At a Glance...

Learning Situation 1: Property Hunting

Total duration: approximately 30 minutes

Material

• hoop
• wooden or plastic three-dimensional objects: cubes, square-based prisms, rectangle-based prism, triangle-based pyramid, square-based pyramids, spheres, cones and cylinders
• bag
• Appendix 1.1

Active Learning (Exploration)

Provide students with the following three-dimensional objects: spheres, cylinders, cones, cubes, square-based prisms, rectangle-based prism, triangle-based pyramid and square-based pyramids. Tell students to:

• choose a three-dimensional object;
• sit in a circle;
• place their three-dimensional object in front of them.

Put all the statements listed in Appendix 1.1 in a bag, pick one at random and read it.

Ask students if their three dimensional object has the attribute.

Pick another statement and proceed in the same way.

Examples of Success Criteria

The student:

• names the three-dimensional objects (cubes, prisms, cones, cylinders, pyramids);
• recognizes that the three-dimensional object has the named property or attribute;
• uses faces, edges, vertices, and angles to compare these three-dimensional objects;
• sorts these three-dimensional objects by comparing their faces, edges, vertices, and angles;
• uses the words vertex, edge, face and angle to describe these three-dimensional objects.

Differentiated Instruction

The activity can be modified to meet different student needs.

Follow-Up at Home

At home, students can go on a three-dimensional object hunt by locating various objects that are shaped like a cone, cylinder, cube, sphere, square-based prism, rectangle-based prism, triangle-based pyramid, square-based pyramid.

Source: translated from Guide d’enseignement efficace des mathématiques de la 1^re à la 3^e année, Géométrie et sens de l'espace, p. 73-76.

Learning Situation 2: A Three-Dimensional Train!

Total duration: approximately 1 hour

Material

• three-dimensional objects: cubes, cones, cylinders, spheres, square-based pyramids, triangle-based pyramids, rectangle-based pyramids, pentagon-based pyramids, hexagon-based pyramids, octagon-based pyramids, square-based prisms, rectangle-based prisms, hexagon-based prisms
• cardboard boxes to represent the locomotives
• sheets of 28 cm x 43 cm paper
• adhesive tape
• glue
• scissors
• Appendix 2PF.3, 8 copies prepared with headings shown below
• Appendix 2PF.4, cut out

Before Learning (Warm-Up)

Ask students to sit in a circle.

Distribute a three-dimensional object to each student and ask them to think about how we would name it.

Ensure that all three-dimensional objects have been assigned.

Tell students that they will be making trains of three-dimensional objects.

Create a locomotive poster, using Appendix 2PF.3, with the phrase, “I have vertices.”

Present the poster to the class and ask a student to read the property written on the locomotive.

Ask students if their three-dimensional object has this property and to place it inside the circle if it does.

Ask the following questions of the students who placed their three-dimensional object in the circle:

• What is the name of your three-dimensional object?
• Why is it part of this train?

Image A locomotive made of geometric shapes, inside is labeled: "I have vertices." The following are next to the locomotive: "prism with a rectangular base", "prism with a cube or square base", "prism with a hexagonal base", "prism with a square base", "prism with a triangular base."

Point out that all the three-dimensional objects in the train have one property in common.

Ask the following question: How are these two three-dimensional objects similar?

Proceed in the same way with other properties.

I have a curved surface.

All my faces are square.

Image A locomotive built with geometric shapes inside is labeled: "All my sides are square." Followed by, "a small square-based cube," "a large square-based cube," "a small square-based cube," "a large square-based cube."

I have at least one circle-shaped face.

Image A locomotive built with geometric shapes inside is labeled: "I have at least one circle-shaped surface." Followed by: "a small cylinder," "a large cylinder," "a small cylinder," "a large cylinder."

I have triangular faces.

Image A locomotive built with geometric shapes, inside is labeled: "I have triangular faces." Followed by "a hexagonal-based pyramid," "a square-based pyramid," "a triangular-based pyramid," "a hexagonal-based pyramid."

I have no vertices.

Image A locomotive built with geometric shapes, inside is labeled: "I have no vertex." Followed by "a large cylinder," "a small sphere," "a large sphere," "a small cylinder."

I only have one vertex.

Image A locomotive built with geometric shapes inside is labeled: "I only have one vertex." Followed by "small cones," "small cone," "large cones."

I have more than six edges.

Image A locomotive built with geometric shapes inside is labeled: "I have more than six edges." Followed by "a prism with a rectangular base," "a cube," "a pyramid with a hexagonal base," "a pyramid with a square base."

Active Learning (Exploration)

Specify that each car (three-dimensional object) must have something in common with the car in front of it, and something in common with the car behind it.

Form teams of four students.

