CSS Primary Standard “Mathematics” 51 iv. 6 9 /25 ÷ 8 9 /19 Solution: 6 9 /25 ÷ 8 9 /19 => 159/25 x 19/161 => (159 x 19) / (25 x 161) 3021/4025 Q 3: Divide and write the answer in simple form: i. 15/16 x 3/8 ÷ 9/7 Solution: 15/16 x 3/8 ÷ 9/7 = 15/16 x 3/8 x 7/9 = (15 x 3 x 7) / (16 x 8 x 9) = 315/1152 = 105/384 = 35 / 128 ii. 12/15 x 5/25 ÷ 6/33 Solution: 12/15 x 5/25 ÷ 6/33 = 12/15 x 5/25 x 33/6 = 4/5 x 1/5 x 11/2 = (4 x 1 x 11) / (5 x 5 x 2) = 44/50 = 22/15 iii. 1 5 /13 x 619/17÷ 1 8 /11 Solution: 1 5 /13 x 619/17÷ 1 8 /11 = 18/13 x 121/17 ÷ 19/11 = 18/13 x 121/17 x 11/19 = (18 x 121 x 11) / (13 x 17 x 19) = 23958/4199 iv. 6 3 /17 x 55 /43 ÷ 35 /43 Solution: 6 3 /17 x 55 /43 ÷ 3 5 /43 = 105/17 x 220/43 ÷ 134/43 = 105/17 x 220/43 x 43/134 = 105/17 x 220/43 x 43/134 = (105 x 220 x 1)/(17 x 1 x 134) = 23100/2278 = 11550/1139 Week 1, 2, & 3 Fractions Lesson # 4 Learning outcomes: Students should be able to: ☻ To add and subtract two and more fractions with different denominators. ☻ To multiply a fraction by a number and demonstrate with the help of diagram. ☻ To multiply a fraction by another fraction. ☻ To multiply two or more fractions involving brackets (proper, improper and mixed fractions). ☻ To verify distributive laws. ☻ To solve real life problems involving multiplication of fractions. ☻ To divide a fraction by a number.
CSS Primary Standard “Mathematics” 52 ☻ To divide a fraction by another fraction (proper, improper and mixed). ☻ To solve real life problems involving division of fractions. ☻ To simplify expressions involving fraction using BODMAS rule. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: ☻ Use the explanation as given on pages # 41, 42 and 43 to use and apply the BODMAS rule. Exercise 3d Q 1: Simplify the following: i. ½ + 3/6 x 4/9 ÷ 6/5 – 10/13 Solution: ½ + 3/6 x 4/9 ÷ 6/5 – 10/13 = ½ + 3/6 x 4/9 x 5/6 – 10/13 = ½ + 1/2 x 4/9 x 5/6 – 10/13 = ½ + (1x4x5)/(2 x 9 x 6) – 10/13 = ½ + 20/108 – 10/13 = ½ + 10/54 – 10/13 = ½ + 5/27 – 10/13 = (27 + 10)/54 – 10/13 = 37/54 – 10/13 = 481- 540/702 = - 59/702 ii. 8 4 /15 ÷ (6/25 – 8/15 x 3/19) Solution: 8 4 /15 ÷ (6/25 – 8/15 x 3/19) = 124/15 ÷ (6/25 – 24/285) = 124/15 ÷ (6/25 – 8/95) = 124/15 ÷ (570 – 200/2375) = 124/15 ÷ (370 /2375) = 124/15÷ 74/475 = 124/15 x 475/74 = 58900/1110 = 5890/111 iii. ½ + {3/6 x [19 /18 – 6 3 /12 ÷ 4]}
CSS Primary Standard “Mathematics” 53 Solution: ½ + {3/6 x [19 /18 – 6 3 /12 ÷ 4]} = ½ + {3/6 x (19 /18 – 6 3 /12 ÷ 4)} = ½ + {3/6 x (27/18 – 75/12 ÷ 4)} = ½ + {3/6 x (27/18 – 75/12 x ¼)} = ½ + {3/6 x (27/18 – 75/48)} = ½ + {3/6 x (3/2 – 25/16)} = ½ + {3/6 x (24 - 25/16)} = ½ + {3/6 x (- 1/16)} = ½ + {-3/96} = ½ - 3/96 = 48 – 3 / 96 = 45/96 = 15/32 iv. 1 8 /9 + (23 /6 + 8/5 ÷ 8/10) Solution: 1 8 /9 + (23 /6 + 8/5 ÷ 8/10) = 1 8 /9 + (23 /6 + 8/5 ÷ 8/10) = 1 8 /9 + (23 /6 + 8/5 x 10/8) = 1 8 /9 + (15/6 + 8/5 x 10/8) = 1 8 /9 + (15/6 + 2) = 17/9 + (15 + 12)/6) = 17/9 + (9/2) = 17/9 + 9/2 = 34 + 81/18 = 115/18 v. 15/17 x [3/5 + {2/5 ÷ (11/2 x 31/6 – 1/15 x 6/13)}] Solution: 15/17 x [3/5 + {2/5 ÷ (11/2 x 31/6 – 1/15 x 6/13)}] = 15/17 x [3/5 + {2/5 ÷ (11 /2 x 31 /6 – 1/15 x 6/13)}] = 15/17 x [3/5 + {2/5 ÷ (11 /2 x 31 /6 – 2/65)}] = 15/17 x [3/5 + {2/5 ÷ (1/2 x 19/2 – 2/65)}] = 15/17 x [3/5 + {2/5 ÷ (19/4 – 2/65)}] = 15/17 x [3/5 + {2/5 ÷ (1235 - 8/260)}] = 15/17 x [3/5 + {2/5 ÷ 1227/260}] = 15/17 x [3/5 + 104/1227] = 15/17 x 4201/1227 = 63015/20859 vi. 1 1 /9 – [ 53 /4 x {32 /9 x 11 /2 ÷ (11 /2 + 11 /8 – 6)}]
CSS Primary Standard “Mathematics” 54 Solution: 1 1 /9 – [ 53 /4 x {32 /9 x 11 /2 ÷ (11 /2 + 11 /8 – 6)}] = 10/9 – [ 23/4 x {29/9 x 3/2 ÷ (3/2 + 9/8 – 6)}] = 10/9 – [ 23/4 x {29/9 x 3/2 ÷ (-27/8)}] = 10/9 – [ 23/4 x {29/9 x 3/2 ÷ (-27/8)}] = 10/9 – [ -6003/64] = 1244/81 vii. 6 1 /31 + [81 /3 x {51 /2 ÷ (1/2 + 11 /3 – 6 1 /5 ÷ 13/15)}] Solution: 6 1 /31 + [81 /3 x {51 /2 ÷ (1/2 + 11 /3 – 6 1 /5 ÷ 13/15)}] = 6 1 /31 + [81 /3 x {51 /2 ÷ (1/2 + 11 /3 – 6 1 /15 ÷ 13/15)}] = 187/31 + [25/3 x {11/2 ÷ (1/2 + 11 /3 – 91/15 ÷ 13/15)}] = 187/31 + [25/3 x {11/2 ÷ {1/2 + 4/3 – 91/5 x 15/13)}] = 187/31 + [25/3 x {11/2 ÷ {1/2 + 4/3 – 7 91/13}] = 187/31 + [25/3 x {11/2 ÷ -31/6}] = 187/31 + [25/3 x – 33/31] = 187 / 31 - 275/31 = -88 / 31 viii. 3 1 /4 + [42 /5 + {61 /12 x (1/5 + 11 /5 + 23 /25 ÷ 1/5)}] Solution: 3 1 /4 + [42 /5 + {61 /12 x (1/5 + 11 /5 + 23 /25 ÷ 1/5)}] = 13/4 + [22/5 + {73/12 x (1/5 + 6/5 + 53/25 x 5/1)}] = 13/4 + [22/5 + {73/12 x (1/5 + 6/5 + 53/5)}] = 13/4 + [22/5 + {73/12 x (60/5)}] = 13/4 + [22/5 + {73/12 x 60/5}] = 13/4 + [22/5 + 73/1] = 13/4 + [387/5] = 13/4 + 387/5 = 1613/20 ix. 8 3 /7 x [1/9 x {31 /2 ÷ (1/2 – 2/13 + 4/13)}] Solution: 8 3 /7 x [1/9 x {31 /2 ÷ (1/2 – 2/13 + 4/13)}] = 59/7 x [1/9 x {7/2 ÷ (1/2 – 2/13 + 4/13)}] = 59/7 x [1/9 x {7/2 ÷ (21/26 – 2/13)}] = 59/7 x [1/9 x {7/2 ÷ 17/26}] = 59/7 x [1/9 x {7/2 x 26/17}] = 59/7 x [1/9 x {91/17}] = 59/7 x [1/9 x 91/17] = 59/7 x [1/9 x 91/17]
CSS Primary Standard “Mathematics” 55 = 59/7 x 91/153 = 13 x 59 / 153 = 767/153 Review Exercise 3 Q 1: Choose the correct answer and fill the circle: 1. A fraction having numerator is less than the denominator is called .………... Proper Fraction Improper Fraction Mixed Fraction Rational Fraction 2. A fraction having denominator is greater than the numerator is called .………... Proper Fraction Improper Fraction Mixed Fraction Rational Fraction 3. Adding 1/3 and 2/3 gives: 2 1 3 4 4. Subtracting 2/3 and 1/3 gives: ½ 1/3 2/3 1 5. Multiplying 1/3 by 5 gives: 1/15 1 2 /3 2/15 8/15 5. Dividing 1/3 by 5 gives: 1 2 /3 1/15 2/15 8/15 7. In fraction expression we use……. operation first. addition subtraction multiplication division 8. 1/5 + 7/10: 9/13 19/11 9/11 9/10 9. 5/17 – 2/17: 3/17 2/17 4/17 1/17 Q 2: Add the following: i. 1 3 /8 + 11 /2 + 23 /11 Solution: 1 3 /8 + 11 /2 + 23 /11 = 11/8 + 3/2 + 25/11 = (121 + 132 + 200) / 88
CSS Primary Standard “Mathematics” 56 = 453/88 ii. 6 2 /17 + 815/17 + 89 /34 Solution: 6 2 /17 + 815/17 + 89 /34 = 104/17 + 151/17 + 281/34 = (208 + 302 + 281)/34 = 791/34 iii. 8 1 /3 + 81 /9 + 11 /9 Solution 8 1 /3 + 81 /9 + 11 /9 = 25/3 + 73/9 + 10/9 = (75 + 73 + 10)/ 9 = 158/9 iv. 6 1 /4 + 3 + 41 /2 Solution: 6 1 /4 + 3 + 41 /2 = 25/4 + 3/1 + 9/2 = (25 + 12 + 18) / 4 = 55/4 Q 3: Subtract the following: i. 9 9 /19 – 1 1 /8 Solution: 9 9 /19 – 1 1 /8 = 180/19 – 9/8 = (180 x 8) – (9 x 19)/152 = (1440 – 171)/ 152 = 1269 / 152 ii. 131 /40 – 1/15 Solution: 131 /40 – 1/15 = 521/40 – 1/15 = (7815 – 40) / 15 = 7775/600 = 1551/120 iii. 1 1 /2 – 6 1 /3 Solution: 1 1 /2 – 6 1 /3 = 3/2 – 19/3 = (9 – 38)/ 6
