mathematics

PHIDEL GROUP OF SCHOOLS, LAGOS Subject: MATHEMATICS Term: FIRST TERM Session : 2022/2023 Class : GRADE SEVEN Educator: Mr. KAMAL

Whole numbers Whole numbers [Cont.] Time Fractions Fractions, Decimals Fractions [Cont.] and Percentages MID-TERM BREAK Sequences Algebraic Expressions Estimation and and Equations Approximation REVISION/EXAMINATION EXAMINATION

YR 7: WK 1 8/9/2023 10:23:41 AM LESSON OBJECTIVES: WEEK 1 TOPIC At the end of the WHOLE NUMBERS>> lesson, students should be able to: INTRODUCTION  Identify and write the HOME PAGE place values of KEY NOTES: numbers Place value , roman and Arabic numerals  Count and write large numbers in words and figures  Identify numbers in millions, billions and trillions  Write in Roman and Arabic numerals.

YR 7: WK 1 8/9/2023 10:23:41 AM PLACE VALUES 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, 5 8 3 4 means TH H T U 5 8 34 5 thousands, 8 hundreds, 3 tens, and 4 units

YR 7: WK 1 WHOLE NUMBERS 8/9/2023 10:23:41 AM (b) for decimal fraction, we count the places to the right from the decimal point as tenths, hundredths, thousandths etc. See the illustration below: For example, 1 5 6 . 7 9 8 means 1 → hundred 5 → tens 6 → units . → decimal 7 → tenths 9 → hundredths 8 → thousandths

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:42 AM EXAMPLE 1 What is the place value of each of the following? (a) the 9 in 10269 (b) the 2 in 2984 SOLUTION tTH TH H T U (a) the 9 in 1 0 2 6 9 is = 9 units TH H T U (b) the 2 in 2 9 8 4 is = 2 thousands

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:42 AM EXAMPLE 2 What is the place value of each of the following? (a) the 8 in 1.85 (b) the 0 in 16.08tenths SOLUTION hundredths (a) the 8 in tenths hundredths 1 . 8 5 is = 8 tenths (b) the 0 in 1 6. 0 8 is = 0 tenths

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:42 AM EXAMPLE 3 What is the value of each digit in 3 865 742 SOLUTION 38 6 5 742 Th HTU M H. T.Th Th Word Form Three million Digit Value Eight hundred thousand 3 3 000 000 8 800 000 6 60 000 Sixty thousand 5 5 000 Five thousand 7 700 Seven hundred 4 40 Forty 2 2 Two

YR 7: WK 1 TOPIC: WHOLE NUMBERS Evaluation 8/9/2023 10:23:42 AM Question 1 NEW GENERAL Question 5 MATHEMATICS Question 6 Pg. 8, Ex. 1g Question 2 Question 3 Question 7 Question 4

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:43 AM COUNTING AND WRITING IN MILLIONS, BILLIONS AND TRILLIONS The figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are called digits 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 million 100 000 000 One billion 1 000 000 000 One trillion 1 000 000 000 000

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:43 AM Large numbers can be read easily by grouping the digits in threes starting from the right hand side as shown below. T hB tB B hM tM M hTH tTH TH h tu 25 8 00 0 74 8 90 Thus 25 800 074 890 reads twenty five billion, eight hundred million, seventy four thousand, eight hundred and ninety.

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:43 AM EXAMPLE 1 Write the number 5 365 987 654 321 in words T hB tB B hM tM M hTH tTH TH h tu 5 3 65 98 7 6 54 321 Five trillion, three hundred and sixty five billion, nine hundred and eighty seven million, six hundred and fifty four thousand, three hundred and twenty one.

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:43 AM EXAMPLE 2 904 540 370 750 in words Write the number T hB tB B hM tM M hTH tTH TH h tu 9 04 54 0 3 70 7 50 Nine hundred and four billion, five hundred and forty million, three hundred and seventy thousand, seven hundred and fifty.

YR 7: WK 1 TOPIC: WHOLE NUMBERS Evaluation 8/9/2023 10:23:44 AM Write the following numbers in words Question 1 857568307 Question 2 258142 Question 3 8512230 Question 4 67651853

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:45 AM EXAMPLE 1 Write in figures twelve billion, three hundred and nine million, ninety five thousand, six hundred and sixty three Twelve billion = = 12 000 000 000 three hundred and nine million 309 000 000 ninety five thousand = 95 000 six hundred and sixty three = 663 12 309 095 663

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:45 AM EXAMPLE 2 Write in figures six trillion, four hundred and thirty billion, one hundred and five million, two hundred and one thousand and fifty four Six trillion = 6 000 000 000 000 four hundred and thirty billion = 430 000 000 000 one hundred and five million = 105 000 000 201 000 two hundred and one thousand = 54 fifty four = 6 430 105 201 054

