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TOPIC ANALYSIS

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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

Foundations of Mathematics

Pre-calculus

Pre-calculus

Grade

6

7

8

9

10

11

12

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

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

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

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

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

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

6

7

8

9

10

11

12

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

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

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

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

6

7

8

9

10

11

12

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.

- 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

- 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

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

6

7

8

9

10

11

12

- 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

- 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

Examples

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

6

7

8

9

10

11

12

Angles:

Geometry and Measurement

Circle

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.

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

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?

Calculate the length of AC to the nearest tenth of a centimeter .

Li is making a kite for a festival, as show in the diagram.

- 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?

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

- 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

It is expected that students will:

Demonstrate an understanding of the limitations of

measuring instruments, including:

• precision

• accuracy

• uncertainty

• tolerance

and solve problems.

Measurement:

Money, hours, moths, years, and rates.

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.