CSS Primary Standard “Mathematics” 57 = -29/6 iv. 8 8 /19 – 5 1 /19 Solution: 8 8 /19 – 5 1 /19 = 160/19 – 96/19 = (160 – 96) / 19 = 64 / 19 Q 4: Multiply the following: i. 6/19 x 25 Solution: 6/19 x 25 = (6 x 25)/ 19 = 150/19 ii. 5/8 x 1/9 Solution: 5/8 x 1/9 = (5 x 1) / (8 x 9) = 5/72 iii. 2 1 /3 x (51 /6 x 62 /9) Solution: 2 1 /3 x (51 /6 x 62 /9) = 7/3 x (31/6 x 56/9) = 7/3 x (31 x 56)/(6 x 9) = 7/3 x 868/27 = 6076 / 81 iv. 6 1 /6 x (51 /5 x 61 /3) Solution: 6 1 /6 x (51 /5 x 61 /3) = 37/6 x (26/5 x 19/3) = 37/6 x (494/15) = 37/6 x 494/ 15 = 18276/90 Q 5: Divide the following: i. 1 5 /8 ÷ 1/3 Solution: 1 5 /8 ÷ 1/3 = 13/8 ÷ 1/3 = 13/8 x 3 = 39/8 ii. 23/5 ÷ 2/5 Solution: 2 3 /5 ÷ 2/5
CSS Primary Standard “Mathematics” 58 = 13/5 ÷ 2/5 = 13/5 x 5/2 = 13/2 iii. 2 1 /3 ÷ (51 /5 ÷ 2/5) Solution: 2 1 /3 ÷ (51 /5 ÷ 2/5) = 7/3 ÷ (26/5 ÷ 2/5) = 7/3 ÷ (26/5 x 5/2) = 7/3 ÷ 13 = 7/3 x 1/13 = 7/39 iv. 41/6 x (23/8 ÷ 61/6) Solution: 4 1 /6 x (23 /8 ÷ 6 1 /6) = 25/6 x (19/8 ÷ 37/6) = 25/6 x (19/8 x 6/37) = 25/6 x 57/148 = 1425/888 = 475/296 Q 6: Solve the following: i. 9 3 /5 – { 11 /5 – (29 /11 x 1/3 ÷ 6)} Solution: 9 3 /5 – { 11 /5 – (29 /11 x 1/3 ÷ 6)} = 48/5 – {6/5 – (31/11 x 1/3 ÷ 6)} = 48/5 – {6/5 – (31/11 x 1/3 x 1/6)} = 48/5 – {6/5 – (31/198)} = 48/5 – 1033/990 = (9504 – 1033)/ 990 = 8471/990 ii. 3 1 /8 x [51 /6 – {1/5 x (61 /8 ÷ 4)}] Solution: 3 1 /8 x [51 /6 – {1/5 x (61 /8 ÷ 4)}] = 25/8 x [31/6 – {1/5 x (49/8÷ 4)}] = 25/8 x [31/6 – {1/5 x (49/8x 1/4)}] = 25/8 x [31/6 – 49/160] = 25/8 x [2480 – 147/480] = 25/8 x 2333/480 = 11665/768 Q 7: Solution:
CSS Primary Standard “Mathematics” 59 Zahid ate pizza on dinner time = 1 1 /2 = 3/2 His friend ate pizza = 2 1 /3 = 7/3 Pizza they eat together = 11/2 + 21/3 = 3/2 + 7/3 = (9 + 14)/6 = 23/6 Q 8: Solution: Zohaib ate cake = ¾ of cake Raffia ate cake = ¾ x ½ of cake Rafia ate = ¾ - 3/8 = 3/8 of cake Q 9: Solution: Alina ate pizza = 3/8 part of pizza Anoral ate pizza = ¼ part of pizza Alina ate more than Anoral = 3/8 – ¼ = 1/8 part more than Anoral pizza Q 10: Solution: Rida bought petrol = 2 1 /10 liters of petrol = 21/10 liters Namra bought petrol = 4 1 /5 liters of petrol = 21/5 liters a) How much petrol did they buy altogether = ? = 21/10 + 21/5 = 63/10 liters b) How much more petrol did Namra buy then Rida? = 21/5 – 21/10 = 21/10 liters Week 4 & 5 Decimals and Percentages Lesson # 1 Teaching Objectives: ☻ To introduce like and unlike decimals. ☻ To add and subtract decimals. ☻ To introduce multiplication of decimals. ☻ To introduce division of decimals. ☻ To apply BODMAS rules to decimals. ☻ To convert fractions to decimals and vice versa. ☻ To practice rounding off to a given decimal place.
CSS Primary Standard “Mathematics” 60 ☻ To introduce percentage as a special type of fraction. Learning outcomes: Students should be able to: ☻ To add and subtract decimals. ☻ To recognize like and unlike decimals. ☻ To multiply decimals by 10, 100 and 1000. ☻ To divide decimals by 10, 100 and 1000. ☻ To multiply a decimal with a whole number. ☻ To divide a decimal with a whole number. ☻ To multiply a decimal by tenth and hundredths only. ☻ To multiply a decimal by a decimal. ☻ To divide a decimal by a decimal. ☻ To use division to change fraction into decimal. ☻ To simplify decimal expressions involving brackets. ☻ To round off decimal up to specified number of decimal places. ☻ To convert fractions to decimal and vice versa. ☻ To solve real life problems involving decimal. ☻ To recognize percentage as a special kind of fraction. ☻ To convert percentage to fraction and to decimal and vice versa. ☻ To solve real life problems involving percentages. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: ☻ Use the explanation as given on pages # 48, 49 and 50 to understand the concept of Addition and Subtraction of decimals. ☻ Use the explanation as given on pages # 51 to understand the concept of Like and Unlike decimals. ☻ Use the explanation as given on pages # 51 to understand multiplication and division of decimals by 10, 100 and 100. ☻ Use the explanation as given on pages # 53 to understand multiplication and division by a whole number. ☻ Use the explanation as given on pages # 54 to understand division of decimal with a whole number. ☻ Use the explanation as given on pages # 55 to understand multiplication of decimal by tenths and hundredths and by a decimal with three decimal places. ☻ Use the explanation as given on pages # 55 to understand the division of decimal by a
CSS Primary Standard “Mathematics” 61 decimal. ☻ Use the explanation as given on pages # 56 to understand the division of decimal by a decimal using direct division by moving decimal positions. ☻ Use the explanation as given on pages # 56 to understand to change fraction into decimal using division. ☻ Use the explanation as given on pages # 57 to understand the simplification of decimal expressions involving brackets. ☻ Use the explanation as given on pages # 57 to understand the rounding of decimals. Exercise 4a Q 1: Solve: i. T h H T O T H T h ii . T h H T O T H T h ii i. T h H T O T H T h 1 3 . 2 1 8 8 1 . 9 2 4 6 2 8 4 . 5 9 4 + 5 8 . 4 3 + 4 2 8 . 0 5 3 + 8 5 6 . 3 2 4 7 1 . 6 4 1 3 0 9 . 9 7 7 7 1 4 0 . 9 1 8 iv . T h H T O T H T h v . T h H T O T H T h T h H T O T H T h 3 1 . 2 8 1 2 1 . 3 8 9 4 6 1 . 3 1 4 2 1 . 6 2 0 + 8 4 1 . 2 4 0 + 4 1 1 . 1 4 2 1 3 3 3 . 8 3 0 9 5 4 1 5 1 Q 2: Solve: i. Th H T O T H Th ii. Th H T O T H Th 13 11 5 17 14 2 3 9 . 2 4 1 2 9 4 . 6 8 4 - 1 1 2 . 1 6 2 - 1 3 2 . 1 8 9 1 2 7 . 0 4 9 1 6 2 . 4 9 5 iv. Th H T O T H Th v. Th H T O T H Th 7 12 16 2 10 18 3 11 4 8 3 . 6 9 2 3 1 8 . 1 4 1 - 1 2 4 . 8 4 1 - 2 4 9 . 1 1 2 3 5 8 . 8 5 1 0 6 9 . 0 2 9 v. Th H T O T H Th
