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TOPIC ANALYSIS

TOPIC ANALYSIS. Measurement. Mathematics. Mathematics. Mathematics. Mathematics. Foundations of Mathematics and Pre-calculus. Apprenticeship and Workplace Mathematics. Apprenticeship and Workplace Mathematics. Apprenticeship and Workplace Mathematics. Foundations of Mathematics.

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TOPIC ANALYSIS

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  1. TOPIC ANALYSIS Measurement

  2. Mathematics Mathematics Mathematics Mathematics Foundations of Mathematics and Pre-calculus Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Foundations of Mathematics Foundations of Mathematics Pre-calculus Pre-calculus Grade New Math Pathways and Courses 6 7 8 9 10 11 12

  3. Grade 6 Volume Area Angles Perimeter Triangles Quadrilaterals examples of angles in the environment classifying angles according to their measure using 45°, 90°, and 180° as reference angles determining angle measures in degrees drawing and labeling angles sum of interior angles is 180° scalene, isosceles, equilateral, right, obtuse, acute perimeter of triangles the sum of interior angles is 360° polygons rectangles right rectangular prisms

  4. Polygons The sum of interior angles is 180° Right rectangular prisms Reference angles: 45°, 90°, and 180° All the type of triangles Grade 7 Grade 6 The sum of interior angles is 360° Angle measures are in degrees Rectangles Area Angles Volume Perimeter Triangles Circles Quadrilaterals radius & diameter π & circumference sum of the central angles constructing circles with a given radius or diameter problems involving the radii, diameters, and circumferences of circles triangles parallelograms circles

  5. π & circumference The sum of interior angles is 360° The sum of interior angles is 180° Right rectangular prisms Polygons Reference angles: 45°, 90°, and 180° All the types of triangles parallelograms Grade 8 Grade 6 Grade 7 The sum of central angles radius & diameter Angle measures are in degrees circles triangles Rectangles Circles Triangles Volume Angles Area Perimeter Quadrilaterals Pythagorean theorem right rectangular prisms right triangular prisms right cylinders Surface area draw and construct nets for 3-D objects right prisms right cylinders

  6. Polygons π & circumference The sum of interior angles is 180° Right rectangular prisms Reference angles: 45°, 90°, and 180° All of the triangles parallelograms Grade 8 Grade 7 Grade 9 Grade 6 The sum of central angles The sum of interior angles is 360° Angle measures are in degrees radius & diameter Right rectangular prisms triangles circles Pythagorean theorem right cylinders Right triangular prisms Right cylinders Nets for 3D objects right prisms Rectangles Surface Area Area Triangles Volume Angles Perimeter Circles scale diagrams of 2-D shapes Quadrilaterals the measure of the central angle = 2x measure of the inscribed angle the perpendicular from the centre of a circle to a chord bisects the chord 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 surface area of composite 3-D objects

  7. π & circumference The sum of interior angles is 180° Reference angles: 45°, 90°, and 180° tangent to a circle right rectangular prisms the inscribed angles subtended by the same arc are congruent Angle measures are in degrees the perpendicular from the centre to a chord bisects the chord Polygons The sum of central angles parallelograms Grade 7 Grade 8 Grade 9 Grade 6 radius & diameter central / inscribed angle The sum of interior angles is 360° rectangles Nets for 3D objects right cylinders right cylinders triangles Pythagorean theorem right rectangular prisms right triangular prisms circles right prisms Any triangle surface area of composite 3-D objects Triangles Volume Surface Area Area scale diagrams of 2-D shapes Angles Perimeter Quadrilaterals Circles Angle measures are in degrees m cm km Hours money m2 cm2 km2 m3 cm3 km3

  8. Mathematics Mathematics Mathematics Mathematics Foundations of Mathematics and Pre-calculus Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Foundations of Mathematics Foundations of Mathematics Pre-calculus Pre-calculus Grade New Math Pathways and Courses 6 7 8 9 10 11 12

