JSS 3 Third Term Mathematics Scheme of Work with Lesson Notes
THIRD TERM: E – LEARNING NOTES
J S 3 (BASIC 9)
SUBJECT: MATHEMATICS
SCHEME OF WORK
WEEK TOPIC
- Measures of Central Tendency: Revision of previous work on mean, median and mode. Calculating the Median of a given data. Finding the Mode of given data. Calculate the Mean of any given data.
- Data Presentation: Pie chart, Bar chart, Histogram – Representation of information on pie charts, Bar chart, etc.
- Use of measures of Central Tendency to analyze information on drug abuse. Meaning and importance of voting. Counting of votes. Analysis of voting using measures of central tendency.
4-6. General Revision of Basic 7 – 9 works.
- Mock BECE/JSCE.
8-12. Basic Education Certificate Examination (JSCE).
BASIC TEXT BOOKS:
- New General Mathematics for Junior Secondary Schools Book 3. By M.F. Macrae et al.
- Exam Focus: Mathematics for JSCE – By DonatusIgbokwe et al
- Funtional Mathematics for JSS Book 3. By T.M Asiru et al
WEEK 1:
TOPIC: MEASURES OF CENTRAL TENDENCY (REVISION)
CONTENT:
- Mean: The average score of a given data.
- Median: The score at the middle after rearranging either ascending or
descending order.
- Mode: The score with the highest frequency.
Examples:
- Find the measures of central tendency of the data below.
8, 10, 13, 11, 7, 8, 2, 8, 6
Solution:
Mean:
To find the mean of the data above, you may not need to rearranged. Just add up the data and divide by the total number they are.
Mean
Median:
First rearrange the data either in ascending or descending order.
Ascending order: 2, 6, 7, 8, 8, 8, 10, 11, 13
Descending order: 13, 11, 10, 8, 8, 8, 7, 6, 2
Using median position:()th
Where is the number of data.
Median position th5th (Meaning that, the median is at the 5th position). Count 5 from any of the ends.
Hence, the median = 8
MODE:
Mode is the number or score that appears most, i.e, number or score with the highest frequency.
Since ‘8’ appears most, hence, the mode is 8.
FURTHER EXAMPLES
Example 2:
The below table shows the age of under 18 youths caught taking Indian hemp by the police at a T-junction near Olobeja with the following frequency of wrapped Indian hemp found in their possession.
| Age(yrs) | 13 | 14 | 15 | 16 | 17 |
| Frequency of wrapped Indian hemp | 1 | 2 | 5 | 7 | 15 |
Find the: (i). mean (ii). median (iii). mode of the frequency of the wrapped Indian hemp.
Solution:
Since the data are many, adding up the numbers and then divide by the total number would take a lot of time. So, we need a frequency table.
| Age | Frequency | Cum.freq | |
| 13 | 1 | 1 | 13 |
| 14 | 2 | 3 | 28 |
| 15 | 5 | 8 | 75 |
| 16 | 7 | 15 | 112 |
| 17 | 15 | 30 | 255 |
| Ʃ | Ʃ483 |
The total sum of frequency must be the same with the last number in the cumulative frequency column; i.e, 30.
MEAN
Mean
MEDIAN
First and foremost, let’s find the position of the median.
Position)thth
We count ‘15.5th’ along the frequency column from any of the ends.
It lies in the age ‘16’. Hence, the median is 16yrs.
MODE
Check for the highest frequency along the frequency column.
It is ‘15’. Right?
What age has 15?
Hence, the mode is 17yrs
Example 3:
The marks of 20 students in a mathematics test score out of 10 are as follows:
5, 8, 6, 7, 4, 9, 5, 7, 7, 0, 2, 1, 3, 9, 8, 4, 6, 7, 8, 1
Prepare a frequency table for the distribution and find the measure of central tendency.