CSS Primary Standard “Mathematics” 62 3 10 17 12 8 11 4 4 1 8 . 2 9 1 3 4 9 . 6 2 8 4 0 6 8 . 6 6 3 Q 3: Identify the like and unlike decimals: i. 3.14, 18.34 Like Decimals ii. 432. 691, 841.214 Unlike Decimals iii. 214.313, 24.9845 Like Decimals iv. 0.521, 31.849 Like Decimals v. 418.003, 1.321 Like Decimals vi. 14.151, 321. 84 Unlike Decimals Q 4: Multiply the following by 10, 100 and 1000. i. 3.142 Step 1: 3.142 x 10 = 31.42 Step 2: 3.142 x 100 = 314.2 Step 1: 3.142 x 1000 = 3142 ii. 12.4168 Step 1: 12.4168 x 10 = 124.168 Step 2: 12.4168 x 100 = 1241.68 Step 1: 12.4168 x 1000 = 12416.8 iii. 0.59864 Step 1: 0.59864 x 10 = 5.9864 Step 2: 0.59864 x 100 = 59.864 Step 1: 0.59864 x 1000 = 598.64 iv. 1.8942 Step 1: 1.8942 x 10 = 18.942 Step 2: 1.8942 x 100 = 189.42 Step 1: 1.8942 x 1000 = 1894.2 v. 16.4923 Step 1: 16.4923 x 10 = 164.923 Step 2: 16.4923 x 100 = 1649.23 Step 1: 16.4923 x 1000 = 16492.3 vi. 13.48419 Step 1: 13.48419 x 10 = 134.8419 Step 2: 13.48419 x 100 = 1348.419 Step 1: 13.48419 x 1000 = 13484.19 Q 5: Divide the following by 10, 100 and 1000. i. 942.684
CSS Primary Standard “Mathematics” 63 Step 1: 942.684 ÷ 10 = 94.2684 Step 2: 942.684 ÷ 100 = 9.42684 Step 1: 942.684 ÷ 1000 = 0.942684 ii. 1214.16 Step 1: 1214.16 ÷ 10 = 121.416 Step 2: 1214.16 ÷ 100 = 12.1416 Step 1: 1214.16 ÷ 1000 = 1.21416 iii. 141.161 Step 1: 141.161 ÷ 10 = 14.1161 Step 2: 141.161 ÷ 100 = 1.41161 Step 1: 141.161 ÷ 1000 = 0.141161 iv. 4884.428 Step 1: 4884.428 ÷ 10 = 488.4428 Step 2: 4884.428 ÷ 100 = 48.84428 Step 1: 4884.428 ÷ 1000 = 4.884428 v. 29.384 Step 1: 29.384 ÷ 10 = 2.9384 Step 2: 29.384 ÷ 100 = 0.29384 Step 1: 29.384 ÷ 1000 = 0.029384 vi. 0.008 Step 1: 0.008 ÷ 10 = 0.0008 Step 2: 0.008 ÷ 100 = 0.00008 Step 1: 0.008 ÷ 1000 = 0.000008 Q 6: Multiply the following: i. 14.62 x 5 ii. 481, 382 x 100 2 3 1 1 4 2 1 4 . 6 2 3 2 9 . 4 x 5 2 . 5 7 3 1 0 1 6 4 7 0 Put decimal after two place. 6 5 8 8 0 7 3 . 1 0 7 2 3 5 0 Put decimal after 2 places. Q 7: Divide the following: i. 132.16 ÷ 2 Solution: 132.16 ÷ 2 = 132.16 x ½ = 13216/100 x ½ = 13216/200 = 6608/100 = 66.08
CSS Primary Standard “Mathematics” 64 ii. 241.2192 ÷ 2 Solution: 241.2192 ÷ 1.2 = 2412192/10000 ÷ 12/10 = 2412192/10000 x 10/12 = 24121920/120000 = 2412192/12000 = 1206096/6000 = 603048/3000 = 301524/1500 = 150762/750 = 75381/375 = 201.016 iii. 791.0724÷ 3.66 Solution: 791.0724÷ 3.66 = 791.0724÷ 3.66 = 7910724/10000 ÷ 366/100 = 7910724/10000 x 100/366 = 7910724 x 100 / 10000 x 366 = 791072400/3660000 = 7910724/36600 = 3955362/18300 = 1977681/9150 = 216.14 iv. 790.77÷ 6.13 Solution: 790.77÷ 6.13 = 790.77÷ 6.13 = 79077/100 ÷ 613/100 = 79077/100 x 100/613 = 79077/613 = 129 v. 448.7496÷ 1.52 Solution: 448.7496÷ 1.52 = 448.7496÷ 1.52 = 4487496/10000 ÷ 152/100 = 4487496/10000 x 100/152 = 448749600/15200000 = 4487496/15200 = 2243748/7600 = 112187/3800 = 295.23 vi 1708.448 ÷ 2.9 Solution: 1708.448 ÷ 2.9 = 1708.448 ÷ 2.9
CSS Primary Standard “Mathematics” 65 = 1708448/1000÷ 29/10 = 1708448 x 10/29 x 1000 = 17084480/29000 = 1708448/2900 = 589.12 Q 8: Convert the following fractions as decimals, and classify them as terminating or nonterminating decimals: i. 1 5 /8 = 13/8 = 1.625 (terminating) ii. 1/3 = 0.3333… = 0.3333.. (non-terminating) iii. 2/5 = 0.4 = 0.4 (Terminating) iv. 14/15 = 0.9333.. = 0.9333.. (non-terminating) v. 151/9 = 136/9 = 15.111.. (non-terminating) Q 9: Simplify the following: i. 5.8 + (6.2 – 15.13) Solution: 5.8 + (6.2 – 15.13) = 5.8 + (6.2 – 15.13) = 5.8 + (-8.93) = 5.8 – 8.93 = - 3.13 ii. 14.8 – (3.9 + 8.16 – 14.3) Solution: 14.8 – (3.9 + 8.16 – 14.3) = 14.8 – (3.9 + 8.16 – 14.3) = 14.8 – (12.06 – 14.3) = 14.8 – (-2.24) = 17.04 iii. 13.25 x {2.12 + (18.6 – 9.2 ÷ 3.2)} Solution: 13.25 x {2.12 + (18.6 – 9.2 ÷ 3.2)} = 13.25 x {2.12 + (18.6 – 9.2 ÷ 3.2)} = 13.25 x {2.12 + (18.6 – 9.2 x 1/3.2)} = 13.25 x {2.12 + (18.6 – 2.875)} = 13.25 x {2.12 + (15.725)} = 13.25 x {17.845} = 13.25 x 17.845 = 236.44 iv. 14.10 ÷ [2.58 x {13.13 + (14.169 – 24.12)}] Solution: 14.10 ÷ [2.58 x {13.13 + (14.169 – 24.12)}] = 14.10 ÷ [2.58 x {13.13 + (14.169 – 24.12)}] = 14.10 ÷ [2.58 x {13.13 – 9.951}] = 14.10 ÷ [2.58 x 3.179]
CSS Primary Standard “Mathematics” 66 = 14.10 ÷ 8.20182 = 1.71913 v. 28.63 + [3.14 – {12.56 + (184.93 – 162.13)}] Solution: 28.63 + [3.14 – {12.56 + (184.93 – 162.13)}] = 28.63 + [3.14 – {12.56 + (184.93 – 162.13)}] = 28.63 + [3.14 – {12.56 +22.8}] = 28.63 – 32.22 = -3.59 Q 10: Change the following fractions into decimals if required then round off the decimal to the whole number, 1 decimal place, 2 decimal places and 3 decimal places: i. 5/18 Solution: 5/18 = 0.27 0.3 0.28 0.278 ii. 135 /19 Solution: 135 /19 = 252/19 = 13.25315 13.3 13.26 13.263 iii. 8.5694321 Solution: 8.5694321 = 8.6 8.57 8.569 iv. 13.41050213 Solution: 13.41050213 13.4 13.41 13.410 Q 11: The difference of two number = 214.386 First number = 184.692 Second Number = ? Second Number = Difference of two numbers + First Number Second Number = 214.386 + 184.692 = 399.078 Q 12: Cost of an egg = Rs. 9.75 Cost of half dozen (6) eggs = ? = 9.75 x 6 = Rs. 58.5 Q 13: Mass of Marble tile = 6.08 kg Mass of Granite tile = 3.58 kg Mass of 525 marble tile = 525 x 6.08 = 3192 kgs Mass of 52 Granite tile = 52 x 3.58 = 186.16 kgs Total Mass of tiles = 3192 + 186.16
CSS Primary Standard “Mathematics” 67 = 3378.16 kgs Week 4 & 5 Decimals and Percentages Lesson # 2 Teaching Objectives: ☻ To introduce like and unlike decimals. ☻ To add and subtract decimals. ☻ To introduce multiplication of decimals. ☻ To introduce division of decimals. ☻ To apply BODMAS rules to decimals. ☻ To convert fractions to decimals and vice versa. ☻ To practice rounding off to a given decimal place. ☻ To introduce percentage as a special type of fraction. Learning outcomes: Students should be able to: ☻ To add and subtract decimals. ☻ To recognize like and unlike decimals. ☻ To multiply decimals by 10, 100 and 1000. ☻ To divide decimals by 10, 100 and 1000. ☻ To multiply a decimal with a whole number. ☻ To divide a decimal with a whole number. ☻ To multiply a decimal by tenth and hundredths only. ☻ To multiply a decimal by a decimal. ☻ To divide a decimal by a decimal. ☻ To use division to change fraction into decimal. ☻ To simplify decimal expressions involving brackets. ☻ To round off decimal up to specified number of decimal places. ☻ To convert fractions to decimal and vice versa. ☻ To solve real life problems involving decimal. ☻ To recognize percentage as a special kind of fraction. ☻ To convert percentage to fraction and to decimal and vice versa. ☻ To solve real life problems involving percentages. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser.
