CSS Primary Standard “Mathematics” 101 ii. 3 : 6 :: 4 : X Solution: 3 x X = 6 x 4 => 3X = 24 => X = 24/3 = 8 iii. 6 : X :: 4 : 5 Solution: 4 x X = 6 x 5 => 4 X = 30 => X = 30/4 = 7.5 vi. X : 8 :: 6 : 10 Solution: 10 x X = 6 x 8 => 10 X = 48 => X = 48/10 = 4.8 Q 3: Cost of 3 chairs = Rs. 1800 Cost of 12 chair = ? 3 : 12 :: 1800 : X 3 x X = 12 x 1800 3X = 12 x 1800 X = 12 x 1800/3 = 7200 Q 4: Cost of 9 m long cloth = Rs. 5000 Cost of 3 m long cloth = ? 9 : 3 :: 5000 : X 9X = 3 x 5000 X = 15000/9 = Rs. 1666.67 Q 5: Number of girls in the school = 40 Number of boys in the school = 60 Number of boys : Number of girls 60 : 40 6 : 4 3 : 2 Q 6: Ratio of water and milk = 1:7 Milk = 10 liters 1 : 10 :: 7 : X = x = 10 x 7 = X = 70 liters of water Q 7: Number of mobiles produced in 2 days = 1000 Number of mobiles produced in 23 days = ? 2 : 23 :: 1000 : X
CSS Primary Standard “Mathematics” 102 2X = 23 x 1000 X = 23 x 1000/2 = 11500 mobiles will be produced in 23 days Q 8: 9 days food available for = 68 person Food available for (68 + 12) person = ? 9 : 80 :: X : 68 80 X = 68 x 9 X = 68 x 9/80 X = 7.65 (approximately 8 days) Review Exercise 6 Q 1: Choose the correct answer and fill the circle: 1. The composition between .………... quantities of the same kind is called ratio. two one four three 2. If the price of a bubble is 5 rupees, then the price of 5 such bubbles will be…… 15 20 25 30 3. Farah travels with the constant speed. She covers 2 km in one hour. She will cover 8 km in……….. 1 4 2 3 4. Proportion is equality between two…….. quantities ratios variables proportions 5. 33 : 22 = …………. 11:12 3:2 9:15 4:5 6. The ratio of boys to the girls in the class is 3:4. If there are 27 boys, then the girls will be……. 12 36 45 40 7. The unit of ratio is……. m km cm no unit 8. The increase / decrease in quantity because of increase/decrease in other quantity is called ……….proportion. continued indirect none of these direct
CSS Primary Standard “Mathematics” 103 9. The increase / decrease in quantity because of decrease/ increase in other quantity is called ……….proportion. continued indirect none of these direct 10. The value of one toy is Rs. 84, the value of 3 toys of same kind is Rs. …… 252 162 182 172 Q 2: Price of 15 cups = Rs. 800 Price of 1 cup = ? 15 : 1 :: 800 : X 15 X = 800 X = 800/15 X = Rs. 53.33 Q 3: Laiba bought 15 notebooks = Rs. 1500 Cost of 31 notebooks = ? 15 : 31 :: 1500 : X 15 X = 1500 x 31 X = (1500 x 31) / 15 X = Rs. 3100 Q 4: Aleezay can eat 24 almonds in = 7 minutes Aleezay can eat 35 almonds in = ? 24 : 35 :: 7 : X 24 X = 35 x 7 X = (35 x 7) / 24 = 10.20 minutes Q 5: Price of mango = Rs. 120 Price of apple = Rs. 160 Ratio = ? Price of Mango : Price of Apple 120 : 160 12 : 16 6 : 8 3 : 4 So ratio of mango and apple is = 3:4 Price of 5 kg of apples = 5 x 160 = Rs. 800 Price of 3 kg of apples = 5 x 120 = Rs. 360 Q 6: 7 person can fill a water tank in = 5 hours 4 person can fill a water tank in = ?
