MATHEMATICS JSS 1
WEEK: 1
TOPIC: Recording of Numbers
OBJECTIVES: At the end of the lesson the students should be able to:
i. Identify the place value in a number
ii. Explain if a number is small or large.
CONTENT: Large and small numbers
INSTRUCTIONAL MATERIALS: pebbles, bottle tops, large seeds etc.
PROCEDURES:
Step 1: Numbers are recorded using place-value system, where the position of a digit
in a number represents its value.
Every digit in the place-value system tells the number of times ones, tens, hundreds,
thousands, ten thousands, hundred thousands, millions, ten millions, hundred
millions, billions, ten billions, hundred billions, trillions is taken
The table below shows whole numbers from which large numbers are obtained
Quantity in words
Quantity in
numbers
Units
Tens
Hundreds
Thousands
Ten thousands
Hundred thousands
Millions
Ten millions
Hundred millions
Billions
Ten billions
Hundred billions
Trillions
1
10
100
1000
10000
100000
1000000
10000000
100000000
1000000000
10000000000
100000000000
1000000000000
No of
digits
1
2
3
4
5
6
7
8
9
10
11
12
13
Step 2: In the place value system, it is very important to write units under
units, tens under tens, hundreds under hundreds, etc.
Decimal points are used to separate whole number from fractions
Example 1:
Thousand
Hundred
Ten
Unit
(7)
(5)
(3)
1
(8)
Example 2:
Hundreds
Tens
Units
Decimal Place
Ten
Hundredths
8
26
Thousandths
.5
9
4
Decimal fractions from which whole numbers are obtained.
Examples 3: Write the name and decimal fractions of the following number:
88888
12345
Ans: Starting from the 5th 8 to 1st
Name
decimal fraction
8 tenth
0.8
8 hundredths
0.08
8 thousandths
0.008
8 ten thousandths
0.0008
8 hundred thousandths 0.00008
EXERCISES:
1. Write the 28th thousandths as decimal fraction
Ans: 28 thousandths
1 thousandth x 28
0.001 x 28
0.028
2. Write
865
as decimal fraction
100, 000
Ans: 0.00865
3. A cubic metre of 100cm by 100cm l x b x h
i.e. 100 x 100 x 100
Volume of cubic metre
= 100 0000
4. Write 407526 in the place value system
Ans:
Hundred thousand
Ten thousand Thousand
4
0
7
Hundreds
5
Tens
2
WEEK: 2
TOPIC: Other Bases of Counting (Seven and Sixty)
OBJECTIVES: At the end of the lesson the students should be able to:
i. Identify other bases of counting other than ten.
ii. Give example of instance where those bases are used
iii. Explain how such counting are used in some electronics gadget
2
CONTENT: Things counted in base seven and sixty and their application
Example of other bases of counting and how they are applied
INSTRUCTIONAL MATERIALS: Number chart
PROCEDURE:
Step 1:Bases 7and60 counting
Students should answer the following
(1) What did you count in bases 7 (ANS: Time)
(2) What did you count in bases sixty (ANS: Time)
SEVEN DAYS MAKE ONE WEEK
60 seconds make 1 minute
60 minutes make 1 hour
(3) Time is the interval between two events and time is constant (k) all the time
Other bases of counting are base ten, base eight, base two (binary).
Apart from time, base 60 counting is applied in the rating of the old 60 watts electric
bulb, base two binary is applied in: - blender; computer. e.t.c.
Step 2: Examples of calculations on base 7 system and sixty systems respectively.
Example1: Find the total of 1week, 5days, 6days and 3weeks, 4days in
weeks and days
Days only
SOLUTION
i. week
day
1
5
6
3
4
6
1
6 weeks
1day
ii. In days
6x7+1 day
=
42+1
=
43days
Example 2: Today is Wednesday, what day of the week, will it be in 160 days time
Solution
160 =22 weeks
6days
7
After 22 weeks, it will be another Wednesday, so count from that Wednesday 6 more
days, this will give you Tuesday.