  9. Apprenticeship and Workplace Mathematics 10 Volume m3 mm3 cm3 km3 liters SI Length m mm cm km Area m2 mm2 cm2 km2 Mass kg g tones Temperature C° • Relationship between SI and imperial units • Ex: 1 inc is approximately 2.5 cm. • Convert a given measurement from SI to imperial units and vice versa • Solve problems that involve SI and imperial measurements, including decimal and fractional measurements. • SI system and its relationship to base ten. • Match the prefixes used for SI units of measurement with the powers of ten • Identify the base units and the relationship among the related units linear regular, composite and irregular 2D shapes and 3D objects Imperial System Volume in3 ft3 yd3 mi3 gallons Mass lbs Temperature °F Length in ft yd mi Area in2 ft2 yd2 mi2 • Pythagorean theorem in right triangles • sine, cosine, tangent ratio in right triangles • acute, right, obtuse, straight and reflex angles • drawing, replicating, constructing, bisecting

  10. Surface area Volume Imperial System Imperial System SI Solving problems that involve two and three right triangles SI Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics 10 • conversion within the systems • conversion between the systems • decimal and fractional measurements. • Linear ,regular, composite and irregular • 2D shapes and 3D objects • Pythagorean theorem in right triangles • sine, cosine, tangent in right triangles 11 • surface area of 3-D objects, including spheres • difference between volume and surface area • relationship between area and surface area • dimensional changes - surface area • cones, cylinders, pyramids, spheres and composite 3-D objects using measuring tools such as rulers, measuring tape, calipers and micrometers • capacity of prisms, cones, pyramids, spheres and cylinders, using measuring tools and methods, such as graduated cylinders, measuring cups, measuring spoons • dimensional changes -volume

  11. Surface area Volume Imperial System SI Solving problems that involve two and three right triangles • Pythagorean theorem in right triangles • sine, cosine, tangent in right triangles Imperial System SI Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics 10 • conversion within the systems • conversion between the systems • decimal and fractional measurements. • Linear ,regular, composite and irregular • 2D shapes and 3D objects 11 using measuring tools: rulers, tape measures, calipers and micrometers Demonstrate an understanding of the limitations of measuring instruments: • precision • accuracy • uncertainty • tolerance 12 Solve problems by using the sine law and cosine law Solve problems that involve triangles, quadrilaterals, regular polygons

  12. Mathematics Mathematics Mathematics Mathematics Foundations of Mathematics and Pre-calculus Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Foundations of Mathematics Foundations of Mathematics Pre-calculus Pre-calculus Grade New Math Pathways and Courses 6 7 8 9 10 11 12

  13. Imperial System Surface area Volume SI Foundations of Mathematics and Pre-calculus 10 • conversion within the systems • conversion between the systems • Linear ,regular, composite and irregular • 2D shapes and 3D objects • right cones • right cylinders • right prisms • right pyramids • spheres Apply the primary trigonometric ratios (sine, cosine, tangent) in right triangles.

  14. Apply sine, cosine, tangent in right triangles Surface area Volume Imperial System SI Foundations of Mathematics and Pre-calculus Foundations of Mathematics 10 • conversion within the systems • conversion between the systems • Linear ,regular, composite and irregular • 2D shapes and 3D objects 11 km/h m/s $/kg $/lbs $/L words/min Application of rates Scale factor, given one dimension of a 2Dshapes and 3d objects Relationships among scale factors, areas, surface areas and volumes of similar 2-D shapes and 3-D objects. Properties of angles and triangles Solve problems that involve the cosine law and the sine law, including the ambiguous case

  15. Apply sine, cosine, tangent in right triangles Measurements: Money, hours, moths, years, and rates. Surface area Volume Imperial System SI Foundations of Mathematics and Pre-calculus Foundations of Mathematics Foundations of Mathematics 10 • conversion within the systems • conversion between the systems • Linear ,regular, composite and irregular • 2D shapes and 3D objects km/h m/s $/kg $/lbs $/L words/min 11 Application of rates Scale factor, given one dimension of a 2Dshapes and 3d objects Relationships among scale factors, areas, surface areas and volumes of similar 2-D shapes and 3-D objects. Properties of angles and triangles Solve problems that involve the cosine law and the sine law, including the ambiguous case 12

