4. Quantitative Reasonings – as stated in the pupil’s quantitative books or textbooks
By the end of the lesson, the pupils should have attained the following objectives (cognitive, affective and psychomotor) and should be able to –
1. measure length and angles.
2. use Pythagoras rule to find the unknown length of a right – angled triangle.
3. solve many quantitative aptitude problems involving Pythagoras rule.
The teacher will teach the lesson with the aid of:
1. Measuring rules and tapes
2. Mathematical sets
3. Chart of Pythagoras rules.
METHOD OF TEACHING – Choose a suitable and appropriate methods for the lessons.
Note – Irrespective of choosing methods of teaching, always introduce an activities that will arouse pupil’s interest or lead them to the lessons.
1. Scheme of Work
2. 9 – Years Basic Education Curriculum
3. Course Book
4. All Relevant Material
5. Online Information
CONTENT OF THE LESSON
LESSON ONE – INTRODUCTION
Teacher’s/Pupil’s Activities 1 – Introduction to Lengths and Angles
1. Draw a line of 5 cm or more.
2. Name the line AB.
3. Draw another line from point A or B.
4. Name the third point, C.
Teacher’s remark – Length AB is the distance between A and B. The point A is called a vertex, where two or more lines meet. At the same point A, an angle is formed and it’s called angle A or <BAC.
An angle is formed when two lines meet at a shared point. That’s, the space between two or lines at a shared point. As shown below.
Teacher’s/Pupil’s Activities 2 – Measuring Lengths and Angles
Guide the pupils to measure the length AB, AC, XY and XZ. And also, measure angle A and X.
LESSON TWO – TYPES OF TRIANGLES
Teacher’s/Pupil’s Activities – Drawing a triangle
1. Draw a line and name it, line AB.
2. Drawing another line at the point A and name it, AC.
3. Draw another line from the B to C.
4. What shape does it formed?
5. Define the _____________.
This is a triangle.
Expect a response like this, a triangle is a shape with three (3) lines.
Teacher’s remark – Expand their definition of triangle. A triangle is a figure (shape) that has three sides and three angles. A triangle also has three (3) vertices.
Pupil’s Activities 2 – Measuring the Lengths and Angles of Triangles and take down their records.
Pupil’s Activities 3 – Describe the lengths and angles of each each triangle measured.
First triangle, all the lengths and angles are equal.
Second triangle, two of the lengths and angles are equal
Third triangle, none of the three (3) lengths and angles are equal.
Teacher’s remark – There are three (3) types of triangle based on lengths (sides) and angles. These triangles are equilateral triangle (all the lengths and angles are equal). Isosceles triangle (two of its lengths and angles are equal) and scalene triangle (no lengths or angles are equal).
LESSON THREE – INTRODUCTION TO PYTHAGORAS RULE
Teacher’s/Pupil’s Activities 1 – The lengths and Angles of Right – angled Triangle
Measure the lengths and angles of the triangle below.
Pupil’s Records – All the three lengths are with different measurements. Two angles measured 45º each and third angle measured 90º
Teacher’s remark – The triangle is called right – angled triangle. It is called right – angled triangle because it has one of its angles to be 90º. The longest length is known as hypotenuse.
Pupil’s Activities 2 – Identify the hypotenuse of the following right – angled triangle.
Pupil’s Activities 3 – Quantitative Reasoning on Pythagoras Rule
Sample – 3² + 4² = 5²
3 x 3 + 4 x 4 = 5 x 5
9 + 16 = 25
1. ____ + 12² = 13²
2. 7² + ____ = 25²
3. 8² + 4² = ____
Teacher’s/Pupil’s Activities 3 – Marking and correction
LESSON FOUR – PYTHAGORAS RULES
Teacher’s/Pupil’s Activities 1 – Discuss the Pythagoras Rule with Pupils
A² + B² = C²
A² = 9 = 3 x 3 = 3²
B² = 16 = 4 X 4 = 4²
C² = 25 = 5 x 5 = 5²
Teacher’s/Pupil’s Activities 2 – Application of Pythagoras Rule
First right – angled triangle
A² + B² = C²
A = 6, B = 8 and C = c
That’s, 6² + 8² = c²
6 x 6 + 8 x 8 = c²
36 + 64 = c²
100 = c²
10² = c² or √100 = c
c = 10.
To deliver the lesson, the teacher adopts the following steps:
1. To introduce the lesson, the teacher revises the previous lesson. Based on this, he/she asks the pupils some questions;
2. Guides pupils to draw a right angled triangle with side 3cm, 4cm and 5cm.
Pupil’s Activities – Draw the right angled triangle.
3. Guides pupils to identify the hypotenuse, opposite and the adjacent sides of the right angled triangle.
Pupil’s Activities – Identify the hypotenuse, opposite and the adjacent sides of the right angled triangle.
4. Guides the pupils to use Pythagoras rule to calculate the unknown side i.e. a² + b² = c² where a and bare the adjacent and opposite sides of the triangles and c is the hypotenuse.
Pupil’s Activities – Use Pythagoras theory a² + b² = c² to calculate the unknown side.
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