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 & Number      Relations & Functions 1     Relations & Functions 2     Relations & 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:

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

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.

Powers of 10

Multiplying by Powers of 10

Prefix Matching Game

 

Length Conversions

 

Ron Blond (International System of Units)

***Link: LearnAlberta (Ron Blond)

Area Conversions

Volume Conversions

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

Imperial Length Conversions

source

Imperial Length to SI Conversions

source

SI Length to Imperial Conversions

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:

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:

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.

 

March, 2008 http://www.education.alberta.ca/media/655889/math10to12.pdf

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