YR 7: WK 1 TOPIC: WHOLE NUMBERS Evaluation 8/9/2023 10:23:45 AM Write the following words in figures Question 1 Eight million, nine hundred and forty five thousand, and twenty. QTuwesotiobni2llion, seven hundred and eighty million, four hundred and fifty nine thousand, eight hundred and twenty five. Question 3 Fifteen billion, three hundred and nine million, ninety one thousand, seven hundred and sixty three. Question 4

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:45 AM ROMAN NUMERALS Roman numerals are series of letters that the romans use as their numerical system. It is one of the ancient ways of writing numbers. 1I 20 XX 2 II 40 XL 3 III 50 L 4 IV 60 LX 5V 90 XC 6 VI 100 C 7 VII 400 CD 8 VIII 500 D 9 IX 900 CM 10 X 1000 M

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:45 AM Notice that in Roman system, when we have a smaller numeral before a larger one, we SUBTRACT (IV means V – I = 4) whereas when we have a smaller numeral after the larger one, we ADD (XI means X + I = 11) EXAMPLE 1 Change this roman numeral DCCCIX to ordinary number SOLUTION D= 500 CCC = + 300 IX = 9 DCCCIX = 809

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:46 AM EXAMPLE 2 Convert 1984 to Roman Numerals SOLUTION Break 1984 into 1000, 900, 80 and 4, then do each conversion 1000 = M 900 = + CM 80 = 4= LXXX IV 1984 = MCMLXXXIV

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:46 AM EXAMPLE 3 Change this roman numeral CMDXXIV to ordinary number SOLUTION CM = 900 D= 500 XX = IV = + 20 4 CMDXXIV = 1424

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:46 AM EXAMPLE 4 Convert 2782 to Roman Numerals SOLUTION 2000 = MM 700 = + DCC 80 = LXXX 2= II 2782 = MMDCCLXXXII

YR 7: WK 1 TOPIC: WHOLE NUMBERS Evaluation 8/9/2023 10:23:46 AM Question 1 Convert 9759 to Roman Numerals Question 2 Change this roman numeral MMMCDLXXI to ordinary number Question 3 Convert 2989 to Roman Numerals Question 4 Change this roman numeral MMMCCCLIV to ordinary number

PHIDEL GROUP OF SCHOOLS, LAGOS Any Questions?

YR 7: WK 2 8/9/2023 10:23:47 AM LESSON OBJECTIVES: WEEK 2 TOPIC At the end of the lesson, students WHOLE NUMBERS>> CONTD should be able to: HOME PAGE  Arrange numbers in KEY NOTES: order of magnitude lowest common multiple, highest common factor  Find the factors and multiples of a number  Find the LCM and HCF of two or more numbers  Apply numbers to real life activities.

YR 7: WK 2 TOPIC: WHOLE NUMBERS>> INTRODUCTION 8/9/2023 10:23:48 AM ORDERING OF 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

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:48 AM SOLUTION 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 smallest number is 2 670 781 and the largest number is 3 498 567. EXAMPLE 2 Arrange these numbers in order of size magnitude starting with the smallest: 13456786, 24567432, 38479871, 24558011, 13498069, 38478817.

YR 7: WK 1 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:48 AM 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, 38 478 817, 38 479 871

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:48 AM TRY THIS 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.

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:48 AM FACTORS AND MULTIPLES OF NUMBERS FACTORS Factors are whole numbers that divide exactly into another whole number WITHOUT a remainder. Factors of numbers can be determined by their FACTOR PAIRS. EXAMPLES Find the factors of these numbers: 1) 32 2) 48 3) 120

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:48 AM 1) The factor pairs of 32 are: ������������ = ������ × ������������ ������������ = ������ × ������������ ������������ = ������ × ������ The factors of 32 are 1, 2, 4, 8, 16 and 32(see the arrows)

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:49 AM 2) The factor pairs of 48 are: ������������ = ������ × ������������ ������������ = ������ × ������������ ������������ = ������ × ������������ ������������ = ������ × ������������ ������������ = ������ × ������ The factors of 48 are :1, 2, 3, 4, 6, 8, 12, 16 , 24 and 48(see the arrows)

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:49 AM 3) The factor pairs of 120 are: 120 = 1 x 120 120 = 2 x 60 120 = 3 x 40 120 = 4x 30 120 = 5x 24 120 = 6x 20 120 = 8x 15 120 = 10 x 12 The factors of 120 are: 1, 2, 3, 4, 5,6, 8,10, 12, 15 , 20,24 ,30, 40, 60 and 120 (see the arrows)

YR 7: WK 2 TOPIC: WHOLE NUMBERS Evaluation 8/9/2023 10:23:49 AM Question 1 NEW Question 2 GENERAL MATHS Pg. 15, Ex. 3a Question 3 Question 4

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:50 AM MULTIPLES Multiples mean finding the product of a positive integer with another positive integer. Simply put, when a whole number multiples another whole number, the result obtained is called the multiple of either of those numbers. EXAMPLE 1 Find the next five multiples of 4. SOLUTION 4x2=8 4 x 4 = 16 4 x 6 = 24 4 x 3 = 12 4 x 5 = 20 :. The next five multiples of 4 are 8, 12, 16, 20 and 24.

