Math-4

51 CSS Primary Standard “Mathematics” yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part I Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (3c) Q 1: Solve the following: i. 3 4 21 16 37 9 1 4 7 28 28 28 ii. 11 5 22 5 27 1 1 13 26 26 26 26 iii. 1 1 7 25 14 25 39 3 3 6 9 2 4 2 4 4 4 4 iv. 1 2 1 1 9 7 7 27 49 83 20 1 2 3 3 7 3 3 7 3 21 21 21 Q 2: Solve the following: i. 3 1 3– 2 1 – 8 4 8 8 ii. 1 2 17 2 17 – 4 13 5 2 – – 1 8 4 8 4 8 8 8 iii. 8 1 134 22 134 – 66 68 5 6 – 3 – 3 21 7 21 7 21 21 21 iv. 5 1 21 9 21– 9 12 1 2 –1 1 8 8 8 8 8 8 2 Q 3: Solve the following: i. 1 2 1 1 1 1 2 2 5 9 5 10 2 5 5 2 10 10 ii. 1 1 1 6 7 25 36 – 70 125 91 1 – 2 4 5 3 6 5 3 6 30 30 iii. 11 2 11 76 7 11 380 – 91 55 344 19 5 –1 5 13 5 13 13 5 13 65 65 65 Q 4: Verify the commutative property of addition: i. 1 3 3 1 2 5 5 2 Solution:

52 CSS Primary Standard “Mathematics” L.H.S. R.H.S. 1 3 5 6 11 2 5 10 10 ……. (A) 3 1 6 5 11 5 2 10 10 ……. (B) As, L.H.S. = R.H.S. So, commutative property of addition is satisfied. ii. 4 2 2 4 7 5 5 7 L.H.S. R.H.S. 4 2 20 14 34 7 5 35 35 ……. (A) 2 4 14 20 34 5 7 35 35 ……. (B) As, L.H.S. = R.H.S. So, commutative property of addition is satisfied. Q 5: Verify the Associative Property of Addition: i. 3 2 1 3 2 1 5 3 3 5 3 3 L.H.S. 3 2 1 9 10 1 19 1 19 5 24 8 5 3 3 15 3 15 3 15 15 5 ……. (A) R.H.S. 3 2 1 3 2 1 3 3 9 15 24 8 5 3 3 5 3 5 3 15 15 5 ……. (B) As, L.H.S. = R.H.S. So, associative property of addition is satisfied. ii. 1 3 5 1 3 5 11 22 11 11 22 11 L.H.S. 1 3 5 2 3 5 5 5 15 11 22 11 22 11 22 11 22 ……. (A) R.H.S. 1 3 5 1 3 10 1 13 2 13 15 11 22 11 11 22 11 22 22 22 ……. (B) As, L.H.S. = R.H.S. So, associative property of addition is satisfied. Q 6: Piece of wire 1 = 11 37 1 m = m 26 26 Piece of wire 2 = 17 m 26 Total Length of wire = 37 17 54 27 1 + 2 m 26 26 26 13 13

53 CSS Primary Standard “Mathematics” Q 7: Waqar ate water melon = 1 8 , Saif ate water melon = 3 8 Total melon they eat = ? = 1 3 1 3 4 1 + 8 8 8 8 2 So, they eat half water melon altogether. Q 8: Capacity of a bucket = 2 32 6 L = L 5 5 It contains water = 4 L How much more water can be filled = ? = 32 4 32 – 20 12 2 – 2 L 5 1 5 5 5 Q 9: Given time for Wahab = 5 33 4 hours hours 7 7 Time to complete mathematics test = 13 hours 10 Time to complete history test = 33 13 330 91 239 29 3 hours 7 10 70 70 70 Q 10: Time spend to watch TV = 5 hours 10 , Time to play game = 1 hours 5 Difference in time = ? Difference in time = 5 1 5 2 3 – hours 10 5 10 10 Lesson # 4 Procedure: Use the explanation as given on pages # 48, 49 and 50 to explain the concepts of Multiplication of fractions to the students. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v

54 CSS Primary Standard “Mathematics” Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (3d) Q 1: Solve the following: i. 3 3 5 15 7 5 1 8 8 8 8 ii. 5 1 5 7 2 14 iii. 6 18 7 3 1 11 11 11 iv. 1 3 41 3 123 18 8 3 5 7 5 7 35 35 v. 1 2 64 8 512 8 9 2 24 7 3 7 3 21 21 vi. 1 2 26 8 208 13 5 2 13 5 3 5 3 15 15 vii. 1 3 1 100 3 1 300 150 9 11 19 2 11 19 2 418 209 Q 2: Prove the following (commutative property) i. 3 2 2 3 5 7 7 5 Solution: L.H.S. R.H.S. 3 2 6 5 7 35 ……. (A) 2 3 6 7 5 35 ……. (B) As, L.H.S. = R.H.S. So, commutative property of multiplication is satisfied. ii. 1 1 1 1 9 3 3 9 2 7 7 2 Solution: L.H.S. 1 1 19 22 418 209 6 9 3 29 2 7 2 7 14 7 7 ……. (A) R.H.S. 1 1 22 19 418 209 6 3 9 29 7 2 7 2 14 7 7 ……. (B) As, L.H.S. = R.H.S. So, commutative property of multiplication is satisfied. iii. 1 9 9 1 2 2 3 7 7 3 Solution: L.H.S. 1 9 7 9 9 2 3 3 7 3 7 3 ……. (A) R.H.S. 9 1 9 7 9 2 3 7 3 7 3 3 ……. (B) As, L.H.S. = R.H.S. So, commutative property of multiplication is satisfied.

55 CSS Primary Standard “Mathematics” iv. 1 1 1 1 5 2 2 5 2 2 2 2 Solution: L.H.S. 1 1 11 5 55 3 5 2 13 2 2 2 2 4 4 ……. (A) R.H.S. 1 1 5 11 55 3 2 5 13 2 2 2 2 4 4 ……. (B) As, L.H.S. = R.H.S. So, commutative property of multiplication is satisfied. Q 3: Prove the following (Associative Property): i. 1 1 1 1 1 1 9 3 4 9 3 4 2 2 3 2 2 3 Solution: L.H.S. 1 1 1 19 7 13 19 91 1729 1 9 3 4 144 2 2 3 2 2 3 2 6 12 12 ……. (A) R.H.S. 1 1 1 19 7 13 133 13 1729 1 9 3 4 144 2 2 3 2 2 3 4 3 12 12 ……. (B) As, L.H.S. = R.H.S. So, associative property of multiplication is satisfied. ii. 1 1 1 1 1 1 2 3 4 2 3 4 2 7 5 2 7 5 Solution: L.H.S. 1 1 1 5 22 21 5 66 2 3 4 33 2 7 5 2 7 5 2 5 ……. (A) R.H.S. 1 1 1 5 22 21 55 21 2 3 4 33 2 7 5 2 7 5 7 5 ……. (B) As, L.H.S. = R.H.S. So, associative property of multiplication is satisfied. iii. 22 5 8 22 5 8 23 6 9 23 6 9 Solution: L.H.S. 22 5 8 22 40 22 20 440 23 6 9 23 54 23 27 621 ……. (A)

56 CSS Primary Standard “Mathematics” R.H.S. 22 5 8 55 8 440 23 6 9 69 9 621 ……. (B) As, L.H.S. = R.H.S. So, associative property of multiplication is satisfied. Q 4: Waqas drinks water daily = 1 2 5 liters = 11 5 liters Water drinks in 8 days = ? = 11 88 3 8 17 liters 5 5 5 Q 5: Length of the side = 1 3 cm 5 = 16 5 cm Width of the side = 1 2 5 cm = 11 5 cm Area = ? Area = Length of the side × Width of the side = 16 11 176 1 2 7 cm 5 5 25 25 Q 6: Rainfalls = 3 5 of days Total days = 365 days Number of rainy days = 3 5 × 365 = 219 days Lesson # 5 Procedure: Use the explanation as given on pages # 51, 52 and 53 to explain the concepts of Division of fractions to the students. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom.

