WHOLE NUMBERS NOTATION AND NUMERATION OF NUMBERS
FIRST TERMÂ
LEARNING NOTES
CLASS: JSS 2 (BASIC 8)
SCHEME OF WORK WITH LESSON NOTESÂ
Subject:Â
MATHEMATICS
Term:
FIRST TERMÂ
Week:
WEEK 1
Class:
JSS 2 (BASIC 8)
Previous lesson:Â
The pupils have previous knowledge of
that was taught as a topic during the last lesson.
Topic :
WHOLE NUMBERS NOTATION AND NUMERATION OF NUMBERS
Behavioural objectives:
At the end of the lesson, the pupils should be able to
 Explain use of whole numbers
 Express whole numbers in standard form
 Convert decimal numbers to standard form
 Changing from standard form to ordinary numbers
 Express numbers in Indices or in index form
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Instructional Materials:
 Wall charts
 Pictures
 Related Online Video
 Flash Cards
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
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WHOLE NUMBERS
TOPICS
 Whole numbers in standard form
 Decimal numbers in standard form
 Changing from standard form to ordinary numbers
 Indices
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WHOLE NUMBERS IN STANDARD FORM
A number is said to be in standard form if it is expressed in the form of AÂ Ã— 10^{n}. Where 1< A < 10 and n is an integer (positive or negative whole numbers). Standard form is very useful in the field of sciences and social sciences for easy presentations and analysis. Examples of numbers in standard form include: 4 Ã— 10^{9}, 5.8 Ã— 10^{2}, 5.62 Ã— 10^{4}, etc.
Examples:
 Write the following in standard form:
(a) 90 000 000
(b) 6 000 000 000 000 000 000
(c) 34256.189
(d) 879.45
Solutions:
(a) 90 000 000 = 9 Ã— 10 000 000 = 9 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 = 9 Ã— 10^{7}
(b) 6 Ã— 1000 000 000 000 000 000 = 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10Â = 6 Ã— 10^{18}
(c) 34256.189 = 3.4256189 Ã— 10 000 = 3.4256189 Ã— 10^{4}
(d) 879.45 = 8.7945 Ã— 100 =Â Â 8.7945 10 Ã— 10 = 8.7945 Ã— 10^{2}
 Express each of the following in ordinary forms or full figures:
(a) 7.879 Ã— 10^{5}
(b) 6.209 Ã— 10^{4}
(c) 4.231 Ã— 10^{6}
Solutions:
(a) 7.879 Ã— 10^{5 }= 7.879 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 = 7.879 Ã— 100 000 = 787900
(b) 6.209 Ã— 10^{4 }= 6.209 Ã— 10 Ã— 10 Ã— 10 Ã— 10 = 6.209 Ã— 10 000 = 62090
(c) 4.231 Ã— 10^{6 }= 4.231 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 = 4.231 Ã— 1 000 000 = 42310000
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CLASS ACTIVITY
 Express the following numbers in standard forms.
(a) 50130002
(b) 0.0000032901
(c) 3518 Ã— 1000000
(d) 0.000400254
(e) 0.000000000235
 Rewrite each of the following in ordinary forms.
(a) 00009 Ã— 10^{5}
(b) 8.543 Ã— 10^{4Â }
(c) 6.653 Ã— 10^{6}
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DECIMAL NUMBERS IN STANDARD FORM
Decimal numbers are always written with decimal points. The decimal point is represented with a point. The number of figures that are after the decimal point indicates the number of decimal places that we have in the figure.
SamplesÂ
 0.345 There is three decimal places in 0.345
 34.5 there is one decimal place in 34.5
 385.0934 there is four decimal places in 385.0934
Decimal fractions can be expressed in standard form using negative powers of ten (10). This means that the values of when a decimal number is expressed in standard forms are negative. To do this, we move the decimal point to Right Hand Side (RHS) in tenth.
Examples:
 Express each of these numbers in standard form.
(a) 0.0008
(b) 0.0000 000 7
(c) 0. 000 036
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 Write the following as decimal fractions and standard forms:
(a) 16 thousandths
(b) 60 millionths
Solutions:
(a) 16 thousandths = 1 thousandth Ã— 16 = 0.001 Ã— 16 = 0.0016
In standard form: 0.0016 = 1.6 Ã— 10^{3}
(b) 60 millionths = 1 millionth Ã— 60 = 0.000001 Ã— 60 = 6 Ã— 10^{5}
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Class activity
 Rewrite each of the following numbers in figures and put them in standard forms.
(a) 7 thousand
(b) two and one quarter billion
(c) 35 thousandths
(d) 783 millionths
 Express the following in standard form.
(a) 00000027
(b) 0.000765
(c) 0.0000000000000098
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CHANGING FROM STANDARD FORM TO ORDINARY NUMBERS
Examples:
Express each of the following in ordinary forms or full figures:
(a). 7.879 Ã— 10^{5}
(b). 6.209 Ã— 10^{4}
(c). 4.231 Ã— 10^{6}
Solutions:
(a). 7.879 Ã— 10^{5 }= 7.879 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 = 7.879 Ã— 100 000 = 787900
(b). 6.209 Ã— 10^{4 }= 6.209 Ã— 10 Ã— 10 Ã— 10 Ã— 10 = 6.209 Ã— 10 000 = 62090
(c). 4.231 Ã— 10^{6 }= 4.231 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 Ã— 10 = 4.231 Ã— 1 000 000 = 42310000
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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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EVALUATION:

 Express the following in standard form:
(a) 000 0004
(b) 720 000 000
(c) 0.000 000 052
(d) 85 000 000 000
 Express the following in ordinary form
(a) 3 Ã— 10^{8}
(b) 2.6 Ã— 10^{7}
(c) 4.4 Ã— 10^{9}
(d) 3.4 Ã— 10^{5}
 Express the following to decimal fractions
(a) 5 Ã— 10^{3}
(b) 2.4 Ã— 10^{4}
(c) 8.8 Ã— 10^{5}
 Express the following decimals in standard form
(a) 000 005
(b) 0.0008
(c) 0.000 000 005
 Simplify the following:
(a) a^{11} Ã· a^{9 }
(b) 3 x 10^{6} Ã— 5 Ã— 10^{3}
(c) 2a^{1Â }Ã— (3a)^{2}
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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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