CSS Primary Standard “Mathematics” 68 Classroom Activity: ☻ Use the explanation as given on pages # 62, 63 to understand the concept of Conversion of fraction to percentage and Conversion of percentage to fraction and decimal. Exercise 4b Q 1: Shade the part of the figure according to the given factors: Q 2: Convert the following fractions into percentages: i. 13/100 = 13% ii. 17/50 Solution: 17/50 = 17 x 2/50 x 2 = 34/100 = 34 % iii. 2 9 /10 Solution: = 29/10 = 29 x 10/10 x 10 = 290/100 = 290 % iv. 9/300 Solution: 9/300 (Divide and multiply by 3) = 3/100 = 3% Express each of the following as a fraction in the simplest form: i. 15 % = 15/100 = 3/2 ii. 75 = 75/100 = ¾ iii. 35 % = 35/100 = 7/10 iv. 3.5 % = 35/1000 = 7/200 Q 4: Total balls = 50 balls Red balls = 20 Green balls = 10 Black balls = 20 Percentage of red balls = 20/50 = 40 % Percentage of green balls = 10/50 = 20 % Percentage of black balls = 20/50 = 40 % Q 5: Total number of fruits in the basket = 25 Total bananas = 10 Total Apples = 15 Percentage of Apples = 15/25 = 60 % Percentage of Bananas = 10/25 = 40 %
CSS Primary Standard “Mathematics” 69 Q 6: The actual price of the dress = Rs. 2500 Discount offered = 25 % = 25/100 = ¼ Amount of discount = 2500 x ¼ = 625 The amount Nasreen pay for = 2500 – 625 = 1875 Q 7: Total strength in class-5 is = 75 students Absent students = 10 Students who were present = 75 – 10 = 65 % of students who were present = 65/75 x 100 = 86.67 % % of students who were absent = 10/75 x 100 = 13.33 % Review Exercise 4 Q 1: Choose the correct answer and fill the circle: 1. If decimal have different number of digits to the right of the decimal point is called .………... unlike decimal like decimal fractional decimal none of these 1. If decimal have same number of digits to the right of the decimal point is called .………... unlike decimal like decimal fractional decimal none of these 3. 4.5 x 10 is: 0.45 45 450 4500 4. 4.5 x 100 is: 0.45 450 45 4500 5. Percentage is a special kind of ………..fraction: common rational proper improper 6. 10% of 100 is: 30 10 20 100 7. The division of decimal by 1000 displaces the decimal point from its original position. two place to right two place to left three place to right three place to left 8. The multiplication of decimal by 1000 displaces the decimal point from its original position. two place to right two place to left
CSS Primary Standard “Mathematics” 70 three place to left three place to right 9. 4.5 ÷ 1000 : 0.0045 0.45 0.00045 0.045 Q 2: Solve 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 T h . 5 2 3 4 9 . 6 8 2 5 6 8 9 . 3 2 4 + 3 . 2 1 + 2 . 5 9 6 + 8 4 9 . 3 2 4 3 . 7 3 8 4 . 3 2 1 . 5 8 4 3 6 . 5 9 9 6 5 3 9 . 2 2 8 i. Th H T O T H Th ii. Th H T O T H Th 1 16 8 11 0 14 7 10 15 2 6 9 . 1 4 8 1 4 3 8 . 1 5 - 1 8 0 . 9 2 4 - 5 1 2 . 3 9 0 8 8 . 2 2 4 9 2 5 . 7 6 iv. Th H T O T H Th v. Th H T O T H Th 2 12 3 11 3 12 2 10 18 3 11 3 2 4 . 1 4 2 3 1 8 . 1 4 1 - 4 3 . 9 2 4 - 2 4 9 . 1 1 2 2 8 0 . 2 1 8 0 6 9 . 0 2 9 Q 3: Solve the following: i. 3.624 x 100 => 362.4 ii. 0.8943 x 10 => 8.943 iii. 15.138 ÷ 100 => 0.15138 iv. 128.53 x 3.27 => 420.2931 v. 344.543 ÷ 0.42 => 820.340 vi. 42.843 ÷ 3.42 => 12. 527 Q 4: Convert the following fractions into decimals and classify them as terminating or nonterminating decimals. i. 1 2 /5 = 7/5 = 1.4 (terminating) ii. 3 1 /8 = 25/8 = 3.33333..(non-terminating) iii. 1425/8 = 1141/8 = 142. 625 (terminating) iv. 102/103 = 0.99029… (non-terminating) Q 5: Solve the following: i. 3.5 + [62.52 – {2.5 + (2.92 x 5.6)}] Solution: 3.5 + [62.52 – {2.5 + (2.92 x 5.6)}]
CSS Primary Standard “Mathematics” 71 = 3.5 + [62.52 – {2.5 + (2.92 x 5.6)}] = 3.5 + [62.52 – {2.5 + 16.35}] = 3.5 + [62.52 –18.852] = 3.5 + 43.66 = 47.168 ii. 18.3 x [23.14 + {8.6 – (9.6 ÷ 3.2)}] Solution: 18.3 x [23.14 + {8.6 – (9.6 ÷ 3.2)}] = 18.3 x [23.14 + {8.6 – (9.6 ÷ 3.2)}] = 18.3 x [23.14 + {8.6 – (9.6 x 1/3.2)}] = 18.3 x [23.14 + {8.6 – 3}] = 18.3 x [23.14 + 5.6] = 18.3 x 28.74 = 525.942 Q 6: Convert the following fractions into decimal and round it off to a) 1 decimal place b) 2 decimal places c) 3 decimal places i. 3/5 => = 0.6 = 0.60 = 0.600 ii. 89/13 => 113/13 = 8.7 = 8.69 = 8.692 iii. 8.9825 = 9 = 9.0 = 8.983 iv. 38.59214 = 38.6 = 38.59 = 38.592 Q 7: Express each of the following into the fractions in simplest form: i. 35 % => 35/100 => 7/20 ii. 8.4 % => 8.4/100 => 21/250 iii. 15% => 15/100 => 3/20 iv. 0.5 % => 0.5/100 => 1/200 Q 8: Total length of the wire = 35.55 meters Cut into 5 equal parts = 35.55 x 1/5 => 7.11 meters Price of each part of wire = Rs. 12.68 Cost of wire = 12.68 x 5 => Rs. 63.4 Q 9: Total people living in the village = 4000 % of women = 36 % % of children = 18 % Number of women = 4000 x 36/100 = 1440 Number of children = 4000 x 18/100 = 720
CSS Primary Standard “Mathematics” 72 Number of men = 4000 – 1440 – 720 = 1840 Percentage of men in village = 1840/4000 x 100 = 46 % Men are the highest number from all people. Week 6 Monthly Test / Revision of Unit # 3 & 4 Week 7, 8, 9 & 10 Distance, Time and Temperature Lesson # 1 Teaching Objectives: ☻ To explain conversion from one unit of length to another. ☻ To practice conversion between units of time. ☻ To introduce smaller and larger units of length and time. ☻ To add and subtract by converting unlike units to like units. ☻ To introduce measurement of temperature. ☻ To introduce the Fahrenheit and Celsius temperature scales. ☻ To explain conversion between the Fahrenheit and Celsius temperature scales. Learning outcomes: Students should be able to: ☻ To convert measures given in kilometers to meters. ☻ To convert measures given in meters to centimeters. ☻ To convert measures given in centimeters to millimeters and vice versa. ☻ Apply the correct units of measurement. ☻ Convert from one unit to another. ☻ Apply conversion of units to real-life problems. ☻ Use the units of temperature and inter-convert them correctly. ☻ Add and subtract measure of distance. ☻ Solve real life problems involving conversion, addition and subtraction of units of distance. ☻ Convert hours to minutes, minutes to seconds and vice versa. ☻ Add and subtract units of time with carrying borrowing. ☻ Convert years to months, months to days, weeks to days and vice versa. ☻ Solve real life problems involving conversion, addition and subtraction of unit of time. ☻ Recognize units of temperature in Fahrenheit and Celsius. ☻ Solve real life problems involving conversion, addition and subtraction of units of
CSS Primary Standard “Mathematics” 73 temperature. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: ☻ The concepts of length and time have already been introduced in the earlier books. In this book the ideas are revisited and the students are introduced to the units of temperature. Choosing the right unit of measuring a particular object has already been dealt with in the earlier books and by now the students are ready to convert a given measurement to a suitable unit. ☻ Begin the lesson by revising the various units of length as an oral activity. Recall the prefixes for the various units of the length commonly used, and what they represent. ☻ The commonly used measurements of length (weight and mass) are: millimeters, milligrams, milliliters, centimeters, grams, liters, meters, , kiloliters and kilometers. ☻ A millimeter (mm) is used for measurement of small lengths, such as thickness of the soft cover of a book. It is a tiny measurement. ☻ 1 centimeter = 10 millimeter. ☻ A centimeter (cm) is used for measurements of thickness 10 times that of 1 mm, e.g. the thickness of an eraser or the width of a nail on your hand. Centimeters are used to measure the width of a table or the thickness of a door. ☻ 1 meter = 100 centimeters. ☻ A meter used to measure lengths 100 times that of 1, e.g. the height of the roof, the width of a floor. ☻ 1 kilometer = 1000 meters. ☻ A kilometer (kilo) means „thousand‟ and is used to measure lengths 1000 times that of 1 km, e.g. the distance between 2 cities, the distance that a car travels in an hour. ☻ Do plenty of oral work in class as revision. ☻ Keep the figures simple so that the students can focus on the conversion. ☻ Ask questions like: o How many Km are there in 10 km? o Convert 13 mm into cm? o How many m in 45 cm? o How many cm in 4 m? o How many m in 0.2 km? ☻ Since the measurement of length uses the metric (or decimal) system, all calculations should be easy for the students. Ask them to calculate the conversions mentally and differentiate the problems that require multiplication from those that require division.