57 CSS Primary Standard “Mathematics” Exercise (3e) Q 1: Solve the following: i. 1 1 1 3 1 6 3 6 1 2 ii. 5 2 4 2 2 2 5 5 iii. 11 2 11 17 189 5 7 13 17 13 2 26 26 iv. 14 2 14 17 7 17 17 17 2 v. 9 9 1 9 16 11 11 16 176 vi. 3 8 1 1 1 8 5 5 8 5 vii. 1 2 28 3 28 13 3 1 1 9 3 9 5 15 15 viii. 1 1 13 2 13 1 2 4 6 2 6 1 3 3 ix. 5 3 5 11 5 4 20 2 9 4 9 4 9 11 99 x. 1 2 1 5 5 3 5 3 2 6 xi. 5 3 12 4 16 2 1 2 7 4 7 3 7 7 xii. 4 2 14 9 126 16 2 1 2 5 9 5 11 55 55 Q 2: Length of the book shelf = 1 5 3 feet 16 3 feet Size of book = 5 11 feet Number of books = ? Number of books = size of book shelf ÷ size of book = 16 5 16 11 176 11.73 3 11 3 5 15 (almost 11 books) Q 3: Size of pizza = 1 4 1 pizza pizza 3 3 Divide in = 2 people = 4 1 4 2 3 2 6 3 part of pizza for each Q 4: Fabrics need to make pillow = 1 4 of yards Fabric available = 12 yards Number of pillows = 1 12 12 4 48 pillows 4 Q 5: Length of string = 1 11 5 meters meters 2 2 Number of pieces to cut in = 4 Length of each string = 11 11 1 11 3 4 1 meters 2 2 4 8 8

58 CSS Primary Standard “Mathematics” Review Exercise Q 1: Write the following fractions and then write in increasing and decreasing order: i. 1 4 ii. 3 8 iii. 3 12 Increasing order: 1 4 , 3 12 , 3 8 Decreasing order: 3 8 , 3 12 1 4 , Q 2: Solve and write answer in the simplest form: i. 3 5 3 5 8 11 7 7 7 7 7 ii. 8 2 17 2 17 2 15 5 2 1 – – 1 9 9 9 9 9 9 3 3 iii. 1 2 9 17 45 68 113 13 2 3 5 4 5 4 5 20 20 20 iv. 1 1 19 10 19 10 9 2 –1 1 9 9 9 9 9 9 v. 8 2 16 9 3 27 vi. 1 1 3 1 3 1 2 8 2 8 16 vii. 1 7 1 7 1 2 6 6 2 12 viii. 5 3 4 53 13 4 265 78 24 319 19 8 2 – – 10 6 5 5 6 5 5 30 30 30 Q 3: Pocket money to buy books = 3 7 Pocket money to help the poors = 1 14 Money spend altogether = 3 1 6 1 7 1 7 14 14 14 2 of pocket money Q 4: Emaan used plain cloth = 3 15 3 m m 4 4 Emaan used printed cloth = 3 24 3 m m 7 7 Total cloth = 15 24 105 96 201 5 + 7 4 7 28 28 28 Q 5: Total pizza ate altogether = 13 16 of pizza Hamza ate pizza = 1 4 of pizza, Emaan ate pizza = 3 16 of pizza Anoral ate pizza = ? = 13 1 3 13 4 3 6 3 part of pizza 16 4 16 16 16 16 16 8 Q 6: Total cloth available = 1 41 20 m m 2 2 Cloth required per dress = 1 5 2 m m 2 2 = 41 2 41 × 8dresses 2 5 5

59 CSS Primary Standard “Mathematics” Unit No. 4 Decimals and Fractions Lesson # 1 Teaching Objectives: To introduce the concept of decimals: another way of writing fractions. To introduce addition and subtraction of decimals. To introduce multiplication of decimals. To introduce division of decimals. Learning Outcomes: The students will be able to: Explain clearly that decimals are a different form of fractions. Perform addition and subtraction of decimals with correct use of place value. Perform multiplication of decimal numbers. Perform division of decimal numbers. Teaching Materials: CSS Primary Standard Mathematics Book 4. Writing Board. Marker. Eraser. Background: Decimals are a very important concept which the students will have to use in every sphere throughout their lives. To use decimals confidently, the students have to be familiar with decimal notation, what each position signifies, its implications, vulgar equivalences and the place value of each number in decimal representation. Procedure: Start the lesson by talking about the significance of the fact that the decimal number system is based on 10. Also, expose them to the idea that this is not the only system used by man, there is the binary system (base of 2) used by computers, hexadecimal system (base of 6), octal system (base of 8), etc. The Mayans used the base of 20 as there are 20 toes and fingers. The Yuki language has an 8 base counting system as the speakers count by using the gaps between the fingers instead of the fingers themselves. Talk about the reason for using the base of 10. The most significant aspect of 10 is the 0. All other numbers were displayed in nature in some form or another. Man found a way to form a symbol for ‘nothing’ or ‘nil’. Then followed 10 and the place values of units, tens, hundreds and so on, before going into decimal fractions. Once the place value of 0 was established, the concept of 10 came very naturally to men, as they had 10 fingers to count on. Start the lesson about decimals, by dividing the students into groups of 3 or 4 each. Give

60 CSS Primary Standard “Mathematics” group an object (such as slabs of chocolate with 10 pieces in each, or bracelets with 10 beads each, or packets of biscuits with 10 biscuits in each, or strips of clips each with 10 clips on it) that can easily be divided into 10. Ask them to divide each item into 10 parts. Then ask each group to hold up different portions of the whole. For example, 3 tenths of a whole strip of clips written as 3/10. Students are familiar with the fact that each of the parts is 1/10 or one-tenth of the whole. Explain that another method of writing the same fraction 1/10 is known as the decimal numeral system (or base 10, or denary). 1/10 is written as 0.1. Tell them that a decimal fraction is a form of writing fractions where the denominator of the fraction is a multiple of 10, such as 100, 1000…i.e. the fraction is written in the form of 3/10 , 7/100 or 9/1000. Tell them that it is an extension of the number system (where we count in tens) to the right, getting 1/10, 1/100 , 1/1000 , of the number as you move to the right of the decimal point. Tell them that the number on the left of the decimal point shows whole numbers with which the students are familiar. The first number on the right side of the decimal points signifies tenths, the next digit is hundredths, and the next digit is thousandths and so on. As the students hold up different parts of the whole, such as 9/10 , write the decimal representation of the vulgar fraction on the board: 0.9. As you write the decimal fraction, explain the significance of the DOT. A dot is used to separate the decimal fractions from the whole numbers. Also, explain and practice the correct method of reading a decimal number. Tell them that one-tenth or 1/10 is written as 0.1 and read as ‘zero point one’. The place value of 1 as the 1stdigit to the right of the decimal point signifies ‘1 divided by 10’ or 1/10. Tell them that similarly, 2/10 signifies two-tenths, and can be written as 0.2 and said as ‘zero point two’. The place value of 2 is tenths, i.e. 2 parts of 10 parts of the whole. The prefix deci-stands for 10. Tell them that for example: 2.5 is read as two point five; 2 wholes and 5 tenths. It means 2 wholes and 5 parts out of 10. Similarly, 10/10 is one whole and the decimal representation would be 1.0. Tell them that once the value of each position is clearly understood, addition and subtraction should not be a problem. Ask them which number is bigger: 0.459 or 0.495? Can you subtract 0.395 from 0.359? Can you add the 2 numbers? Tel them that multiplication is a little more complex. If 4 children eat 1.5 bars of chocolates each, how many bars of chocolates were eaten? This means: 4 × 1.5 = 4 times 15 tenths = 60 tenths = 6 whole bars. 4 × 1.5 = 4 times 1 whole + 4 times 5 tenths = 4 wholes and 2 wholes = 6 whole bars. The decimal point in the multiplicand and the

61 CSS Primary Standard “Mathematics” product must be placed one below the other. This will be explained more clearly with more than 1 place of decimal later. Moreover use the explanation as given on pages # 55, 56, 57 and 58 to explain the concepts of decimals. Fun activities: Snag a Spoon! A Math Game What You Need: White paper Marker Spoons What You Do: 1. With your fifth grader, cut sheets of white paper into 52 playing cards. Divide the cards into 13 sets of 4. 2. For each of the 13 sets, choose a decimal, such as 0.25, and write it on one of the cards. On the rest of the cards in the set, write equivalent percents or fractions. For example, one set of cards would be: 0.25, 25%, 25/100, 25%. 3. As you are making the game, explain decimal and fraction equivalents by applying them to money and referring to place value, an important component in understanding decimals. For example, explain that $ 0.25 = 25 cents. 25 cents = 25 pennies. There are 100 pennies in a dollar. Therefore, $ 0.25 (25 cents) = 25/100. Next, explain decimal and percent equivalents. For example, remind your child that 0.25 = 25/100. 25/100 means “25 per 100”. “Cent” means 100 (in Latin) 25/100 = 25 percent or 25% 4. Once the playing cards are complete, shuffle and gather a few more players. In the middle of the table, place one less spoon than the number of players. For example, if there are 5 players, use 4 spoons. Deal 4 cards to each player and explain the rules. 5. The object is to get “4 equivalents of a kind”, for example .30, 30/100, 30%, .30. The dealer will begin by taking the top card from the deck. She will look at it and decide if she wants to keep it or pass it. If she keeps it, she must discard one of her cards and pass it face-down to the next player. If she doesn’t want it, she simply passes the card facedown to the next player. 6. Play continues in a circle until one player gets “4 equivalents of a kind”. That player grabs a spoon – trying to do so secretly. As soon as another player notices someone has grabbed a spoon, he should grab one, too! Suddenly, everyone will be grabbing for a spoon! The player who does not get a spoon is out. Remove one and continue playing until there are no spoons left – whoever gets the last one is the champion! Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v

62 CSS Primary Standard “Mathematics” Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (4a) Q 1: 53.549 Q 2: i. Tens Ones Tenth Hundredths Thousandths 0 . 5 8 6 ii. Tens Ones Tenth Hundredths Thousandths 3 . 4 1 iii. Tens Ones Tenth Hundredths Thousandths 9 1 . 8 4 6 iv. Tens Ones Tenth Hundredths Thousandths 3 . 0 0 6 v. Tens Ones Tenth Hundredths Thousandths 8 . 5 5 9 vi. Tens Ones Tenth Hundredths Thousandths 8 . 4 4 1 vii. Tens Ones Tenth Hundredths Thousandths 4 . 4 0 2 Q 3: Write the following numbers as decimal fraction: i. 241 2.41 100 ii. 321 0.321 1000 iii. 3 0.003 1000 iv. 24 0.024 1000 v. 94.1 0.941 100 Q 4: Write the following numbers as common fractions: i. 212 106 53 0.212 1000 500 250 ii. 341 0.341 1000 iii. 2560 256 128 64 2.560 1000 100 50 25 iv. 84650 8465 1693 84.650 1000 100 20 v. 95082 47541 95.082 1000 500 vi. 3221 3.221 1000 vii. 84319 84.319 1000 Q 5: What does each digit stands for in the decimal fractions given below? i. 0.001 ii. 0.001 iii. 0.08 iv. 0.002 v. 0.003 0.050 0.020 0.50 0.010 0.020 0.800 0.600 0.400 0.200 3.000 5.000 9.000 3.000

