E1.1Describe and classify cylinders, pyramids, and prisms according to their geometric properties, including plane and rotational symmetry.
Activity 1: Exciting Packages!
In this activity students see that several determining factors in the choice of packaging for any product are related to the properties of geometric shapes and objects. A few days before the start of the activity, the teacher should ask the students to bring an empty package of any product from home (for example, cereal box, tin can, jam jar). Without showing it to the others, each student writes on a piece of paper a geometric property of the three-dimensional object corresponding to their chosen packaging (for example, “My packaging has a curved surface.”). On the day of the activity, teachers use various strategies to form teams of two to four (for example, group students who have written the same property). When all the teams are formed, the students reveal within their team the packaging they have brought, name the corresponding three-dimensional object or a related three-dimensional object and describe it according to its properties. They then discuss as a team the similarities and differences between the three-dimensional objects. Each team member should explain why he or she thinks the manufacturer chose this packaging for their product (for example, strong packaging, easy to handle, storage, transport, high capacity, low cost of production; see the proposition below related to the attribute measurements). Each team then chooses one of the packages presented and discusses its advantages and disadvantages. During the discussion, each team presents its conclusions to the class.
Source: translated from Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, Géométrie et sens de l'espace, Fascicule 1, p. 39.
To Establish Links with Attribute Measurements
- Allow students to apply different problem-solving strategies to calculate the surface area and volume of their empty package.
- Make the following materials available: ruler, string, rope, tape measure, calculator, paper.
- Ask them to calculate the surface area and volume with two different metric units. It is important that the student draws a sketch of the package noting the measurements obtained.
- Provide feedback on students' strategies and generalizations. Emphasize the use of correct mathematical vocabulary associated with the three-dimensional object representing the package.
Sample Questions:
- What do you notice about the area calculated with two different metric units? about the volume?
- Did you deconstruct (unfold) your boxes to find the surface area? Did you create your own formula? Explain your formula or strategy.
Activity 2: What Am I Thinking?
Write questions on small cardboard rectangles and store them in a clear plastic bag with a zipper. Add the instruction sheet. Prepare several bags.
Students can take turns taking the bags home.
Another suggestion: Prepare questions to be posted randomly on the interactive board.
Sample Questions:
- I have two congruent and parallel circular shaped bases. The parallel lines that join my two bases are not perpendicular to them. Answer: The oblique circular cylinder.
- All my cross sections produce a similar scaled down version of my base. Answer: The pyramid.
- I am a three-dimensional object. I have an apex. My base is triangular. Answer: The triangle-based pyramid or tetrahedron.
Instructions
This game is played by two or more people.
- One person pulls out a card and reads aloud the first property or description of the object.
- The other person has to guess what three-dimensional object it is.
- If they do not give the right answer, a second clue is given, and so on.
- The roles are reversed as soon as a three-dimensional object is found. Other descriptions can be invented to continue the activity.
Source: adapted and translated from L'@telier - Ressources pédagogiques en ligne (atelier.on.ca).