51 y Activit Write the time with a.m. or p.m. Examples: Write a.m. or p.m. with given time: a. 9’O clock in the morning. 9:00 a.m. b. 9’O clock in the evening. 9:00 p.m. c. 10:30 in the morning. 10:30 a.m. d. 10:30 in the evening. 10:30 p.m. e. 1’O clock at noon. 1:00 p.m. f. 1’O clock after midnight. 1:00 a.m. a. 3:30 in the after noon. ___________________ b. 8: 00’O clock at night. ___________________ c. 5’O clock at Fajr prayer. ___________________ d. 11:59 before noon. ___________________ e. 12:01 after midnight. ___________________ f. 3’O clock at night. ___________________ 24-Hours Format There is another method for representing time. It is called 24 hoursformat. In this system, midnight (12:00 a.m.) is considered as 00:00 hrs. and one hour after it is represented by 01:00 hrs. 1:00 p.m. is represented as 13:00 hrs. 8:00 p.m. is represented as 20:00 hrs. and 12:00 midnight is represented as 24:00 hrs. a.m time is represented as it as. For our conveyance, we can think that 12 hours is added after a.m. It means 1:00 pm is equal to 1 + 12 = 13 hr, 2:00 p.m. is equal to 2 + 12 = 14 hrs, etc. I know the Answer! 3:30 p.m. 8:00 p.m. 5:00 a.m. 11:59 a.m. 12:01 a.m. 3:00 a.m.
52 Example 1: Write the given time in 24-hours format: a. 3 : 30 a.m. ___________________ b. 2 : 14 p.m . ___________________ c. 8 : 35 p.m. ___________________ d. 11 : 19 p.m. ___________________ e. 11 : 30 p.m. ___________________ Example 2: Write the given time in 12-hours format. a. 02 : 15 hrs ___________________ b. 06 : 30 hrs ___________________ c. 13 : 30 hrs ___________________ d. 16 : 45 hrs ___________________ e. 21 : 15 hrs ___________________ y Activit 1 Write the given time in 12-hours format. y Activit 2 Write the given time in 24-hours format. a. 13 : 45 hrs ___________________ b. 14 : 50 hrs ___________________ c. 16 : 10 hrs ___________________ d. 17 : 00 hrs ___________________ e. 19 : 05 hrs ___________________ a. 3 : 13 a.m. ___________________ b. 11 : 45 a.m. ___________________ c. 1 : 45 p.m. ___________________ d. 2 : 00 p.m . ___________________ e. 10 : 00 p.m. ___________________ 3:30 hours 14:14 hours 20:30 hours 23:19 hours 23:30 hours 2:15 a.m 6:30 a.m 1:30 p.m 4:45 p.m 9:15 p.m 1:45 p.m. 2:50 p.m. 4:10 p.m. 5:00 p.m. 7:05 p.m. 3:13 hours 11:45 hours 13:45 hours 14:00 hours 22:00 hours
53 Addition and Subtraction of Time Addition Example 2: Solution: Solution: An hour has 60 minutes and one minute has 60 seconds. We can add or subtract time as shown in examples. Example 1: Add 3 hr and 45 min to 4 hr and 10 min. So, answer is 7 hr and 55 minutes Add 3 hr 35 min and 4 hr 45 min. We know that 60 min = 1 hr But in this example these are 80 minutes. i.e. It is more than one hour. Now divide it in hour and minutes. So minutes can be written as: 80 min = 60 min + 20 min. or 80 min = 1 hr + 20 min Now take 1 hr to the column of hr as a carry. i.e hr min 3 35 + 4 45 7 80 80 min = 1 hr 20 min hr min 7 80 + 20 8 20 1 Hence, the answer to 8 hrs 20 min. Example 3: Solution: hr min 3 45 + 4 10 7 55 hr min 2 35 + 6 55 8 90 hr min 8 60 + 30 9 30 1 Add the given times. 2 hrs 35 min and 6 hrs 55 min.
54 Hence, answer is 9 hrs 30 min 90 min = =60 min + 30 min = 1 hr + 30 min Subtraction We can also subtract time. In normal subtraction we borrow 10 but in case of time we always borrow 60. Look at these examples. Example 1: Subtract 3 hrs 40 min from 5 hr 45 min. Solution: Example 2: Subtract 2 hr 35 min from 4 hr 20 min. Solution: 35 minutes cannot be subtracted from 20 minutes, so we borrow 1 hour from 4 hrs when it reaches at min column it will become 60 min because 1 hr = 60 min hr min 4 60 1 hr = 60 min 20 Now add 60 and 20 min. We get 80 min. Now subtract 35 min from 80 min and 2 hrs from 3 hrs. 3 hr min 5 45 – 3 40 2 05 hr min 4 20 – 2 35 hr min 3 80 – 2 35 So, the answer is 1 hr 45 min. 1 45 So the answer is 2 hours 05 minutes.