63 CSS Primary Standard “Mathematics” Lesson # 2 Use the explanation as given on pages # 59, 60 and 61 to explain the concepts of Conversion between fractions and decimals. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part Iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (4b) Q 1: Explain the following fractions into decimal fractions: i. 3 10 = 0.3 ii. 2 100 = 0.02 iii. 55 100 = 0.55 iv. 35 10 = 3.5 v. 2 5 = 0.4 vi. 1 19 9 2 2 9.5 vii. 1 25001 25 25.001 1000 1000 viii. 1 151 6 6.04 25 25 ix. 1 751 3 3.004 250 250 x. 1 501 1 1.002 500 500 Q 2: Convert the following decimals into a fraction: i. 5 1 0.5 10 2 ii. 240 2 2.40 2 100 5 iii. 1001 1 1.001 1 1000 1000 iv. 500 1 0.500 1000 2 v. 9500 95 1 9.500 9 1000 10 2 vi. 5513 513 5.513 5 1000 1000 vii. 8651 651 8.651 8 1000 1000 viii. 921 0.921 1000 ix. 231 31 2.31 2 100 100 x. 8451 51 84.51 84 100 100 xi. 921531 531 921.531 921 1000 1000

64 CSS Primary Standard “Mathematics” Lesson # 3 Use the explanation as given on pages # 62 and 63 to explain the concepts of Addition and Subtraction fractions and decimals. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (4c) Q 1: Add the following: i. Th H T O T H Th ii. Th H T O T H Th iii. Th H T O T H Th 5 2 . 6 0 9 2 . 5 0 4 . 6 0 + 3 1 . 0 1 + 3 . 2 0 + 8 . 4 0 8 3 . 6 1 9 5 . 7 0 1 3 . 0 0 iv. Th H T O T H Th v. Th H T O T H Th vi. Th H T O T H Th 9 . 6 1 6 . 5 8 3 3 . 0 1 + 7 . 2 5 + 9 . 4 1 + 4 5 . 8 6 1 6 . 8 6 1 5 . 9 9 7 8 . 8 7 vii. Th H T O T H Th viii. Th H T O T H Th 9 1 . 2 1 6 1 . 2 4 + 3 . 5 1 + 3 1 . 4 0 9 4 . 7 2 9 2 . 6 4 Q 2: Subtract the following: i. Th H T O T H Th ii. Th H T O T H Th iii. Th H T O T H Th 8 15 9 5 . 4 0 3 3 . 2 1 4 8 . 6 9 - 6 8 . 4 0 - 2 1 . 2 1 - 3 0 . 4 0 2 7 . 0 0 1 2 . 0 0 1 8 . 2 9

65 CSS Primary Standard “Mathematics” iv. Th H T O T H Th v. Th H T O T H Th vi. Th H T O T H Th 7 13 9 10 2 14 3 11 12 11 8 4 . 0 0 3 4 . 6 3 4 2 . 3 1 - 6 9 . 0 2 - 0 5 . 2 0 - 0 3 . 9 5 1 4 . 9 8 2 9 . 4 3 3 8 . 3 6 vii. Th H T O T H Th viii. Th H T O T H Th ix. Th H T O T H Th 5 14 13 18 17 10 6 4 . 8 4 5 4 . 8 4 5 6 . 8 0 - 0 9 . 5 3 - 1 5 . 9 3 - 1 5 . 9 3 5 5 . 3 1 4 8 . 9 1 4 0 . 8 7 Q 3: Height of Anees = 5.33 feet Height of Amina = 0.54 feet more than Anees Height of Amina = ? i. Th H T O T H Th 5 . 3 3 + 0 . 5 4 5 . 8 7 So, Height of Amina = 5.87 feet Q 4: Fatima bought for her own house = 54.60 m Fatima bought for her uncle’s house = 13.25 m Total wire altogether = ? i. Th H T O T H Th 5 4 . 6 0 + 1 3 . 2 5 6 7 . 8 5 Total wire altogether = 67.85 meters Q 5: Aleezay ran on Sunday = 130.60 m Aleezay ran on Monday = 229.50 m Aleezy ran on Tuesday = 133.94 m Total distance covered = ? i. Th H T O T H Th 1 3 0 . 6 0 2 2 9 . 5 0 + 1 3 3 . 9 4 4 9 4 . 0 4 Q 6: Kausar’s previous weight = 99.50 kg Kausar lost weight = 12.5 kg Kausar’s new weight = ?

66 CSS Primary Standard “Mathematics” i. Th H T O T H Th 9 9 . 5 0 - 1 2 . 5 0 8 7 . 0 0 Kausar’s new weight = 87.00 kg Q 7: Aleem’s Weight = 84.50 kg Rehan’s weight = 90.00 kg Difference in weight = ? i. Th H T O T H Th 8 9 10 9 0 . 0 0 - 8 4 . 5 0 5 . 5 0 Difference in weight = 5.5 kg Lesson # 4 Use the explanation as given on pages # 64, 65, 66 and 67 to explain the concepts of Multiplication and Division of fractions and decimals. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (4d) Q 1: Multiply the below decimals by 10, 100 and 1000. i. 3.50 × 10 = 35 ii. 12.62 × 10 = 126.2 3.50 × 100 = 350 12.62 × 100 = 1262 3.50 × 1000 = 3500 12.62 × 1000 = 12620 iii. 9.52 × 10 = 95.2 iv. 32.31 × 10 = 323.1 9.52 × 100 = 952 32.31 × 100 = 3231

67 CSS Primary Standard “Mathematics” 9.52 × 1000 = 9520 32.31 × 1000 = 32310 v. 92.62 × 10 = 926.2 vi. 84.60 × 10 = 846.0 92.62 × 100 = 9262 84.60 × 100 = 8460 92.62 × 1000 = 92620 84.60 × 1000 = 84600 vii. 54.62 × 10 = 546.2 viii. 17.81 × 10 = 178.1 54.62 × 100 = 5462 17.81 × 100 = 1781 54.62 × 1000 = 54620 17.81 × 1000 = 17810 ix. 3.5 × 10 = 35 x. 18.10 × 10 = 181.0 3.5 × 100 = 350 18.10 × 100 = 1810 3.5 × 1000 = 3500 18.10 × 1000 = 18100 Q 2: Solve the following: i. 13.13 × 5 1313 100 × 5 = 6565 100 = 65.65 ii. 24.16 × 52 2416 100 × 52 = 125632 100 = 1256.32 iii. 34.53 × 13 3453 100 × 13 = 44889 100 = 448.89 iv. 56.24 × 32 5624 100 × 32 = 179968 100 = 1799.68 v. 24.14 × 16 2414 100 × 16 = 38624 100 = 386.24 Q 3: Solve the following: i. 13.50 ÷ 2 13.50 × 1 2 = 1350 100 × 1 2 6.75 ii. 19.62 ÷ 3 1962 100 × 1 3 6.54 iii. 55.68 ÷ 8 5568 100 × 1 8 6.96 iv. 99.15 ÷ 3 9915 1 100 3 33.05 v. 100.62 ÷ 2 10062 1 100 2 50.31 vi. 143.622 ÷ 3 143622 1 1000 3 47.874 vii. 134.589 ÷ 3 134589 1 1000 3 44.863 viii. 16.12÷ 2 1612 1 100 2 8.06 ix. 49.49 ÷ 7 4949 1 100 7 7.07 x. 18.95 ÷ 5 1895 1 100 5 3.79 xi. 16.120 ÷ 8 16120 1 1000 8 2.015 Q 4: Mass of a book = 752.95 grams Mass of 25 such books = ? Mass of 25 such books = 752.95 × 25 75295 25 100 = Rs. 18823.75

68 CSS Primary Standard “Mathematics” Q 5: Distance covered by Anoral in 2 hours = 94.60 km Distance covered by Anoral in 1 hour = ? Distance covered by Anoral in 1 hour = 94.60 ÷ 2 94.60 × 1 2 47.30 kilometers Review Exercise 4 Q 1: Choose the correct answer and fill the circle: i. Which of the following is a decimal fraction? 5 8 18 5 3 1 5 2.18 ii. The figure shows: 1.9 0.09 10.009 0.9 iii. 2.31 + 1.05 = 4.36 4.35 3.34 3.36 iv. 8.64 – 7.12 = 2.56 3.52 2.52 1.52 v. 5.85 × 100 = 58.5 5850 15.850 585 vi. 19.82 ÷ 2 9.94 9.93 5850 9.91 Q 2: Identify the fraction and decimals in the following: i. 3 13 = Proper Fraction ii. 5.86 = Decimal Fraction iii. 1 1 13 = Mixed Fraction iv. 8.64 = Decimal Fraction Q 3: Solve the following: i. 3.84 + 1.60 + 2.03 = 7.47 ii. 35.84 – 12.68 = 23.16 iii. 38.9 × 1000 = 38900 iv. 8.60 × 31 = 860 100 × 31 266.6 v. 801.96 ÷6 = 80196 100 × 1 6 133.66 vi. 15.68 × 10 = 156.8 Q 4: Price of half dozen (6 eggs) = Rs. 75 Price of 8 eggs = 75 6 × 8 = Rs.100