Example 3: find the number off second days in 3 minutes, 49s
Solution
3x60+49
=180+49
229s
Example 4: Add the following together
Wk day
Wkday
Wk day
4
4
1
5
1
1
2
2
6
1
5
6
4
4
3
Wkday
4
4
1
3
3
2
6
1
6
0
CLASS EXERCISE:
1. Add the following together
Hr
min
hr
2
12
1
1
49
4
0
2
min
34
45
20
sec
28
50
18
2. Find the number of minutes in
(i) 2405 (ii) 5 hours
ASSIGNMENT:
1. A baby is 3wks 4days, what is his age in days
Ans: 25days
2. Suppose today is Thursday, what day of the week will it be after?
i. 20 days ANS Wednesday
ii. 50 days ANS Friday
iii. 70 days ANS Thursdays
iv. 100 days ANS Saturday
3. Find the number of seconds in the following:
i. 2 minutes
ANS 120 seconds
ii. 10 min 54sec
ANS 654 seconds
iii. 3 mins 22sec
ANS 202 seconds
iv. 1 hour
ANS 360 seconds
WEEK 3
TOPIC: Tally system, Roman numeral,Simple code, Place value.
OBJECTIVES: At the end of the lesson the student should be able to:
i. Mention the common number system
ii. Give example of them
iii. Solve some of the problem based on the number system.
PROCEDURE:
Step 1: The teacher leads the students to revise the history of counting in local
language and the international base ten systems.
Step 2: The teacher leads them to write down numbers using the (i) tally system (ii)
simple code and (iii) roman numeral
Step 3: The teacher leads the students to use these systems to solve problems.
CONTENT:
In the development of numbers system, the tally marks were the first numbers symbol
used as numerals. The early man use tally marks to represent the number of things
they had. These marks were scratched on stone, walls or cut on sticks.
1.
Ans. = 8
Ans. =18
Ans. = 23
Present the following ordinary numbers in tally marks
1.
37
2.
41
3.
16
4
Roman numeral
The system is one of the recent ways of writing numbers which is in use today. In this
system, capital letters of English alphabets are used for the numerals. e.g.
I stand for unit;X stands for 1; L stand for 5; C stand for 100
Hence we have the following
1-I
4 - IV
7 - VII
10 - X
2 - II
5-V
8 - VIII
11 - XI
3 - III
6 - VI
9 - IX
12 - X11
20- XX
30- XXX
40- XL
50- L
60- LX
70- LXX
80- LXXX
90- XC
100- C
400- CD
500-D
1000- M
Roman numeral can be used for clocks, watches and chapters in books
EXAMPLE 1: Find the number represented by (1) XXV (2) XLVII (3) CCXC
(4) MCMLXXIV.
SOLUTIONS
(1). XX = 20
(2). XL = 40
(3). CC = 200
(4). M = 1000
V=5
VII = 7
XC = 90
CM = 900
XXV = 25
XLVII = 47
CCXC = 290
LXX = 70
IV = 14
MCMLXXIV = 1,974
EXAMPLE 2: Write the following in roman numerals:
1. 18
2. 139
3. 1999
Solution
1). 10 = X
(2). 100 = C
(3). 1000 = M
8 = VIII
30 = XXX
900 = CM
18 = XVIII
9 = IX
90 = XC
139 =CXXXIX
9 = IX
1999 = MCMXCIX
EXAMPLE 3: What number does MDCLXXVIII represent?
