Program of Studies: [Math 10C] [Math 10-3] [Math 10-4] [Math 20-1] [Math 20-2] [Math 20-3] [Math 20-4] [Math 30-1] [Math 30-2] [Math 30-3]

## MATHEMATICS 10C

[C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation

[PS] Problem Solving
[R] Reasoning
[T] Technology
[V] Visualization

### Measurement      Algebra & NumberRelations & Functions 1Relations & Functions 2Relations & Functions 3

General Outcome: Develop spatial sense and proportional reasoning.

Specific Outcomes: It is expected that students will:

1. Solve problems that involve linear measurement, using:
• SI and imperial units of measure
• estimation strategies
• measurement strategies.
[ME, PS, V]

1.1 Provide referents for linear measurements, including millimetre, centimetre, metre, kilometre, inch, foot, yard and mile, and explain the choices.

• thickness of a dime - millimetre
• diameter of a dime - centimetre
• height of a door knob from the floor - metre
• distance you could walk comfortably in 15 minutes - kilometer
• width of a thumb across the joint - inch
• adult foot length - foot
• one adult pace - yard
• distance walked in 20 minutes - mile

1.2 Compare SI and imperial units, using referents.
1.3 Estimate a linear measure, using a referent, and explain the process used.
1.4 Justify the choice of units used for determining a measurement in a problem-solving context.
1.5 Solve problems that involve linear measure, using instruments such as rulers, calipers or tape measures.

 Vernier Calipers

 Micrometer Calipers

1.6 Describe and explain a personal strategy used to determine a linear measurement; e.g., circumference of a bottle, length of a curve, perimeter of the base of an irregular 3-D object.

1. Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.
[C, ME, PS]

2.1 Explain how proportional reasoning can be used to convert a measurement within or between SI and imperial systems.
2.2 Solve a problem that involves the conversion of units within or between SI and imperial systems.

## Volume Conversions

2.3 Verify, using unit analysis, a conversion within or between SI and imperial systems, and explain the conversion.

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## Imperial Area Conversions

2.4 Justify, using mental mathematics, the reasonableness of a solution to a conversion problem.

1. Solve problems, using SI and imperial units, that involve the surface area and volume of 3-D objects, including:
• right cones
• right cylinders
• right prisms
• right pyramids
• spheres.
[CN, PS, R, V]

3.1 Sketch a diagram to represent a problem that involves surface area or volume.
3.2 Determine the surface area of a right cone, right cylinder, right prism, right pyramid or sphere, using an object or its labelled diagram.

3.3 Determine the volume of a right cone, right cylinder, right prism, right pyramid or sphere, using an object or its labelled diagram.

3.4 Determine an unknown dimension of a right cone, right cylinder, right prism, right pyramid or sphere, given the object's surface area or volume and the remaining dimensions.
3.5 Solve a problem that involves surface area or volume, given a diagram of a composite 3-D object.
3.6 Describe the relationship between the volumes of:

• right cones and right cylinders with the same base and height
• right pyramids and right prisms with the same base and height

1. Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.
[C, CN, PS, R, T, V]

4.1 Explain the relationships between similar right triangles and the definitions of the primary trigonometric ratios.

The following applet provides an introduction to trigonometry:

Select [Continue]. Look at the sine, cosine and tangent ratios displayed. Move the scale slider to generate similar triangles. Note that the trigonometry ratios for similar triangles are the same.

4.2 Identify the hypotenuse of a right triangle and the opposite and adjacent sides for a given acute angle in the triangle

4.3 Solve right triangles.

4.4 Solve a problem that involves one or more right triangles by applying the primary trigonometric ratios or the Pythagorean theorem.

Select [Practice].

 There are 18 question types for right triangles. Select [Next Type] to see another question type. These types are organized in groups of three: 1-3 Pythagorean Theorem 4-6 trigonometry ratio from a given angle 7-9 trigonometry ratio given two sides 10-12 calculate acute angle given two sides 13-15 calculate the numerator of the trigonometry function 16-18 calculate the denominator of the trigonometry function [New Problem] generates additional questions of the same type. [Check/Explain] provides a solution and calculator keystrokes for the type/question selected.

4.5 Solve a problem that involves indirect and direct measurement, using the trigonometric ratios, the Pythagorean theorem and measurement instruments such as a clinometer or metre stick.

2008 Program of Studies with Achievement Indicators: http://education.alberta.ca/media/823110/math10to12_ind.pdf

Authorized Resources: http://www.education.alberta.ca/teachers/program/math/educator/resources.aspx