69 CSS Primary Standard “Mathematics” Unit No. 5 Measurements Lesson # 1 Teaching Objectives: To introduce standard units of measurement. To explain conversion of units of length, weight, and capacity. Learning Outcomes: The students will be able to: Identify the standard units of measurement of length, weight, and capacity. Apply the correct units of measurement. Convert one unit to another. Apply conversion of units to real life problems. Teaching Materials: CSS Primary Standard Mathematics Book 4. Writing Board. Marker. Eraser. Procedure: Begin by asking what is length and how can we measure it. Explain the concept of Length, Conversion of the unit of length as explained on pages # 69 and 70. Fun activities: 1) Size Up Your Stuffed Animal: A Measurement What You Need: A favorite stuffed toy or doll Kitchen string Ruler, with both centimeters and inches Approximately 40 plastic linking blocks or cubes, depending on the size of the toy Balance scale Bathroom or food scale Lined or graph paper to record results (optional) What You Do: 1. Open the activity. Share with your child that she is going to get to learn more about her toy friend by using her measuring skills to find the toy's weight, its height, and its measurement around. 2. Make predictions. Let your child take a look at her stuffed toy and make predictions. Encourage her to think about how tall it is, how big around it is, and how much she thinks it weighs. You can use the lined paper to create a chart and record the various measurements and estimates. Creating a chart for the results of each measurement (the estimate and the actual) is a good visual and can be a starting point to discuss the difference between estimates and actual measurements.

70 CSS Primary Standard “Mathematics” 3. Find the height of the toy. Using blocks, have your child estimate how many blocks or cubes tall she thinks her toy is. Stack the blocks to figure out the toy's actual height. If you're keeping a chart, record your results. Follow the same procedure with both the inch side and centimeter side of the ruler: have her estimate first, perform the actual measurement, then record the results. Discuss how close her estimates were with the actual measurements. 4. Find the distance around the toy. Ask your child to estimate how many cubes it will take to measure around the toy like a belt. After she makes her estimate, take the kitchen string, wrap it around the toy, and cut it when it circles the toy once. Now, use the measuring tools to measure the length of the string. Measure the string using the cubes first. 5. Record and discuss the results compared to her estimate. Follow the same steps and measure the string using both the inch and centimeter sides of the ruler. Discuss with her which of her estimates was the closest. 6. Find out how much the toy weighs. Again, encourage your child to estimate the number of cubes she thinks her toy friend weighs. Use the balance scale: place the toy on one side of the scale, and keep adding cubes to the other side until the scale balances. Let your child figure out the difference between her estimate and the toy's actual weight; you may want to help her set up a subtraction problem for this. Follow the same procedure to figure out the weight of the toy in pounds. Have her make an estimate, then place her toy on the food or bathroom scale. 7. Discuss. Discuss your findings. Were the predictions correct? Were the estimates accurate? What are the differences between the estimate and the actual measurements? 2) Play the Measuring Game What You Need: Deck of cards with the face cards (jacks, queens, and kings) removed Metric ruler Pencil 2 sheets of white paper Scissors Markers Penny What You Do: 1. Have your child trace a penny on white paper, cut out the circle and draw an ant on the cut-out circle. 2. Shuffle and place the deck face down on the table. 3. Have him place his ant at the bottom of a sheet of white paper that's positioned vertically. 4. Encourage him to draw the first card. Have him measure the distance from his ant in a straight line up the page, drawing both a line to the end point and marking the end of the line with a pencil dot. (Example: If he draws a 5 card, he measures a line 5 centimeters long and draws a dot at the end of the line.) 5. Have him write the number of centimeters his ant traveled next to the drawn line. 6. Move the ant up the line and have him stop on the dot. 7. Continue drawing cards and measuring until the ant reaches the top of the page. 3) Variation: Create an abstract line drawing by allowing your child to measure out an ant path, or maze. How many centimeter measurements and lines does it take to complete a full ant path?

71 CSS Primary Standard “Mathematics” 4) Measurement Scavenger Hunt: What You Need: 6-10 paper strips of various lengths labeled A, B, C or 1, 2, 3 etc. Unlined sheets of paper Pencil Computer (optional) What You Do: 1. Prepare 6-10 paper strips by simply cutting strips of paper from white unlined paper or construction paper, approximately 1/2 inch wide and various lengths long. Label each strip with either a number or letter (A-J or 1-10) 2. Using an unlined sheet of paper and either a computer or a pencil create a chart. The chart will need boxes large enough to record either pictures or a list of the items you will find on your measurement scavenger hunt corresponding to particular strips. Boxes should be approximately 2 inches wide and 3 inches tall. Label each box consistent with the paper strips. (A-J or 1-10) 3. Using the strips of paper, explain to your child that his job will be to search the house looking for items that are the same length as the strips. You may need to demonstrate for him how to measure an item. Using any item found in your home and any one of the paper strips, show him the proper way to measure the item by placing one end of the strip at one end of the item, pulling the strip down over the item to see if it and the strip are the same size. Explain to him that if the strip is longer or shorter than the item you are measuring that they are not the same size, and he'll need to continue searching for something. 4. As he searches and measures, have him use the chart to record the items he finds that are the same length as that particular strip. He may record the item by drawing a picture of the item or simply writing the name of the item (or he can write both.) Measure using as many strips as he would like and revisit the activity next time using different strips. The goal of this activity is to build confidence with basic measuring skills before introducing more common tools such as rulers, measuring sticks and tapes with standard units of measurement. He'll be running from room to room searching for the items to measure! Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom.

72 CSS Primary Standard “Mathematics” Exercise (5a) Q 1: Fill in the blanks. i. 23 m = 2300 cm ii. 14 km = 14,000,000 mm iii. 18m = 1800 cm iv. 24 km = 24000m v. 14km = 1,400,000 cm vi. 15.6 km = 1,560,000 cm vii. 13.5 km = 13500m viii. 23.9 cm = 239 mm Q 2: Convert these lengths from km to cm and m. i. 32 km 32,000 m 3,200,000 cm ii. 16 km 16,000 m 1,600,000 cm iii. 1.2 km 12,00 m 1,200,000 cm iv. 16.14 km 16,140 m 1,614,000 cm v. 13.56 km 13,560 m 1,356,000 cm vi. 105.6 km 105,600 m 10, 560,000 vii. 142.3 km 142,300 m 14, 230, 000 Q 3: Laiba jumps = 2m 45 cm = 2(100) + 45 cm = 245 cms Q 4: Distance from Lahore to Multan = 350 km Distance from Lahore to Multan in m = 350 × 1000 = 350000 m Distance from Lahore to Multan in cm = 350 × 1000 × 100 = 3500000 cm Exercise (5b) Q 1: Write vertically and add the following: i. km m cm H T O H T O T O 5 1 5 1 4 + 1 4 0 2 1 8 1 9 1 7 3 2 19 km 17 m 32 cm ii. km m cm H T O H T O T O 1 9 1 6 1 8 + 1 2 1 3 1 2 3 1 2 9 3 0 31 km 29 m 30 cm iii. km m cm H T O H T O T O 1 4 1 9 1 3 + 1 2 2 8 5 4 2 6 4 7 6 7 26 km 47 m 67 cm

73 CSS Primary Standard “Mathematics” iv. km m cm H T O H T O T O 5 6 1 3 1 2 + 0 0 1 9 1 4 5 6 3 2 2 6 56 km 32 m 26 cm Q 2: Add the following: i. km m cm H T O H T O T O 0 0 5 4 0 3 + 9 4 0 4 0 4 9 4 5 8 0 7 94 km 58 m 07 cm ii. km m cm H T O H T O T O 1 8 1 1 0 5 + 1 3 1 2 0 1 3 1 2 3 0 6 31 km 23 m 06 cm iii. km m cm H T O H T O T O 2 4 1 6 0 5 + 1 0 1 0 0 3 3 4 2 6 0 8 34 km 26 m 08 cm iv. km m cm H T O H T O T O 7 1 1 3 0 5 + 1 6 9 4 0 3 8 7 1 0 7 0 8 87 km 107 m 08 cm v. km m cm H T O H T O T O 1 2 1 4 0 4 + 6 1 1 1 0 2 7 3 2 5 0 6 73 km 25 m 06 cm

74 CSS Primary Standard “Mathematics” vi. km m cm H T O H T O T O 1 3 1 6 0 5 + 2 5 1 2 0 4 3 8 2 8 0 9 38 km 28 m 09 cm Q 3: Write vertically and subtract the following: i. km m cm H T O H T O T O 1 4 1 9 0 9 - 0 2 2 1 0 3 1 1 9 8 8 0 6 11 km 988 m 06 cm ii. km m cm H T O H T O T O 9 8 1 5 0 5 - 4 2 0 3 0 2 5 6 1 2 0 3 56 km 12 m 03 cm iii. km m cm H T O H T O T O 0 15 1 5 1 3 0 0 - 0 8 0 3 0 0 7 1 0 0 0 7 km 10 m iv. km m cm H T O H T O T O 5 14 0 15 6 4 1 2 1 5 - 1 5 1 0 0 7 4 9 0 2 0 8 49 km 02 m 08 cm Q 4: Subtract the following: i. km m cm H T O H T O T O 5 11 5 5 6 1 1 2 - 2 4 1 3 1 0 3 1 4 8 0 2 31 km 48 m 02 cm