Solution
M 1000
D
500
C
100
L
50
XX
20
VIII
8
MDCLXXVIII = 1678
CLASS EXERCISES:
1. What number does CCXC represent?
Solution
CC = 200
XC = 90
CCXC = 290
2. Write 1934 in Roman Numerals
Solution
1000 =
M
900 = CM
30 = XXX
4 = IV
1934 = MCMXXXIV
5
ASSIGNMENT: Write the following numbers in Roman Numerals:
Ans (Not to be given with the assignment)
(a) 12 = XII
(b) 18 = XVIII
(c) 19 = XIX
(d) 26 = XXVI
(e) 39 = XXXIX
(f) 41 = XL
(g) 200 = CC
(h) 175 = CLXXV
(i) 294 = CCXCIV
(j) 512 = DXII
(k) 1422 = MCDXXII
(l) 1999 = MDCDXCIX or MCDXXII
(MIM would be a good guess)
6
MATHEMATICS JSS 2
WEEK: 1
TOPIC: Arithmetic in the home and office (Personal Arithmetic – Interest)
OBJECTIVE: At the end of the lesson the students should be able to; solve simple
problems on simple interest
CONTENT: Personal arithmetic: simple edition
INSTRUCTIONAL MATERIAL: New general mathematics for junior secondary school
book 2, UBE edition by MF MACRAE, ETAL
PROCEDURE:
Step 1: Introduction to the lesson; simple interest is the extra money given to people
to encourage them to save money. For example; saving account in banks give
simple interest.
Step 2: Example of calculations on simple interest.
Example 1: If a person saves N10, 000 for a year and the interest rate is 8%
per annum. Calculate the simple interest
Solution
The interest rate will be
8x10, 000
100
= N800
Thus N800 is the simple interest.
Example 2: Find the simple interest on N60, 000 for 5 years at 9% per annum.
Solution
Yearly interest = 9% of N60, 000
9 x 60,000
100
= 5400
Interest for 5 years will be
5400 x 5
= 27,000
Example 3: Find the simple interest on N40, 000 for 1 year per annum
Solution
Yearly interest is 5% of N40, 000
5 x 40,000
100
= N2000
Example 4: Find the simple interest for N10, 000 for 2 years at 4% per annum
Yearly interest 4% of N9000
4x 1000
100
= N400
Interest for 2 years 400 x2
= N800
Step 3: The formula for simple interest is PTR
100
Where
P = Principal
T = Time
R = Rate
7
Example 5: Find the simple interest for N25000 for 3 years at 5% per annum (p.a.)
P = 25000
T = 3 years
R = 5%
Simple interest 1 = 25000 x 3 x15
100
= N3750
CLASS EXERCISE:
1. Find the simple interest for N70, 000 for 1 year at 4%
Ans: N2800
2. N10, 000 for 4 years at 4½ %
Ans. N1800
3. N30, 000 for 2 years at 5%
Ans. 3000
ASSIGNMENT:
Find the simple interest for
1. N20, 000 for 4 years at 6% per annum
Ans. N4800
2. N70, 000 for 3 years at 5% per annum
Ans. N10500
3. N60, 000 for 2½ years at 5% per annum
Ans. N7500
4. N35000 for 4 years at 3% per annum
Ans. N4200
5. N5000 for 3 years at 4% per annum.
Ans. N1800.
8
MATHEMATICS JSS 2
WEEK: 2
TOPIC: Arithmetic in the home and office (simple interest part II)
OBJECTIVE: At the end of this lesson the students should be able to; solve simple
problems on simple interest (i.e. simple interest)
CONTENTS: Simple interest part II
INSTRUCTIONAL MATERIALS: New general mathematics for junior secondary school
book 2, UBE edition by MF MACRAE, ETAL
PROCEDURE:
Step 1: Introduction to the lesson
People that borrow money pay interest to the lender based on agreed term or modality
of pay back
Step 2: Examples of calculation on simple interest part II
Examples I: a man borrows N1600, 000 to buy a house. He is charged interest at a
rate of 11% per annum. In the first year he paid the interest on the loan, he also paid
back N100,000 of the money borrowed. How much did he pay back altogether? If he
paid this amount by monthly installments. How much did he pay per month? How
much did he still owe?
Solution:
Interest on N1600, 000 for one year.
