Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Identify and name common 2D shapes and 3D objects.
• Describe the properties of these shapes and objects.
• Understand the difference between 2D and 3D.
• Draw 2D shapes and 3D objects.
• Calculate the perimeter of 2D shapes.

Lesson summary

This week, we're diving into the exciting world of geometry! Geometry is all about shapes, sizes, positions, and properties of things. We see geometry everywhere around us, from the rectangular shape of your textbooks and desks to the circular wheels of a taxi. In South Africa, understanding geometry is crucial for many things, like building houses that are safe and strong (understanding shapes like triangles in roof supports is vital), designing beautiful patterns for traditional crafts (understanding shapes like squares and circles to create aesthetically pleasing designs), and even planning urban spaces effectively.

Lesson notes

2D Shapes (Two-Dimensional) 2D shapes are flat shapes that only have length and width. They have no thickness or depth. Think of a drawing on a piece of paper – that's a 2D shape!

Square: A square is a 4-sided shape where all sides are equal in length and all angles are right angles (90 degrees).

Rectangle: A rectangle is also a 4-sided shape, but only the opposite sides are equal in length. All angles are also right angles (90 degrees). Think of a door.

Triangle: A triangle is a 3-sided shape.

There are different types of triangles: Equilateral triangle: All three sides are equal in length, and all three angles are equal (60 degrees).

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

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

Right-angled triangle: One of the angles is a right angle (90 degrees).

Circle: A circle is a round shape where all points on the shape are the same distance from the center.

Parallelogram: A parallelogram is a 4-sided shape where opposite sides are parallel and equal in length. The opposite angles are also equal. 3D Objects (Three-Dimensional) 3D objects have length, width, and height (or depth). They take up space. Think of a soccer ball or a brick – these are 3D objects!

Cube: A cube is a 3D object with six square faces. All sides are equal in length, and all angles are right angles. Think of a dice.

Rectangular Prism (Cuboid): A rectangular prism is a 3D object with six rectangular faces. Like a cube, all angles are right angles, but the sides are not necessarily equal. Think of a shoebox.

Sphere: A sphere is a round 3D object where all points on the surface are the same distance from the center. Think of a soccer ball.

Cylinder: A cylinder has two circular faces and one curved surface. Think of a can of beans.

Pyramid: A pyramid has a base that is a polygon (a shape with straight sides) and triangular faces that meet at a point called the apex.

Square-based Pyramid: The base is a square.

Triangular-based Pyramid (Tetrahedron): The base is a triangle. Properties of 2D Shapes and 3D Objects Sides: The straight lines that make up a 2D shape.

Angles: The space between two lines that meet at a point (vertex).

Faces: The flat surfaces of a 3D object.

Edges: The lines where two faces of a 3D object meet.

Vertices: The points where edges of a 3D object meet (corners). Perimeter of 2D shapes The perimeter of a 2D shape is the total distance around its outside. To calculate the perimeter, we add the lengths of all the sides together.

Example 1: Square A square has sides of 5cm each. What is its perimeter?

Solution: Perimeter = 5cm + 5cm + 5cm + 5cm = 20cm Example 2: Rectangle A rectangle has length 8cm and width 3cm. What is its perimeter?

Solution: Perimeter = 8cm + 3cm + 8cm + 3cm = 22cm Example 3: Triangle A triangle has sides of 4cm, 6cm and 7cm. What is its perimeter?

Solution: Perimeter = 4cm + 6cm + 7cm = 17cm Example 4: 3D objects from nets: Imagine a cardboard box for a fridge. It's delivered flat, as a 'net' of 2D shapes. When folded correctly, you create a 3D rectangular prism! Likewise you can create different 3D shapes by folding nets of triangles and squares. Guided Practice (With Solutions)

Question 1: Identify the shape below and state the number of sides and angles. Also, state its perimeter. ``` _____ | | 4cm |_____| 4cm ``` Solution: Shape: Square Number of Sides: 4 Number of Angles: 4 (all right angles)

Perimeter: 4cm + 4cm + 4cm + 4cm = 16cm Question 2: Identify the object and describe its faces, edges, and vertices.

Imagine a standard dice Solution: Object: Cube Faces: 6 square faces Edges: 12 edges Vertices: 8 vertices Question 3: Draw a rectangle on squared paper with a length of 6 units and a width of 3 units. Calculate the perimeter.

Solution: Draw a rectangle using the squares on the paper, ensuring the length is 6 squares and the width is 3 squares.

Perimeter: 6 units + 3 units + 6 units + 3 units = 18 units Question 4: A triangular street sign has side lengths of 50cm, 50cm, and 70cm. What is its perimeter? What type of triangle is it?

Solution: Perimeter: 50cm + 50cm + 70cm = 170cm Type of Triangle: Isosceles triangle (because two sides are equal) Independent Practice (Questions Only) Name three objects you see around your classroom or home that are examples of 3D shapes. Draw a circle on squared paper using a compass. A rectangular swimming pool is 10m long and 5m wide. What is its perimeter? A pyramid has a square base with sides of 3cm each, and its triangular faces are all identical. What shapes make up the pyramid? What is the difference between a square and a cube? Describe the properties of a cylinder, including its faces and edges. Draw a net (flat pattern) that can be folded to make a cube. A farmer wants to fence his triangular field. The sides of the field are 12m, 15m and 20m. What is the total length of fencing he needs?