55 y Activit 2 Subtract these. y Activit 1 Add these. hr min 6 25 + 3 25 9 50 a. hr min 4 35 + 2 50 7 25 b. hr min 6 30 + 2 40 9 10 c. hr min 4 25 + 3 35 8 00 d. hr min 2 50 + 2 45 5 35 e. hr min 3 20 + 2 25 5 45 f. hr min 7 77 + 4 23 12 40 g. hr min 8 70 + 1 30 10 40 h. hr min 9 40 + 2 40 12 20 i. hr min 8 45 – 2 35 6 10 a. hr min 6 15 – 2 25 3 50 b. hr min 4 20 – 1 30 2 50 c. hr min 6 40 – 4 25 2 15 d. hr min 9 45 – 5 35 4 10 e. hr min 5 30 – 2 40 2 50 f. hr min 7 35 – 1 25 6 10 g. hr min 8 25 – 4 15 4 10 h.
56 1. Put a.m. or p.m. with the time in the given statements. a. I wake up at 7:00 __________ of the morning. b. The Sun rises at 5:45 __________. c. The Sun sets at 7:10__________. d. I slept at 10:30 __________ last night. e. After 11:59 at night, it is one minute to 12 _________ . f. My father returns from his job at 6:30__________ in the evening. g. The recess time in our school is 10:30 __________. h. On Friday, I reached home at 12:15 __________ from school. i. I listened news last night at 9:00 __________. 2. Convert 12-hours time format into 24-hours time format. 3. Convert 24-hours time format into 12-hours time format. Exercise a. 6 : 15 a.m ____________ b. 6 : 15 p.m __________ c. 12 : 00 noon ____________ d. 1 : 15 a.m __________ e. 3 : 45 a.m ____________ f. 8 : 20 p.m __________ g. 8 : 20 a.m ____________ h. 8 : 45 a.m __________ i. 10 : 00 p.m ____________ j. 12 : 15 p.m __________ a. 13 : 15 ____________ b. 23 : 05 __________ c. 18 : 45 ____________ d. 13 : 13 __________ e. 20 : 00 ____________ f. 24 : 00 __________ g. 23 : 59 ____________ h. 18 : 18 __________ i. 21 : 12 ____________ j. 22 : 30 __________ am am pm pm am pm pm am pm 6:15 hours 12:00 hours 3:45 hours 8:20 hours 22:00 hours 18:15 hours 1:15 hours 20:20 hours 8:45 hours 12:15 hours 11:05 pm 1:13 pm 12:00 am 6:18 pm 10:30 pm 1:15 pm 6:45 pm 8:00 pm 11:59 pm 9:12 pm
57 4. Add the following. 5. Subtract the following. hr min 4 35 + 2 20 6 55 a. hr min 4 20 + 6 28 10 48 b. hr min 3 20 + 2 25 5 45 c. hr min 6 25 + 2 25 8 50 d. hr min 4 25 + 3 45 8 10 e. hr min 6 35 + 7 35 14 10 f. hr min 5 45 + 2 35 8 20 g. hr min 3 55 + 2 45 6 40 h. hr min 4 88 + 3 22 8 50 i. hr min 8 45 – 2 22 6 23 a. hr min 9 57 – 3 28 6 29 b. hr min 6 49 – 2 42 4 07 c. hr min 8 42 – 3 36 5 06 d. hr min 6 35 – 4 45 1 50 e. hr min 5 25 – 3 40 1 45 f. hr min 8 20 – 5 35 2 45 g. hr min 10 35 – 9 55 0 40 h. hr min 8 00 – 2 55 5 05 i.
