Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Identify and describe properties of common 2D shapes.
• Draw 2D shapes accurately using a ruler.
• Identify and draw lines of symmetry in 2D shapes.
• Determine if a shape is symmetrical or asymmetrical.
• Create symmetrical patterns using 2D shapes.

Lesson summary

Geometry helps us understand the world around us. From the shape of our houses to the patterns in a Shweshwe cloth, shapes and symmetry are everywhere! In Grade 4, we build on what you already know about shapes and learn to describe them accurately. This week, we're focusing on two-dimensional (2D) shapes and the fascinating idea of symmetry. Understanding 2D shapes helps us design things, understand patterns, and even solve puzzles. Symmetry helps us appreciate balance and beauty in nature and art. Think about the South African flag – it has interesting shapes and even some symmetry!

Lesson notes

2D Shapes: A 2D shape is a flat shape that only has two dimensions: length and width. It doesn't have thickness or depth. Think of a drawing on a piece of paper – that's a 2D shape!

Let's look at some common ones: Square: A square has four sides that are all equal in length. It also has four corners, which we call vertices (plural of vertex). Each vertex forms a right angle (90 degrees). Imagine the tiles on your kitchen floor – many of them are squares!

Properties: 4 equal sides, 4 vertices, 4 right angles Rectangle: A rectangle has four sides, but only the opposite sides are equal in length. It also has four vertices, each forming a right angle. Think of a door or a chalkboard.

Properties: 4 sides (opposite sides equal), 4 vertices, 4 right angles Circle: A circle is a round shape with no corners or straight sides. It's defined by a single point in the middle (the center) and all points on the circle are the same distance from the center. Think of the sun or a plate.

Properties: No sides, no vertices, defined by its center and radius.

Triangle: A triangle has three sides and three vertices.

There are different types of triangles: Equilateral Triangle: All three sides are equal.

Isosceles Triangle: Two sides are equal.

Scalene Triangle: No sides are equal. Think of a slice of watermelon or the support beams of a bridge.

Properties: 3 sides, 3 vertices.

Pentagon: A pentagon has five sides and five vertices.

Properties: 5 sides, 5 vertices Hexagon: A hexagon has six sides and six vertices. Think of the cells in a beehive.

Properties: 6 sides, 6 vertices Symmetry: Symmetry means that a shape is balanced or the same on both sides. We can draw a line through a symmetrical shape so that if you fold it along that line, the two halves match exactly. This line is called the line of symmetry or the axis of symmetry.

Line of Symmetry: An imaginary line that divides a shape into two identical halves.

Symmetrical Shape: A shape that has at least one line of symmetry.

Asymmetrical Shape: A shape that has no lines of symmetry.

Examples: Square: A square has four lines of symmetry: one horizontal, one vertical, and two diagonal.

Rectangle: A rectangle has two lines of symmetry: one horizontal and one vertical.

Circle: A circle has an infinite number of lines of symmetry because you can draw a line through the center in any direction and still have matching halves.

Triangle (Equilateral): An equilateral triangle has three lines of symmetry.

Triangle (Isosceles): An isosceles triangle has one line of symmetry.

Triangle (Scalene): A scalene triangle has no lines of symmetry.

Drawing Shapes Accurately: To draw shapes accurately, you'll need a ruler, a pencil, and sometimes a protractor (for measuring angles, but that's more advanced).

Square: Use a ruler to draw one side of a specific length (e.g., 5cm). Then, use the ruler to draw the other three sides, making sure they are all the same length and meet at right angles.

Rectangle: Use a ruler to draw one side of a specific length (e.g., 8cm). Then, draw a perpendicular line (at a right angle) to create one of the shorter sides (e.g., 3cm). Repeat to complete the rectangle.

Circle: Use a compass. Place the point of the compass at the center of where you want the circle. Adjust the distance between the point and the pencil to the radius (distance from the center to the edge) you want. Then, draw the circle by rotating the compass around the center point. Guided Practice (With Solutions)

Question 1: Draw a rectangle with a length of 7cm and a width of 3cm. Then, draw its lines of symmetry.

Solution: Use a ruler to draw a horizontal line that is 7cm long. At each end of the line, draw a perpendicular line (at a right angle) that is 3cm long. Connect the top ends of these lines to complete the rectangle. Draw a horizontal line of symmetry exactly in the middle of the rectangle (1.5cm from the top and bottom). Draw a vertical line of symmetry exactly in the middle of the rectangle (3.5cm from the left and right sides).

Commentary: We use a ruler to ensure accuracy when drawing the rectangle. The lines of symmetry must divide the rectangle exactly in half, both horizontally and vertically.

Question 2: Look at the shape below: (Imagine an equilateral triangle is described here). How many sides and vertices does it have? Is it symmetrical? If so, draw its lines of symmetry.

Solution: The shape is an equilateral triangle. It has 3 sides. It has 3 vertices. It is symmetrical. It has three lines of symmetry, each going from a vertex to the midpoint of the opposite side.

Commentary: Identifying the shape is crucial. Understanding the properties of an equilateral triangle (all sides equal, all angles equal) helps determine its symmetry.

Question 3: Which of the following shapes are symmetrical?