You will find below on this page JSS1 Mathematics e-note for 1st term. This will be very helpful for you in planning your lessons for your students. Do enjoy your Academic Session.
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WEEK ONE
TOPIC: WHOLE NUMBERS
CONTENT
- Introduction
- System of Counting
- Counting in Millions
- Counting in Billions and Trillions
INTRODUCTION
- Counting
It is likely that mathematics began when people started to count and measure. Counting and measuring are part of everyday life.
Ancient people used fingers and toes to help them count or group numbers in different number bases. This led them to collect numbers in groups: sometimes 5s (fingers of one hand), sometimes 10s (both hands) and even in 20s (hands and feet). When people group numbers in 5s, we say they use a base five method. The most common bases used were five, ten and twenty. For example, a person with thirty two cows would say ‘I have six fives and two cows’ when counting in base ten. The most widely used base is base ten also called the denary system.
Other bases of counting: seven and sixty
7 days = 1 week
60 seconds = 1 minute
60 minutes = 1 hour
In English, ‘dozen’ means 12, ‘score’ means 20 and ‘gross’ means 144
System of Counting
- Tally System
Tally marks were probably the first numerals.
The ancient people employed tally marks to count large numbers. The tally marks were scratched on stones or sometimes cut on sticks but today we use tally marks to count or record large data, especially in statistics.
A tally mark of 5 is written by putting a line across a tally count of 4.
i.e = 4 and = 5
Example 1
Draw the tally marks for each of the following numbers:
- 34 (b) 15
Solution
- 34 =
15 =
EVALUATION
During a dry season, it did not rain for 128 days. How many weeks and days is this?
- What is the number represented by
- Draw the tally marks for each of the following numbers: (a) 43 (b) 52
- Roman numerals
The Romans used capital letters of the alphabets to represent numbers. Many people believe that the Romans used the fingers to represent numbers as follows:
I for one finger, II for two fingers, III for three fingers, V for five fingers and X for the combination of two hands ( or two V’s) .
The Roman also used L for fifty, C for hundred, D for five hundred and M for one thousand as shown below.
| Hindu-Arabic | Roman Numeral | Hindu-Arabic | Roman Numeral |
| 1 | I | 20 | XX |
| 2 | II | 40 | XL |
| 3 | III | 50 | L |
| 4 | IV | 60 | LX |
| 5 | V | 90 | XC |
| 6 | VI | 100 | C |
| 7 | VII | 400 | CD |
| 8 | VIII | 500 | D |
| 9 | IX | 900 | CM |
| 10 | X | 1000 | M |
The Roman used the subtraction and addition method to obtain other numerals. For example
- IV means V- I i.e. 5- 4 = 4
- VI means V+ I, i.e. 5 + 1 = 6
- IX means X- I, i.e. 10 – 1 = 9
- XXIV means XX + IV = 20 + 4 = 24
- CD means D- C = 500 – 100 = 400
- MC means M + C = 1000 + 100 = 1100
Example 1
Change the following numbers to Roman numerals: (a) 2459 (b) 3282
Solution
- 2459— 2000 = MM
400 = CD
50 = L
9 = IX
2459 = MMCDLIX
- 3282 = 3000 + 200 + 80 + 2
= MMM CC LXXX II
i.e 3282 = MMMCCLXXXII
EVALUATION
- Write the following Roman figures in natural ( or counting) numbers:
- MMMCLIV (b) MMCDLXXI (c) MCMIX (d) DCCCIV
- Write the following natural numbers in Roman figures:
- 2659 (b) 1009 (c) 3498 (d) 1584
- The Counting board
A counting board is a block of stone or wood ruled in columns. Loose counters, pebbles, stones or seeds in the columns show the value of the numbers in the columns.
Counters in the right-hand column (U) represent units, counters in the next column (T) represent tens, and so on.
TH | H | T | U |
| ●●● | ● | ||
| ●● | ●●●● | ●●●● |
2 7 5
The diagram below is a counting board showing the number 275.
- The Abacus
An abacus is a frame consisting of beads or disks that can be moved up or down (i.e. slide) on a series of wires or strings. Each wire has its own value. Both abacus and counting board work in the same way when carrying out calculations.
Example 1
M HTH TH H T U
| 3 | |||
An Abacus showing 2703
- Place Value of Numbers
Numbers of units, tens, hundreds,…….., are each represented by a single numeral.
(a).For a whole number:
– the units place is at the right-hand end of the number.
– the tens place is next to the units place on the left, and so on
For example: 5834 means ↓
5 thousands, 8 hundreds, 3 tens, and 4 units.
See the illustration below:
5 8 3 4
(b) for decimal fraction, we count the places to the right from the decimal point as tenths, hundredths, thousandths, etc.
See the illustration below:
↓ ↓ ↓ ↓ ↓
6 . 7 9 8
6 → units
. → decimal
7 → tenths
9 → hundredths
8 → thousandths
Example 1:
What is the place value of each of the following?
