Week Note for the Week Ending

Class: Year 7(seven)

Subject: Mathematics

Topic: whole number

Age: 11+

Sex: Mixed

Duration: 40 Minutes

Period: one (1)

Instructional Materials: Marker, Marker’s board, lesson note, and a chart illustrating the different number system

Instructional Objectives: At the end of the lesson, the students should be able to:

i. discuss the history of counting

ii. discuss the history of counting in Egypt
iii. relate the Egyptian numeral with the modern system of counting
iv. apply the roman system of counting to standard numerals
v. define and apply place value in arranging numbers
vi. Count in million, billion, and trillion.

Entry Behaviour: The teacher enters the class, exchanges greetings with the students before arousing their interest in the
days lesson

Presentation of lesson

Step One:(Revision)

The teacher revises some of previous lessons the students took in year 5 that are related to the topic. such as roman
numerals, place values etc, with the students, there after he arouses the students interest in the day’s lesson

Step Two:(Introduction)

The teacher introduces the new lesson “whole numbers” to the students, by discussing briefly the history of 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
Tally System of Counting
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:
(a) 34 =
(b) 15 =
Solution
a. 34 =|||| |||| |||| |||| |||| |||| ||||
b. 15 = |||| ||||
||||

Step Three :( Explanation an solving)

The teacher guides the students as he apply the roman system of counting to standard numerals.

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

1. IV means V- I i.e. 5- 4 = 4
2. VI means V+ I, i.e. 5 + 1 = 6
3. IX means X- I, i.e. 10 – 1 = 9
4. XXIV means XX + IV = 20 + 4 = 24 5.
CD means D- C = 500 – 100 = 400
6. MC means M + C = 1000 + 100 = 1100
 Example 1

Change the following numbers to Roman numerals: (a) 2459 (b)

3282

Solution
1. 2459--- 2000 = MM

400 = CD

50 = L

9 = IX

2459 = MMCDLIX

1. 3282 = 3000 + 200 + 80 +2

= MMM CC LXXX II

Therefore 3282 = MMMCCLXXXII

Step four :( Evaluation)

The teacher evaluate the lesson y asking questions that are relevant to lesson, such as:

1. During a dry season, it did not rain for 128 days. How many weeks and days is this?
2. Draw the tally marks for each of the following numbers: (a) 43 (b) 52
3. Write the following Roman figures in natural ( or counting) numbers:
(a) MMMCLIV (b) MMCDLXXI (c)MCMIX (d)DCCCIV
4. Write the following natural numbers in Roman figures:
(a)2659(b) 1009(c) 3498(d) 1584

Period Two (2)

Sub-topic:

Presentation of lesson:

Step One: (Revision): the teacher revises the previous lesson “the counting system” with the student before arousing
their interest in the day’s lesson

Step Two: (Introdution): the teacher introduces the new lesson “place value” by defining it and explains

place value

Place value is the basis of the entire number system. It is the system in which the position of a digit in a number,
determines its value. The order of place value from right to left is units, tens, hundreds, thousands, ten thousand, a
hundred thousand, million. Ten million, a hundred million, one billion and so on.

Step Three :( solving):

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?

(i) the 9 in 1026 (ii) the 2 in 2984

Solution
(i) the 9 in 10269 is = 9 units or nine units
(ii) the 2 in 2984 is = 2 thousands or two thousands
Example 2:
What is the value of each of the following?
(i) the 8 in 1.852 (ii). the 0 in 16.08
Solution

(i) The 8 in 1.85 is = 8 tenths or eight tenths

(ii) 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
 38 6 5 7 4 2
M H. T.T Th H T U
Th h
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
Step four :( Evaluation):

The teacher evaluate the lesson by asking questions that are relevant to lesson, such as:

i. The place value of 5 in 5763 is ……………

ii. What is the place value 1 in 5.691?

iii. Give the value of each digit in 489 734

Period Three (3)

Sub-topic: counting in millions, billions, and trillions

Presentation of lesson:

Step One: (Revision): the teacher revises the previous lesson “the counting system” with the student before arousing
their interest in the day’s lesson.

Step Two: (Introdution): the teacher introduces the new lesson by telling the students the number of digits in
millions, billions, and trillions.

Step Three: (explaination): the teacher guides the students as e

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 100 000 000
million
 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 1
Write the following in figures:
i. twelve billion, three hundred and nine million, ninety five thousand, six hundred
and sixty three
ii. six trillion, four hundred and thirty billion, one hundred and five million, two hundred and one
thousand and fifty four
iii. nine hundred and four billion, five hundred and forty million, three hundred and seventy
thousand, seven hundred and fifty
iv.nine hundred and four billion, five hundred and forty million, three hundred and seventy
thousand, seven hundred and fifty

Solution

i. You can work it out as follows:

Twelve billion = 12 000 000 000

Three hundred and nine = 309 000 000
million
Ninety five thousand = 95 000
Six hundred and sixty three= 663
Adding = 12 309 095 663

ii. Six Trillion = 6 000 000 000 000

Four hundred and thirty = 430 000 000 000
billion
One hundred and five = 105 000 000
million
Two hundred and one = 201 000
thousand
Fifty four = 54
Adding = 6 430 105 201 054

iii.Nine hundred and four = 904 000 000 000

billion
Five hundred and forty = 540 000 000
million
Three hundred and seventy = 370 000
thousand
Seven hundred and fifty = 750
Adding = 904 540 370 750
 Step four :( Evaluation):

1. Write the following in figures:

i. Ninety nine million, eighty thousand, nine hundred and forty one.
ii. Fifteen trillion, six hundred and seventy one billion, three hundred and ninety one million,
eighty eight thousand, five hundred and fifty five.
2. 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

WEEKEND ASSIGNMENT

1. The value of 8 in 18214 is (a) 8 units (b) 8 tens ( c) 8 hundreds ( d) 8 thousands (e) 8 ten
thousands
2. The Roman numerals CXCIV represents the number (a) 194 (b) 186 (c ) 214 (d) 215 (e) 216.
3. What is the number represented by ? (a) 32 (b) 40 (c) 28 (d) 39
4. The value of 7 in 3.673 is (a) 7tenths (b) 7 hundredths ( c ) 7 units ( d) 7 hundredth. 5.
Three million and four in figures is (a) 300004 (b) 300040 (c) 30000004 (d) 3000004
THEORY

1. Change this Roman figure to natural numbers:

(i) MMCDLXXI (ii) MMMCLIV

2. Write the following in figures:

(i) fifteen trillion, six hundred and seventy one billion, three hundred and ninety one
million, eighty eight thousand, five hundred and fifty five.

(ii) three hundred and twenty-nine billion, five hundred and sixty two million, eight hundred
and one thousand, four hundred and thirty thr