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:50 AM EXAMPLE 2 Find the next five multiples of 6. SOLUTION 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36 :. The next five multiples of 6 are 12, 18, 24 , 30 and 36.

YR 7: WK 2 TOPIC: WHOLE NUMBERS Evaluation 8/9/2023 10:23:50 AM Question 1 NEW GENERAL Question 2 MATHS Pg. 19, Ex. 3g Nos 3, 4, 5 and 6. Question 3 Question 4

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:50 AM LOWEST COMMON MULTIPLES(LCM) The lowest common multiple of two or more numbers is the lowest multiple they have in common. For example, the common multiples of 3 and 4 are 12, 24, 36 etc. The smallest of these multiples is 12.This means that the LCM is 12

YR 7: WK 2 TOPIC: WHOLE NUMBERS LOWEST COMMON MULTIPLES (LCM) The lowest common multiple of two or more numbers is the lowest multiple they have in common. For example, the common multiples of 3 and 4 are 12, 24, 36 etc. The smallest of these multiples is 12.This means that the LCM is 12

EXAMPLE 1 TOPIC: WHOLE NUMBERS SOLUTION ������������������������ ������ℎ������ ������������������ ������������ 24 ������������������ 36 2 24 36 2 12 18 26 33 9 31 9 3 1 1 ∴ LCM of 24 and 36 = ������ × ������ × ������ × ������ × ������ = ������������

EXAMPLE 2 TOPIC: WHOLE NUMBERS SOLUTION ������������������������ ������ℎ������ ������������������ ������������ 8, 9 ������������������ 12 2 8 9 12 24 9 6 22 9 3 31 9 3 31 3 1 11 1 ∴ LCM of 8, 9 and 12 = ������ × ������ × ������ × ������ × ������ = ������������

EXAMPLE 3 TOPIC: WHOLE NUMBERS ������������������������ ������ℎ������ ������������������ ������������ ������������ , 28 , 36 ������������������ 50 SOLUTION 2 24 28 36 50 2 12 14 18 25 26 7 9 25 3 3 7 9 25 3 1 7 3 25 5 1 7 1 25 51 7 1 5 71 7 1 1 111 ∴ LCM of 24, 28, 36 and 50 = 1������������ × ������������ × ������������ × ������ = ������������������������������

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:52 AM HIGHEST COMMON FACTORS (HCF) The highest common factor of two or more numbers is the highest factor common to them. EXAMPLE 1 Find the HCF of 24 and 30. Use numbers that is a factor of the given numbers by dividing until there is no common factor again. SOLUTION 2 24 30 3 12 15 45 ∴HCF of 30 and 24 = ������ × ������ = ������

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:52 AM EXAMPLE 2 Find the HCF of 48 and 60. SOLUTION 2 48 60 2 24 30 3 12 15 45 ∴HCF of 48 and 60 = ������ × ������ × ������ = ������������

YR 7: WK 2 TOPIC: WHOLE NUMBERS 8/9/2023 10:23:52 AM EXAMPLE 3 Find the HCF of 340, 360 and 140. SOLUTION 2 340 360 140 2 170 180 70 5 85 90 35 18 17 7 ∴ HCF of 340, 360 & 140 = ������ × ������ × ������ = ������������

YR 7: WK 2 TOPIC: WHOLE NUMBERS Evaluation 8/9/2023 10:23:53 AM Question 1 New General Question 2 maths Bk 1, Pg 18, Ex 3f Question 3 Nos 2d, 2e , 2f , 2g and 2h. Question 4

PHIDEL GROUP OF SCHOOLS, LAGOS Any Questions?

YR 7: WK 3 8/9/2023 10:23:53 AM LESSON OBJECTIVES: WEEK 3 TOPIC At the end of the TIME lesson, students should be able to: HOME PAGE  Know the KEY NOTES: relationships time, clock ,year, months, weeks, hour, minutes , between units of seconds time  Understand the 12- hour and 24-hour clock systems  Interpret timetables  Calculate time intervals.

YR 7: WK 3 TOPIC: TIME 8/9/2023 10:23:53 AM MEASURING TIME The earth is spinning on an imaginary line known as its axis. It takes the earth 24 hours to spin once on its own axis,thus 1day= 24hours. For the earth to go round the sun, it takes approximately 36541 days. This means, 1 year is approximately 36514 days. Furthermore, the moon travels around the earth once every ≈ 29 days, hence 1 lunar month ≈ 29 days. The standard unit of time is the second (s). 60 seconds (s) = 1 minute (min) 1hr = 3600secs. 60 minutes = 1 hour (hr) 24hrs = 1 day.

YR 7: WK 3 TOPIC: TIME 8/9/2023 10:23:53 AM It is also useful to know the following: 52 weeks = 1 year (yr) 12 months = 1 year 365 days = 1 year. 366days = 1 leap year (Note: Leap year occurs every 4 years) 1 decade = 10years. 1 century = 100years. 1 millennium = 1000years.