= 11% of N1600, 000
= 11/100 x 1600,000
= 11 x 16000
= N176000
Total money paid on first year
= 176 000
+ 100 000
N 276 000
Monthly payments = 276000
12
= 23,000
The man now owes
1600, 000
- 1000, 000
N1500, 000
Example 2:
Find the total amount to be paid (i.e. loan + interest) on the following
1. N500 for 2 weeks at N100 interest per week
1st week interest N500 = N100
2nd week interest N500 = N100
Total amount of interest = N200
Total amount paid back is 500+ 200
= N700
2. N2000 for 3weeks at N1 on each N10
Interest per week
No of N10 in N2000 = 2000
10
= 200
Amount of interest for 1st week is 200x 1= 200
9
Amount of interest for 2nd week is 200 x 1 = 200
Amount of interest for 3rd week is 200 x 1 = 200
Total interest = N600.
Total amount paid back is
N2000
+ 600
2600
Example 3:
A woman borrows N4000 on a short term loan. She is charged interest of N on each
N10 per week.How much does he pay back altogether if she borrow the money for (a) 1
week (b) 3 weeks (c) 10 weeks
Answer:
Total money borrowed = N4000
No of N10 interests N4, 000 = 4, 000
10
= 400
Hence for each N10 interest = N400
For 1 week is 400 x 1 = 400
For 3weeks is 400 x 3 = 1200
For 10 weeks is 400 x 10 = 4000
So the money paid back
(a) 1 week is (b) 3 weeks is 4000
(c) 10 weeks is 4000
4000+ 1200 + 4000
+ 400N5200 N 8000
N 4400
CLASS EXERCISE: Find the amount to be paid back on the following loans
a. N10, 000 for 12 year at 9% simple interest per annum
Ans= N1090
b. N60, 000 for 3 years 7 ½ % simple interest per annum
Ans= N73500
c. N10, 000 for 15 years at 8% simple interest per annum.
Ans= N22, 000
ASSIGNMENT:
1. A woman borrowed N600, 000 to pay for car. She agreed to pay the money over
2(yrs.) years paying simple interest at 9% per annum
Calculate the simple interest on N600, 000 at 9% per annum for 2 years
Answer N108000
Hence find the total amount she paid back.
Answer N708000
If the total amount is paid back in monthly installments over 2 years each mouth?
Answer = N29500
2. A woman borrowed N2000 for 4weeks. She agreed to pay N2500 back at the end of
the 4 weeks.
How much interest does she pay over the 4 weeks?
Answer N500
How much interest does she pay per week?
Answer N125
Find the percentage rate of interest per week that she pays.
Answer 6¼%
10
MATHEMATICS JSS 2
WEEK: 3
TOPIC: Arithmetic in the home and office (income tax).
OBJECTIVE: At the end of the lesson students should be able toexplain income
tax, calculate income tax
CONTENT: Income tax
INSTRUCTIONAL MATERIALS: New general mathematics for junior secondary school
book 2, UBE edition by MF MACRAE, ETAL
PROCEDURE: Introduction to the lesson
Step 1: All responsible citizen in every nation pay income tax to the government.
Income tax is a part of their income. To understand effective calculation of income tax
you need to note the following. The process of paying tax is called PAYE i.e. pay as you
earn. The government uses tax to pay for public services such as:
Defence,
Education,
Health,
Transport.
Method of calculating taxes varies from country to county but the method usually is
similar to the following example:
TYPICAL PAYE TAX SYSTEM
Each month, all earners pay tax on their taxable income.
Taxable income is
Total income – (minus) allowance for any wages or salary earner
Table 3a contains a typical rate of tax, for various income bands.
Tax bands on monthly income
1st N20, 000
Over 20,000 and up to 40,000
Rate of tax
10%
15%
Over 40,000 and up to 60,000
20%
Over 60,000
25%
Allowance are as follows:Personal allowance N6000
Child allowance N25, 000 for each child under 10years of age (for a maximum of 4
children); Dependent relatives allowance, maximum of N4000.
If both parent are working, only one parent claim the child allowance of an earner.
Step 2: Method on how to attempt to calculate income tax, always follow these steps:
Note personal allowance of earner.
