Second Term Lesson Note for Week Five
Class : JSS 3
Subject : Mathematics
Topic : Variation (Meaning and types)
Duration : 80 Minutes
Period : Double Period
Reference Book :
- Essential Mathematics for Junior Secondary School, JSS 3 (Basic 9).
- Lagos State Unified schemes of work for Junior Secondary School, JSS 1 – 3.
- Online Resources
Instructional Material : Chart showing the variation sign and types of variation.
Learning Objectives : By the end of the lesson learners will be able to :
i. Explain the meaning of variation.
ii. Identify and list types of variations.
iii. Describe the direct and inverse variations, with examples.
Content :
VARIATION
Variation may be described as the relationship that exist between two or more quantities in which a change in one quantity leads to a change in the other(s)
Variation can be classified into;
- Direct Variation
- Inverse Variation
- Joint Variation and
- Partial variation
DIRECT VARIATION
Direct Variation occurs when two variables x and y are related directly, here an increase or decrease in x results into a proportional increase or decrease in the other.
For example :
If y varies directly as x, then y α x
The symbol α ‘’ means “is proportion to” or “varies directly with”. This symbol can be change to an “= “sign by introducing a constant K.
y α x
Y = kx. ( where k is a constant)
Example 1 :
M varies directly as L. Given that M = 6 and L = 2. Find :
i. The relationship between M and L
ii. The value of L when M = 15
Solution :
M α L
M = KL
6 = K 2
K = 6/2
K = 3.
M = 3L is the relationship between M and L.
ii. M = 3L, M = 15, then
15 = 3 L
L = 15/3
Therefore, L = 5
INVERSE VARIATION
Two variables are said to be inverse proportion when their product is a constant.
If the value of y varies as a result of the variation of Z such that y x Z is always a constant, then y is said to vary inversely with Z. Inverse variation is written as y , y = where K is the constant.
Example 2 :
If P varies inversely with A where P = 4 and A = 8, find the constant and write down the equation.
Solution
P α 1/A
P = K/ A
PA = K
4 x 8 = K
K = 32
The equation connecting P and A.
P = 32/ A ( This can also be called formula connecting P and A).
Evaluation :
1. The circumference, C of a circle is directly proportional to its diameter, d and when C = 66, d = 21.
(a) Find the relationship between the circumference of a circle and its diameter
(b) Find the value of d when C = 44.
2. The intensity I of a wave varies inversely as the square of the distance d from the source. If I = 250 when d = 30, find :
(a) I in terms of d
(b) the value of I when d = 25
(c) the value of d when I = 10.
Conclusion : At the end of the lesson, the teacher marks the learners notebook and makes necessary corrections.
Assignment :
1. If x varies directly as √y and x = 5 when y = 169, find:
(a) the value of the constant of proportionality
(b) the formula connecting x and y
(c) the value of x when y = 9.
2. P varies inversely as q³ and p = 8 when q = 2.5. Find :
(a) the relationship between p and q
(b) the value of q when p = 216.