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

Linked Source - Ron Blond

 Micrometer Calipers

Linked Source - Ron Blond

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.

## Ron Blond (International System of Units)

***Link: LearnAlberta (Ron Blond)

## Volume Conversions

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

source

source

source

## 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.

Link: LearnAlberta

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

Link: LearnAlberta

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

Link: LearnAlberta

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.

Linked Source: LearnAlberta

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.

Link: LearnAlberta

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