Whole Numbers Continued: Problems solving in quantitative aptitude reasoning using large numbers
Subject :Â
Mathematics
Term :
First Term
Week:
Week Two
Class :
JSS 1
Previous lesson :Â
The pupils have previous knowledge of Whole Numbers Counting and Writing (i) Millions (ii) Billions (iii) Trillions
Topic :
Whole Numbers Continued: Problems solving in quantitative aptitude reasoning using large numbers
Behavioural objectives :
At the end of the lesson, the pupils should be able to
 Write figures in thousands , millions or billions
 expand any given numbers
 calculate the place values of any given number
 express Roman figures in Hindu Arabic numerals
 express figures in Roman figures
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Instructional Materials :
 Wall charts
 Pictures
 Related Online Video
 Flash Cards
 Abacus
 Numeric Table Chart
Methods of Teaching :
 ClassÂ Discussion
 Group Discussion
 Asking Questions
 Explanation
 Role Modelling
 Role Delegation
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Reference Materials :
 Scheme of Work
 Online Information
 Textbooks
 Workbooks
 9 Year Basic Education Curriculum
 Workbooks
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Content :
WEEK TWO
TOPIC: WHOLE NUMBERS
CONTENT
 Ordering Large Numbers
 Using Mixture of Digits and Words with Large Numbers
 Problems Solving in Quantitative Aptitude Reasoning (QR) using large numbers
Ordering Large Numbers
Any 2digit number is larger than every unit number, e.g 11 is larger than 9. Any 3digit number is larger than every 2digit number; e.g 132 is greater than 86, and so on.
When a set of numbers are given, it is useful to rearrange the numbers in such a way that those that start in such a way that those that start with the same digit can be compared.
Example 1
Find the smallest and the largest number from the following set of numbers:
2 675 571, 3 498 567, 2 670 781, 3 497 859
Solution
Comparing numbers that start with 2
compare digits in this column
2 6 7 5 5 7 1
smaller number
2 6 7 0 7 8 1
smallest digit
Comparing numbers that start with 3
largest digit
larger number
3 4 9 8 5 6 7
3 4 9 7 8 5 9
The smallest number is 2 670 781 and the largest number is 3 498 567.
The numbers in the example above can also be arranged in order of size starting with the smallest as follows:
2 670 781, 2 675 571, 3 497 859, 3 498 567
This arrangement is also called ascending order. The reverse is known as descending order.
Example 2
Arrange these numbers in order of size magnitude) starting with the smallest: 13456786, 24567432, 38479871, 24558011, 13498069, 38478817.
Solution
Always group large numbers in threes.
Arranging the numbers that start with 1 in order of size: 13 456 786, 13 498 069
Arranging the numbers that start with 2: 24 558 011, 24 567 432
Arranging the numbers that start with 3: 38 478 817, 38 479 871
Hence, arranging these numbers in order of magnitude gives: 13 456 786, 13 498 069, 24 558 011, 24 567 432, 24 558 011, 24 567 432
EVALUATION
 Arrange the following numbers in ascending order: 89728567, 89704567, 89693670, 89776909, 89735890.
 Arrange the following numbers in descending order: 217679057, 497378939, 234656452, 21023404895, 2100998969.
Using Mixture of Digits and Words with Large Numbers
People often get confused when reading and writing large numbers. To avoid the confusion, the editors of newspapers use a combination of digits and words to show large numbers. For example, 1 million people, $ 1.5 billion, N 3.6 trillion.
Some newspapers headlines are as follows:
 Unemployment soaring to 10.7 million
 HIV rose to an estimated 23 million in 2010
 Cost of ID rises to Â£10 billion in the UK.
Example 1
Write these numbers as a mixture of digits and words:
 Â£30 000 000 (b) N75 000 000 000 (c) $460 000 000 (d) Â£3 400 000 000 000
Solution
 Â£30 000 000 = Â£30 x 1 000 000
= Â£30 million
 N 75 000 000 000 = N 75 x 1 000 000 000
= N 75 billion
 $460 000 000 = $460 x 1 000 000
= $460 million
 Â£3 400 000 000 000 = Â£3.4 x 1 000 000 000 000
= Â£3.4 trillion
Example 2
Write the following numbers in digits
 3.6 million (b) 2 billion
Solution
 3.6 million = 3.6 x 1 000 000
= 3 600 000
 2 billion = 2.75 x 1 000 000 000
= 2 750 000 000
Large Numbers (QR)
The S. I system of units is an internationally agreed method of measuring quantities such as length, mass, capacity and time.
Example 1.
Express the following in millimeter.
(a) 173 cm (b) 5.9km (c ) 200m
Solution
 173 cm to mm
Since 1cm = 10mm
Then, 173cm = 173 x 10
= 1 730mm
 5.9km to mm
1cm = 10mm, 100cm = 1m, 1000m = 1km. Therefore, 1 000 000mm = 1 km

 km = 5.9 x 1 000 000mm
= 5 900 000 or 5.9 million(mm)
 200m to mm
1m = 1000mm
200m = 200 x 1 000mm
= 200 000mm or 200 thousand (mm)
EVALUATION
 Write these numbers in digits only and group the digits of your answers in threes.
 billion (b) Â£0.85 trillion (c) million litres
 Write these numbers as a mixture of digits and words: (a) 780 000 barrels (b) 900 000 km (c) $ 900 000 000
 Change the following to the unit in brackets: (a) 5000kg (grams) (b) 1250 litres ( mL)
READING ASSIGNMENT
 Essential Mathematics for JSS1 by AJS Oluwasanmi page2335.
 New General Mathematics for JSS 1 by M. F Macrae et al pg 1520.
WEEKEND ASSIGNMENT

 What is the value of 1.2 km in metres? (a) 120m (b) 1 200m (c ) 12 000m (d ) 120 000m
 Which of the following numbers is the largest?(a) 727345565 (b) 727245565 (c)727445565 (d) 726778876.
 million in digits only is (a) $1 200 000 (b) $1 140 000 (c) $1 250 000 (d) $125 000
 Le 5 600 000 in digits and words is (a) Le 56 million (b) Le 5.6 billion (c) Le 0.56 billion (d) Le 5.6 million
 13 500 000mm in km is (a) 13.5 km (b) 1.35 km (c) 1350 km (d) 13500 km
THEORY
 Write these numbers in digits only: (a) Le 0.5 billion (b) $ 9.1 million
 Write down the missing number (QR):
 100 987 331, 101 987 331, 102 987 331, __________, __________, 105 987 331
 980 231 680, 980 231 682, ________, 980 231 686, ____________, 980 231 690.
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Presentation
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The topic is presented step by step
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Step 1:
The class teacher revises the previous topics
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Step 2.
He introduces the new topic
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Step 3:
The class teacher allows the pupils to give their own examples and he corrects them when the needs arise
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Conclusion
The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.
The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.
He or she does the necessary corrections when and whereÂ the needs arise.
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