Any one earning N6000 a mouth or less will not pay income tax
Find the allowance
Calculate the taxable income
Calculate the tax
11
Step 3: Example of calculation on income tax
Example1:
A man’s income is N52, 800 per month. He has 3 children, a dependent relatives
whose claim is 3700. Calculate the amount of tax he pays
Solution:
N
Personal allowance
6000
Child allowance 3 x 2500
7500
Dependant relatives
3700
Total allowance
17200
Taxable income
52800
-17200
35600
Taxable income = N20, 000 +15600
Tax 10% of 2,000 + 15% of N156, 00
N2000 +2340
= N4340.
Example 2:
Using the PAYE tax system above table 3a.
Copy and complete table bellow
No
Monthly income
Allowance
N
N
N
a.
28,900
10, 000
b.
48,080
25,000
c.
73,160
27,260
d.
10,1040
32,200
e.
38,270
31,780
f.
18,960
23,000
Taxable income
N
18,900
18,080
45,900
68,840
6,490
None
CLASS EXERCISE: Calculate the tax payable on the total income in example 2
(a) N1890 (b) N1808 (c) N6180 (d) N11210 (e) N649 (f) 0
ASSIGNMENT: A person with five children earns N61320 per month
Calculate the tax allowance – ANS N16, 000
Calculate the taxable income =ANS N45, 320
Calculate the taxable income tax paid = ANS N5798
Calculate the income after tax is paid answer ANS = N55522
13
MATHEMATICS JSS 3
WEEK: 1
TOPIC: COMPOUND INTEREST
SUB-TOPIC: Revision on simple interest.
OBJECTIVES: At the end of the lesson, the student should be able to find
simple interest given the principal, rate and time. Recall and use the Simple interest
formula: Find the amount, given time and rate apply the principles of simple interest
to
daily
life
problems
including
inflation
and
deflation
INSTRUCTIONAL MATERIAL:
(i) Naria notes.
(ii) Cheque Book
(iii) Pass Book
(iv) Reference.
New General Mathematics for junior Secondary school by M.F. Macrae et al
CONTENT:
Simple Interest means payment given for saving money or price paid for borrowing
money.
FORMULA:
I=
Where:
P-Principal (sum of money saved)
R-Annual rate of interest (given as a percentage)
T-This is the time for which the money is saved or borrowed
EXAMPLE 1:
Find the simple interest on 6000 for 4years at 3% per annum
I=
= 6000 × 3 × 4
100
= 60 × 12
= N720
EXAMPLE 2:
Find the S.I. of the following:
(1) 3000 for 4yrs at 8%
I=
=30 4
= N960
EXERCISE
1. Find S.I. on 52000 for 5yrs of 7% =N1820
2. FindS.I. on1250 for 4yrs at 9% =N810
3. Find S.I. on 1600 for 3 yrs at 6% =N336
4. Find S.I. on 8200 for 6yrs at 7 % =N3690
5. Find S.I. on 6880 for 2yrs at 5% =N688
14
6. Find S.I. on 21210 for 3 yrs at 6% =N4242
7. Find S.I. on $47520 for 6yrs at 6 % =$178.20
8. Find S.I. on $131.70 for 6yrs at 4 % =$212.49.
ASSIGNMENT
Find S.I on N500 for 32yrs at 4 % =N2160
Find S.I on $787 for 3yrs at 9% $212.49
WEEK: 1 Continues
TOPIC: Finding the amount given as the principal,time,and rate.
OBJECTIVE: At the end of the lesson,the student should be able to
(i) Define amount
(ii) Find amount given principal and interest.
(iii) Find amount given principal,rate,and time.
INSTRUCTIONAL MATERIAL:
(i)Naira notes
(ii)Cheque books
(iii)Pass Books.
CONTENT
Amount is the sum of the principal and interest,E.g.
Principal
N6000
Interest
720
Amount
6720
EXAMPLE: Find the amount if the principal is N34320 for 5yrs at 6 % per annum.