CSS Primary Standard “Mathematics” 104 7 : 4 :: X : 5 4X = 7 x 5 X = 35/4 = 9 hours 45 minutes Week 1, 2, & 3 Geometry Lesson # 1 Teaching Objectives: Students should be able to: ☻ To demonstrate the use of a protractor to construct a right angle, straight angle, and reflex angle. ☻ To explain adjacent angles, complementary angles, supplementary angles. ☻ To define a triangle. ☻ To explain classification of triangles based on i) sides ii) angles. ☻ To show construction of triangles • to define quadrilaterals. ☻ To demonstrate construction of a square and a rectangle using a set-square and ruler. Teaching Objectives: Students should be able to: ☻ Use a protractor to construct angles. ☻ Differentiate between complementary and supplementary angles. ☻ Calculate the complement and supplement of a given angle. ☻ Define and classify triangles based on the sizes of their angles and lengths of sides. ☻ Construct a triangle using a pair of compasses and a ruler when the lengths of its 3 sides are given. ☻ Identify and define quadrilaterals • construct a quadrilateral using set-square and a ruler. Teaching Materials: CSS Primary Standard Mathematics Book 5. Geometry box. Ruler. Set-squares. Clock with moveable hands. Board and markers/chalk. Classroom Activity: ☻ Use the explanation as given on pages # 93, 94 and 95 to explain the concepts of angles, types of angles, and construction of right angle, straight angle and reflex angle. ☻ Use the explanation as given on page # 96 to explain the concepts of adjacent,
CSS Primary Standard “Mathematics” 105 complementary and supplementary angles. Exercise 7a Q 1: Activity based. Q 2: Activity based. Q 3: i. Not complementary nor supplementary. ii. Complementary angles iii. Supplementary angles iv. Complementary angles v. Supplementary angles Week 1, 2, & 3 Geometry Lesson # 2 Teaching Objectives: Students should be able to: ☻ To demonstrate the use of a protractor to construct a right angle, straight angle, and reflex angle. ☻ To explain adjacent angles, complementary angles, supplementary angles. ☻ To define a triangle. ☻ To explain classification of triangles based on i) sides ii) angles. ☻ To show construction of triangles • to define quadrilaterals. ☻ To demonstrate construction of a square and a rectangle using a set-square and ruler. Teaching Objectives: Students should be able to: ☻ Use a protractor to construct angles. ☻ Differentiate between complementary and supplementary angles. ☻ Calculate the complement and supplement of a given angle. ☻ Define and classify triangles based on the sizes of their angles and lengths of sides. ☻ Construct a triangle using a pair of compasses and a ruler when the lengths of its 3 sides are given. ☻ Identify and define quadrilaterals • construct a quadrilateral using set-square and a ruler. Teaching Materials: CSS Primary Standard Mathematics Book 5. Geometry box. Ruler.
CSS Primary Standard “Mathematics” 106 Set-squares. Clock with moveable hands. Board and markers/chalk. Classroom Activity: ☻ Use the explanation as given on pages # 98, 99, 100, 101, 102, 103 and 104 to explain the concepts of Triangles, types of triangles (w.r.t) sides and angles. ☻ Use the explanation as given on pages # 98, 99, 100, 101, 102, 103 and 104 to explain the construction of different types of triangles. Exercise 7b Q 1: i. Isosceles triangle ii. Isosceles triangle iii. Equilateral triangle iv. Scalene triangle v. Equilateral triangle vi. Scalene triangle Q 2: Activity Based Q 3: Activity Based Q 4: Activity Based Week 1, 2, & 3 Geometry Lesson # 3 Teaching Objectives: Students should be able to: ☻ To demonstrate the use of a protractor to construct a right angle, straight angle, and reflex angle. ☻ To explain adjacent angles, complementary angles, supplementary angles. ☻ To define a triangle. ☻ To explain classification of triangles based on i) sides ii) angles. ☻ To show construction of triangles • to define quadrilaterals. ☻ To demonstrate construction of a square and a rectangle using a set-square and ruler. Teaching Objectives: Students should be able to: ☻ Use a protractor to construct angles. ☻ Differentiate between complementary and supplementary angles. ☻ Calculate the complement and supplement of a given angle. ☻ Define and classify triangles based on the sizes of their angles and lengths of sides. ☻ Construct a triangle using a pair of compasses and a ruler when the lengths of its 3 sides
