Math 10 Common

Unit 1: Measurement

General Outcome 1: Develop spatial sense and proportional reasoning.

In this unit, you will solve problems involving ...

Chapter 1 Measurement Systems

Big Ideas

When you have completed this chapter, you will be able to...

Specific Outcome: It is expected that students will:

1. Solve problems that involve linear measurement, using:

[ME, PS, V]

Open Specific Outcome 1.1 General Notes

General Notes

Students have been working with SI units of measure since Grade 3. While the SI system of measure is the official measurement system in Canada, students need to have some exposure to and experience with imperial units of measure. Some commerce in Canada, primarily involving imports from and exports to the U.S., is still conducted in imperial units.

This is the first time that imperial units are formally addressed in the Kindergarten to Grade 12 curriculum.

In measurement, a referent is described as something common that provides students with a reference for a unit of measure. While there are some commonly used measurement referents, e.g., 1 foot is approximately the length of an adult’s foot, students are expected to develop their own referents for the basic units of length in each system.

Measurements in imperial units should generally be expressed in fraction form. This outcome is not intended to assess operations on fractions but can be used to reinforce students’ understanding of fractions.

A personal strategy must be efficient and accurate and the student must be able to explain it. A student may develop his or her own personal strategy or adopt a strategy developed by another student. The student must be able to explain his or her strategy to others.

Students have been encouraged to develop personal strategies throughout the Kindergarten to Grade 9 mathematics program and may employ some nontraditional methods in solving problems. Provided they meet the criteria above, these personal strategies should be accepted.

It is expected that students will use a variety of measuring instruments.

Open Achievement Indicators

Achievement Indicators

Acceptable Standard

Standard of Excellence

1.1.1 Provide referents for linear measurements, including millimetre, centimetre, metre, kilometre, inch, foot, yard and mile, and explain the choices. Use referents for millimetre, centimetre, metre, inch, foot and yard and explain the choice. Use referents for kilometre and mile and explain the choice.
1.1.2 Compare SI and imperial units, using referents. **
1.1.3 Estimate a linear measure, using a referent, and explain the process used **
1.1.4 Justify the choice of units used for determining a measurement in a problem-solving context. **
1.1.5 Solve problems that involve linear measure, using instruments such as rulers, calipers or tape measures. **
1.1.6 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. Describe and give a partial explanation of the personal strategy used. Describe and give a detailed explanation of the personal strategy used.

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1.1 SI Measurement

Focus on...

SI (Systeme International d'Unites)

A system of measurement in which all units are based on multiples of ten

The metre is the basic unit of length

Units

Abbreviation

Multiplying Factor

kilometre km 1000
hectometre hm 100
decametre dam 10
metre m 1
decimetre dm 0.1
centimetre cm 0.01
millimetre mm 0.0001

With SI conversions only the decimal moves, the number does not change. This is the advantage of all conversions based on tens.

Referent

An item that an individual uses as a measurement unit for estimating.

A personal measurement unit that you can use to estimate measurements in standard units, such as SI units.





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1.2 Imperial Measurement

Focus on...

Imperial system

A system of measurement based on British units

In the imperial system, common units for linear measurement are the inch (in.), foot (ft), yard (yd), and mile (mi). The imperial units for length are related according to the following conversions:





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1.3 Converting Between SI and Imperial Systems

Focus on...

If an exact conversion between systems is required, use:

When solving problems involving measurement, it is crucial to work with the same units