Measurement      Geometry 1-2    3-4    5-6     Number      Algebra

## MATHEMATICS 10-3

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

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

### Measurement

General Outcome: Develop spatial sense through direct and indirect measurement.

Specific Outcomes: It is expected that students will:

1. Demonstrate an understanding of the Système International (SI) by:
• describing the relationships of the units for length, area, volume,capacity, mass and temperature
• applying strategies to convert SI units to imperial units.
[C, CN, ME, V]

(It is intended that this outcome be limited to the base units and the prefixes milli, centi, deci, deca, hecto and kilo.)
1.1 Explain how the SI system was developed, and explain its relationship to base ten.

## Multiplying by Powers of 10

1.2 Identify the base units of measurement in the SI system, and determine the relationship among the related units of each type of measurement.

## Temperature Difference

1.3 Identify contexts that involve the SI system.
1.4 Match the prefixes used for SI units of measurement with the powers of ten.

## Prefix Matching Game

1.5 Explain, using examples, how and why decimals are used in the SI system.
1.6 Provide an approximate measurement in SI units for a measurement given in imperial units; e.g., 1 inch is approximately 2.5 cm.
1.7 Write a given linear measurement expressed in one SI unit in another SI unit.

## Length Conversions

1.8 Convert a given measurement from SI to imperial units by using proportional reasoning (including formulas); e.g., Celsius to Fahrenheit, centimetres to inches.

1. Demonstrate an understanding of the imperial system by:
• describing the relationships of the units for length, area, volume, capacity, mass and temperature
• comparing the American and British imperial units for capacity
• applying strategies to convert imperial units to SI units.
[C, CN, ME, V]

2.1 Explain how the imperial system was developed.
2.2 Identify commonly used units in the imperial system, and determine the relationships among the related units.

## Imperial Weight Conversions

2.3 Identify contexts that involve the imperial system.
2.4 Explain, using examples, how and why fractions are used in the imperial system.
2.5 Compare the American and British imperial measurement systems; e.g., gallons, bushels, tons.
2.6 Provide an approximate measure in imperial units for a measurement given in SI units; e.g., 1 litre is approximately 1/4 US gallon.
2.7 Write a given linear measurement expressed in one imperial unit in another imperial unit.

2.8 Convert a given measure from imperial to SI units by using proportional reasoning (including formulas); e.g., Fahrenheit to Celsius, inches to centimetres.

## Volume (SI to Imperial)

1. Solve and verify problems that involve SI and imperial linear measurements, including decimal and fractional measurements.
[CN, ME, PS, V]

(It is intended that the four arithmetic operations on decimals and fractions be integrated into
the problems.)
3.1 Identify a referent for a given common SI or imperial unit of linear measurement.
3.2 Estimate a linear measurement, using a referent.
3.3 Measure inside diameters, outside diameters, lengths, widths of various given objects, and distances, using various measuring instruments.
3.4 Estimate the dimensions of a given regular 3-D object or 2-D shape, using a referent; e.g., the height of the desk is about three rulers long, so the desk is approximately three feet high.

## Cone - HTML code controls type

3.5 Solve a linear measurement problem including perimeter, circumference, and length + width + height (used in shipping and air travel).

## Perimeter Linear Measurement

3.6 Determine the operation that should be used to solve a linear measurement problem.
3.7 Provide an example of a situation in which a fractional linear measurement would be divided by a fraction.
3.8 Determine, using a variety of strategies, the midpoint of a linear measurement such as length, width, height, depth, diagonal and diameter of a 3-D object, and explain the strategies.
3.9 Determine if a solution to a problem that involves linear measurement is reasonable.

1. Solve problems that involve SI and imperial area measurements of regular, composite and irregular 2-D shapes and 3-D objects, including decimal and fractional measurements, and verify the solutions.
[ME, PS, R, V]

(It is intended that the four arithmetic operations on decimals and fractions be integrated into the problems.)
4.1 Identify and compare referents for area measurements in SI and imperial units.

4.2 Estimate an area measurement, using a referent.
4.3 Identify a situation where a given SI or imperial area unit would be used.
4.4 Estimate the area of a given regular, composite or irregular 2-D shape, using an SI square grid and an imperial square grid.

2. ## Area of a Trapezoid - average length of parallel sides - grid not present

4.5 Solve a contextual problem that involves the area of a regular, a composite or an irregular 2-D shape.
4.6 Write a given area measurement expressed in one SI unit squared in another SI unit squared.

## SI Volume

4.7 Write a given area measurement expressed in one imperial unit squared in another imperial unit squared.

## Imperial Volume

4.8 Solve a problem, using formulas for determining the areas of regular, composite and irregular 2-D shapes, including circles.

## Area of a Rectangle

4.9 Solve a problem that involves determining the surface area of 3-D objects, including right cylinders and cones.