Provide each team with three-dimensional objects and a locomotive poster.

Specify that each car (three-dimensional object) must have one property in common with the car in front of it and one property in common with the car behind it.

Show a cube and place it behind the locomotive.

Ask students to choose a three-dimensional object to be the second car.

Examples of three-dimensional objects with a property in common with the cube:

• The square-based prism, because it has at least one square face.
• The square-based pyramid, because it has at least two congruent faces.
• The rectangle-based prism, because it has twelve edges.

Place the square-based prism after the cube.

Ask the following questions.

• Why can this three-dimensional object follow the cube?
• How are these three-dimensional objects similar?
• What other three-dimensional objects can be placed after the cube? Why?

Ask students to choose a three-dimensional object as the third car.

Examples of three-dimensional objects with a property in common with the square-based prism:

• The square-based pyramid, because it has at least one square face.
• The rectangle-based prism, because it has twelve edges.

Place the square-based pyramid after the square-based prism.

Ask the following questions:

• Why can this three-dimensional object follow the square-based prism?
• How are these three-dimensional objects similar?
• What other three-dimensional objects can be placed after the square-based prism? Why? Ask students to choose a three-dimensional object as the fourth car.

Examples of three-dimensional objects that have a property in common with the square-based pyramid:

• The pyramid with a triangular base, because it has triangular faces.
• The hexagonal based prism, because it has congruent faces.

Place the hexagonal based pyramid in the train after the square based pyramid.

Ask the following questions:

• Why can this three-dimensional object follow the square-based pyramid?
• How are these three-dimensional objects similar?
• What other three-dimensional objects can be placed after the square-based pyramid? Why?

Point out that the three-dimensional objects are different from each other.

Give each team eight to ten different three-dimensional objects.

Ask them to build the longest train possible with the three-dimensional objects.

Remind students that each car is linked to the next and the previous one by something they have in common.

The three-dimensional objects that cannot be included in the train represent people watching the train or cars go by and waiting for another locomotive.

Circulate and provide support as needed, by asking questions such as:

• Why did you choose this three-dimensional object as your first car?
• Why can we place this three-dimensional object between these two cars?
• Is there another three-dimensional object that could replace this car? Why?
• Why can't this three-dimensional object be part of the train?
• Can you modify the train to insert this three-dimensional object?
• What strategy did you use to solve this problem?

Check the train built by each team.

Consolidation of Learning

Provide each team with a large sheet of paper and a copy of Appendix 2PF.4.

Explain to students that they are going to represent their train using the drawings of the three-dimensional objects and their locomotive.

Tell students:

• to glue the locomotive on the large sheet;
• to cut out the three-dimensional objects;
• to place the three-dimensional objects after the locomotive in the same order as those in the train constructed earlier;
• to place the drawings of the unused three-dimensional objects under the train.

Example

Image locomotive built with geometric shapes followed by "a cube," "a rectangular-based prism," "a square-based pyramid," "a hexagonal-based pyramid."

Unused three-dimensional objects:

Have a team present their train and justify the order of the cars using specific terminology (for example, names of three-dimensional objects, common property, three-dimensional object that precedes, three-dimensional object that follows, face, surface, edge, vertex).

Note: It is not necessary for all teams to present their trains on the same day. The presentation of the trains can take place over several days. After all the presentations, the trains can be colored and laminated. It may be useful to refer to them when reviewing.

Examples of Success Criteria

The student:

• names the sorted three-dimensional objects;
• sorts three-dimensional objects according to a given attribute or a given property;
• compares one three-dimensional object with another (for example, same property, different property);
• uses appropriate vocabulary in explanations (for example, for attributes: dimensions, color, height; for properties: number of edges, vertices, faces, surfaces).

Differentiated Instruction

The activity can be modified to meet the needs of the students.

Follow-Up at Home

Students can take turns taking their team's train home and explaining it to their parents, or the train presentation can be recorded and sent home.

Source: translated from Guide d’enseignement efficace des mathématiques de la 1^re à la 3^e année, Géométrie et sens de l'espace, p. 119-127.

Learning Situation 3: It’s Three-Dimensional!

Total duration: approximately 3 hours

Materials

• scissors
• transparent adhesive tape
• 1 sphere, 1 cone and 1 cylinder per team of two
• 2 hoops per team of two
• Appendix 3I.1 (a) to (l) on construction paper
• Appendix 3I.2
• Appendix 3I.3 (a) and (b)

Active Learning (Exploration)

Provide a large enough space for this activity.

Form teams of two.

Give each team a sphere, a cylinder and a cone, two hoops and the two sets of labels.

