Second Term Lesson Note for Week Two
Class : JSS 2 / Basic 8
Subject : Mathematics
Topic : Word Problems leading to Algebraic Expressions
Duration : 80 Minutes
Period : Double Periods
Reference Book :
Essential Mathematics for Junior Secondary Schools, JSS 2.
Lagos State Unified schemes of work for Junior Secondary Schools, (JSS 1 – 3).
Online Resources
Instructional Material :
Learning Objectives : By the end of the lesson learners will be able to :
i. Explain the concept of word problem.
ii. Explain what is an algebraic expression.
iii. Solve word problems involving algebraic expressions.
Content :
WORD PROBLEM LEADING TO ALGEBRAIC EXPRESSION
Sometimes you may be asked to solve problem given in words. To do this you need to convert the words into an algebraic equation and then solve it.
The following points will show you what to do.
a. Read the equation carefully and then decide what the unknown number is
b. Where necessary, change all the unit of measurement to the same unit
c. Use a letter to represent the unknown
d. Use the information provided to write the required equation
e. Solve the equation as usual
f. Use the solution obtained to answer the questions in words
g. You can check your answer as usual.
Example 1 : I think of a number, add 5 to it and multiply the result by 3, the answer is 36. What is the number?
Solution:
Note the rules above. Follow the steps.
Let the number be x, add 5 to it, then it becomes x + 5, multiply by 3, we have
3(x + 5), the answer is 36.
Open the bracket 3(x + 5) = 36 [use the 3 to multiply the equation]
3x + 15 = 36 [subtract 15 from both side]
3x + 15 – 15 = 36 – 15
3x = 21[divide both side by 3
3x/3 = 21/3
x = 7
To Check if the answer is correct, substitute it in the equation :
3(7 + 5)
= 3 x 12
= 36
Example 2 : The sum of a number and 9 is multiplied by -2 and the answer is -8. Find the number
Solution :
Let x be the number, x + 9, multiply by -2,
-2(x + 9), the answer is -8
-2(x + 9) = -8 [open the bracket]
-2x -18 = -8
Collect the like term
-2x = -8 + 18 [the sign we change to positive]
-2x = 10
Divide both sides by -2
-2x/-2 = 10/-2
x = -5
To Check if the answer x = – 5 is correct, put it into the equation :
-2( x + 9)
= -2(-5 + 9)
= -2(+4)
= -8
Example 3 : The smallest of three consecutive odd number is n, if their sum is 27. Find the three numbers.
Solution :
Let the first number be n, second number to be n+2, third number be n+4.
Note that odd numbers are 1, 3, 5, 7, the difference between each number is 2.
N+N+2+N+4 = 27
Collect the like term
3N + 6 = 27 [subtract 6 from both sides]
3N = 27 – 6
3N = 21
Divide both sides by 3
3N/3 = 21/3
N = 7
If N =7,
then N+2= 7+2 = 9,
while N + 4 = 7 + 4 = 11
Therefore the consecutive numbers are 7, 9, and 11 respectively.
EVAULATION: Translate the following statement into algebraic equations and then solve them
Think of a number, and 5, the result is 10. What is the number?
Two market women shared a basket full of oranges in order to sell them. The share of the first woman is twice the other. If there are 300 oranges in the basket. What is the share of each woman?
The sum of three consecutive even numbers is 60. Find the numbers.
ASSIGNMENT: PAGE 159 EXERCISE 13.5 NO 4, 6,8,15, AND 18