I = 34320
100
I=
=N10725
Interest = 10725
Principal=32320
43045
15
EXERCISE
Find the amount of the following:
(i)
N500 for 1yrs at 6% =N530
(ii)
N7000 for 2yrs at 7 % =N8050
(iii) N4800 for 3yrs at 6% =N720
(iv)
N45000 for 4yrs at 4% =N52200
(v)
N360 for 5 yrs at 7% =N498.60
(vi)
$423.68 for 6yrs 3m at 2 % =N489.88
ASSIGNMENT: Find the simple interest on
1. N800 for 1yrs at 8% =N864
2. N15000 for 20yrs at 6 % =N337500
3. $112.80 for 7 yrs at 7 % =$176.25
4. $172.35 for 3yrs 4m at 8% =$218.31
Note: Do not give the answers along with the assignment it is just to guide when
correction is made.
WEEK: 2
TOPIC:Introduction of Compound Interest
OBJECTIVES:At the end of the lesson the student should be able to:i. Define compound interest
ii. Solve simple problems on compound interest
iii. Differentiate between compound interest and S.Ii.e Simple
interest.
CONTENT
Simple interest is computed by formula
S.I=
While compound interest is computed thus:Principal SimpleInterest (S.I)
Example: Find the compound interest on N30,000 for 2yrs at 4%
1st year
S.I=
I1 =N1200.0
Amount at the end of the first year is: N 30000
+ 1200
N 31200
16
New principal=N31200
2nd year Principal is N31200
S.I on
=N1248
I2 = N1248
Amount at the end of the 2nd year is
+ 1248
32,448
Total compound interest=32448
-30000
N2448
CLASS WORK:
1.Find the compound interest for 2yrs at 8% per annum. Ans: I1 = 4800;
I2 = 5184. Compound Interest at N9984
2.Find the amt N5000 becomes if saved for 3yrs at 6%.Ans: N5955.08
3.Find the amount and the compound interest for each of the following.
4.N40, 000 for 2yrs at 8% per annum (Ans 466.56)
5.N50, 000 for 2yrs at 6% (Ans 56180)
ASSIGNMENT:
Find the compound interest of:
i. N1000 for 3yrs at 8% P.A N1331
ii. N6000 for 3yrs at 5% P.A N6945.75
iii. N5000 for 3yrs at 8% P.A N6298.56
iv. N10,000 for 3yrs at 7% P.A N12250
WEEK: 3
TOPIC:Compound interest;Mortgage, Depression, andInflation
OBJECTIVE:At the end of the lesson,the students should be able to:
Calculate compound interest based on mortgage.
Calculate compound interest based on depression
Calculate compound interest based on inflation.
CONTENT
Mortgage-This refers to loan for house purchase. The borrower pays both interest and
principal back.This reduces the principal gradually.
EXAMPLE:
A man borrows N900, 000 to buy a borrows N 900, 000 to buy a house at 8% p.a.
Compound interest. He pays N92, 000 at the end of each year, how much does he still
owe at the end of 3yrs.
Steps to follow:
Step 1: Calculate the amount with interest added each year.
Step II: Subtract the repayment and carry the remaining amounts to the next
year.
Step III: Calculate the interest again and repeat the process until the third
year.
17
Workings:N
1st year: Principal
8% interest
880, 000
2nd year
Principal 880, 000
% interest
950, 400
92, 000
3rd year
900, 000
72, 000
972, 000
92, 000
70, 400
85840.0
Principal
858, 400
B/f
858, 400
8% interest 68, 672
927, 072
Repayment 92, 000
835, 072
Class Work:
A woman burrowed N 450, 000 to buy a house at 4% p.a. compute the interest she
pays. She pays back N46, 000 at the end of each year. How much does she still owe at
the end of 2yrs?
Workings:
1st year
N
Principal
450, 000
4% interest
18, 000
Amount 468, 000
Repayment 46, 000
422, 000
2nd year interest16,880
438, 880
46, 000
Payment
392, 880
ASSIGNMENT: Solve problems on Depreciation and inflation.
REVISION
18