Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Identify and classify 2D shapes and 3D objects.
• Describe the properties of 2D shapes (sides, angles, symmetry).
• Describe the properties of 3D objects (faces, edges, vertices).
• Distinguish between prisms and pyramids.
• Draw nets for simple 3D objects.

Lesson summary

Geometry is all around us, from the shapes of our houses to the design of our soccer balls. Understanding geometry helps us make sense of the world and allows us to solve practical problems in everyday life. In South Africa, geometric principles are vital for architecture, construction, design, and even understanding the patterns in traditional artwork and crafts. This week, we will begin our journey into understanding the properties of 2D shapes (like squares and circles) and 3D objects (like cubes and cylinders).

Lesson notes

2D Shapes (Plane Shapes) 2D shapes are flat shapes that only have length and width. They exist on a plane and have no thickness.

Some common 2D shapes are: Triangles: Three-sided polygons.

Equilateral Triangle: All three sides are equal in length, and all three angles are 60°.

Isosceles Triangle: Two sides are equal in length, and the two angles opposite those sides are equal.

Scalene Triangle: All three sides are of different lengths, and all three angles are different.

Right-angled Triangle: One angle is 90°. The side opposite the right angle is called the hypotenuse.

Quadrilaterals: Four-sided polygons.

Square: Four equal sides and four right angles (90°). All sides are lines of symmetry, as are the diagonals.

Rectangle: Two pairs of equal sides and four right angles (90°). Has two lines of symmetry.

Parallelogram: Two pairs of parallel sides. Opposite sides and opposite angles are equal.

Rhombus: Four equal sides. Opposite sides are parallel and opposite angles are equal.

Trapezium/Trapezoid: Only one pair of parallel sides.

Circles: A set of points equidistant from a central point.

Radius: The distance from the center of the circle to any point on the circle.

Diameter: The distance across the circle through the center (twice the radius).

Circumference: The distance around the circle.

Example 1: A window in a shack is in the shape of a triangle. One angle is 90 degrees, and the other two angles are 45 degrees each. What type of triangle is it?

Solution: Since one angle is 90 degrees, it is a right-angled triangle. Since the other two angles are equal, it is also an isosceles triangle.

Therefore, it is a right-angled isosceles triangle.

Example 2: A farmer has a field in the shape of a quadrilateral. All four sides are equal in length, but the angles are not 90 degrees. What type of quadrilateral is it?

Solution: Since all four sides are equal, and it's a quadrilateral, it must be either a square or a rhombus.

However, because the angles are NOT 90 degrees, it cannot be a square.

Therefore, the field is in the shape of a rhombus. 3D Objects (Solid Shapes) 3D objects have length, width, and height (or depth). They occupy space.

Some common 3D objects are: Cube: Six square faces, 12 edges, and 8 vertices (corners). All faces are congruent squares.

Cuboid: Six rectangular faces, 12 edges, and 8 vertices. (Think of a rectangular box).

Note: A cube is a special type of cuboid where all sides are equal.

Sphere: A perfectly round 3D object where every point on the surface is equidistant from the center. It has no faces, edges, or vertices.

Cylinder: Two circular faces and one curved surface. It has two edges and no vertices.

Pyramid: A base (which can be any polygon) and triangular faces that meet at a point called the apex. Named according to the shape of its base (e.g., a square-based pyramid has a square base and four triangular faces).

Cone: A circular base and one curved surface that tapers to a point (the apex). It has one circular face, one curved surface, one edge, and one vertex. Prisms vs.

Pyramids: Prisms: Have two identical bases connected by rectangular faces. They are named according to the shape of their bases (e.g., a triangular prism has two triangular bases and three rectangular faces).

Pyramids: Have one base and triangular faces that meet at a point (the apex).

Example 3: A brick used for building a house is a 3D object with six rectangular faces. What is the name of this object?

Solution: This is a cuboid (or a rectangular prism).

Example 4: A traditional Zulu hut often has a conical roof. What is the shape of the roof?

Solution: The roof is in the shape of a cone.

Nets of 3D Objects: A net is a 2D shape that can be folded to form a 3D object. For example, a net of a cube consists of six squares connected in a way that they can be folded to form a cube. Drawing nets helps us visualize how 2D shapes relate to 3D objects. Guided Practice (With Solutions)

Question 1: Identify the following shape: It has four sides, all sides are equal, and all angles are right angles.

Solution: This shape is a square. It is a quadrilateral with four equal sides and four 90-degree angles.

Question 2: A shape has one circular face and a curved surface that tapers to a point. What 3D object is it?

Solution: This is a cone. The circular face is the base, and the curved surface connects the base to the apex.

Question 3: Draw a possible net for a cube.

Solution: There are many possible nets for a cube. One common example is a "T" shape: ``` [] [][][][] [] ``` Each `[]` represents a square. Imagine folding the top and bottom squares up, and then folding the left and right squares around to form the sides of the cube.

Question 4: A building block has 6 faces, 8 vertices, and 12 edges, and all the faces are rectangles. What 3D shape is the building block?

Solution: This is a cuboid (or rectangular prism). The number of faces, vertices, and edges matches the properties of a cuboid.