Outcome #4
Measurement
Embedded Files
Description
This outcome covers the following:
Perimeter/Circumference and Area of Composite Shapes
Side Length Relationship for right angle triangles (Pythagorean Theorem)
Volume and Surface Area for Prisms, Pyramids, Cylinders and Cones (compare differences when changing one or more dimensions)
Relationship between volume of prisms/pyramids and cylinders/cones
Curriculum Expectations: E1.1, E1.2, E1.4, E1.5, E1.6
Notes:
It is recommended that teachers only provide formulas for the area of rectangles, triangles and circles. Volume of prisms = Area of Base x Height. Volume of Pyramid and Cone is equal to 1/3 of the corresponding prism. Try to avoid using the standard EQAO formula sheet.
Circle and Triangle Properties are not being formally assessed (E1.2)
Emerging
Emerging
I can determine Perimeter/Circumference and area of composite shapes.
I can use side-length relationships for a right triangle to solve for an unknown side.
Notes/Examples:
Eg. Determine the area and perimeter of the following shape:
Eg. Determine the length of the unknown side
Developing
Developing
I can solve for area and perimeter of composite shapes that involve right triangle relationships.
I can calculate the volume of prisms and cylinders.
Notes/Examples:
Eg. This community garden space needs to be fenced on all sides. Determine the length of fencing needed:
Eg. What is the area and perimeter of this figure?
Proficient
Proficient
I can apply the relationship between the volume of prisms and pyramids and between the volume of cylinders and cones.
I can show how changing one or more dimensions of a two-dimensional shape and three-dimension object affects perimeter/circumference, area, surface area, and/or volume (using technology when appropriate).
Notes/Examples:
Eg. If a prism has a volume of 300 cm3, what is the volume of the pyramid with the same base and height?
In a cylinder, how does the volume change if the height is doubled? (tripled?) How does the volume change if the radius is doubled? (tripled?)
Eg. Calculate the volume of the pyramid below:
Exceeding
Exceeding
I can solve multi-step problems to determine the perimeter and area of composite shapes and the volume of three-dimensional objects including pyramids and cones in various units of measure.
Notes/Examples:
Eg. Frozen ice cream treats are sold in cone-shaped containers. The containers have a slant height of 12.3 cm and have a 2.5 cm radius. Calculate the volume of the ice cream treat.
Extending
Extending
I can consistently solve a variety of measurement problems involving different units.
Notes/Examples:
Sample Problem: Volume of two tanks with different units and comparing the sizes. One imperial and one metric.
Eg. What would be the volume of a pyramid with the exact same base and height of the shape shown here? (pick a shape that has not been done)
Sample Assessments
(Approaching Standard)
(Approaching Standard)
(Reaching Standard)
(Reaching Standard)
(Reaching Standard -> Extending Understanding)
(Reaching Standard -> Extending Understanding)
Lesson Ideas
Area, Perimeter and Volume - Traffic Light Activity
Area, Perimeter and Volume - Traffic Light Activity
This web based activity has students answer measurement questions as they explore different buildings around the world.
Students play this game with the goal of cutting a shape into two equal areas. This is a short activity for students to try as they visualize areas.
Coding Activities
Alter: Volume of a Cylinder
Alter: Volume of a Cylinder
This program asks the user to input the radius and height of a cylinder and then outputs the volume.
Extensions:
Determine the volume of a pyramid or sphere
Determine the surface area of the cylinder
Given the volume and height of the cylinder, determine the radius
Alter: Investigate a Circle Property I
Alter: Investigate a Circle Property I
This program checks to see if an inscribed angle and a central angle could subtend the same chord, however the if condition is missing!
Fill in the condition statement to make the program run correctly.
Alter: Investigate a Circle Property II
Alter: Investigate a Circle Property II
This program checks to see if two inscribed angles could subtend the same chord, however the if condition is missing!
Fill in the condition statement to make the program run correctly.
Desmos Classroom Activities
This activity is a nice recap where students investigate the relationship between the area of the squares on the sides of a right angled triangle without giving the explicit formula for Pythagorean theorem.
In this activity, students will use the Pythagorean Theorem. They will discover that the theorem only works for right triangles. Then use their knowledge to solve some real world problems.
This is a 3-act to examine the relationships between the volumes of prisms, cylinders and pyramids and cones, based on the work and videos of Kyle Pearce.
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