Whole Numbers Continued: Problems solving in quantitative aptitude reasoning using large numbers

Subject :

Mathematics

Term :

First Term

Week:

Week Two

Class :

JSS 1

Previous lesson :

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

Instructional Materials :

• Wall charts
• Pictures
• Related Online Video
• Flash Cards
• Abacus
• Numeric Table Chart

Methods of Teaching :

• Class Discussion
• Group Discussion
• Explanation
• Role Modelling
• Role Delegation

Reference Materials :

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• 9 Year Basic Education Curriculum
• Workbooks

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 2-digit number is larger than every unit number, e.g 11 is larger than 9. Any 3-digit number is larger than every 2-digit 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

compare digits in this column

2 6 7 5 5 7 1

smaller number

2 6 7 0 7 8 1

smallest digit

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

1. Arrange the following numbers in ascending order: 89728567, 89704567, 89693670, 89776909, 89735890.
2. 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 £10 billion in the UK.

Example 1

Write these numbers as a mixture of digits and words:

1. £30 000 000 (b) N75 000 000 000 (c) \$460 000 000 (d) £3 400 000 000 000

Solution

1. £30 000 000 = £30 x 1 000 000

= £30 million

1. N 75 000 000 000 = N 75 x 1 000 000 000

= N 75 billion

1. \$460 000 000 = \$460 x 1 000 000

= \$460 million

1. £3 400 000 000 000 = £3.4 x 1 000 000 000 000

= £3.4 trillion

Example 2

Write the following numbers in digits

1. 3.6 million (b) 2 billion

Solution

1. 3.6 million = 3.6 x 1 000 000

= 3 600 000

1. 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

1. 173 cm to mm

Since 1cm = 10mm

Then, 173cm = 173 x 10

= 1 730mm

1. 5.9km to mm

1cm = 10mm, 100cm = 1m, 1000m = 1km. Therefore, 1 000 000mm = 1 km

1. km = 5.9 x 1 000 000mm

= 5 900 000 or 5.9 million(mm)

1. 200m to mm

1m = 1000mm

200m = 200 x 1 000mm

= 200 000mm or 200 thousand (mm)

EVALUATION

1. Write these numbers in digits only and group the digits of your answers in threes.
2. billion (b) £0.85 trillion (c) million litres
3. Write these numbers as a mixture of digits and words: (a) 780 000 barrels (b) 900 000 km (c) \$ 900 000 000
4. Change the following to the unit in brackets: (a) 5000kg (grams) (b) 1250 litres ( mL)

1. Essential Mathematics for JSS1 by AJS Oluwasanmi page23-35.
2. New General Mathematics for JSS 1 by M. F Macrae et al pg 15-20.

WEEKEND ASSIGNMENT

1. What is the value of 1.2 km in metres? (a) 120m (b) 1 200m (c ) 12 000m (d ) 120 000m
2. Which of the following numbers is the largest?(a) 727345565 (b) 727245565 (c)727445565 (d) 726778876.
3. million in digits only is (a) \$1 200 000 (b) \$1 140 000 (c) \$1 250 000 (d) \$125 000
4. 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
5. 13 500 000mm in km is (a) 13.5 km (b) 1.35 km (c) 1350 km (d) 13500 km

THEORY

1. Write these numbers in digits only: (a) Le 0.5 billion (b) \$ 9.1 million
2. Write down the missing number (QR):
3. 100 987 331, 101 987 331, 102 987 331, __________, __________, 105 987 331
4. 980 231 680, 980 231 682, ________, 980 231 686, ____________, 980 231 690.

Presentation

The topic is presented step by step

Step 1:

The class teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

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 where  the needs arise.

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