- the 9 in 10269
- the 2 in 2984
Solution:
- the 9 in 10269 is = 9 units or nine units
- the 2 in 2984 is = 2 thousands or two thousands
Example 2
What is the value of each of the following?
- the 8 in 1.85
- the 0 in 16.08
Solution:
- the 8 in 1.85 is = 8 tenths or eight tenths
- the 0 in 16.08 is =0 in tenths or zero tenths
Example 3
What is the value of each digit in 3 865 742
Solution
| 3 | 8 | 6 | 5 | 7 | 4 | 2 | |||
M | H. Th | T.Th | Th | H | T | U | |||
| Digit | Value | Word Form | |||||||
| 3 | 3 000 000 | Three million | |||||||
| 8 | 800 000 | Eight hundred thousand | |||||||
| 6 | 60 000 | Sixty thousand | |||||||
| 5 | 5 000 | Five thousand | |||||||
| 7 | 700 | Seven hundred | |||||||
| 4 | 40 | Forty | |||||||
| 2 | 2 | Two | |||||||
EVALUATION
1 (a) The place value of 5 in 5763 is ……………
(b)What is the place value 1 in 5.691?
2. Give the value of each digit in 489 734
3. Write down the number shown in the following figures:
(a)
READING ASSIGNMENT
- Essential Mathematics for JSS1 by AJS Oluwasanmi page 3-7
- New General Mathematic for Jss1 by M. F. Macrae et al page 17-18.
Counting and Writing in millions, billions and trillions
The figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are called digits or units.
The table below gives the names and values of some large numbers.
| Name | Value |
| One thousand | 1 000 |
| Ten thousand | 10 000 |
| One hundred thousand | 100 000 |
| One million | 1 000 000 |
| Ten million | 10 000 000 |
| One hundred million | 100 000 000 |
| One billion | 1 000 000 000 |
| One trillion | 1 000 000 000 000 |
Large numbers can be read easily by grouping the digits in threes starting from the right hand side as shown below.
Billion Million TH H T U
25 800 074 4 3 0
The 1st gap separates hundreds from thousands and the second gap separates thousands from millions and the third gap separates million from billion.
Thus 25 800 074 430 reads twenty five billion, eight hundred million, seventy four thousand, eight hundred and ninety.
Example
Write the following in figures:
- twelve billion, three hundred and nine million, ninety five thousand, six hundred and sixty three
- six trillion, four hundred and thirty billion, one hundred and five million, two hundred and one thousand and fifty four
- nine hundred and four billion, five hundred and forty million, three hundred and seventy thousand, seven hundred and fifty
Solution
- You can work it out as follows:
| Twelve billion | = 12 000 000 000 |
| Three hundred and nine million | = 309 000 000 |
| Ninety five thousand | = 95 000 |
| Six hundred and sixty three | = 663 |
| Adding |
| Six Trillion | = 6 000 000 000 000 |
| Four hundred and thirty billion | = 430 000 000 000 |
| One hundred and five million | = 105 000 000 |
| Two hundred and one thousand | = 201 000 |
| Fifty four | = 54 |
| Adding |
| Nine hundred and four billion | = 904 000 000 000 |
| Five hundred and forty million | = 540 000 000 |
| Three hundred and seventy thousand | = 370 000 |
| Seven hundred and fifty | = 750 |
| Adding |
EVALUATION
- Write the following in figures:
- Ninety nine million, eighty thousand, nine hundred and forty one.
- Fifteen trillion, six hundred and seventy one billion, three hundred and ninety one million, eighty eight thousand, five hundred and fifty five.
- Write in figures, the number referred to in the statement: Last year a bank made a profit of ‘two hundred and twenty billion, five hundred and one thousand, four hundred and ninety three Naira (
N)
WEEKEND ASSIGNMENT
- The value of 8 in 18214 is (a) 8 units (b) 8 tens ( c) 8 hundreds ( d) 8 thousands (e) 8 ten thousands
- The Roman numerals CXCIV represents the number (a) 194 (b) 186 (c ) 214 (d) 215 (e) 216.
What is the number represented by ? (a) 32 (b) 40 (c) 28 (d) 39
- The value of 7 in 3.673 is (a) 7tenths (b) 7 hundredths ( c ) 7 units ( d) 7 hundredth.
- Three million and four in figures is (a) 300004 (b) 300040 (c) 30000004 (d) 3000004
THEORY
- Change this Roman figure to natural numbers
(i) MMCDLXXI (ii) MMMCLIV
- Write the following in figures:
(a) fifteen trillion, six hundred and seventy one billion, three hundred and ninety one million, eighty eight thousand, five hundred and fifty five.
(b) three hundred and twenty-nine billion, five hundred and sixty two million, eight hundred and one thousand, four hundred and thirty three.
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