58 Geometry Point: Line: Ray: Take a pencil and a notebook. Draw a dot on the page. Wow! you have drawn a geometrical figure called point. Point: A point is a small dot which has no length or width. It is just a sign. Usually a point is represented by a capital English letter. Line: A line is a set of pints joined together with no end point. A line has no fixed length. Actually a line has infinite length. A line is represented by two arrow heads at its corners. These arrow heads show that line is increasing in this direction. It is represented by two ways. Ray: If we cut a line at any point it is divided into two rays. A ray has one end point and the other side has an other arrow head. This arrow head shows that the ray is increasing in this direction. Student’s Learning Outcomes: After studying this unit, students will be able to: describe basic concepts of geometry. draw basic shapes of geometry, compare different geometrical objects. differentiate between different type os angles. Unit 8 . A . C . X A B X Y
59 A B O X Line Segments: A line segment is a piece of line with fixed length. A line segment has two end points and each end point has a fixed name. For example: You have a scale (ruler) in your geometry box. We use this instrument to draw straight lines with the help of pencil. Draw a dot ‘.’ on the page. (fig i) Now place O of scale at this dot (remember we are using only cm side of our scale). (fig ii) Now we have to draw a line of 6 cm, place your pencil at 0 of scale (which ......... with dot. ), and drag the pencil to 6 cm sign. Now remove the scale. Name the points of this line segment and write its length. (fig iii) A 4 cm B X 6 cm Y . . . . Dot How to Draw a Line Segment fig i fig ii fig iii
60 Examples: Draw a line segment to join these points together. Measure the line segment with your ruler and write its length. A 3 cm B P 6 cm Q y Activit 1 Join points to draw a line segment with your ruler and write its length. (a) A B (b) E F (c) P Q y Activit 2 Draw a line segment of given lengths. (a) CD = 10 cm (b) CD = 8 cm (c) CD = 6 cm (d) CD = 4 cm (e) CD = 3 cm 5 cm 7 cm 10 cm C D 10 cm C D 8 cm C D 6 cm C D 4 cm C D 3 cm
61 Angle Types of Angles Angle When two rays meet at an initial point, they form an angle. In other words, union of two rays is called angle. An angle has two arms. One arm is called initial arm or initial ray and other arm is called terminal arm or terminal ray. The point at which they meet is called vertex. An angle is denoted by sign. In fig (i) it is AOB (or BOA) and in fig (ii) it is PQR (or RQP). Types of Angles There are many types of angles according to movement of their arms, such as: O A B Q P R fig (i) fig (ii) Right Angle Obtuse Angle Straight Angle Reflex Angle Terminal arm Initial arm Acute Angle
62 Step 1: Step 2: Angles are measured with the help of a geometrical instrument called protractor. It is a ‘D’ shaped instrument. It has small scales from 0 to O 180 . Every angle is measured in O degrees. The sign of a degree is ‘ ‘. Let there is an angle we have to measure it. Here are the steps to measure the angle: Step 1: Place the protractor on the given angle such that its centre is at vertex O and zero of protractor exactly on ray OA. Step 2: Now read from O (from ray OA) and reach to the ray OB. Read the degree on the protractor. It is O 45 . Remove the protractor and write the angle. O It is written as AOB = 45 How to Measure an Angle y Activit 1 Measure the given angles and write them. Q P R PQR = __________ a. B A C ABC = __________ b. O A B 45 A B
63 How to Draw an Angle Step1: Step2: Now count from Step 3: Now remove the Step 4: Name this point B. O Example 1: Draw an angle of 30 . Step1: Draw a line segment of suitable length. Place your protractor centre point at O. Step2: Now count from point A (on the protractor) and reach at 30 degree. Put a dot at 30. Step 3: Now remove the protractor and join the dot to point O with the help of a ruler. Step 4: Name this point B. Draw arrow heads at point A and point B. O AOB = 30 is required angle. O A O A B O 30 O A O A O A
64 Step1: Step2: Now count from Step 3: Now remove the Step 4: Name this point Z. O Example 2: Draw an angle of 120 . Step1: Draw a line segment of suitable length. Place your protractor centre point at O. Step2: Now count from point Y (on the protractor) and reach at 120 degree. Put a dot at 120. Step 3: Now remove the protractor and join the dot to point O with the help of a ruler. Step 4: Name this point Z. Draw arrow heads at point Y and point Z. O YOZ = 120 is required angle. O Y O Y O Y O Y O Y Z O 120
65 1. Measure the distance between given points and write the length below them. Exercise a. A B C D AB = 4 cm CD = 6 cm b. c. E F EF = 7 cm O P OP = 10 cm d. e. J K JK = 12 cm 2. Join the dots to draw a straight line and write the length. OP = 5 cm a. UV = 6 cm b. LM = 7 cm c. XY = 4 cm d. ST = 10 cm e. O P U V L M S T X Y
66 3. Measure the given angles. O A B O E F O G H O L M O Q P O Q R O X Y O U V a. b. c. d. e. f. g. h. O UOV = 120 O XOY = 140 O QOR = 100 O QOP = 90 O LOM = 75 O EOF = 45 O GOH = 60 O AOB = 30
67 4. Draw the given angles with the help of ruler and protractor. a. b. c. d. e. f. g. h. O ABC = 20 O DEF = 30 O PQR = 45 O LMN = 60 O UVW = 70 O ABC = 110 O XYZ = 90 O DEF = 120 B A C E D F Q P R M L N V U W Y X Z B A C E D F