CSS Primary Standard “Mathematics” 74 Once the students are confident with conversions, move on to the number operations with measurements in different units of length. ☻ Explain them the method to convert one unit of length into other smaller or bigger unit of length. ☻ Explain them the way to Add or Subtract measure of distance as explained on pages # 70 and 71. Exercise 5a Q 1: Write the following measures: i. 32 km = 32000 meters ii. 1.84 meters = 0.00184 kms iii. 14.6 cms = 0.000146 kms iv. 294 mm = 29.4 cm v. 12 cm = 120 mm vi. 12.984 mm = 0.000012984 kms Q 2: i. Add 3 km, 315 m to 8 km, 212 m i. kms m cm mm H T O H T O T O O 3 3 1 5 8 2 1 2 1 1 5 2 7 11 kms and 527 meters. ii. Add 3 km, 315 m to 8 km, 212 m i. Kms m cm mm H T O H T O T O O 1 9 1 3 1 2 1 9 1 4 2 4 5 4 1 6 5 5 8 6 65 kms and 586 meters.
CSS Primary Standard “Mathematics” 75 iii. Add, 115 m, 35 cm and 214 m, 94 cm and 5 m, 16cm i. Kms m cm mm H T O H T O T O O 1 1 5 3 5 2 1 4 9 4 5 1 6 3 3 5 4 5 335 meters and 45 cms. iv. Add, 115 m, 35 cm and 214 m, 94 cm and 5 m, 16cm i. Kms m cm mm H T O H T O T O O 2 1 8 5 8 1 1 5 1 4 3 2 4 0 9 6 5 7 8 1 657 meters and 81 cms. iv. Add, 113 m, 14 cm, 4mm and 29 m, 54 cm, 3mm. i. Kms m cm mm H T O H T O T O O 1 1 3 1 4 4 2 9 5 4 3 1 4 2 6 8 7 142 meters and 68 cms and 7 mm. Q 3: i. Subtract 16km, 102 m from 92 km, 215 m. i. Kms m cm mm H T O H T O T O O 8 12 9 2 2 1 5 1 6 1 0 2 7 6 1 1 3 76 kilometers and 113 meters.
CSS Primary Standard “Mathematics” 76 ii. Subtract 13m, 84 cm 9mm from 29m,21 cm, 6mm. i. Kms m cm mm H T O H T O T O O 8 11 10 16 2 9 2 1 6 1 3 8 4 9 1 5 3 6 7 15 meters, 36 centimeters and 7 mm. iii. Subtract 14 cm 5mm from 29cm, 6mm. i. Kms m cm mm H T O H T O T O O 2 9 6 1 4 5 1 5 1 15 cms, 1mms. iv. Subtract 94m, 85 cm from 185m, 39cm. i. Kms m cm mm H T O H T O T O O 0 18 4 13 1 8 5 3 9 9 4 8 5 9 0 5 4 90 meters, 54 cms. v. Subtract 26km, 841m, 94 cm from 94 km, 329m, 41 cm. i. Kms m cm mm H T O H T O T O O 8 13 12 12 8 13 11 9 4 3 2 9 4 1 2 6 8 4 1 9 4 6 7 4 8 7 4 7 67 kms, 487 meters, 47 cms. Q 4: Zoya covered by bus = 38 kms, 586 m Zoya covered by car = 82 kms, 324 m Kms m H T O H T O 3 8 5 8 6 8 2 3 2 4 1 2 0 9 1 0
CSS Primary Standard “Mathematics” 77 120 kilometers and 910 meters. Q 5: Length of the swimming pool = 340 meters 5 cms Width of the swimming pool = 200 meters 15 cms Total Length of the swimming pool = m cm H T O H T O 3 4 0 5 2 0 0 1 5 5 4 0 2 0 Difference between length and width = m cm H T O H T O 3 9 10 3 4 0 0 5 2 0 0 1 5 1 3 9 9 0 Week 7, 8, 9 & 10 Distance, Time and Temperature Lesson # 2 Teaching Objectives: ☻ To explain conversion from one unit of length to another. ☻ To practice conversion between units of time. ☻ To introduce smaller and larger units of length and time. ☻ To add and subtract by converting unlike units to like units. ☻ To introduce measurement of temperature. ☻ To introduce the Fahrenheit and Celsius temperature scales. ☻ To explain conversion between the Fahrenheit and Celsius temperature scales. Learning outcomes: Students should be able to: ☻ To convert measures given in kilometers to meters. ☻ To convert measures given in meters to centimeters. ☻ To convert measures given in centimeters to millimeters and vice versa. ☻ Apply the correct units of measurement. ☻ Convert from one unit to another. ☻ Apply conversion of units to real-life problems. ☻ Use the units of temperature and inter-convert them correctly.
CSS Primary Standard “Mathematics” 78 ☻ Add and subtract measure of distance. ☻ Solve real life problems involving conversion, addition and subtraction of units of distance. ☻ Convert hours to minutes, minutes to seconds and vice versa. ☻ Add and subtract units of time with carrying borrowing. ☻ Convert years to months, months to days, weeks to days and vice versa. ☻ Solve real life problems involving conversion, addition and subtraction of unit of time. ☻ Recognize units of temperature in Fahrenheit and Celsius. ☻ Solve real life problems involving conversion, addition and subtraction of units of temperature. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: ☻ Explain the page # 72, 73, 74, 75 and 76 to the students as described in the book. Exercise 5b Q 1: Convert the following: i. 1 hour = 60 minutes = 3600 seconds ii. 10 hours 36 minutes = 636 minutes = 38160 seconds iii. 13 hours 20 minutes 12 sec = 48012 seconds iv. 360 minutes = 6 hours v. 120 seconds = 2 minutes = 1/30 hour vi. 9152 seconds = 1528 /15 minutes = 2 122/225 hours Q 2: Convert the following: i. 4 years = 48 months ii. 1 months = 450 days iii. 64 week 2 days = 450 days iv. 94 days = 13 week, 3 days v. 3843 days = 128 months, 3 days vi. 391 months = 32 years, 7 mon
CSS Primary Standard “Mathematics” 79 Q 3: i. Add 3 hours, 12 minutes, 16 seconds and 3 hours, 12 minutes, 16 seconds. Hours Minutes Seconds T O T O T O 3 1 2 1 6 3 1 2 1 6 4 2 4 3 2 4 hours, 24 minutes, 32 seconds. ii. Add 0 hours, 24 minutes, 19 seconds and 2 hours, 13 minutes, 43 seconds and 1 hour, 14 minutes, 16 seconds. Hours Minutes Seconds T O T O T O 0 2 4 1 9 2 1 3 4 3 1 1 4 1 6 3 5 2 1 8 3 hours, 52 minutes, 18 seconds. iii. Add 38 hours, 24 minutes, 19 seconds and 16 hours, 49 minutes, 38 seconds. Hours Minutes Seconds T O T O T O 3 8 2 4 1 9 1 6 4 9 3 8 5 5 1 3 5 7 55 hours, 13 minutes, 57 seconds. iv. Add 1 hours, 58 minutes, 13 seconds and 0 hours, 24 minutes, 16 seconds and 3 hour, 19 minutes, 14 seconds. Hours Minutes Seconds T O T O T O 1 5 8 1 3 0 2 4 1 6 3 1 9 1 4 5 4 1 4 3 5 hours, 41 minutes, 43 seconds.
CSS Primary Standard “Mathematics” 80 Q 4: i. Subtract 2 hours, 11 minutes, 5 seconds from 12 hours, 43 minutes, 16 seconds. Hours Minutes Seconds T O T O T O 1 2 4 3 1 6 2 1 1 0 5 1 0 3 2 1 1 10 hours, 32 minutes, 11 seconds. ii. Subtract 8 hours, 48 minutes, 34 seconds from 19 hours, 39 minutes, 13 seconds. Hours Minutes Seconds T O T O T O 8 9 8 6 13 1 9 3 9 1 3 8 4 8 3 4 1 0 5 0 3 9 10 hours, 50 minutes, 39 seconds. iii. Subtract 5 hours, 34 minutes, 12 seconds from 14 hours, 15 minutes, 18 seconds. Hours Minutes Seconds T O T O T O 0 13 7 1 4 1 5 1 8 5 3 4 1 2 0 8 4 1 0 6 8 hours, 41 minutes, 06 seconds. iv. Subtract 59 minutes, 16 seconds from 1 hour, 53 minutes, 18 seconds. Hours Minutes Seconds T O T O T O 0 10 13 1 5 3 1 8 0 5 9 1 6 0 0 5 4 0 2 54 minutes, 02 seconds. Q 5: Alina drove the car for = 3 hours, 35 minutes and 17 seconds. Alina‟s brother drove the car = 2 hours, 20 minutes, 10 seconds a) How much time they spend altogether = Hours Minutes Seconds T O T O T O 3 3 5 1 7 2 2 0 1 0
CSS Primary Standard “Mathematics” 81 5 5 5 2 7 5 hours, 55 minutes, 27 seconds. b) How much more time Alina drove more than her brother = Hours Minutes Seconds T O T O T O 3 3 5 1 7 2 2 0 1 0 1 1 5 0 7 1 hours, 15 minutes, 07 seconds. Q 6: The age of Waqar is = 26 years and 5 months. Age of Waqar in days = (26 x 365) + (5 x 30) = 9490 + 150 = 9640 days Age of Waqar in seconds = (26 x 365) + (5 x 30) = 9490 + 150 = 9640 days = (9640 x 24 x 60 x 60) = 832, 896, 000 seconds. Week 7, 8, 9 & 10 Distance, Time and Temperature Lesson # 3 Teaching Objectives: ☻ To explain conversion from one unit of length to another. ☻ To practice conversion between units of time. ☻ To introduce smaller and larger units of length and time. ☻ To add and subtract by converting unlike units to like units. ☻ To introduce measurement of temperature. ☻ To introduce the Fahrenheit and Celsius temperature scales. ☻ To explain conversion between the Fahrenheit and Celsius temperature scales. Learning outcomes: Students should be able to: ☻ To convert measures given in kilometers to meters. ☻ To convert measures given in meters to centimeters. ☻ To convert measures given in centimeters to millimeters and vice versa. ☻ Apply the correct units of measurement. ☻ Convert from one unit to another.
