# Properties of plane shapes like Rhombus, Square, Rectangle in relation to real life situations Primary 5 Third Term Lesson Notes Mathematics Week 3

** Subject : Mathematics **

Term : Third Term

Class :Primary 5

Week : Week 2

Topic : Properties of plane shapes like Rhombus, Square, Rectangle in relation to real life situations

Previous Lesson

### Learning Objectives:

By the end of this lesson, students should be able to:

- Identify and describe the properties of plane shapes like rhombus, square, and rectangle in relation to real-life situations.
- Recognize and state the basic properties of quadrilaterals.
- Understand the component parts of a circle with a specific radius using real-life objects.

### Embedded Core Skills:

- Critical thinking: Analyzing and identifying properties of shapes and their applications in real-life situations.
- Communication: Expressing ideas clearly and using appropriate mathematical vocabulary.
- Problem-solving: Applying knowledge of shapes and their properties to solve problems.

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### Learning Materials:

- Chart paper or whiteboard
- Markers or chalk
- Real-life objects representing different shapes (e.g., square tiles, rectangular books, a kite, circular objects like plates, clock, etc.)
- Worksheets or handouts with exercises related to the topics covered

Content

Good morning, class! Today, we’re going to explore the properties of some plane shapes, namely the rhombus, square, and rectangle, and understand how they relate to real-life situations. Let’s dive in!

Let’s start with the rhombus. A rhombus is a four-sided shape with opposite sides that are parallel and equal in length. It also has opposite angles that are equal. When it comes to real-life situations, the shape of a kite is an excellent example of a rhombus. If you’ve ever flown a kite, you may have noticed that the string is attached to the kite at two different points, forming two opposite equal angles. This gives the kite its rhombus shape.

Moving on to the square, I’m sure you’re all familiar with this shape. A square is a four-sided shape with all sides of equal length, and all angles are right angles, which means they measure 90 degrees. Many objects around us are shaped like squares. For instance, think of a tile on the floor or the screen of your tablet or smartphone. These objects have square shapes because their sides are equal in length, and all their angles are right angles.

Now let’s talk about the rectangle. A rectangle is also a four-sided shape, just like the square, but it has opposite sides that are equal in length, and all angles are right angles. Many objects in our daily lives have a rectangular shape. Look at your notebooks, doors, windows, or even the TV screen. They all have a rectangular shape because they have opposite sides that are equal, and all the angles are right angles.

Understanding the properties of these shapes helps us identify and classify objects around us. It also allows us to solve problems related to these shapes. For example, if you’re planning to tile your room, knowing that the shape of the tiles is a square will help you calculate how many tiles you need based on the dimensions of the room.

So, remember, a rhombus has opposite sides that are parallel and equal, a square has all sides equal and right angles, and a rectangle has opposite sides that are equal and right angles as well. Recognizing these shapes and their properties can be useful in various real-life situations.

I hope this explanation helps you understand the properties of these plane shapes and how they relate to real-life situations. If you have any questions, please feel free to ask!

**3 **DIMENSIONAL SHAPES

A prism is solid with a uniform cross-section. The top and bottom faces are the same. Cubes,

cuboids and cylinders are prisms.

Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides. A right triangular prism has rectangular sides, otherwise it is oblique. A uniform triangular prism is a right triangular prism with equilateral bases, and square sides.

to

(Rectangular prism)

a rectangular cuboid, all angles are right angles, and opposite faces of a cuboid are equal.

Cuboid

(Square prism)

Cube

A square prism is a three-dimensional shape cuboid figure whose bases are squares. The opposite sides and angles are congruent to each other. In the given figure, the bases of the prism are square, and therefore, it is called a square prism.

(Circular prism)

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cylinder

A pyramid is a solid with a non-uniform cross-section. The top has only one vertex. In a

prism the number of vertices at the top is the same with the number of vertices at the

bottom. Consider the following solids.

Triangular-based pyramid

Square-based

pyramid Rectangular-based pyramid

Circular-based pyramid (cone)

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Remember:

A vertex is a point where three or more edges meet. It is a corner point of a 3-D shape.

