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 

  1. Apply Pythagoras’ rule or theorem to find the unknown length of a given right-angled triangle
  2. Identify Pythagorean triplets
  3. 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)

See the source image

Examples1.

10mm = 1cm

Therefore 18cm = 18 × 10mm = 180mm

  1. 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

  1. Find the length of the hypotenuse of a right-angled triangle if the lengths of the other two sides are 12cm and 16cm respectively.
  2. 3. A right-angled triangle has its hypotenuse as 10cm and one other side as 8cm. Calculate the length of the third side
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