Solution:
| Score | Tally | |||
| 0 | 1 | / | 1 | 0 |
| 1 | 2 | // | 3 | 2 |
| 2 | 1 | / | 4 | 2 |
| 3 | 1 | / | 5 | 3 |
| 4 | 2 | // | 7 | 8 |
| 5 | 2 | // | 9 | 10 |
| 6 | 2 | // | 11 | 12 |
| 7 | 4 | //// | 15 | 28 |
| 8 | 3 | /// | 18 | 24 |
| 9 | 2 | // | 20 | 18 |
| Ʃ20 | Ʃ107 |
Mean
MEDIAN
position)th 10.5th position.
By counting 10.5th from any of the ends,
The median = 6.
MODE
The mode = 7.
WEEKEND ASSIGNMENT:
Functional Mathematics for JSS.Book3. Ex.12.1,pg 188 No. 3,6-10; Ex.12.3,pg 192 No.5&6.
New General Mathematics for JSS Book3. Ex. 16b pg 156 No. 4-6
WEEK 2:
TOPIC: DATA PRESENTATION
CONTENT:
- Pie chart
- Bar chart
- Histogram
- Pictogram
- Bar line, etc
SUB TOPIC: REPRESENTATION OF INFORMATION ON PIE CHARTS.
A pie chart is a tool for data representation usually in the form of a circle and divided into sectors such that the angle at the centre is proportional to the frequency representing the item.
Example:
- The table below shows the number of fruits sold in a day by a fruit seller.
| Types of fruits | Number |
| Apples | 120 |
| Bananas | 150 |
| Mangoes | 120 |
| Oranges | 150 |
| Pawpaws | 50 |
| Pineapples | 130 |
Illustrate the information on a pie chart.
Solution:
Total number of fruits
We need to convert the fruits’ numbers to degrees ie the sectorial angles
For Apples: 0
For Bananas: 0
For Mangoes: 0
For Oranges: 0
For Pawpaws: 0
For Pineapples: 0
A pie chart showing the distribution of fruits
SUB TOPIC: REPRESENTATION OF INFORMATION ON BAR CHARTS.
A bar chart is a tool for data representation usually made up of rectangular bars of different height conveying the proportion of the frequencies of items being represented. They are simply blocks with equal spaces in between bars used to represent data.
Example:
- The following records represent the number of different motor cycles (Okada) purchased in a year from one dealer:
| Motor cycle | No. of Purchases |
| Suzuki | 50,000 |
| Honda | 80,000 |
| Simba | 30,000 |
| Jincheng | 35,000 |
| Cargo | 17,000 |
Prepare a bar chart to illustrate the information. How many motor cycles were purchased?
×1000
90
80
70
60
50
40
30
20
10
0
Suzuki Honda SimbaJinchengCargo Motor cycle
SUB TOPIC: REPRESENTATION OF INFORMATION ON HISTOGRAM.
A histogram is a tool for data representation usually made up of rectangular bars of different height conveying the proportion of the frequencies of items being represented without spaces in between bars.
Example:
The below table shows the number of students admitted in a University according to departments.
| Departments | No. of Students |
| Microbiology | 85 |
| Physics | 25 |
| Mathematics | 40 |
| Chemistry | 15 |
| Biochemistry | 20 |
| Biology | 105 |
Illustrate the information on a histogram.
Solution:
No. of Std
110
100
90
80
70
60
50
40
30
20
10
0
MicrobioPhyMath Chem Bio chem Bio Departments
WEEKEND ASSIGNMENT:
Functional Mathematics for JSS Book3. Ex.13.2, pg 197 No. 3, 5,6,9,10
New General Mathematicss for JSS Book3 pg 153 No. 2-5
WEEK 3:
TOPIC: USE OF MEASURES OF CENTRAL TENDENCY
- TO ANALYZE INFORMATION ON DRUG ABUSE.
The knowledge of measure of central tendency could help in analyzing the abuse of drugs among students as well as the youth. Specifically, it will help in:
- finding out the most drug used;
- finding out the least drug used;
iii. finding out the rate of drug abuse among the youth
- finding out how drugs are used among the youth and in the society at large.
Examples:
- The following data represent the frequencies at which some senior secondary students abuse drugs.
a). 33, 5, 8, 8, 10, 10, 10, 13, 15.
b). 4, 8, 9, 10, 13, 13, 15, 16, 16.