75 CSS Primary Standard “Mathematics” ii. km m cm H T O H T O T O 0 13 0 10 7 8 1 3 1 0 - 1 2 0 9 0 5 6 6 0 4 0 5 66 km 04 m 05 cm iii. km m cm H T O H T O T O 0 9 9 0 16 1 0 0 0 5 1 6 - 9 2 1 0 0 8 0 0 7 9 9 5 0 8 7 km 95 m 08 cm iv. km m cm H T O H T O T O 0 10 13 1 1 3 0 0 0 5 0 9 8 0 0 0 2 0 1 5 0 0 0 3 15 km 03 cm Q 5: Length of the wall = 15m 15 cm Length of second wall = 12m 13 cm H T O T O 1 5 1 5 + 1 2 1 3 2 7 2 8 27 m 28 cm Q 6: Distance from Lahore to Multan = 350 km 50 m 12 cm. Distance from Multan to Bahawalpur = 50 km 35 m 90 cm Total Distance = ? km m cm H T O H T O T O 3 5 0 5 0 1 2 5 0 3 5 9 0 4 0 0 8 6 0 2 400 km 86 m 02 cm Total Distance = 400 km 86 m 02 cm

76 CSS Primary Standard “Mathematics” Q 7: Saimiya’s height = 1 m 46 cm Aleezay’s height = 1 m 94 cm Difference in height = ? H T O T O 8 14 1 9 4 + 1 4 6 4 8 48 cm Difference in height = 48 cm Q 8: Total distance = 14 km 450 m Distance already covered = 3km 250 m Distance to be covered = ? km m H T O H T O 1 4 4 5 0 3 2 5 0 1 1 2 0 0 11 km 200 m Distance to be covered = 11 km 200 m Q 9: Anees bought total cloth for curtains of drawing room = 15 m 256 cm Anees bought total cloth for curtains of bedroom = 8 m 56 cm More clothes needed for drawing room curtains = ? m cm H T O H T O 1 5 2 5 6 - 8 5 6 7 2 0 0 More clothes needed for drawing room curtains = 7m 200cm Lesson # 2 Procedure: Explain the concept of Mass/ Weight and Addition and Subtraction of Mass/weight as given on pages # 73, 74, 75 and 76. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be:

77 CSS Primary Standard “Mathematics” Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (5c) Q 1: What is the approximate mass of each object? Activity based. Q 2: Convert from kg to g. i. 5200 g ii. 16509 g iii. 18000 g iv. 13619 g v. 24610 g Q 3: Shazmeen’s weight = 57 kg 520 g Shazmeen’s weight in grams = ? We know that: 57 kg = 57000 g So, 57 kg 520 g = 57000 + 520 57520 g Q 4: Kousar’s weight = 99 kg 734 g Shazmeen’s weight in grams = ? We know that: 99 kg = 99000 g So, 99 kg 734 g = 99000 + 734 99734 g Exercise (5d) Q 1: Add the following: i. kg g H T O H T O 1 4 4 1 1 2 + 1 3 1 1 8 1 5 7 2 3 0 157 kg 230 g ii. kg g H T O H T O 1 0 1 3 9 + 9 5 1 2 1 9 6 5 1 196 kg 51 g

78 CSS Primary Standard “Mathematics” iii. kg g H T O H T O 1 8 1 1 9 + 1 3 1 0 2 1 9 4 1 2 1 194 kg 121 g iv. kg g H T O H T O 1 7 1 2 2 1 5 0 1 7 1 6 7 1 3 9 167 kg 139 g v. kg g H T O H T O 9 2 4 1 3 + 5 1 1 0 0 9 7 5 1 1 3 975 kg 113 g vi. kg g H T O H T O 1 5 6 9 2 1 3 2 5 8 + 1 5 6 4 2 0 4 0 4 3 945 kg 113 g Q 2: Subtract the following: i. kg g H T O H T O 1 1 2 11 1 2 1 5 3 1 - 1 6 0 1 3 1 0 5 5 1 8 105 kg 518 g ii. kg g H T O H T O 2 15 2 3 5 2 1 1 1 0 6 1 1 1 1 2 9 1 0 0 129 kg 100 g

79 CSS Primary Standard “Mathematics” iii. kg g H T O H T O 0 14 15 2 9 4 1 5 5 1 2 1 9 6 1 7 3 5 9 173 kg 59 g vi. kg g H T O H T O 4 15 5 5 1 6 - 2 6 1 4 2 9 0 2 29 kg 2 g v. kg g H T O H T O 8 11 14 11 9 2 5 1 5 4 3 6 5 2 5 1 5 5 9 9 0 3 559 kg 903 g vi. kg g H T O H T O 4 10 4 14 8 2 5 0 5 4 3 2 1 1 0 5 5 0 3 9 4 9 503 kg 949 g Q 3: Mass of Sugar = 354 kg 213 g Mass of flour = 95 kg 54 g Total mass of sugar and flour = ? kg g H T O H T O 3 5 4 2 1 3 + 9 5 0 5 4 4 4 9 2 6 7 449 kg 267 g Total mass of sugar and flour = 449 kg 267 g Q 4: Mass of two bags = 59 kg 24 g Mass of one bag = 22 kg 31 g

80 CSS Primary Standard “Mathematics” Mass of other bag = ? kg g H T O H T O 8 12 5 9 2 4 2 2 3 1 3 6 9 3 36 kg 93 g Mass of other bag = 36 kg 93 g Q 5: Mass of chicken = 5 kg 216 g Mass of rice bags = 15 kg 219 g Total Mass = 5kg 2 16g + 15 kg 219g = 26 kg 80 g Kg g H T O H T O 1 5 2 1 6 1 5 2 1 9 2 0 4 3 5 Total Mass of chicken and rice = 31 kg and 296 g Q 6: Total flour Mrs. Namra has = 15 kg Flour used for making cake = 3 kg 520 g Flour used for making bread = 2 kg 600 g Total flour used = ? kg g H T O H T O 3 5 2 0 + 2 6 0 0 6 1 2 0 Total flour used = 6 kg 120 g Flour left = 15 kg – 6 kg 120 g = 8 kg 880 g Q 7: Mass of first rock = 908 kg 430 g Total mass of two rocks = 3234 kg 530 g Mass of other rock = ? kg g Th H T O H T O 2 1 2 14 3 2 3 4 5 3 0 9 0 8 4 3 0 2 3 2 6 9 0 0 Mass of other rock = 2326 kg 900 g

81 CSS Primary Standard “Mathematics” Lesson # 3 Procedure: Explain the concept of Volume/ Capacity and Addition and Subtraction of Volume/ Capacity as given on pages # 77 and 78. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (5e) Q 1: Convert from liters to milliliters: i. 513 liters = 513000 mL ii. 2.5 liters = 2500 mL iii. 16.25 liters = 16250 mL iv. 14.55 liters = 14550 mL v. 199.5 liters = 199500 mL vi. 5.689 liters = 5689 mL vii. 181.321 liters = 181321 mL viii. 16.295 liters = 16295 mL Q 2: The water bottle of seema contains = 5 liters 321 mL Capacity in liters = ? Capacity in mL = ? Capacity in liters = 5.321 liter Capacity in mL = 5321 ml Q 3: Capacity of the oil tanker = 40500 liters Capacity in mL = ? Capacity in mL = 40500 × 1000 = 40500000 mL Q 4: Measure capacity of beaker in mL = 100 mL Measure capacity of beaker in liter = ? Measure capacity of beaker in liter = 100 × 1/1000 = 0.1 liters Exercise (5f) Q 1: Write vertically and add the following:

82 CSS Primary Standard “Mathematics” i. L mL H T O H T O 2 0 5 3 0 0 + 5 4 9 5 0 3 6 0 2 5 0 360 L, 250 mL ii. L mL H T O H T O 5 3 0 2 1 0 1 3 9 4 0 0 6 6 9 6 1 0 669 L, 610 ml iii. L mL H T O H T O 2 9 5 3 5 0 6 1 4 1 0 0 9 0 9 4 5 0 909L, 450 mL vi. L mL Th H T O H T O 3 5 6 3 3 2 0 + 1 3 2 0 6 1 3 6 9 5 3 8 1 3695 L, 381 mL Q 2: Solve the following: ii. L mL H T O H T O 6 8 9 5 - 2 4 3 2 4 4 6 3 44 L, 63 mL i. L mL H T O H T O 3 9 10 4 10 4 0 0 2 5 0 2 5 1 1 1 2 1 4 9 1 3 8 149 L, 138 mL

83 CSS Primary Standard “Mathematics” iii. L mL H T O H T O 0 13 1 9 2 1 3 5 1 0 0 5 0 0 9 2 0 8 5 92 L, 85 mL iv. L mL H T O H T O 4 11 8 11 11 2 5 1 9 2 1 1 2 5 2 4 6 1 2 6 6 7 5 126 L, 675mL Q 3: Total milk brought by Emaan = 3000 mL Milk drank by Emaan on first day = 550 mL Milk drank by second day by Emaan = 620 mL How much milk is left = ? Total milk drank in 2 days = 550mL + 620 mL = 1170 mL Total milk left now = 3000 – 1170 = 1830 mL Q 4: Capacity of the drum = 1000 liters Oil filled in the drum = 519 liters How much oil can be filled now = ? = 1000 – 519 = 481 liters of oil Q 5: Capacity of each mug = 725 mL Number of mugs = ? Tea in 7 mugs = 725 mL +725 mL +725 mL +725 mL +725 mL +725 mL +725 mL = 5075 mL Tea left in bucket = 1 liter = 1000 mL Capacity of the bucket = 5075 mL + 1000 mL = 6075 mL = 6 liters 75 mL Lesson # 4 Teaching Objectives: To explain conversion of units of time.

