Whole Numbers: Counting and Writing in Millions, Billions, and Trillions Mathematics JSS 1 First Term Lesson Notes Week 1

Mathematics JSS 1 First Term Lesson Notes Week 1

Subject: Mathematics
Class: JSS 1
Term: First Term
Week: 1
Age: 11-12 years
Topic: Whole Numbers: Counting and Writing in Millions, Billions, and Trillions
Sub-topic: i. Millions ii. Billions iii. Trillions
Duration: 40 minutes

Behavioural Objectives:

By the end of the lesson, students should be able to:

1. Understand the concept of whole numbers.
2. Count and write whole numbers in millions, billions, and trillions.
3. Differentiate between millions, billions, and trillions in terms of place values.

Keywords:

• Whole numbers
• Millions
• Billions
• Trillions
• Place value

Set Induction (5 minutes):

The teacher shows a chart of large numbers starting from thousands to trillions and asks students what they think comes after millions.

Entry Behaviour:

Students are familiar with counting and writing numbers up to thousands.

Learning Resources and Materials:

1. Place value chart
2. Flashcards showing numbers in millions, billions, and trillions
3. Number line

Building Background/Connection to Prior Knowledge:

Students have been taught how to count and write numbers up to thousands. This lesson will extend their knowledge to larger numbers.

Embedded Core Skills:

• Numeracy
• Problem-solving
• Analytical thinking

Instructional Materials:

1. Chalkboard or whiteboard
2. Markers or chalk
3. Printed number charts
4. Place value tables

Content:

Counting and Writing Numbers in Millions, Billions, and Trillions

1. Millions:
   • The place value of a million is after the hundred thousand place.
   • Example: 1,000,000 (One million)
   • Numbers like 2,345,000 (Two million, three hundred forty-five thousand).
2. Billions:
   • The place value of a billion is after the hundred million place.
   • Example: 1,000,000,000 (One billion)
   • Numbers like 3,456,000,000 (Three billion, four hundred fifty-six million).
3. Trillions:
   • The place value of a trillion is after the hundred billion place.
   • Example: 1,000,000,000,000 (One trillion)
   • Numbers like 5,678,000,000,000 (Five trillion, six hundred seventy-eight billion).

Place Value Table:

WEEK ONE

TOPIC: WHOLE NUMBERS

CONTENT

• Introduction

• System of Counting

• Counting in Millions

• Counting inBillions 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:

1. 34     (b) 15

Solution

1. 34 = 
2. 15 = 

EVALUATION

1. During a dry season, it did not rain for 128 days. How many weeks and days is this?
2. What is the number represented by
3. 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.

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

i.e 3282 = MMMCCLXXXII

EVALUATION

1. Write the following Roman figures in natural ( or counting) numbers:

1. MMMCLIV     (b) MMCDLXXI   (c) MCMIX     (d) DCCCIV

1. Write the following natural numbers in Roman figures:

1. 2659     (b) 1009     (c) 3498     (d) 1584

Questions:

1. 1,000,000 is called ______.
   a) Million
   b) Billion
   c) Trillion
   d) Thousand
2. The place value after a billion is ______.
   a) Million
   b) Trillion
   c) Quadrillion
   d) None of the above
3. A trillion has how many zeros?
   a) 6
   b) 9
   c) 12
   d) 15
4. 2,000,000 is written as two ______.
   a) Billion
   b) Million
   c) Trillion
   d) Thousand
5. 1,000,000,000 is known as ______.
   a) One billion
   b) One trillion
   c) One million
   d) One thousand
6. Which of these is larger? ______
   a) Million
   b) Billion
   c) Thousand
   d) Hundred
7. The place value after million is ______.
   a) Billion
   b) Hundred thousand
   c) Trillion
   d) Hundred million
8. How many millions make one billion?
   a) 1,000
   b) 10
   c) 1
   d) 100
9. The number 4,500,000 is four million, five hundred ______.
   a) Billion
   b) Thousand
   c) Million
   d) Trillion
10. The number 1,000,000,000,000 is called ______.
    a) One million
    b) One billion
    c) One trillion
    d) One thousand
11. 3,000,000,000 is three ______.
    a) Million
    b) Trillion
    c) Billion
    d) Thousand
12. 1,234,000 is written as one million, two hundred thirty-four ______.
    a) Billion
    b) Trillion
    c) Million
    d) Thousand
13. A trillion is how many millions?
    a) 100
    b) 1,000
    c) 10,000
    d) 1,000,000
14. Which of these numbers has nine zeros?
    a) Trillion
    b) Billion
    c) Million
    d) Thousand
15. The number 12,345,000 is written as ______.
    a) Twelve billion, three hundred forty-five million
    b) Twelve million, three hundred forty-five thousand
    c) Twelve million, three hundred forty-five
    d) Twelve billion, three hundred forty-five thousand

