1.4.11 Determine if a solution to a problem that involves an area measurement is reasonable.

G Geometry

  • G.1 Develop spatial sense.

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

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

        • G.1.1.1.a guess and check

        • G.1.1.1.b look for a pattern

        • G.1.1.1.c make a systematic list

        • G.1.1.1.d draw or model

        • G.1.1.1.e eliminate possibilities

        • G.1.1.1.f simplify the original problem

        • G.1.1.1.g work backward

        • G.1.1.1.h develop alternative approaches.

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

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

    • G.1.2 Demonstrate an understanding of the Pythagorean theorem by:

      • G.1.2.a identifying situations that involve right triangles

      • G.1.2.b verifying the formula

      • G.1.2.c applying the formula

      • G.1.2.d solving problems.

      • G.1.2.1 Explain, using illustrations, why the Pythagorean theorem only applies to right triangles.

      • G.1.2.2 Verify the Pythagorean theorem, using examples and counterexamples, including drawings, concrete materials and technology.

      • G.1.2.3 Describe historical and contemporary applications of the Pythagorean theorem.

      • G.1.2.4 Determine if a given triangle is a right triangle, using the Pythagorean theorem.

      • G.1.2.5 Explain why a triangle with the side length ratio of 3:4:5 is a right triangle.

      • G.1.2.6 Explain how the ratio of 3:4:5 can be used to determine if a corner of a given 3-D object is square (90º) or if a given parallelogram is a rectangle.

      • G.1.2.7 Solve a problem, using the Pythagorean theorem.

    • G.1.3 Demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons.

      • G.1.3.1 Determine, using angle measurements, if two or more regular or irregular polygons are similar.

      • G.1.3.2 Determine, using ratios of side lengths, if two or more regular or irregular polygons are similar.

      • G.1.3.3 Explain why two given polygons are not similar.

      • G.1.3.4 Explain the relationships between the corresponding sides of two polygons that have corresponding angles of equal measure.

      • G.1.3.5 Draw a polygon that is similar to a given polygon.

      • G.1.3.6 Explain why two or more right triangles with a shared acute angle are similar.

      • G.1.3.7 Solve a contextual problem that involves similarity of polygons.

    • G.1.4 Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by:

      • G.1.4.a applying similarity to right triangles

      • G.1.4.b generalizing patterns from similar right triangles

      • G.1.4.c applying the primary trigonometric ratios

      • G.1.4.d solving problems.

      • G.1.4.1 Show, for a specified acute angle in a set of similar right triangles, that the ratios of the length of the side opposite to the length of the side adjacent are equal, and generalize a formula for the tangent ratio.

      • G.1.4.2 Show, for a specified acute angle in a set of similar right triangles, that the ratios of the length of the side opposite to the length of the hypotenuse are equal, and generalize a formula for the sine ratio.

      • G.1.4.3 Show, for a specified acute angle in a set of similar right triangles, that the ratios of the length of the side adjacent to the length of the hypotenuse are equal, and generalize a formula for the cosine ratio.

      • G.1.4.4 Identify situations where the trigonometric ratios are used for indirect measurement of angles and lengths.

      • G.1.4.5 Solve a contextual problem that involves right triangles, using the primary trigonometric ratios.

      • G.1.4.6 Determine if a solution to a problem that involves primary trigonometric ratios is reasonable.

    • G.1.5 Solve problems that involve parallel, perpendicular and transversal lines, and pairs of angles formed between them.

      • G.1.5.1 Sort a set of lines as perpendicular, parallel or neither, and justify this sorting.

      • G.1.5.2 Illustrate and describe complementary and supplementary angles.

      • G.1.5.3 Identify, in a set of angles, adjacent angles that are not complementary or supplementary.

      • G.1.5.4 Identify and name pairs of angles formed by parallel lines and a transversal, including corresponding angles, vertically opposite angles, alternate interior angles, alternate exterior angles, interior angles on same side of transversal and exterior angles on same side of transversal.

      • G.1.5.5 Explain and illustrate the relationships of angles formed by parallel lines and a transversal.

      • G.1.5.6 Explain, using examples, why the angle relationships do not apply when the lines are not parallel.

