Linear Measurement or Length
Class:- Basic 6
Subject:- Mathematics
Week:- 3
Topic: Length
Behavioral objective:-
At the end of the lesson the pupils should be able to:-
1. Recognize and convert the units of Length measurements from one units to another
- Apply Pythagoras’ rule or theorem to find the unknown length of a given right-angled triangle
- Identify Pythagorean triplets
- 4. Find the heights and distances of objects
Instructional material/Reference material:-
Online Materials
Textbooks
Scheme of Work By Lagos state
Pictures of Triangles
Building Background /connection to prior knowledge :
Students are familiar with the various ways of measuring length in their previous lessons
Content:-
LENGTH
The standard unit of length are:–
10 millimetres (mm) make one centimetre
10 centimetres (cm) make one decimetre
10 decimetres (dm) make one metre
100 centimetre make one metre
1000 metres make one kilometre
The measurements can also be written in inverse way in this way
10 millimetres (mm) = 1 centimetre (cm)
1000 millimetres = 1 metre
100 centimetres = 1 metre
10 Decimetres 1 Metre
1000 metres = 1 kilometre (km)
Examples1.
10mm = 1cm
Therefore 18cm = 18 × 10mm = 180mm
- 1000m = 1km 1.08km = 1.08 × 1000m = 1080m
Examples
1} 10mm = 1cm
∴ 280mm = 280 ÷ 10cm
= 28cm
2} 100cm = 1m ∴ 185cm = 185 ÷ 100m = 1.85m
Pythagoras theorem
Study the diagrams below
Triangles ABC, LMN and XYZ are right-angled triangles
.Bˆ, Mˆ and Yˆ are right angles (i.e. 90º)
The side facing (opposite) each right angle is the longest side.
This side is called the hypotenuse.
That is, AC, LN and XZ are the hypotenuses of triangles ABC, LMN and XYZ respectively.
ABC is a right-angled triangle with Bˆ = 90º
AB = 3cm, BC = 4cm and AC = 5cm
Area of red square = 3cm × 3cm = 9cm
2 Area of blue square = 4cm × 4cm = 16cm2
Area of red square + Area of blue square 9cm2 + 16cm2 = 25cm2Area of black square = 5cm × 5cm = 25cm2
From the calculation, you will see that the area of the black square equals the sum of the areas of both the red square and blue square.This is called the Pythagoras theorem. In this right-angled triangle ABC,
pythagoras’ theorem tells you that area Y (black) = area R (red) + area B (blue)Pythagoras’ theorem
In any right-angled triangle, the area of the square on the hypotenuse side is equal to the sum of the areas of the squares on the other two sides
Application of Pythagoras’ theorem to calculate the missing side of a right-angled triangle
Pythagoras’ theorem is usually written using the lengths of the sides of the triangle.In this right-angled triangle ABC, Pythagoras’ theorem tells you that
b2 = a2 + c2
The square of the hypotenuse side is
equal to the sum of the squares of the other two sides.This rule is used to find an unknown side of a right-angled triangle when the other two sides are given.
Example1. Study how the length of the side marked y is found.
Hypotenuse = 13cm∴ 132 = y2 + 52
∴ 169 = y2 + 25
169 – 25 = y
2√144 = y2
∴ y2 = 144y
= 144
= 12cm
Evaluation:-
1. Convert 3000 cm to kilomètres
- Find the length of the hypotenuse of a right-angled triangle if the lengths of the other two sides are 12cm and 16cm respectively.
- 3. A right-angled triangle has its hypotenuse as 10cm and one other side as 8cm. Calculate the length of the third side