Find the mode for the drug abuse. What is its significant?
Solution:
a). The highest occurring score is 10. So, the mode for the first set of data is 10.
b). The second set of data is bimodal; i.e, it has two modes for drug abuse, 13 and 16.
The
- The table below shows the rate at which some teenagers abuse drugs:
| Name | Ade | Uche | Adamu | Bako | Binta |
| Frequency | 12 | 13 | 15 | 13 | 12 |
Find the mode for the drug abuse.
Solution:
Adamu consumes 15 times which is more than the rest of the people. So, Adamu is the mode for this set of data.
- The following data shows the ages of some youths that take drugs:
23yrs, 19yrs, 18yrs, 30yrs
15yrs, 21yrs, 19yrs, 24yrs
25yrs, 31yrs, 17yrs, 20yrs
a). Find the median ages of the youths that take drugs.
b). Find the mean age of the youth.
Solution:
a). Rearrange in either ascending or descending order.
15yrs, 17yrs, 18yrs, 19yrs, 19yrs, 20yrs, 21yrs, 23yrs, 24yrs, 25yrs, 30yrs, 31yrs.
Counting from left or right, 20yrs and 21yrs are at the middle.
Thus, median age
Alternatively,
Using median position: thth position.
Now, count ‘6.5th‘ from any of the ends.
Median age 20.5yrs
b). The mean age is the addition of all the ages divided by the number they are.
i.e, (15+17+18+19+19+20+21+23+24+25+30+31)/12 = 262/12 = 21.8yrs.
MEANING AND IMPORTANCE OF VOTING.
VOTING is a usually formal expression of opinion or will in response to a proposed decision; especially one given as an indication of approval or disapproval of a proposal, motion, or candidate for office. It is a fundamental right for every citizen of a country in a civilized and democratic nation.
THE IMPORTANCE OF VOTING AND COUNTING OF VOTES include:
- It is a tool for selecting representatives in modern democracies.
- It teaches about one’s obligation as a citizen of a country to be voted for or to vote in order to elect a leader in a free and fair manner without fear or favour.
iii. It helps to detest favouritism, arrogance and tyrannism (act of using power over someone cruelly or unfairly).
- It helps to give room for true representation through the majority.
- ANALYSIS OF VOTING USING MEASURES OF CENTRAL TENDENCY
We can analyse voting using the measures of central tendency, which are:
- Mean
- Median and
Example:
The following figures represent the number of voters that voted from 2003 to 2008.
| YEAR | NO. OF VOTERS |
| 2003 | 89,000 |
| 2004 | 101,000 |
| 2005 | 115,000 |
| 2006 | 131,000 |
| 2007 | 151,000 |
| 2008 | 96,000 |
a). What is the total number of voters?
b). Find the mean of the voters.
c). In what year did the people vote most?
d). In what year did the people vote least?
e). How many people voted in years 2003 and 2004?
Solution:
a). Total number of voters
b). Mean .
c). Year 2007
d). Year 2003.
e). Number of voters in 2003 and 2004
EVALUTION:
The total votes cast at different centres are as follows:
5000, 7000, 9000, 10000, 12000, 17000, 18000, 15000, 9000, 18000.
Find a. the mean of the votes cast.
- the median of the votes cast.
- the mode of the votes cast.
WEEKEND ASSIGNMENT:
Functional Mathematics for JSS Book3: Ex.12.3, pg 192 No. 3-6.
WEEKEND READING:
Functional Mathematics for JSS Book3: pg 186 – 213.
NOTE: Teachers should use the Nelson Functional Mathematics for JSS WorkBook3 during the weekend study.
WEEK 4 -6
TOPIC: GENERAL REVISION OF BASIC 7 – 9 WORKS.
NOTE: Teachers should ensure comprhensive revision of Basic7 to 9 works is done with the students using past questions of Federal and State JSSCE.
WEEK 7: MOCK BECE/JSSCE
WEEK 8 -12: BASIC EDUCATION CERTIFICATE EXAMINATION (JSCE).
