Space and Geometry: Three-DimensionalSpace

|| QT Elements

SGS2.1 Makes, compares, describes and names three-dimensional objects including pyramids, and represents them in drawings.

  • Identifies and names three-dimensional objects such as prisms, pyramids, cylinders, cones and spheres.
  • Identifies and discusses the properties of three-dimensional objects.
  • Compares and describes features of prisms, pyramids, cylinders, cones and spheres.
  • Makes models of prisms, pyramids, cylinders, cones and spheres.
  • Recognising similarities and differences between prisms, pyramids, cylinders, cones and spheres.
  • Describe cross-sections of three-dimensional objects.
  • Predicts possible sections and cross-sections of an object.

Lesson 1
Three Dimensional Objects
Introduce 3D concepts and discuss 3D objects, what is a 3D object? These shapes are solid or hollow.They have three dimensions, length, width and height. Ask students if they can name some 3D shapes.

Revise pyramids, prisms, spheres and cylinders and cones. Define prisms, a 3D object with two identical ends and all other faces being rectangles. Define pyramids, a 3D object with a base and all other faces being triangles. Show students examples of pyramids and prisms and allow them to guess the object.

Discuss the shapes that the students have identified. Discuss the properties of the shapes such as the number of faces, edges and vertices. (Revise faces, edges and vertices with students). To assist students understanding, choose a 3D shape and identify and discuss its properties as a class. Allow students to identify its faces, edges and vertices.

Students are given a selection of prisms and pyramids to look at. In pairs/groups students are to investigate the number of faces, edges and vertices of each shape. Students are given a table to record the findings (Worksheet 1).

Answer questions provided on the worksheet as a class or students complete individually.

Resources: Worksheet 1, 3D Shapes

Lesson 2
Cross section
Introductory Activity
Review the names of the 3D shapes and list the names on the board.
Students will complete a short game to revise what they had learnt in lesson 1.
GAME: 3D Shape Concentration

In pairs the students shuffle the cards and place them in rows picture side down. The first student turns over any two cards. If the shape card matches the word form card then the student takes the two cards and continues playing. If the two cards do not match, the next play goes to the other student. Play continues until all matches have been made. The student with the most cards at the end of the game is the winner.

Main Activity
Introduce cross-sections by asking if any students know what they are. Discuss cross-sections to the class. (A cross section is the face you get when you make one slice through an object).
Teacher demonstrates with a plasticine model by cutting to show the cross-section. Display a cube made from playdough to the class. Explain to the students that a straight cut in any direction through an object would result in displaying a face and that this face is called a section. Provide pairs of students with paper and pencils and ask them to predict and draw the resulting section. Cut the cube as suggested and have the students compare the section to their drawings.
Have the pairs of students join to form a group of four. Provide each group with a playdough model of a cube or any other shape. Instruct the students to mark a cut on their model, then discuss, predict and draw the resulting section. Have the students repeat this process for one or two additional sections. Encourage the students to visualise and discuss the features of each section in order to draw the section accurately (optional activity).
After the students have had adequate time to complete the task, invite a group to share the drawing of one of its sections. Have them indicate where the cut on the cube or other shape would occur and explain how their group predicted the resulting section. If other groups have marked a similar cut on their shape, ask them to compare their drawings.

In pairs students will complete findings of other shapes on the worksheet provided. (Worksheet 2)

Students complete extra cross-sections worksheet if finished before time.
Example: A cylinder has a cross-section which is circular. This means that if acylinder was sliced, all the slices would be circles.
Explain that cross-sections of both prism and pyramids are identical in shape to their ends. Pyramid cross-sections become smaller as they approach the apex.
Resources: 3D Shape game, Worksheet 2, Playdough, worksheet 3

Lesson 3
Making 3D objects
Teacher guided:
Students use art straws and plasticine/blue tack to construct 3D objects and record properties in terms of mathematical vocabulary. Challenge with different numbers of art straws and balls of plasticine/blue tack. Students will then identify the properties of the shapes they have made.
  • How many faces does it have?
  • How many edges?
  • How many (vertices)?

Extra Activities and Resources:

  • Students create their own, “What 3D object am I” game. Students write down properties of a 3D objects on blank cards (students also draw the object). Students then play with other students and try to guess what 3D object it is.

Resources:Straws, plasticine/blue tack, images of 3D shapes (worksheet 4)

ICT Games