Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Identify and classify 2D shapes and 3D objects
• Calculate the perimeter of squares, rectangles, and triangles
• Calculate the area of squares and rectangles
• Describe the nets of common 3D objects
• Distinguish between different types of triangles

Lesson summary

Welcome to Week 4 of our Mathematics journey! This week, we're diving into the fascinating world of 2D shapes and 3D objects. Geometry isn't just about shapes; it's about understanding the world around us. From the houses we live in, to the soccer balls we play with, geometry is everywhere. In South Africa, geometry plays a crucial role in architecture (think of the design of traditional rondavels or modern skyscrapers), construction (building roads and bridges), and even arts and crafts (creating patterns and designs). Understanding these concepts will empower you to better understand and appreciate the spaces and objects that make up your daily life.

Lesson notes

2.1 2D Shapes 2D shapes, also known as flat shapes, exist only in two dimensions: length and width. They have no thickness.

Let's explore some key 2D shapes: Triangles: Triangles are polygons with three sides and three angles. The sum of the angles in any triangle is always 180°.

Equilateral Triangle:* All three sides are equal, and all three angles are equal (60° each). Think of the triangular gable of a traditional Cape Dutch house.

Isosceles Triangle:* Two sides are equal, and the angles opposite those sides are equal.

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

Right-angled Triangle:* One angle is 90°. This is essential for understanding concepts like the height of buildings.

Quadrilaterals: Quadrilaterals are polygons with four sides and four angles. The sum of the angles in any quadrilateral is always 360°.

Square:* All four sides are equal, and all four angles are right angles (90°). Many tiles are square.

Rectangle:* Opposite sides are equal, and all four angles are right angles (90°). Think of the shape of a classroom door.

Parallelogram:* Opposite sides are parallel and equal, and opposite angles are equal.

Rhombus:* All four sides are equal, and opposite angles are equal.

Trapezium (Trapezoid):* Only one pair of opposite sides is parallel.

Circle: A circle is a set of all points that are the same distance 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 passing through the center (twice the radius).

Circumference:* The distance around the circle. 2.2 3D Objects 3D objects, also known as solid shapes, exist in three dimensions: length, width, and height.

Cube: A cube has six square faces. All edges are equal in length. Think of a dice or sugar cube.

Rectangular Prism (Cuboid): A rectangular prism has six rectangular faces. Think of a brick or a box of cereal.

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

Sphere: A sphere is a perfectly round 3D object where every point on the surface is equidistant from the center. Think of a soccer ball.

Pyramid: A pyramid has a polygonal base and triangular faces that meet at a single point called the apex.

Square Pyramid:* A pyramid with a square base.

Triangular Pyramid (Tetrahedron):* A pyramid with a triangular base. 2.3 Perimeter and Area Perimeter: The perimeter is the total distance around the outside of a 2D shape. To calculate the perimeter, add up the lengths of all the sides.

Square: Perimeter = 4 side Rectangle: Perimeter = 2 (length + width)

Triangle:* Perimeter = side1 + side2 + side3 Area: The area is the amount of surface a 2D shape covers.

Square: Area = side side = side² Rectangle: Area = length width 2.4 Nets of 3D Objects A net is a 2D pattern that can be folded to form a 3D object. Visualizing and drawing nets helps us understand the surface area of 3D objects. Consider a cube; its net would consist of six connected squares arranged in a way that they can be folded to form the cube.

Example 1: Calculating the Perimeter of a Rectangle A farmer in Limpopo wants to fence his rectangular vegetable garden. The garden is 10 meters long and 5 meters wide. How much fencing does he need?

Solution: Perimeter = 2 (length + width) Perimeter = 2 (10m + 5m) Perimeter = 2 (15m) Perimeter = 30m Therefore, the farmer needs 30 meters of fencing.

Example 2: Calculating the Area of a Square A tile in a bathroom is square shaped with a side length of 20cm. What is the area of the tile?

Solution: Area = side side Area = 20cm 20cm Area = 400 cm² Therefore, the area of the tile is 400 square centimeters.

Example 3: Identifying a 3D object from its Net Consider a net consisting of one square and four triangles all connected to the sides of the square. What 3D object can be formed by folding this net?

Solution: This net can be folded to form a square pyramid. The square forms the base, and the triangles fold upwards to meet at an apex. Guided Practice (With Solutions)

Question 1: A triangular road sign has sides of length 50cm, 50cm, and 80cm. What is the perimeter of the sign?

Solution: Perimeter = side1 + side2 + side3 Perimeter = 50cm + 50cm + 80cm Perimeter = 180cm The perimeter of the sign is 180cm. This is a good example of applying math to road safety!

Question 2: A rectangular school garden is 12 meters long and 8 meters wide. What is the area of the garden?

Solution: Area = length width Area = 12m 8m Area = 96 m² The area of the garden is 96 square meters. This will help determine how much fertilizer is needed.

Question 3: Draw the net of a cube.

Solution: There are multiple ways to draw the net of a cube. A common one is to draw four squares in a row. Then add one square above the second square and another square below the third square. This shape can be folded into a cube. You can find images of different cube nets online if you need more examples.