Specific Outcome: It is expected that students will:
[C, ME, PS]
Conversions between SI and imperial units should be limited to commonly used linear units of measure; e.g., centimetres ? inches or metres ? feet. Unusual conversions, e.g., converting miles to millimetres, should be avoided.
Proportional reasoning solves for an unknown value by comparing it to known values, using ratios. Students are expected to use and explain proportional reasoning when converting units within and between the two measurement systems.
Technology (T) has not been identified as one of the mathematical processes to be emphasized in completing this outcome. Technology may be used, where appropriate, in solving a proportion.
In unit analysis, students apply the process for multiplying and simplifying fractions to verify the units in the final solution to a problem. While the analysis in Achievement Indicator 2.3 will be quite straightforward, teachers may use conversion of units within or between the two measurement systems to introduce students to unit analysis.
Students are not expected to memorize conversion factors. Basic conversion factors, especially those between the SI and imperial systems of measure, e.g., inch ? centimetre, yard ? centimetre, should be provided.
The use of conversion programs is not appropriate.
Achievement Indicators |
Acceptable Standard |
Standard of Excellence |
| 1.2.1 Explain how proportional reasoning can be used to convert a measurement within or between SI and imperial systems. | ** | |
| 1.2.2 Solve a problem that involves the conversion of units within or between SI and imperial systems. | Solve problems that involve converting measures within either the SI or imperial measurement system. | Solve problems that involve converting measures between SI and imperial measurement systems. |
| 1.2.3 Verify, using unit analysis, a conversion within or between SI and imperial systems, and explain the conversion. | ** | |
| 1.2.4 Justify, using mental mathematics, the reasonableness of a solution to a conversion problem. | Justify the reasonableness of a solution to a conversion problem involving SI units. | Justify the reasonableness of a solution to a conversion problem involving imperial units. |
Specific Outcome: It is expected that students will:
[CN, PS, R, V]
Prior knowledge from previous grade levels includes:
The intent of this outcome is to extend the concepts of surface area and volume to right pyramids, right cones and spheres.
The bases of right prisms and pyramids should be restricted to triangles, simple quadrilaterals and regular polygons.
Teachers are expected to develop the formulae for surface area and volume with students.
Figures can have an open side and the external surface area of the figure can still be calculated.
In problems that involve multiple steps, rounding in calculations is to be done only after the last step.
Students are expected to sketch and label diagrams of right prisms and cylinders, right cylinders and cones, and spheres.
Students are expected to write complete, well-organized solutions to problems.
Students are expected to discover the relationship between the volumes of cylinders and cones with the same base and height or prisms and pyramids with the same base and height.
Achievement Indicators |
Acceptable Standard |
Standard of Excellence |
| 1.3.1 Sketch a diagram to represent a problem that involves surface area or volume. | ** | |
| 1.3.2 Determine the surface area of a right cone, right cylinder, right prism, right pyramid or sphere, using an object or its labelled diagram. | Determine the surface area when all of the required dimensions are given. | Determine the surface area when one or more of the required dimensions have to be determined from other given information. |
| 1.3.3 Determine the volume of a right cone, right cylinder, right prism, right pyramid or sphere, using an object or its labelled diagram. | Determine the volume when all of the required dimensions are given. | Determine the volume when one or more of the required dimensions have to be determined from other given information. |
| 1.3.4 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. | Solve a given problem requiring a one-step calculation. | Solve a given problem requiring a multistep calculation. |
| 1.3.5 Solve a problem that involves surface area or volume, given a diagram of a composite 3-D object. | Provide a partial solution to the problem. | Provide a complete solution to the problem. |
3.6 Describe the relationship between the volumes of:
|
** |
The abbreviation for inches is in. or "
The abbreviation for feet is ft. or '
The abbreviation for yards is yd.
Area of a rectangle A = lw
Area of a triangle A = lw/2 = bh/2
Area of a circle A = π r 2
Circumference of a circle C = π d
A three-dimensional object with a circular base and a curved lateral surface that extends from the base to the vertex.
The shortest distance from the base of a cone or pyramid to its highest point
SA cone = π r 2 + π rs
r = radius
s = slant height
A three-dimensional shape that has a consistent cross-section.
The surface that joins the two bases of a three-dimensional object or that joins the base to the highest point.
SA rectangular prism = 2lw + 2lh + 2wh
l = length
w = width
h = height
SA cylinder = 2 π r2 + 2 π rh
r = radius
h = height
A round, ball shaped object.
A set of points in space that are a given distance (radius) from a fixed point (centre)
SA sphere = 4 π r2
r = radius
A three dimensional object with one base and the same number of triangular faces as there are sides on the base
SA pyramid = lw + 2(1/2 ls1) + 2(1/2 ws2)
l = length
w = width
s1 = slant height 1, touching length
s2 = slant height 2, touching width
Highest point on a pyramid
V cone = π r2h/3
r = radius
h = height
V pyramid = lwh/3
l = length
w = width
h = height
V sphere = 4/3 π r2
r = radius