A face is a 2-D shape (known as a plane shape). Examples of 2-D shapes are triangles,

squares, rectangles, parallelograms, kites, circles etc.

An edge is a line where two faces meet.

Lead the class to discover all these from the above drawings of the 3-D shapes.

Solids (3-D shapes) Faces/surfaces (F) Edges (E) Vertices (points where edges meet)

Triangular prism 5 9 6

Triangular-based pyramid 4 6 4

Square prism (cube) 6 12 8

Square-based pyramid 5 8 5

Rectangular prism (cuboid) 6 12 8

Rectangular-based pyramid 5 8 5

Circular prism (cylinder) 3 2 0

Circular-based pyramid (cone) 2 1 1

Exercise

Answer the following questions.

- How many faces has your mathematics textbook?
- Write down two everyday objects which are
- a) cuboids b) cubes c)
- What shapes are the faces of
- a) rectangular prism b) triangular prism?
- What shapes are the faces of
- a) rectangular-based pyramid b) triangular-based pyramid?
- What is the difference between a triangular-based pyramid and a triangular prism?
- What shape are the faces of a cylinder?
- If F stands for faces, E stands for edges and V stands for vertices, what shapes satisfy the

following equations? Question f) is done for you. Use the table on page 335 to help you.

- a) E + F – V = 10 b) E + V – F = 10 c) V + F – E = 2
- d) F + V + E = 20 e) F + E – V = 6 f) F + E + V = 26 = cuboid
- g) F + E + V = 4 h) V + E – F = 6 i) F + E – V = 5

Use the nets of these shapes you have made to answer questions 1 to 18.

- A cube has _____ faces.
- A cube has _____ vertices.
- A cube has _____ edges.

sss4. A cuboid has _____ vertices.

- A cuboid has _____ edges.
- A triangular-based pyramid has _____ triangular faces.
- A triangular-based pyramid has _____ vertices.
- A triangular-based pyramid has _____ edges.
- A square-based pyramid has _____ square faces.
- A square-based pyramid has _____ vertices.
- A square-based pyramid has _____ edges.
- A closed cylinder has _____ circular faces.
- A closed cone has _____ circular faces.
- The curved surface of a cylinder is a _____.
- The curved surface of a cone is a _____.
- A triangular-based prism has _____ vertices.
- The shape of a
*Bournvita*tin is a _____. - Sugar,
*maggi*and dice for playing Ludo game are examples of _____.

Identify and state the meaning Of

– radius

– diameter

– circumference of a circle

– chord

– sector (minor and major)

– segment (minor and major)

A path traced from a fixed point such that the same distance from that point is maintained

is called a circle.

O

This is a circle.

The fixed point O is called the centre of the circle

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Parts of a circle

There are special words to describe different parts of a

circle as shown in the diagram of the circle drawn.

- The distance round the circle is called the

circumference or perimeter.

- A straight line from the centre of a circle to the

circumference of the circle is called a radius.

- A straight line across a circle which starts and ends

at two points on the circumference is called a chord.

- A chord which passes through the centre of a circle

is called a diameter.

- An arc is part of the circumference of a circle.
- The area enclosed by two radii and an arc is called a sector.
- The area enclosed by an arc and a chord is called a segment.
- A straight line which touches the circumference of a circle is called a tangent.

Exercise 1

- Use the circle below to answer the questions.
- Measure radius OA. Copy and complete: OA = !
- Name four other radii. (Radii is the plural of radius.)
- Copy and complete: OY = !, OQ = !, OY = !,

OP = !, OX = !

- Are all the radii of the same length?
- Measure the diameter POQ.
- Name another diameter and find its length.
- Compare the length of a diameter with the length of a radius. What do you observe?

Copy and complete these statements.

- The length of a diameter is the length of a radius.
- The length of a radius is that of a diameter.
- Measure EF and QY. Record their lengths.
- Compare the lengths of EF and QY with the length of POQ and XOY respectively.

What do you observe?

1. Rhombus:

– A rhombus is a four-sided shape.

– It has opposite sides that are parallel and equal in length.

– It also has opposite angles that are equal.