CSS Primary Standard “Mathematics” 82 ☻ Apply conversion of units to real-life problems. ☻ Use the units of temperature and inter-convert them correctly. ☻ Add and subtract measure of distance. ☻ Solve real life problems involving conversion, addition and subtraction of units of distance. ☻ Convert hours to minutes, minutes to seconds and vice versa. ☻ Add and subtract units of time with carrying borrowing. ☻ Convert years to months, months to days, weeks to days and vice versa. ☻ Solve real life problems involving conversion, addition and subtraction of unit of time. ☻ Recognize units of temperature in Fahrenheit and Celsius. ☻ Solve real life problems involving conversion, addition and subtraction of units of temperature. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: ☻ Explain the page # 78, 79, 80 and 81 to the students as described in the book. Exercise 5c Q 1: Convert the following from Fahrenheit to Celsius: i. -12oF Solution: Use the formula to convert Fahrenheit to Celsius = oC = 5/9(o F – 32) = 5/9 (-12 – 32) = 5/9(-44) = -24.44 oC ii. 100oF Solution: Use the formula to convert Fahrenheit to Celsius = oC = 5/9(o F – 32) = 5/9 (100 – 32) = 5/9(68) = 37.77 oC iii. -35 oF Solution: Use the formula to convert Fahrenheit to Celsius = oC = 5/9(o F – 32) = 5/9 (-35 – 32)= 5/9(-67) = - 37.22 oC iv. 64 oF Solution: Use the formula to convert Fahrenheit to Celsius = oC = 5/9(o F – 32) = 5/9 (64 – 32) = 5/9(32) = 17.78 oC
CSS Primary Standard “Mathematics” 83 v. 48 oF Solution: Use the formula to convert Fahrenheit to Celsius = oC = 5/9(o F – 32) = 5/9 (48 – 32) = 5/9(16) = 8.88 oC Q 1: Convert the following from Celsius to Fahrenheit: i. 0 oC Solution: Use the formula to convert Fahrenheit to Celsius = o F = (9/5x oC) + 32 = 9/5 x 0 + 32 = 32o F ii. 100oC Solution: Use the formula to convert Fahrenheit to Celsius = o F = (9/5x oC) + 32 = 9/5 x 100 + 32 = 212o F iii. -38oC Solution: Use the formula to convert Fahrenheit to Celsius = o F = (9/5x oC) + 32 = 9/5 x (-38) + 32 = -36.4 o F iv. 25.50oC Solution: Use the formula to convert Fahrenheit to Celsius = o F = (9/5x oC) + 32 = 9/5 x (25.50) + 32 = 77.9 o F v. 70oC Solution: Use the formula to convert Fahrenheit to Celsius = o F = (9/5x oC) + 32 = 9/5 x (70) + 32 = 158 o F Q 3: Add the following: i. 35oC + 18oC = 53oC ii. 13oC + 14oC = 27oC iii. 219oC + 18o F Convert 18o F to oC first. oC = 5/9 x o F – 32 = 5/9 x 18 – 32 = 10 – 32 = -22oC Convert 219oC to o F = (9/5 x (219)) + 32 = 426.2o F => 219oC + 18o F = 219oC + (-22) = 197oC => 426.2 + 18 = 444.2 o F iv. 144o F + 74o F = 218o F Q 4: Subtract the following: i. 16oC – 2 oC = 14oC ii. 14oC – 84oC = -70oC iii. 183oF – 13oC = 183o F - 55.4oF = 72.2o F
CSS Primary Standard “Mathematics” 84 iv. 88o F – 16oC = 88o F – 60.8o F = 27.2o F v. 139o F – 12oC = 139o F – 53.6o F = 85.4 o F vi. 214o F – 100o F = 114o F i. How much warmer is Colombo than Ottawa? = (30oC – 5 oC) = 25oC ii. How much colder is Skardu than Lahore? = (-9 oC - 26oC) = -35oC iii. What is the temperature of Mumbai at Fahrenheit scale = 93.20o F iv. How much Mumbai is warmer than Glasgow? = (34oC – 7 oC) = 27oC Q 5: Temperature in the morning = -4 o F Temperature in the evening = 13o F Rise in temperature = (13 – (-4) = 13 + 4 = 17o F Review Exercise 5 Q 1: Choose the correct answer and fill the circle: 1. 1km = .………...m 1000 100 100,000 10,000 2. 1km = .………...cm 1000 100 100,000 10,000 3. 1 second = .………...minutes 3600 1/60 1/3600 60 4. Temperature in Fahrenheit o F = …………. 5/9oC + 32 9/5oC + 32 5/9oC - 32 9/5oC - 32 5. Temperature in Fahrenheit oC = …………. 9/5 o (F – 32) 5/9o (F – 32) 5/9o (F + 32) 9/5o (F + 32) 6. 1/7 of a week is: year day week month 7. The normal human body temperature is. 35oC 36oC 34oC 37oC 8. There are seconds in one hour. 60 360 36 3600 9. A second is the unit of time which is 1/60 of :
CSS Primary Standard “Mathematics” 85 minute hour day second 10. In time, “p.m.” stands for: post meridian post master Prime Minister Punjab Minister Q 2: Convert the following measures to: i. 21 km = 21000 meters ii. 132 m = 13200 cms iii. 218 m 14 cm = 21814cm iv. 24 cm 13 mm= 253 mm v. 0.389mm = 0.0389 cm = 0.000389m = 0.000000389 kms vi. 158 seconds = 2 minutes 38 seconds vii. 19 years 3 months = 231 months viii. 52 weeks = 364 days ix. 84o F = 28.9oC x. 69oC = 156.2o F Q 3: i. Add 15 km, 924 m, 13 cm to 94 km, 320 m, 18cm. kms m cm mm H T O H T O T O O 1 5 9 2 4 1 3 + 9 4 3 2 0 1 8 1 0 2 4 4 3 1 10 kms and 244 meters and 31 cms. ii. Add 15 km, 313 m, 19 cm and 105 km, 64 m, 89cm and 14 km, 26 m, 18cm. kms m cm mm H T O H T O T O O 1 5 3 1 3 1 9 1 0 5 6 4 8 9 1 4 2 6 1 8 1 3 4 4 0 4 2 6 134 kms and 404 meters and 26 cms. Q 4:
CSS Primary Standard “Mathematics” 86 i. Subtract 5km, 15 m, 2 cm from 14 km, 324 m, 14 cm. i. Kms m cm mm H T O H T O T O O 0 14 1 14 1 4 3 2 4 1 4 0 5 0 1 5 0 2 0 9 3 0 9 1 2 9 kilometers and 309 meters, 14 cms. ii. Subtract 16km, 821 m, 14 cm from 24 km, 398 m, 20 cm. i. Kms m cm mm H T O H T O T O O 1 13 13 1 10 2 4 3 9 8 2 0 1 6 8 2 1 1 4 0 7 5 7 7 0 6 7 kilometers and 577 meters, 6 cms. Q 5: Length of the cord = 3 kms and 500 meters Length of cord in meters = 3 x (1000) + 500 m = 3000 + 5000 = 3500 meters Q 6: Arslan talked to Sobia = 1 hour, 20 minutes, 30 seconds Sobia talked to Qaiser = 59 minutes 48 seconds Sobia talked in total = Hours Minutes Seconds T O T O T O 1 2 0 3 0 0 5 9 4 8 2 2 0 3 8 2 hours, 20 minutes, 38 seconds. Q 7: Temperature at 12 noon = 30o F Temperature at 9:00 after drop of 25o F = 30o F - 25o F = 5 o F Q 8: Temperature at oC Temperature at o F 26oC 78.8o F 23oC 73.4o F 21oC 69.8o F
CSS Primary Standard “Mathematics” 87 Week 11 Monthly Test / Revision of Unit # 3 and 4 Week 12 Week 13 Revision of Unit # 5 and 6 Week 14 Final Test Model Paper # 1 Instructions: Every question has three 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. (10 Marks) Section A Time Allowed: 45 Minutes Total Marks: 30 1. A fraction having numerator is less than the denominator is called .………... Proper Fraction Improper Fraction Mixed Fraction Rational Fraction 2. A fraction having denominator is greater than the numerator is called .………... Proper Fraction Improper Fraction Mixed Fraction Rational Fraction 3. Adding 1/3 and 2/3 gives: 2 1 3 4 4. Subtracting 2/3 and 1/3 gives: ½ 1/3 2/3 1 5. Multiplying 1/3 by 5 gives: 1/15 1 2 /3 2/15 8/15 5. Dividing 1/3 by 5 gives: 1 2 /3 1/15 2/15 8/15 7. In fraction expression we use……. operation first. addition subtraction multiplication division
CSS Primary Standard “Mathematics” 88 8. 1/5 + 7/10: 9/13 19/11 9/11 9/10 9. 5/17 – 2/17: 3/17 2/17 4/17 1/17. 10. 5/5 + 7/10: 9/13 17/11 9/11 7/10 11. If decimal have different number of digits to the right of the decimal point is called .………... unlike decimal like decimal fractional decimal none of these 12. If decimal have same number of digits to the right of the decimal point is called .………... unlike decimal like decimal fractional decimal none of these 13. 4.5 x 10 is: 0.45 45 450 4500 14. 4.5 x 100 is: 0.45 450 45 4500 15. Percentage is a special kind of ………..fraction: common rational proper improper 16. 10% of 100 is: 30 10 20 100 17. The division of decimal by 1000 displaces the decimal point from its original position. two place to right two place to left three place to right three place to left 18. The multiplication of decimal by 1000 displaces the decimal point from its original position. two place to right two place to left three place to left three place to right 19. 4.5 ÷ 1000 : 0.0045 0.45 0.00045 0.045
CSS Primary Standard “Mathematics” 89 20. 4.5 x 1000 : 0.0045 0.45 0.00045 4500 21. 1km = .………...m 1000 100 100,000 10,000 22. 1km = .………...cm 1000 100 100,000 10,000 23. 1 second = .………...minutes 3600 1/60 1/3600 60 24. Temperature in Fahrenheit o F = …………. 5/9oC + 32 9/5oC + 32 5/9oC - 32 9/5oC - 32 25. Temperature in Fahrenheit oC = …………. 5/9o (F – 32) 5/9o (F – 32) 5/9o (F + 32) 9/5o (F + 32) 26. 1/7 of a week is: year day week month 27. The normal human body temperature is. 35oC 36oC 34oC 37oC 28. There are seconds in one hour. 60 360 36 3600 29. A second is the unit of time which is 1/60 of : minute hour day second 30. In time, “p.m.” stands for: post meridian post master Prime Minister Punjab Minister Part B Time Allowed: 75 Minutes Total Marks: 45 Note:Attempt All questions. All questions carry equal (3) Marks. 16.What number must be subtracted from 7/18 to get the difference of 1/9?