15 FAQs with Answers:

1. What is a million?
   A million is equal to 1,000,000.
2. How many zeros are in a billion?
   There are 9 zeros in a billion.
3. What comes after a million?
   After a million comes a billion.
4. How many millions make up a billion?
   One thousand million equals one billion.
5. What is the value of 1 trillion?
   One trillion is equal to 1,000,000,000,000.
6. How many zeros are in a trillion?
   There are 12 zeros in a trillion.
7. How do you write three million in numerals?
   Three million is written as 3,000,000.
8. What is the difference between a billion and a trillion?
   A trillion is 1,000 times larger than a billion.
9. What comes after a trillion?
   After a trillion comes a quadrillion.
10. How do you write one billion in numerals?
    One billion is written as 1,000,000,000.
11. What is the place value of the number 1 in 1,234,000,000?
    The place value of 1 is one billion.
12. How many zeros are in a million?
    There are 6 zeros in a million.
13. How do you write twelve billion, five hundred thousand in numerals?
    It is written as 12,000,500,000.
14. What is the place value of the number 5 in 5,678,000,000?
    The place value of 5 is five billion.
15. What comes after one billion in place value?
    After one billion comes ten billion.

• 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.

                    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

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?

1. the 9 in 10269
2. the 2 in 2984

Solution:

1. the 9 in 10269 is = 9 units or nine units
2. the 2 in 2984  is = 2 thousands or two thousands

Example 2

What is the value of each of the following?

1. the 8 in  1.85
2. the 0 in 16.08

Solution:

1. the 8 in 1.85 is = 8 tenths or eight tenths
2. 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 

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

1. Essential Mathematics for JSS1 by AJS Oluwasanmi page 3-7
2. 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.

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:

1. twelve billion, three hundred and nine million, ninety five thousand, six hundred and sixty three
2. six trillion, four hundred and thirty billion, one hundred and five million, two hundred and one thousand and fifty four
3. nine hundred and four billion, five hundred and forty million, three hundred and seventy thousand, seven hundred and fifty

Solution

1. You can work it out as follows:

EVALUATION

1. Write the following in figures:

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

1. 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)

Presentation:

Step 1:
The teacher revises the previous knowledge of counting numbers in thousands.

Step 2:
The teacher introduces the concept of counting in millions, billions, and trillions, using charts and examples.

Step 3:
The teacher allows the students to give examples of large numbers and write them on the board, ensuring they understand the place value for millions, billions, and trillions.

Teacher’s Activities:

1. Present numbers in millions, billions, and trillions on the board.
2. Explain the place value system of large numbers.
3. Guide students to count and write large numbers correctly.

Learners’ Activities:

1. Count numbers in millions, billions, and trillions.
2. Write examples of large numbers in their place values.
3. Participate in class discussions by giving their examples.

Assessment:

• The students will write numbers in millions, billions, and trillions.
• They will be asked to count large numbers correctly using place value.

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   

1. 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.

10 Evaluation Questions:

1. What is the value of 1,000,000?
   Answer: One million
2. How many zeros are there in a billion?
   Answer: Nine zeros
3. Write the number for five million.
   Answer: 5,000,000
4. What is 1 trillion in numerals?
   Answer: 1,000,000,000,000
5. How many millions make up a billion?
   Answer: One thousand million
6. What comes after one trillion?
   Answer: Quadrillion
7. How do you write four billion in numerals?
   Answer: 4,000,000,000
8. What is the place value of the digit 2 in 2,456,000,000?
   Answer: Two billion
9. How many zeros are there in a trillion?
   Answer: Twelve zeros
10. Write the number for twelve million.
    Answer: 12,000,000

Conclusion:

The teacher goes around to mark students’ work and offers further explanations as needed.

Captivating Title:

Understanding Large Numbers: Millions, Billions, and Trillions

Focus Keyphrase:

Counting in Millions, Billions, and Trillions

SEO Title:

JSS 1 Mathematics: Counting and Writing in Millions, Billions, and Trillions

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counting-millions-billions-trillions-jss1

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Learn how to count and write large numbers in millions, billions, and trillions in this JSS 1 Mathematics lesson on whole numbers.