– Real-life example: A kite, where the string is attached at two different points, forming two opposite equal angles.

2. Square:

– A square is a four-sided shape.

– All sides of a square are equal in length.

– All angles in a square are right angles (90 degrees).

– Real-life examples: Floor tiles, tablet or smartphone screens.

3. Rectangle:

– A rectangle is a four-sided shape.

– It has opposite sides that are equal in length.

– All angles in a rectangle are right angles (90 degrees).

– Real-life examples: Notebooks, doors, windows, TV screens.

Understanding these key points helps in identifying and classifying objects.

It also enables solving problems related to these shapes, such as calculating the number of tiles needed for tiling a room.

EVALUATION

- A __________ is a four-sided shape with opposite sides that are parallel and equal in length. a) Rhombus b) Square c) Rectangle d) Triangle
- In a __________, all sides are equal in length, and all angles are right angles. a) Rhombus b) Square c) Rectangle d) Circle
- A shape with opposite sides that are equal in length and right angles is called a __________. a) Rhombus b) Square c) Rectangle d) Hexagon
- When flying a kite, the shape formed is a __________. a) Rhombus b) Square c) Rectangle d) Pentagon
- A __________ has opposite angles that are equal. a) Rhombus b) Square c) Rectangle d) Trapezoid
- The shape of a floor tile is often a __________. a) Rhombus b) Square c) Rectangle d) Circle
- All angles in a __________ measure 90 degrees. a) Rhombus b) Square c) Rectangle d) Triangle
- A notebook typically has the shape of a __________. a) Rhombus b) Square c) Rectangle d) Hexagon
- The screen of a smartphone is usually a __________. a) Rhombus b) Square c) Rectangle d) Oval
- A shape with all sides equal, opposite sides parallel, and opposite angles equal is a __________. a) Rhombus b) Square c) Rectangle d) Pentagon

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### Topic: Quadrilaterals

1. Recognizing Quadrilaterals:

– A quadrilateral is a polygon with four sides.

– It is a closed figure formed by connecting four line segments.

– Examples of quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.

2. Basic Properties of Quadrilaterals:

– Four sides: A quadrilateral always has four sides.

– Sum of interior angles: The sum of the interior angles of a quadrilateral is always 360 degrees.

– Diagonals: A quadrilateral has two diagonals, which are line segments connecting opposite vertices.

– Opposite sides: In a quadrilateral, opposite sides are parallel in some cases (e.g., parallelograms) or not parallel in others (e.g., trapezoids).

### Topic: Component Parts of a Circle with Specific Radius

To discuss the component parts of a circle with a specific radius, let’s consider a circle with a radius of 5 units:

1. **Center**: The center is the point in the middle of the circle. It is denoted as point O.

2. **Radius**: The radius is a line segment from the center to any point on the circle’s circumference. In this case, the radius is 5 units long.

3. **Circumference**: The circumference is the distance around the outer edge of the circle. It is calculated using the formula: circumference = 2πr, where r is the radius. For our circle with a radius of 5 units, the circumference would be 2π(5) = 10π units.

4. **Diameter**: The diameter is a line segment that passes through the center and connects two points on the circle’s circumference. It is equal to twice the length of the radius. In our circle, the diameter would be 2(5) = 10 units.

5. **Chord**: A chord is a line segment that connects two points on the circle’s circumference. It can be of any length, but it should not pass through the center.

6. **Arc**: An arc is a portion of the circumference of a circle. It is a curved line connecting two points on the circle.

7. **Sector**: A sector is a region of the circle enclosed by two radii and an arc. It is like a slice of the circle.

By understanding these component parts of a circle, we can better analyze and solve problems related to circles and their properties.