68 Unit 1 Graph Student’s Learning Outcomes: After studying this unit, students will be able to: understand the purpose of graph. read the given graphs. describe the different types of graph. compare the different types of graph. Unit 9 Ali is very fond of animals. He has following animals at home. 3 cats 2 dogs 5 parrots 4 sparrows 6 chickens This diagram is called pictograph. A graph helps us to see the differences quickly and easily. In a pictograph, pictures are used to represent information. Example: Draw a pictograph with given information. Here are the number of students who fail in different subjects. Math 5, Urdu 1, English 4, Islamiat 0, Science 2. Solution: Chickens Sparrows Parrots Dogs Cats Math Urdu English Islamiyat Science
69 This example can also be represented by another way. This way of representing information is called column graph or block graph. Now look at this graph and answer the following questions: 1. How many more students are fail in English than science? ______ 2. In which subject least students are fail? _________ 3. In which subject only one student is fail? _________ 4. Is there any two subjects in which equal numbers of students are fail? _________ 5. In which subject maximum number of students are fail? _________ 6. How many students are fail in all subjects? _________ Subjects: Math Urdu English Islamiat Science y Activit Now look at this graph. It shows birth days of children of a class. Answer the questions. Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 9 8 7 6 5 4 3 2 1 Number of Children Months: 5 4 3 2 1 Number of fail students 2 Urdu Urdu No Math 12
70 This way of representing information is called block graph. Now look at this graph and answer the following questions: 1. In which month, maximum students have their birthday? ________ 2. How many children have their birthday in Jan? _________ 3. Which month has least birthdays? _________ 4. In which months 7 children were born? _________ 5. What are the total birthdays in last 3 months of year? _________ 6. How many total students are there in the class? _________ Bar Graph It is very similar to column graph. The basic difference is that, all bars have same distance between them. Look at this graph, read it carefully and give the answers. It is a bar graph of favourite colours in the classroom. Questions: 1. Which is the most favourite colour of the students? ____ 2. Which is the most 2nd favourite colour of the students? ________________ 3. How many students do like white colour? _________ 4. Which colour is least favourite? _________ 5. How many students have given their colour opinion? _________ 0 1 2 3 4 5 White Red Blue Green Pink Number of Students Favourite colours 5 3 pink red and green blue 9 15 Sept Apr/June 5 Sept
71 Look at the given pictograph and answer the following questions. (Ali has stamps of different countries) y Activit There are many players of different games in a school. Answer the questions from the given bar graph. Questions: 1. How many students like hockey? _____________ 2. Which is the favourite game of the students? _____________ 3. Which games are equally liked? _____________ 4. How many students like hockey and tennis? _____________ 5. Which game is least popular? _____________ 0 10 20 30 40 50 Table Tennis Hockey Tennis Cricket Football Number of Students Games Swimming 60 70 80 Exercise 1. Turkey Nepal UAE UK USA Iran 50 Cricket Hockey/Football 50 + 40 = 90 swimming
72 Read the pictograph and answer the following questions. (Six friends have many toy cars.) 2. Questions: 1. How many tickets of Nepal does Ali have? ___________ 2. Of which country does Ali have the most tickets? ___________ 3. Of which country does Ali have the least tickets? ___________ 4. What are total number of tickets of UK and USA? ___________ 5. How many total tickets does he have? ___________ Questions: 1. What is the total of Fazal and Anas cars? ___________ 2. How many cars do Zaib and Akbar have? ___________ 3. Who has the most cars? ___________ 4. Who is 2nd in having the most cars? ___________ 5. How many cars do all friends have? ___________ 3. Look at the given column graph which shows rainfall in different months and answer the following questions. Fazal Zahid Anas Zaib Akbar Usman March April May June July August 50 mm 40 mm 30 mm 20 mm 10 mm Months: Rainfall 3 UK Iran 12 23 11 8 Zahid Fazal 29
73 Questions: 1. Which month has the least rainfall? _______________ 2. Which month has no rainfall? _______________ 3. Which months have the most rainfall? _______________ 4. What is the maximum rainfall in which month? _______________ 5. In which month, there is 20 mm of rainfall? _______________ 6. In first 3 months, what is the total rainfall? _______________ Maximum temperature of different months are given in bar graph. Read and answer the questions. 4. 0 O 10 c O 20 c O 30 c O 40 c O 50 c January February March April May Temperatur e Favourite colours June Questions: 1. Which is the hottest month? _______________ 2. What is the maximum temperature of the hottest month? _______ 3. Which month is the coldest? _______________ 4. Which months have the same temperature? _______________ 5. O Which month has 20C temperature? _______________ May o 50 c January February and March February and March March May July and August July and August April 30 mm
74 Make a bar graph of number of copies of your five friends on a particular day and then answer the given questions. 0 9 8 7 6 5 4 3 2 1 Number of copies Friends Names Questions: 1. Who has the maximum copies? _______________ 2. Who has the minimum copies? _______________ 3. Who have equal number of copies? _______________ 4. What is the number of you and your best friend copies? _______________ 5. What is the total number of copies? ________ Fun Time ? Hassan Ahmad No one 5 , 7 45 Ali Ahmad Naveed Hassan Yasir