CSS Primary Standard “Mathematics” 90 17.On Saturday Naeem ate pizza at dinner and had 5/12 left over. On Sunday he ate 2/6 of what was left on Saturday. How much pizza did Naeem eat on Sunday? Simplify your answer and write it in proper, improper, whole number of mixed fraction. 18.Saif shares 5/8 of a pizza with his two sisters. Can you help saif divide this pizza into 3 equal parts? How much of the whole pizza does each person will get? 19.Zaid ate 11 /2 of pizza on dinner time and his friends are 21 /3 of pizza. How much pizza did they eat altogether? 20.Zohaib ate ¾ of cake and raffia ate ½ times of Zohaib‟s cake. How much cake did raffia eat? 21.If the difference of two numbers is 214.386 and one of them is 184.692. Find the other number. 22.The cost of an egg is Rs. 9.75. Find the cost of half dozen of eggs. 23.There are 50 balls in the box, 20 balls out of them are red, 10 balls are green and rests are black. What % of the ball is red? What % of the ball is green? What % of the ball is black? 24.There are 25 fruits in the basket. 10 of them are bananas and rest is apples. What % of the fruits are apples? What % of the fruits is bananas? 25.The length of the wire is 35.55 m. Ahmed want to cut this wire into 5 equal parts. Find the length of each part of the wire? If the price of each part of the wire is Rs. 12.68, then find the total cost of the wire? 26.In Shazmeena‟s house a rectangular swimming pool (blue) whose length is 350m 5 cm and width is 200m and 15cm is surrounded by the (green) grass. Find the total length and width of the pool. Also find the difference between length and width. 27.Alina is driving a car. She drove for 3 hours and 35 minutes and 17 seconds. Her brother drives 2 hours 20 minutes and 10 seconds. How much more time Alina drove the car than her brother? And how much time did they spend altogether for driving the car? Also convert the total time into seconds only. 28.The temperature yesterday was -4 o F in the morning and 13oF inn the evening. How much degrees did temperature rise? 29.At the hardware store Arslan asked for an extension cord that was 3km 500 m long. What is the length of the cord in meters? Was this an appropriate length to ask? 30.Arslan talked 1 hour 20 minutes and 30 seconds on mobile with Sobia. After Arslan Sobia talked 59 minutes and 48 seconds with Qaiser. How much more time did Sobia talk with Arslan and Qaiser in all? Model Paper # 2 Instructions: Every question has three possible answers but one is the correct answer.
CSS Primary Standard “Mathematics” 91 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. (10 Marks) Section A Time Allowed: 45 Minutes Total Marks: 30 1. A fraction having numerator is greater than the denominator is called .………... Proper Fraction Improper Fraction Mixed Fraction Rational Fraction 2. A fraction having denominator is less than the numerator is called .………... Proper Fraction Improper Fraction Mixed Fraction Rational Fraction 3. Adding 2/5 and 3/5 gives: 2 1 3 4 4. Subtracting 2/3 and 1/3 gives: ½ 1/3 2/3 1 5. Multiplying 1/2 by 7 gives: 1/15 1 2 /3 7/2 8/15 5. Dividing 1/3 by 5 gives: 1 2 /3 1/15 2/15 8/15 7. In fraction expression we use……. operation at last. addition subtraction multiplication division 8. 1/10 + 9/10: 9/13 19/11 1 9/10 9. 5/13 – 2/13: 3/13 2/17 4/17 1/17. 10. 5/10 + 7/10: 12/10 17/11 9/11 7/10 11. If decimal have same number of digits to the right of the decimal point is called .………... unlike decimal like decimal
CSS Primary Standard “Mathematics” 92 fractional decimal none of these 12. If decimal have different number of digits to the right of the decimal point is called .………... unlike decimal like decimal fractional decimal none of these 13. 4.5 x 100 is: 0.45 45 450 4500 14. 4.5 x 1000 is: 0.45 450 45 4500 15. Percentage is a special kind of ………..fraction: common rational proper improper 16. 10% of 90 is: 30 9 20 100 17. The division of decimal by 100 displaces the decimal point from its original position. two place to right two place to left three place to right three place to left 18. The multiplication of decimal by 10 displaces the decimal point from its original position. two place to right two place to left three place to left three place to right 19. 4.5 ÷ 100 : 0.0045 0.45 0.00045 0.045 20. 4.5 x 100 : 0.0045 0.45 0.00045 450 21. 2km = .………...m 2000 200 200,000 20,000 22. 2km = .………...cm 2000 200 200,000 20,000 23. 1 minute = .………...hours 3600 1/60 1/3600 60 24. Temperature in Fahrenheit o F = ………….
CSS Primary Standard “Mathematics” 93 5/9oC + 32 9/5oC + 32 5/9oC - 32 9/5oC - 32 25. Temperature in Fahrenheit oC = …………. 5/9o (F – 32) 5/9o (F – 32) 5/9o (F + 32) 9/5o (F + 32) 26. 1/24 of a day is: year day hour month 27. The normal human body temperature is. 35oC 36oC 34oC 37oC 28. There are seconds in one minute. 60 360 36 3600 29. A second is the unit of time which is 1/3600 of : minute hour day second 30. In time, “p.m.” stands for: post meridian post master Prime Minister Punjab Minister Part B Time Allowed: 75 Minutes Total Marks: 45 Note:Attempt All questions. All questions carry equal (3) Marks. 16.Abbas bought 32 /5 liters of petrol and Ali bought 83 /10 liters of petrol. a. How much petrol did they buy altogether? b. How much more petrol did Ali bought than Abbas? 17.In survey 41/100 voters planned to vote for party A and 39/100 planned to vote for party B and the rest were undecided. What fraction of voters was undecided? 18.Shazia‟s lemon cookie recipe calls for 5/20 of a cup of sugar. How much sugar would Shazia use to make 2/8 of a batch of cookies? Simplify your answer. 19.Saima spends 3/10 of the whole day in school. She learns and practice Mathematics for 3/7 of the time spends in the school. How much time of the day does she spend for mathematics? 20.Alina ate 3/8 part of a pizza. Anarol ate ¼ part of the pizza. How much pizza did Alina and Anarol eat altogether? 21.A truck carries 52 pieces of granite and 525 pieces of marble floor tiles. The mass of the granite tile is 3.58 kg and the mass of the marble tile is 6.08. Find the total mass of the tile which was carried by the truck.
CSS Primary Standard “Mathematics” 94 22.One day Nasreen went to the market to buy her Eid dress. The actual price of the dress was Rs. 2500. The shop keeper gave her 25 % discount. How much money did she pay to the shop keeper for her dress? 23.The total strength of the class-5 is 75 students. 10 students were absent. a. Find the % of the students who were present? b. Find the % of the students who were absent? 24.There are 4000 people living in a village. 36% of them are women, and 18% of them are children and rests of them are men. Find the number of women, men and children in the village. a. What is the % of men in a village? b. What is highest number from all people. 25.Zoya travelled 38km 586m by bus and 82km 324 m by car. Find the total distance she travelled. 26.Zaid spend 1 hour 30 minutes daily doing exercise and spend 3 hours and 15 minutes in playing cricket. How much more time does zaid spend in playing cricket daily? 27.Waqar is 26 years and 5 months old. Find his age in days. Also find the total seconds of Waqar‟s age. Calculate your own age in seconds. 28.A snow drove the temperature down each 4oC each hour. The thermometer read 8oC before the strom began. What did it read 4 hours later? 29.The temperature at 12 noon was 30o F. By 9:00 pm it had dropped 25o F. What was the emperature at 9:00 pm? 30.During the week, the temperature each day at noon was 26oC, 23oC and 21oC. Find each temperature at Fahrenheit scale? Model Paper # 3 Instructions: Every question has three 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. (10 Marks) Section A Time Allowed: 45 Minutes Total Marks: 30 1. A fraction having numerator is less than the denominator is called .………... Proper Fraction Improper Fraction Mixed Fraction Rational Fraction 2. A fraction having denominator is greater than the numerator is called .………...