84 CSS Primary Standard “Mathematics” To introduce addition, subtraction, and comparison of units of time. Learning Outcomes: The students will be able to: Inter-convert seconds to minutes and to hours. Inter-convert hours to days and to weeks. Add and subtract different units of time. Teaching Materials: CSS Primary Standard Mathematics Book 4. Writing Board. Marker. Eraser. A clock faces with movable hands. An actual clock. A calendar. Time-tables of flight or railway schedules. A TV guide Introduction: Show a clock to the students and ask about its uses. Ask them to prepare a timeline of their daily routine. Ask them about a.m and p.m. Ask them about seconds, minutes and hours. Ask about the day, week and month. Invite them for book reading and solving exercises. Fun activity Make a Clock! What You Need: Old frisbee, or a thick paper plate Markers Scissors or a drill Poster board or heavy paper Paper fasteners (available at any stationery store) Circle-shaped stickers Paper Pencil What You Do: 1. The teacher will start by making a small hole in the center (With a plate, she can use scissors. With a frisbee, she’ll need to use a drill). Let her child know he’s going to make his very own clock and that the frisbee or paper plate will serve as the clock face. If she has an analog watch or clock somewhere in the house, bring it to the table to use as a model. 2. She will ask the child to place one sticker at the top of the “clock face” and one directly opposite, on the bottom. With the marker, have him write the number 12 on the top sticker and the number 6 on the bottom sticker. Now she will ask him to place one sticker on each side, halfway in between the top and bottom. He should write 3 on the right-hand sticker, and 9 on the left-hand sticker. Then, referring your analog clock as a model, she will ask him to fill in the other numbers on the clock using the stickers and his marker. 3. Now it’s time for the clock hands! Using the poster board, cut two arrows—a longer one for the minute hand, and a shorter one for the hour hand. Pierce the ends of the arrows with the paper fastener, slide it through the hole in the center of your clock face, and secure it at the back. 4. Pick a day of the week and, with the child’s help, create a list of his activities. This might include soccer practice, a violin lesson, going to school, a playdate, a shopping trip with

85 CSS Primary Standard “Mathematics” grandma…or just time spent eating a snack. Next to each entry, write the time the activity begins, rounding to the nearest half hour. To make it concrete! The teacher will help the child identify the hour hand and the minute hand on the clock face. Remind her that the hour hand shows the hour and the minute hand shows the minutes. Now, she will make sure she knows which hand of the clock is longer (the minute hand) and which hand of the clock is shorter (the hour hand). Pick an activity and find its time on the clock. Start with the activities that begin on the hour and then move to the activities that are on the half hour. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (5g) Q 1: Convert the following in minutes and seconds: i. 8 hours 20 minutes = 8 × 60 + 20 = 500 minutes = 500 × 60 = 30000 seconds ii. 35 hours 16 min 15 seconds = 35 × 60 + 16 + 15 seconds = 2100 + 16 = 2116 minutes 15 seconds = 2116 × 60 + 15 = 126960 + 15 = 126975 seconds iii. 2 days 3 hours 50 min = (2 × 24 + 3) hours 50 min = 51 hours 50 min = (51 × 60) + 50 = 3060 + 50 = 3110 minutes = 3110 × 60 = 186600 seconds iv. 16 minutes 56 seconds = 16 × 60 + 56 = 960 + 56 = 1016 seconds v. 15 hours 13 min = (15 × 60) min + 13 min = 900 + 13 = 913 minutes = 913 × 60 = 54780 seconds

86 CSS Primary Standard “Mathematics” vi. 1 week, 2 days, 3 hours, 51 minutes = 7 days + 2 days, 3 hours, 51 minutes = 9 days, 3 hours, 51 minutes = (9 × 24)hours + 3 hours, 51 minutes = 216 hours + 3 hours, 51 minutes = 219 hours, 51 minutes = (219 × 60)min, 51 min = 13140 minute + 51 minute = 13191 minutes = (13191 × 60) seconds = 791460 seconds vii. 9 hours 3 minutes 20 seconds = (9 × 60) minutes, 3 minutes, 20 seconds = 543 minutes 20 seconds = (543 × 60) seconds + 20 seconds = 32580 + 20 seconds = 32600 seconds viii. 30 minutes 29 seconds = (30 × 60) seconds + 29 seconds = 1800 + 29 = 1829 seconds Q 2: Convert years to months, months to days and weeks to days. i. 5 years = 5 × 12 = 60 months = 365 × 5 = 1825 days ii. 18 years = 18 × 12 = 216 months = 365 × 18 = 6570 days iii. 42 weeks = (42 × 7) days = 294 days iv. 36 weeks = (36 × 7) days = 252 days v. 12 years = 12 × 12 = 144 months = 365 × 12 = 4380 days Q 3: Age of Alishaba = 12 years 5 months Age in months = ? Age in days = ? Age in months = (12 × 12) months + 5 months = (144 + 5) months = 149 months Age in days = (149 × 365) = 54385 days Q 4: Age of Arslan = 24 years Age in months = ? Age in days = ? Age in hours = ? Age in minutes = ? Age in months = (24 × 12) months = 288 months Age in days = (288 × 30) days = 8760 days Age in hours = (8760 × 24) hours = 210240 hours Age in minutes = (210240 × 60) = 12614400 minutes

87 CSS Primary Standard “Mathematics” Q 5: Solve the following: i. Hours Minutes Seconds T O T O T O 5 1 8 3 0 + 9 3 2 2 0 1 4 5 0 5 0 14 hours, 50 minutes, 50 seconds. ii. Hours Minutes Seconds T O T O T O 1 6 1 3 5 5 1 8 1 4 0 0 3 4 2 7 5 5 34 hours, 27 minutes, 55 seconds. iii. Hours Minutes Seconds T O T O T O 3 9 1 4 2 0 1 5 1 5 1 3 5 4 2 9 3 3 54 hours, 29 minutes, 33 seconds. iv. Hours Minutes Seconds T O T O T O 2 3 4 5 1 5 0 0 1 2 2 5 23 5 7 4 0 23 hours, 57 minutes, 40 seconds. Q 6: Subtract the following: i. Hours Minutes Seconds T O T O T O 0 15 1 5 5 8 9 3 2 0 6 2 6 6 hours, 26. ii. Hours Minutes Seconds T O T O T O 4 14 2 13 1 6 5 4 3 3 0 3 2 6 1 9 1 3 2 8 1 4 13 hours, 28 minutes, 14 seconds.

88 CSS Primary Standard “Mathematics” iii. Hours Minutes Seconds T O T O T O 4 10 3 5 1 6 5 0 1 2 1 3 1 2 2 3 0 3 3 8 23 hours, 03 minutes, 38 seconds. iv. Hours Minutes Seconds T O T O T O 8 15 9 5 3 6 4 2 1 6 3 6 2 0 7 9 0 0 2 2 79 hours, 00 minutes, 22 seconds. Q 7: Mrs. Namra worked on Tuesday = 8 hours 40 minutes Mrs. Namra worked on Wednesday = 8 hours 10 minutes Total hours of work = ? Hours Minutes Seconds T O T O T O 8 4 0 + 8 1 0 1 6 5 0 16 hours, 50 minutes. Total hours of work = 16 hours 50 minutes Q 8: Aleezay take total time to make 3 dresses = 9 hours 55 minutes Time taken to make one dress = 3 hours 45 minutes Time taken to make other two dresses = ? Hours Minutes Seconds T O T O T O 9 5 5 – 3 4 5 6 1 0 6 hours, 10 minutes. Time taken to make other two dresses = 6 hours 10 minutes Review Exercise 5 Q 1: Choose the correct answer and fill the circle: i. 1 km = …………m 100 10 10,000 1000 ii. 2kg = ………g 200 20 20,000 2000

89 CSS Primary Standard “Mathematics” iii. 3l =…….ml 30 30,000 300 3000 iv. 2 years =……….days 830 days 760 days 860 730 days v. 1 day = ……….. minutes 14400 1400 144000 1440 Q 2: Solve the following: i. km m H T O H T O 2 3 + 5 8 7 1 1 7 km 11 m ii. km m H T O H T O 9 5 0 0 + 1 3 0 0 8 2 0 0 8 km 200m iii. kg g H T O H T O 3 5 1 4 + 1 6 1 5 – 5 1 5 2 1 9 0 4 6 1 9 46 kg 19g iv. L mL H T O H T O 0 16 2 15 1 6 3 5 - 8 1 9 8 1 6 8liters16 mL iii. This question will be solved in two steps: Step 1: = 35 kg 14 g + 16 kg 15 g = Result 1 Step 2: = Result 1 – 5kg 10 g Step 1:

90 CSS Primary Standard “Mathematics” kg g H T O H T O 3 5 1 4 + 1 6 1 5 5 1 2 9 51 kg 29 g Step 2: kg g H T O H T O 4 11 5 1 2 9 - 0 5 1 0 4 6 1 9 46 kg 19 g Q 3: Ali bought sugar = 354 kg 213 g Ali bought rice = 95 kg 54 g Total things bought = ? kg g H T O H T O 3 5 4 2 1 3 - 9 5 5 4 4 4 9 2 6 7 449 kg 267 g Q 4: Time taken by Rehman to make 2 doors = 8 hours 15 minutes Time taken by Rehman to make one door = 3 hours 10 minutes Time taken by Rehman to make other door = ? Hours Minutes H T O H T O 8 1 5 3 1 0 5 0 5 5 hours 5 minutes

91 CSS Primary Standard “Mathematics” Model Paper # 1 Instructions: Every question has four possible answers but one is the correct answer. Choose the correct answer and fill the circle. Only use black or blue pen to fill the circle. Filling more than one circle will be considered wrong answer. Section A Time Allowed: 45 Minutes (Objective Type) Total Marks: 30 Q.1: Fill the circle of correct answer. (10 Marks) 1. Factors are those numbers when multiply together give another ……….. number digit alphabet none of the above 2. Two numbers are called co-prime if their only common factor is ………... 1 2 3 4 3. An exact divisor of a number is called ………... number factor alphabet none of the above 4. The product of a number by the numbers 1, 2, 3, 4, is called ………... number digit multiples none of the above 5. The method in which we use to find out the prime factors of a number is called ………... prime factorization co-multiple common factors Ven Diagram Method 6. The number above the line says how many parts we have………... numerator denominator divisor fractions 7. The number below the line says how many parts we have………... numerator denominator divisor fractions. 8. A ……….. is a part of the whole or a collection. numerator denominator divisor fractions. 9. Fractions with same ………… are called like fractions. numerator denominator divisor fractions. 10. Fractions with different denominators are called ………. fractions. like unlike unit equal 11. Which of the following is a decimal fraction? 5 8 18 5 3 1 5 2.18 12. The figure shows: 1.9 0.09 10.009 0.9 13. 2.31 + 1.05 = 4.36 4.35 3.34 3.36

92 CSS Primary Standard “Mathematics” 14. 1 km = …………m 100 10 10,000 1000 15. 2kg = ………g 200 20 20,000 2000 B: Fill in the blanks: (15 Marks) 1. Ascending order means arrange the fraction from lowest to ………. fraction. 2. We use the relative values of numerator and denominator of a fraction to …………… into different types. 3. There are …………… main types of fractions. 4. Any fraction with numerator “1” is called …………… fraction. 5. A fraction with numerator less than the denominator is called …………… fraction. 6. A number that can be written as fraction can also be written as a …………… fraction. 7. Decimal fraction is a kind of fraction in which …………… is 10 or power of 10. 8. We can convert fractions into decimals when …………… is not the power of 10. 9. There are …………… basic operation used in mathematics. 10. …………… means move decimals point three places to the right. 11. We use kilometer to measure the large distances and meter to measure the …...… lengths. 12. There are …………… cm in a meter. 13. To convert large unit into small unit, we …………… 14. During …………… we will subtract the same units. 15. There are …………… minutes in one hour. Section B Time Allowed: 75 Minutes (Subjective Type) Total Marks: 45 Note: Attempt all questions. All questions carry equal (3) Marks. 1. Three drums contain 36 liters, 48 liters and 72 liters of oil. What biggest measure can measure all the different quantities exactly? 2. Find the highest number that exactly divides the numbers 50, 60 and 86. 3. Find the smallest number that is divisible by the number 36, 64 and 74. 4. Anoral has 6 oranges, 8 peaches and 20 pears. She wants to put all the fruit into baskets with each basket having the fruits. What is the greatest number of pieces of fruit Anoral can put in each basket? 5. A piece of wire is 111/16 m and another piece of wire is 17/26 m long. How long the two pieces of are wire altogether? 6. Anoral spend 5/10 hours to watch TV and 1/5 hours to play with her friends. How much more time did she spend in watching TV than playing with her friends. 7. Waqas drinks 21 /5 liters of water daily. How many liters of water will he drink in 8 days? 8. Mrs. Rizwan class is making pillow cases. Each pillow case uses ¼ of a yard fabric. How many pillow cases can they make out of 12 yards of fabric? 9. Anees is 5.33 feet tall and Amina is 0.54 feet taller than Anees. How tall is Amina?

93 CSS Primary Standard “Mathematics” 10. Aleem’s weight is 84.50 kg and Rehan’s weight is 90 kg. What is the difference between Aleem and Rehan’s height? 11. If the price of half dozen eggs is Rs. 75, then find the price of 8 eggs. 12. The length of a wall is 15m, 15cm and the length of second wall is 12m, 13cm. Find the total length of both walls. 13. A man bought 354 kg 213 g of sugar and 95 kg 54 g of flour. What is the total mass of Sugar and flour? 14. Emaan’s mother bought 3000 ml of milk. She drank 550 ml of it on first day and 620 ml of it on 2nd day. How much milk is left? 15. Aleezay took 9 hours 55 minutes to make 3 dresses. She made one dress in 3 hours 45 minutes. How much time did she take to make other two dresses? Model Paper # 2 Instructions: Every question has four possible answers but one is the correct answer. Choose the correct answer and fill the circle. Only use black or blue pen to fill the circle. Filling more than one circle will be considered wrong answer. Section A Time Allowed: 45 Minutes (Objective Type) Total Marks: 30 Q.1: Fill the circle of correct answer. (10 Marks) 1. Ascending means from smallest to the greatest. smallest greatest equal none of the above 2. 3l =…….ml 30 30,000 300 3000 3. 2 years =……….days 830 days 760 days 860 730 days 4. 1 day = ……….. minutes 14400 1400 144000 1440 5. 8.64 – 7.12 = 2.56 3.52 2.52 1.52 6. 5.85 x 100 = 58.5 5850 15.850 585 7. 19.82 ÷ 2 9.94 9.93 5850 9.91

94 CSS Primary Standard “Mathematics” 8. 1 week = …… days 6 7 8 9 9. While addition, we will ………. the same units. subtract multiply add divide 10. The biggest unit of length is: mm km cm m 11. The biggest unit of mass is: mg kg gg g 12. The biggest unit of capacity is: liter micro liter spoon milliliter 13. The biggest unit of time is: day hour week month 14. We measure……. in kg. length volume time mass 15. We measure ………. in seconds. length volume time mass B: Fill in the blanks: (15 Marks) 1. A fraction with numerator greater than or equal to the denominator is called ……….. fraction. 2. Any fraction having same numerator and denominator is also called a ……….. fraction. 3. When we write fraction as a mixed number then the ……….. becomes the numerator. 4. ……….. numbers consist of a whole number and fraction. 5. While adding two fractions, if the sequence of fractions is ……….., the sum remains same. 6. To simplify divide ……….. and denominator by 2. 7. ……….. is the reverse process of multiplication. 8. Always write the final answer in ……….. form. 9. While doing addition or ……….., always put decimal points under the decimal point. 10. ……….. means move decimal point one place to the right. 11. ……….. means move decimal point three place to the right. 12. 39693 is divisible by ……….. 13. We measure the mass/weight in ……….. 14. We measure length in ……….. 15. We measure volume/capacity in ……….. Section B Time Allowed: 75 Minutes (Subjective Type) Total Marks: 45 Note: Attempt all questions. All questions carry equal (3) Marks.

95 CSS Primary Standard “Mathematics” 1. Rabia has two pieces of clothes. One piece is 72 inches wide and other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? 2. Find the least number of mangoes that can be usually shared by 20, 50 and 75 people. 3. Laiba, Tauseef and Nadia walked 24, 42 and 52 meters. What is the minimum distance that each of them can cover equally. 4. Humaira is putting together First Aid kits. She has 12 large bandages and 18 small bandages and she want each kit to be identical with no bandage left over. What is the greatest number of first aid kits Humaira could put together? 5. Express 43/7 as mixed fraction. 6. Rabia ate 1/6 of a pizza, Raheel and Arslan ate 1/3 of the pizza respectively. How much pizza did they eat altogether? 7. Ali spent 23 /8 hours to read mathematics from 41 /1 hours. How much time did he spend for other activates. 8. Waqar ate 1/8 of a watermelon; Saif ate 3/8 of watermelon. How much water melon did they eat altogether? 9. Alina’s height is 182.53 cm and her brother is 5.60 cm taller than her. What is the height of Alina’s brother? 10. Aleezay ran 130.60 m on Sunday, 229.50 m on Monday and 133.94 m on Tuesday. How much distance did she cover in three days? 11. Laiba covers a distance of 350.55 km in 5 hours. How much distance did she cover in one hour? 12. The mass of a book is 752.95 grams. Find the mass of 25 such book. 13. The total length of piece of wire is 14 cm and 54 cm. The wire is cut off into two pieces. If the length of one piece is 2m and 15 cm, find the length of second piece. 14. The mass of the empty box is 1 kg 354 g. Ali is putting vegetables in the box. The weight of vegetables is 9kg 320 grams. What is the weight of box and vegetables altogether? 15. A tea bucket is filled with tea. Ayesha poured the tea into 7 mugs. The capacity of each mug is 725 ml. There is one liter of tea left in the bucket. What is the capacity of the bucket? Model Paper # 3 Instructions: Every question has four possible answers but one is the correct answer. Choose the correct answer and fill the circle. Only use black or blue pen to fill the circle. Filling more than one circle will be considered wrong answer.