Ask students to:

• take out the 12 three-dimensional objects that they have built;
• make a Venn diagram on the floor using two hoops and the first set of labels.
• sort their set of three-dimensional objects (including the sphere, the cylinder and the cone) into the appropriate regions.

Allocate the necessary time for them to complete the work.

Circulate and provide support as needed, by asking questions such as:

• What is the name of this three-dimensional object?
• What categories are you using to sort your set of three-dimensional objects?
• Does this three-dimensional object fit the category?
• Does this three-dimensional object have the properties of it?
• Is there a region that is common to both sets?
• In which region will you put this three-dimensional object? Why?

Check how each team sorted the objects and encourage students to correct themselves if there are any mistakes.

Ensure that students:

• place the hoops on the floor so that there is a common area for both sets;
• place the labels in the appropriate places;
• sort the three-dimensional objects by taking into account the two categories.

Example

The Venn diagram consists of three inner regions and one outer region. The labels are placed on the outside of the diagram.

Provide students with a copy of Appendices 3I.2, 3I.3(a) and 3I.3(b).

Ask them to:

• cut out the first set of three-dimensional objects (Appendix 3I.2) and paste them into Diagram 1 in Appendix 3I.3(a) to represent the classification of three-dimensional objects made on the floor;
• cut out the second set of three-dimensional objects (Appendix 3I.2) and paste them into Diagram 2 in Appendix 3I.3(b) to sort them according to the stated categories.

Consolidation of Learning

Share the results by asking the following questions.

Diagram 1

Image A Venn diagram made up of three interior regions. A rectangle that represents solids. In this space only there is a sphere, a cone, a cylinder, a pyramid with a rectangular base, a pyramid with a triangular base, and a pyramid with a pentagonal base. In the rectangle there are 2 circles. A blue circle represents the solids that have 12 or more edges. In this space only there is: a pyramid with a hexagonal base. A red circle that shows "the side faces of the solids are rectangles with squares partly overlapping". In this space only there is: a prism with a rectangular base. The two circles partly overlap, so a space is created for the solids that have both characteristics. In this space we find: a prism with a rectangular base, a prism with a hexagonal base, a prism with a pentagonal base, a prism with a square base, a cube, a prism with an octagonal base.

• How many regions are there in this Venn diagram?
• What categories were used to sort the three-dimensional objects in this Venn diagram?
• Which three-dimensional objects have side faces that have 12 or more edges?
• In what region of the diagram are these three-dimensional objects placed?
• Which three-dimensional objects have 12 or more edges?
• Which three-dimensional object has faces that are rectangles, including squares, but has fewer than 12 edges?
• Which three-dimensional object has faces that are not rectangles, and 12 or more edges?
• Why are there three-dimensional objects in the outer region of the diagram?

Diagram 2

Image A Venn diagram consists of three inner parts. A rectangle that represents solids. In this space only there are: a sphere, a cone, a cylinder. In the rectangle there are 2 circles. A blue circle representing solids with 12 or more edges. In this space there are: a pyramid with a hexagonal base, a pyramid with a rectangular base, a pyramid with a triangular base, and a pyramid with a pentagonal base. A red circle which shows "the lateral faces of the solids are rectangles including the squares partly overlapping". In this space there is: a prism with a rectangular base, a prism with a rectangular base, a prism with a hexagonal base, a prism with a pentagonal base, a prism with a square base, a cube with all the faces of the squares being congruent, a prism with an octagonal base

• How many regions are there in this Venn diagram?
• What categories were used to sort the three-dimensional objects in this Venn diagram?
• Why is the region labeled “All faces are congruent squares” inside the region labeled “All side faces are rectangles, including squares”?
• Why don't the two regions labeled “All side faces are triangles” and “All side faces are rectangles, including squares” touch?
• Why are the sphere, cone, and cylinder in the outer region of the diagram?
• If you replaced the categories listed as categories on the labels with the names of the three-dimensional objects, which ones could you use?
• How are the prisms similar?
• How are the prisms different?
• Is the cube a prism? Why?
• How are the pyramids similar?
• How are the pyramids different?

Examples of Success Criteria

The student:

• constructs three-dimensional objects;
• names the prisms according to their bases;
• names the pyramids according to their bases;
• sorts three-dimensional objects according to the given categories;
• sorts each three-dimensional object into the appropriate region of the Venn diagram;
• compares three-dimensional objects to each other;
• describes their differences and similarities;
• describes the properties of each major family of three-dimensional objects.
  • Pyramids have at least four vertices. Their side faces are triangular. They have only one base.
  • All prisms have two congruent bases; their side faces are rectangles, including squares.

Differentiated Instruction

Source: translated from Guide d’enseignement efficace des mathématiques de la 1^re à la 3^e année, Géométrie et sens de l'espace, p. 137-144.