  16. Mathematics Mathematics Mathematics Mathematics Foundations of Mathematics and Pre-calculus Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Foundations of Mathematics Foundations of Mathematics Pre-calculus Pre-calculus Grade New Math Pathways and Courses 6 7 8 9 10 11 12

  17. Apply sine, cosine, tangent in right triangles Surface area Volume Imperial System SI Foundations of Mathematics and Pre-calculus Pre-calculus 10 • conversion within the systems • conversion between the systems • Linear ,regular, composite and irregular • 2D shapes and 3D objects 11 angles in standard position (0° to 360°) the three primary trigonometric ratios for angles from 0° to 360° in standard position the cosine law and sine law, including the ambiguous case

  18. Apply sine, cosine, tangent in right triangles Surface area Volume Imperial System SI Foundations of Mathematics and Pre-calculus Pre-calculus Pre-calculus 10 • conversion within the systems • conversion between the systems • Linear ,regular, composite and irregular • 2D shapes and 3D objects 11 • angles in standard position (0° to 360°) • the three primary trigonometric ratios for angles from 0° to 360° in standard position • the cosine law and sine law, including the ambiguous case 12 • angles in standard position, expressed in degrees and radians. • the equation of the unit circle • the six trigonometric ratios for angles expressed in radians and degrees

  19. Measurement Examples

  20. Mathematics Mathematics Mathematics Mathematics Foundations of Mathematics and Pre-calculus Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Apprenticeship and Workplace Mathematics Foundations of Mathematics Foundations of Mathematics Pre-calculus Pre-calculus Grade New Math Pathways and Courses 6 7 8 9 10 11 12

  21. Grade 6 Angles:

  22. Grade 7 Geometry and Measurement Circle

  23. Grade 8 A triangle has side lengths of 5cm, 7cm, and 9cm. • What are the areas of the three squares that can be drawn on the sides of the triangle? • Is the triangle a right triangle? Explain your answer.

  24. Grade 9 The diameter AB of a circle C measures 17 cm. A chord DB=15cm is drawn from point B. Determine the value of AD.

  25. Grade 10 Apprenticeship and Workplace Pilot James is flying his airplane above a cluster of mountains. He knows his altitude is at 23 000 feet when he reaches the peak of the last mountain and the runway for landing begins 14 500 feet from the peak of the mountain. What is the angle of depression needed for Pilot James to be able to see the beginning of the runway after reaching the last mountain?

  26. Grade 10 Foundations and Pre-calculus Calculate the length of AC to the nearest tenth of a centimeter .

  27. Li is making a kite for a festival, as show in the diagram. Grade 11 Apprenticeship and Workplace • What will be the length of the two cross section pieces that form the frame? • Calculate the length of the string the t will form the outer perimeter of the kite. • For each color what area of fabric will be needed?

  28. Grade 11 Foundations Determine the unknown side length or angle measure that is indicated the triangle, to the nearest tenth of a unit.

  29. Grade 11 Pre-calculus • The Point P(4,7) is on the terminal arm of an angle θ in standard position • determine the distance r from the origin to point P • determine the primary trigonometric ratios of θ • determine the measure of θ to the nearest degree

  30. Grade 12 Apprenticeship and Workplace It is expected that students will: Demonstrate an understanding of the limitations of measuring instruments, including: • precision • accuracy • uncertainty • tolerance and solve problems.

  31. Grade 12 Foundations Measurement: Money, hours, moths, years, and rates.

  32. Grade 12 Pre-calculus It is expected that students will: Demonstrate an understanding of angles in standard position, expressed in degrees and radians. Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees. Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians.

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