96 CSS Primary Standard “Mathematics” Section A Time Allowed: 45 Minutes (Objective Type) Total Marks: 30 Q.1: Fill the circle of correct answer. (10 Marks) 1. Factors are those numbers when multiply together give another ……….. number digit alphabet none of the above 2. Two numbers are called co-prime if their only common factor is ………... 1 2 3 4 3. An exact divisor of a number is called ………... number factor alphabet none of the above 4. The product of a number by the numbers 1, 2, 3, 4,… are called ………... number digit multiples none of the above 5. The method in which we use to find out the prime factors of a number is called ………... prime factorization co-multiple common factors Venn diagram method 6. The number above the line says how many parts we have………... numerator denominator divisor fractions 7. The number below the line says how many parts we have………... numerator denominator divisor fractions. 8. A ……….. is a part of the whole or a collection. numerator denominator divisor fractions. 9. While addition, we will ………. the same units. subtract multiply add divide 10. The biggest unit of length is: mm km cm m 11. The biggest unit of mass is: mg kg lg g 12. The biggest unit of capacity is: liter micro liter spoon milliliter 13. The biggest unit of time is: day hour week month 14. We measure……. in kg. length volume time mass 15. We measure ………. in seconds. length volume time mass B: Fill in the blanks: (15 Marks) 1. A fraction with numerator greater than or equal to the denominator is called ……….. fraction. 2. Any fraction having same numerator and denominator is also called a ……….. fraction. 3. When we write fraction as a mixed number then the ……….. becomes the numerator.

97 CSS Primary Standard “Mathematics” 4. ……….. numbers consist of a whole number and fraction. 5. While adding two fractions, if the sequence of fractions is ……….., the sum remains same. 6. To simplify divide ……….. and denominator by 2. 7. ……….. is the reverse process of multiplication. 8. Always write the final answer in ……….. form. 9. There are …………… basic operation used in mathematics. 10. …………… means move decimals point three places to the right. 11. We use kilometer to measure the large distances and meter to measure the ……… length. 12. There are …………… cm in a meter. 13. To convert large unit into small unit, we …………… 14. During …………… we will subtract the same units. 15. There are …………… minutes in one hour. Section B Time Allowed: 75 Minutes (Subjective Type) Total Marks: 45 Note: Attempt All questions. All questions carry equal (3) Marks. 1. The lengths of three tracks are 44m, 88m and 114m. Find the highest length of each track if we want to take equal lengths. 2. Rabia is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use? 3. Find the greatest number that exactly divides 22, 32 and 60. 4. Define Unit, Proper and Improper fraction. 5. The capacity of bucket is 2 6 5 liters. If it contains 4 liters then how much more water can be filled in it? 6. Multiply 3 4 by 2 11 and write the result in simplest form. 7. What is the area of a rectangle if its length is 1 3 5 cm and width is 1 2 5 cm? 8. How many dresses can be made from 201 /2 m cloth, if each dress requires 1 2 2 m cloth? 9. Fatima bought 54.60 m wire for her house and 13.25 m for her uncle’s house. How much wire did she buy altogether? 10. Six month’s ago, kousar weight was 99.50 kg. She lost her weight by 12.5 kg in six months. What is her current weight? 11. The mass of an empty water bottle is 23.50 g. What will be the mass of 12 such empty water bottles?

98 CSS Primary Standard “Mathematics” 12. The total distance between two cities in 94.60 km. Anoral covered this distance in 2 hours. How much distance did she cover in one hour? 13. Farzana is living in Madina. Her house is 14km, 450 m from Masjid Nabvi. She has already covered 3km and 250 m. How much more distance she has to cover to reach Masjid-e-Nabvi? 14. Shazmeen’s weight is 57 kg and 520 grams. Find her weight in grams only. 15. A beaker can measure 100ml of water. Find its measuring capacity in liters. Unit No. 6 Geometry Lesson # 1 Teaching Objectives: To introduce angles and their components. To introduce different types of angles. To explain the use of a protractor. To demonstrate how to draw an angle using angle flippers or protractor. To explain the parts of a circle. To demonstrate how to draw a circle using a ruler and a pair of compasses. To explain the properties of quadrilaterals. To explain different terms connected to quadrilaterals. To introduce types of quadrilaterals. To demonstrate how to construct a square and rectangle using a ruler and set-squares. Learning Outcomes: The students will be able to: Identify an angle and its different parts. State the different types of angles with their properties. Use a protractor to draw angles • identify a circle and its different parts. Draw a circle of a given radius accurately using a pair of compasses. Recognize a quadrilateral by its properties. Use terms connected to quadrilaterals correctly. Recognize the different types of quadrilaterals and differentiate between them. Construct a quadrilateral when its sides are given. Teaching Materials: CSS Primary Standard Mathematics Book 4. Writing Board. Marker. Eraser. Geometry box with its instruments.

99 CSS Primary Standard “Mathematics” Procedure: Greet students and ask them about different shapes they look around themselves. Ask them what they know about a line. Use a Japanese fan to introduce the lesson on angles. Turn one arm of the fan so that the gap between the two arms increases. Tell them angle is the special word used to describe the amount of turn between the two arms. Its symbol is ∠. The unit to measure angles is called degree and is written as Angles have special names. As the teacher widens the gaps between the two arms of the fan, she keeps on naming the different angles: 1. When one arm is horizontally straight and the other is vertically straight, a right angle is formed. 2. When the angle is smaller than a right angle, it is called an acute angle. 3. When an angle is bigger than a right angle, but not big enough to form a straight line, it is called an obtuse angle. 4. When the angle goes beyond the straight line, it is called a reflex angle. The concept of angles can be taught using two strips of paper as well. The fan and the strips can be illustrated as a drawing wherein the arms of the fan or the two strips become the arms BA and BC of the drawing as shown in figure. Point B is referred to as the vertex. This angle can be named as ABC or CBA. The children are then informed that angles can be measured using a protractor. They observe the shape of the protractor and the numbers on it. They see that the numbers go from 0 to 180 both clockwise and anti-clockwise on the semicircular protractor. Tell them that in order to construct an angle, the children have to draw a horizontal, straight, line AB first. They have to place the protractor in such a way that the middle of its bottom line is exactly on A. The teacher calls out a number, say 70. The children put a point, say C, on the paper where they see the number 70 on the protractor and then join the points A and C to make the arm AC of the resulting angle. The measure of this angle is 70° and we write, ∠CAB = 70°. The children then measure and construct several angles using the protractor. Thereafter the teacher demonstrates that when the fan makes a complete turn, a circle is constructed and the central angle of a circle is 360°. Triangle: Children know that a triangle is a shape that has three sides and three vertices. In addition to this, they now know that it has three angles. Triangles can be classified into three groups according to their sides or their angles. Using the paper folding technique, it is easy to see that the 3 angles of any triangle add up to 180°. This fact can also be verified by measuring the 3 angles with a protractor. Any two triangles (with at least one side equal) placed together along the equal side form a quadrilateral. If the four angles of a quadrilateral are torn off, placed together on a sheet of paper and measured, the angles add up to 360° (equal to a full turn of the arm of a Japanese fan). And, there is proof within proof. If any quadrilateral is cut into two parts across either of the two diagonals, two triangles are formed which can be either different in size or equal in size. The angles of each one add up to 180° and the angles of both

100 CSS Primary Standard “Mathematics” triangles add up to 360°. These are interesting experiments to perform, which later go on to show how the two halves of a parallelogram, even though identical in size and shape (congruent), need to be flipped to coincide. Quadrilateral: Children are aware that quadrilaterals are shapes which have four sides. They now know that quadrilaterals have four angles too! With the help of the protractor, the children then measure the four angles of several quadrilaterals. On adding up the measures of each of the four angles of the quadrilateral, children find that the angles add up to 360°. They also notice that squares and rectangles have four right angles. A new word ‘perpendicular’ is introduced to the vocabulary of the children. They are taught that when one line is at right angles to another or crosses another line at right angles, then the two lines are said to be perpendicular to each other e.g. the trees stand 'perpendicular' to the ground, or when we sit, our back should be 'perpendicular' to our thighs etc. Fun Activity: Yoga formations can be used to demonstrate the different angles. A child stands in front of the class and holds two small flags in his/her hand. He/She moves his/her arms around and the children call out the name of the angle formed. The children can also be asked to write down the angle made by the hour hand and the minute hand, at any given time like 1 o’clock, 2 o’clock, and so on. Other similar questions can be asked. What angle is formed when the time is 12 o’clock? How many times during the day do the two hands form an angle of 0o. The two hands of the clock make an angle of 60° at 2 o’clock. At what other time (in whole hours) will the hands make an angle of 60°? Children study the formation of angles between the two hands as the minute hand moves from, say, 4 o’clock to 5 o’clock. Explain the concept of Geometrical Instruments as given on pages # 84, 85 and 86. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (6a) Q 1: Identify the following shapes: i. Set Square ii. Ruler iii. Compass iv. Divider Q 2: Ruler Q 3: Compass