CSS Primary Standard “Mathematics” 95 Proper Fraction Improper Fraction Mixed Fraction Rational Fraction 3. Adding 1/3 and 2/3 gives: 2 1 3 4 4. Subtracting 2/3 and 1/3 gives: ½ 1/3 2/3 1 5. Multiplying 1/3 by 5 gives: 1/15 1 2 /3 2/15 8/15 5. Dividing 1/3 by 5 gives: 1 2 /3 1/15 2/15 8/15 7. In fraction expression we use……. operation first. addition subtraction multiplication division 8. 1/5 + 7/10: 9/13 19/11 9/11 9/10 9. 5/17 – 2/17: 3/17 2/17 4/17 1/17. 10. 5/5 + 7/10: 9/13 17/11 9/11 7/10 11. If decimal have different number of digits to the right of the decimal point is called .………... unlike decimal like decimal fractional decimal none of these 12. If decimal have same number of digits to the right of the decimal point is called .………... unlike decimal like decimal fractional decimal none of these 13. 4.5 x 10 is: 0.45 45 450 4500 14. 4.5 x 100 is: 0.45 450
CSS Primary Standard “Mathematics” 96 45 4500 15. Percentage is a special kind of ………..fraction: common rational proper improper 16. 10% of 90 is: 30 9 20 100 17. The division of decimal by 100 displaces the decimal point from its original position. two place to right two place to left three place to right three place to left 18. The multiplication of decimal by 10 displaces the decimal point from its original position. two place to right two place to left three place to left three place to right 19. 4.5 ÷ 100 : 0.0045 0.45 0.00045 0.045 20. 4.5 x 100 : 0.0045 0.45 0.00045 450 21. 2km = .………...m 2000 200 200,000 20,000 22. 2km = .………...cm 2000 200 200,000 20,000 23. 1 minute = .………...hours 3600 1/60 1/3600 60 24. Temperature in Fahrenheit o F = …………. 5/9oC + 32 9/5oC + 32 5/9oC - 32 9/5oC - 32 25. Temperature in Fahrenheit oC = …………. 5/9o (F – 32) 5/9o (F – 32) 5/9o (F + 32) 9/5o (F + 32) 26. 1/24 of a day is: year day hour month 27. The normal human body temperature is. 35oC 36oC
CSS Primary Standard “Mathematics” 97 34oC 37oC 28. There are seconds in one minute. 60 360 36 3600 29. A second is the unit of time which is 1/3600 of : minute hour day second 30. In time, “p.m.” stands for: post meridian post master Prime Minister Punjab Minister Part B Time Allowed: 75 Minutes Total Marks: 45 Note:Attempt All questions. All questions carry equal (3) Marks. 1. Abbas bought 32 /5 liters of petrol and Ali bought 83 /10 liters of petrol. c. How much petrol did they buy altogether? d. How much more petrol did Ali bought than Abbas? 2. In survey 41/100 voters planned to vote for party A and 39/100 planned to vote for party B and the rest were undecided. What fraction of voters was undecided? 3. Shazia‟s lemon cookie recipe calls for 5/20 of a cup of sugar. How much sugar would Shazia use to make 2/8 of a batch of cookies? Simplify your answer. 4. Saima spends 3/10 of the whole day in school. She learns and practice Mathematics for 3/7 of the time spends in the school. How much time of the day does she spend for mathematics? 5. Alina ate 3/8 part of a pizza. Anarol ate ¼ part of the pizza. How much pizza did Alina and Anarol eat altogether? 6. A truck carries 52 pieces of granite and 525 pieces of marble floor tiles. The mass of the granite tile is 3.58 kg and the mass of the marble tile is 6.08. Find the total mass of the tile which was carried by the truck. 7. One day Nasreen went to the market to buy her Eid dress. The actual price of the dress was Rs. 2500. The shop keeper gave her 25 % discount. How much money did she pay to the shop keeper for her dress? 8. There are 50 balls in the box, 20 balls out of them are red, 10 balls are green and rests are black. What % of the ball is red? What % of the ball is green? What % of the ball is black? 9. There are 25 fruits in the basket. 10 of them are bananas and rest is apples. What % of the fruits are apples? What % of the fruits is bananas? 10.The length of the wire is 35.55 m. Ahmed want to cut this wire into 5 equal parts. Find the length of each part of the wire? If the price of each part of the wire is Rs. 12.68, then find the total cost of the wire?
CSS Primary Standard “Mathematics” 98 11.In Shazmeena‟s house a rectangular swimming pool (blue) whose length is 350m 5 cm and width is 200m and 15cm is surrounded by the (green) grass. Find the total length and width of the pool. Also find the difference between length and width. 12.Alina is driving a car. She drove for 3 hours and 35 minutes and 17 seconds. Her brother drives 2 hours 20 minutes and 10 seconds. How much more time Alina drove the car than her brother? And how much time did they spend altogether for driving the car? Also convert the total time into seconds only. 13.The temperature yesterday was -4 o F in the morning and 13oF inn the evening. How much degrees did temperature rise? 14.At the hardware store Arslan asked for an extension cord that was 3km 500 m long. What is the length of the cord in meters? Was this an appropriate length to ask? 15.Arslan talked 1 hour 20 minutes and 30 seconds on mobile with Sobia. After Arslan Sobia talked 59 minutes and 48 seconds with Qaiser. How much more time did Sobia talk with Arslan and Qaiser in all? Third Term Week 1, 2, & 3 Unitary Method Lesson # 1 Teaching Objectives: Students should be able to: ☻ To compare quantities of the same kind as a ratio. ☻ To compare the relationship between 2 quantities as a proportion. ☻ To introduce direct and inverse proportion. ☻ To introduce percentage ratio • to introduce the unitary method. Teaching Objectives: Students should be able to: ☻ Compare 2 quantities by expressing them as a ratio in the simplest term. ☻ Differentiate quantities which are directly/inversely proportional. ☻ Use the unitary method to solve real life problems (both direct and inverse). ☻ Describe the concept of Unitary Method. ☻ Calculate the value of many objects of the same kind when the value of another of the same type is given. ☻ Calculate the value of a number of same types of objects when the value of another of these types is given. ☻ Define ratio of two numbers.
CSS Primary Standard “Mathematics” 99 ☻ Define and Identify direct and inverse proportion. ☻ Solve real life problems involving direct and inverse proportion. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: ☻ Use the explanation as given on pages # 85 to explain unitary method. Exercise 6a Q 1: Anees went to stationary shop to buy stationery. How much money did he pay in all for below listed items? Name of Items Price of one item Number of items Total price of all items Pencils 15 4 60 Eraser 5 6 30 Notebooks 60 7 420 Registers 120 2 240 Total money needed 750 Q 2: Price of 1 laptop = Rs. 31500 Price of 5 laptops = 31500 x 5 = Rs. 157,500 Q 3: Cost of 1 fancy light = Rs. 329 Cost of 28 fancy lights = 329 x 28 = Rs. 9212 Q 4: Shahbaz receive at each piece of pant = Rs. 1.75 Shahbaz will receive 531 piece of pant = Rs. 1.75 x 531 = Rs. 929. 25 Q 5: Distance covered by Humaira in 6 hours = 450 kilometers Distance covered by Humaira in 1 hours = 450/6 kilometers = 75 kilometers Q 6: The cost of Dozen (12) bananas = Rs. 144 Cost of 1 banana = 144/12 = Rs. 12 Cost of 9 bananas = Rs. 12 x 9 = Rs. 108 Week 1, 2, & 3 Unitary Method Lesson # 2 Teaching Objectives:
CSS Primary Standard “Mathematics” 100 Students should be able to: ☻ To compare quantities of the same kind as a ratio. ☻ To compare the relationship between 2 quantities as a proportion. ☻ To introduce direct and inverse proportion. ☻ To introduce percentage ratio • to introduce the unitary method. Teaching Objectives: Students should be able to: ☻ Compare 2 quantities by expressing them as a ratio in the simplest term. ☻ Differentiate quantities which are directly/inversely proportional. ☻ Use the unitary method to solve real life problems (both direct and inverse). ☻ Describe the concept of Unitary Method. ☻ Calculate the value of many objects of the same kind when the value of another of the same type is given. ☻ Calculate the value of a number of same types of objects when the value of another of these types is given. ☻ Define ratio of two numbers. ☻ Define and Identify direct and inverse proportion. ☻ Solve real life problems involving direct and inverse proportion. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: ☻ Use the explanation as given on pages # 86, 87, 88 and 89 to explain the concepts of Direct and inverse proportion and ratio. Exercise 6b Q 1: Simplify the following ratio in the lowest form: i. 5 : 10 => 1 : 2 ii. 3 : 6 => 1 : 2 iii. 14 : 21 => 2 : 3 iv. 4.6 : 8.4 => 2.3 : 4.2 v. 1/3 : 1/7 => 3 : 7 Q 2: Solve the following using. Product of means = Product of extremes i. 4 : 2 :: X : 4 Solution: 2 x X = 4 x 4 => 2X = 16 => X = 16/2 = 8