      • G.1.5.7 Determine if lines or planes are perpendicular or parallel, e.g., wall perpendicular to floor, and describe the strategy used.

      • G.1.5.8 Determine the measures of angles involving parallel lines and a transversal, using angle relationships.

      • G.1.5.9 Solve a contextual problem that involves angles formed by parallel lines and a transversal (including perpendicular transversals).

    • G.1.6 Demonstrate an understanding of angles, including acute, right, obtuse, straight and reflex, by:

      • G.1.6.a drawing

      • G.1.6.b replicating and constructing

      • G.1.6.c bisecting

      • G.1.6.d solving problems.

      • G.1.6.1 Draw and describe angles with various measures, including acute, right, straight, obtuse and reflex angles.

      • G.1.6.2 Identify referents for angles.

      • G.1.6.3 Sketch a given angle.

      • G.1.6.4 Estimate the measure of a given angle, using 22.5°, 30°, 45°, 60°, 90° and 180° as referent angles.

      • G.1.6.5 Measure, using a protractor, angles in various orientations.

      • G.1.6.6 Explain and illustrate how angles can be replicated in a variety of ways; e.g., Mira, protractor, compass and straightedge, carpenter's square, dynamic geometry software.

      • G.1.6.7 Replicate angles in a variety of ways, with and without technology.

      • G.1.6.8 Bisect an angle, using a variety of methods.

      • G.1.6.9 Solve a contextual problem that involves angles.

N Number

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

    • N.1.1 Solve problems that involve unit pricing and currency exchange, using proportional reasoning.

      • N.1.1.1 Compare the unit price of two or more given items.

      • N.1.1.2 Solve problems that involve determining the best buy, and explain the choice in terms of the cost as well as other factors, such as quality and quantity.

      • N.1.1.3 Compare, using examples, different sales promotion techniques; e.g., deli meat at $2 per 100 g seems less expensive than $20 per kilogram.

      • N.1.1.4 Determine the percent increase or decrease for a given original and new price.

      • N.1.1.5 Solve, using proportional reasoning, a contextual problem that involves currency exchange.

      • N.1.1.6 Explain the difference between the selling rate and purchasing rate for currency exchange.

      • N.1.1.7 Explain how to estimate the cost of items in Canadian currency while in a foreign country, and explain why this may be important.

      • N.1.1.8 Convert between Canadian currency and foreign currencies, using formulas, charts or tables.

    • N.1.2 Demonstrate an understanding of income, including:

      • N.1.2.a wages

      • N.1.2.b salary

      • N.1.2.c contracts

      • N.1.2.d commissions

      • N.1.2.e piecework

      • N.1.2.1 Describe, using examples, various methods of earning income.

      • N.1.2.2 Identify and list jobs that commonly use different methods of earning income; e.g., hourly wage, wage and tips, salary, commission, contract, bonus, shift premiums.

      • N.1.2.3 Determine in decimal form, from a time schedule, the total time worked in hours and minutes, including time and a half and/or double time.

      • N.1.2.4 Determine gross pay from given or calculated hours worked when given:

        • N.1.2.4.a the base hourly wage, with and without tips

        • N.1.2.4.b the base hourly wage, plus overtime (time and a half, double time).

      • N.1.2.5 Determine gross pay for earnings acquired by:

        • N.1.2.5.a base wage, plus commission

        • N.1.2.5.b single commission rate.

      • N.1.2.6 Explain why gross pay and net pay are not the same.

      • N.1.2.7 Determine the Canadian Pension Plan (CPP), Employment Insurance (EI) and income tax deductions for a given gross pay.

      • N.1.2.8 Determine net pay when given deductions; e.g., health plans, uniforms, union dues, charitable donations, payroll tax.

      • N.1.2.9 Investigate, with technology, "what if …" questions related to changes in income; e.g., "What if there is a change in the rate of pay?"

      • N.1.2.10 Identify and correct errors in a solution to a problem that involves gross or net pay.

      • N.1.2.11 Describe the advantages and disadvantages for a given method of earning income; e.g., hourly wage, tips, piecework, salary, commission, contract work.

A Algebra