Evaluation

- A __________ is a polygon with four sides. a) Triangle b) Quadrilateral c) Circle d) Pentagon
- The sum of the interior angles of a quadrilateral is always __________ degrees. a) 90 b) 180 c) 270 d) 360
- A quadrilateral has __________ diagonals. a) No b) One c) Two d) Four
- In a parallelogram, opposite sides are __________. a) Perpendicular b) Equal in length c) Not parallel d) Diagonal
- A quadrilateral with only one pair of parallel sides is called a __________. a) Square b) Rectangle c) Trapezoid d) Rhombus
- The center of a circle is denoted by the letter __________. a) R b) D c) C d) O
- The radius of a circle is a line segment from the center to any point on the __________. a) Perimeter b) Diameter c) Chord d) Circumference
- The circumference of a circle can be calculated using the formula __________. a) Circumference = π × radius b) Circumference = 2 × π × radius c) Circumference = π × diameter d) Circumference = 2 × π × diameter
- The diameter of a circle is equal to __________ times the length of the radius. a) One-half b) The same as c) Double d) Triple
- An arc is a curved line that connects two points on the circle’s __________. a) Perimeter b) Diameter c) Chord d) Circumference

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### Lesson Plan Presentation

Subject: Mathematics

Topic: Properties of Plane Shapes and Component Parts of a Circle

**Presentation**:

**Introduction**: a) Greet the students and briefly recap the previous lesson on shapes. b) Introduce the topics to be covered: properties of plane shapes (rhombus, square, rectangle) in real-life situations, and recognizing quadrilaterals. c) State the learning objectives for the lesson.**Teacher’s Activities**: a) Present information on the properties of plane shapes: i. Explain the properties of a rhombus, square, and rectangle, including their sides, angles, and parallel lines. ii. Give real-life examples of these shapes (e.g., kites, tiles, screens). iii. Use visual aids, diagrams, and objects to reinforce understanding.b) Discuss the properties of quadrilaterals: i. Define a quadrilateral and its characteristics. ii. Explain the sum of interior angles in a quadrilateral (360 degrees), diagonals, and opposite sides.

c) Use real-life objects to discuss the component parts of a circle: i. Introduce the concept of a circle and its basic components (center, radius, diameter, circumference). ii. Demonstrate with real-life objects (e.g., circular plates, clock) to show the center, radius, diameter, circumference, chords, arcs, and sectors

**Learners’ Activities**: a) Engage students by asking questions and encouraging participation. b) Encourage students to observe and discuss real-life objects related to the shapes and circle components presented. c) Provide opportunities for students to work in pairs or small groups to explore and discuss the properties of shapes and components of a circle using the provided objects.

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**Learners’ Activities**: a) Engage students by asking questions and encouraging participation. b) Encourage students to observe and discuss real-life objects related to the shapes and circle components presented. c) Provide opportunities for students to work in pairs or small groups to explore and discuss the properties of shapes and components of a circle using the provided objects.

Assessment:

- During the lesson: a) Observe students’ participation and engagement during discussions and activities. b) Ask questions to check students’ understanding of the properties of shapes and the components of a circle.
- Post-lesson assessment: a) Distribute worksheets or handouts with exercises related to the topics covered. b) Review and assess students’ responses to evaluate their understanding of the concepts

Evaluation Questions:

- What are the properties of a square?
- Name a real-life object that resembles a rhombus.
- What are the opposite sides of a rectangle called?
- What is the sum of interior angles in a quadrilateral?
- Define the term “radius” in relation to a circle.
- How can you calculate the circumference of a circle?
- What is the diameter of a circle if the radius is 8 units?
- Explain the concept of a chord in a circle
- Give an example of a real-life object that represents a circle.
- What are the basic components of a circle?

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. Conclusion:

- Summarize the main points covered in the lesson: properties of plane shapes (rhombus, square, rectangle) in real-life situations, recognizing quadrilaterals, and the components of a circle.
- Highlight the importance of understanding these concepts in everyday life and problem-solving.
- Encourage students to practice identifying shapes and their properties in their surroundings.

VIII. Homework: Assign homework exercises or problems related to the topics covered, such as identifying shapes in everyday objects or solving problems involving circles and quadrilaterals.

IX. Follow-up Activities:

- Review the concepts in the next lesson by revisiting examples and exploring further real-life applications.
- Provide opportunities for students to work collaboratively on shape-related projects or investigations.

Note: The lesson plan can be adapted based on the specific classroom environment, available resources, and time constraints. It is important to provide ample opportunities for student engagement, exploration, and assessment throughout the lesson.