CSS Primary Standard “Mathematics” 107 are given. ☻ Identify and define quadrilaterals • construct a quadrilateral using set-square and a ruler. Teaching Materials: CSS Primary Standard Mathematics Book 5. Geometry box. Ruler. Set-squares. Clock with moveable hands. Board and markers/chalk. Classroom Activity: ☻ Use the explanation as given on pages # 105, 106 and 107 to explain the concepts of Quadrilaterals, Kind of quadrilaterals and construction of quadrilateral. Exercise 7c Q 1: i. Square ii. Rhombus iii. Rectangle iv. Parallelogram v. Trapezium vi. Kite Q 2: Activity Based Q 3: Activity Based Review Exercise 7 Q 1: Choose the correct answer and fill the circle: 1. .………... is an acute angle. 34oC 90oC 103oC none of these 2. .………... is an obtuse angle. 103oC 90oC 34oC none of these 3. .………... is a right angle. 103oC 90oC 103oC none of these 4. Two angles with a common vertex and a common arm is called…….. angles. Supplementary Adjacent Complementary none of these 5. Two angles are said to be…… angles if the sum of both angles is equal to 90o . Supplementary Adjacent
CSS Primary Standard “Mathematics” 108 Complementary none of these 6. Two angles are said to be…… angles if the sum of both angles is equal to 180o . Supplementary Adjacent Complementary none of these 7. A triangle having one angle is equal to 90o is called ……. angle. Right angled Acute angled Obtuse angled Complete angled 8. A quadrilateral with all sides and angles are equal is called…….. Rectangle Kite Parallelogram Square Q 2: Activity Based Q 3: Activity Based Q 4: Activity Based Week 4 & 5 Perimeter and Area Lesson # 1 Teaching Objectives: ☻ To introduce the concept of perimeter and its practical applications. ☻ To introduce the formula for finding the perimeter of a square and a rectangle. ☻ To introduce the concept of area. ☻ To introduce the formula for finding the area of a square and a rectangle. ☻ To explain the application of area in practical situations. ☻ To explain how to calculate the area and perimeter of irregular shapes. Learning Outcomes: Students should be able to: ☻Explain the concept of perimeter and apply it in practical situations. ☻ Use the formula to find the perimeter of a square and a rectangle. ☻Explain the idea of area • use the formula to find the area of a square and a rectangle. ☻Apply the concept of area in practical situations. ☻Find the areas and perimeters of irregular shapes using a square grid and approximation. Teaching Materials: CSS Primary Standard Mathematics Book 5. Geometry box. Ruler. Set-squares. Clock with moveable hands. Board and markers/chalk.
CSS Primary Standard “Mathematics” 109 Classroom Activity: ☻ The concepts of area and perimeter have already been introduced in previous years. In Year 5, the concept is refined and formalized with the introduction of the mathematical formulae for finding the areas and perimeters of 2D shapes, such as a square and a rectangle. ☻ Revise the concepts with some hands-on activity. ☻ Let students explore the concept of perimeter by walking around a garden or around the classroom: they can talk about perimeter in terms of „footsteps‟. Then they can tie ribbons or strong thread around a desk or around the board. The perimeter, in these cases, will be measured in terms of meters or centimeters. ☻ Then, introduce the formula for calculating the perimeter of a square and a rectangle. A square has 4 equal sides, each side with the length of 5 units. So, the perimeter of a square is 4 × length of each side = 4 × 5 = 20 units. ☻ A rectangle has two pairs of equal sides, L being the length, B being the breadth. The perimeter = 2 × length + 2 × breadth = 2(L + B) = 2 (8 + 5) = 2 × 40 = 80 cm. ☻ In real-life situations, to find the perimeter of a square or a rectangular room, students may prefer to add all the 4 sides, rather than apply the formulae. Allow them to do that, until they realize that the use of the formulae makes the problem easier. ☻ Before moving on to area use the activity below to reinforce the distinction between the area and the perimeter of a shape. ☻ REMEMBER: Perimeter is 1-dimension, and area is 2-dimension. ☻ Area: The length (L) of a square is 1 cm, and the breadth (B) is 1 cm. (In a square, L = B) Area = 1 cm2 Perimeter = 4 cm ☻ This means that the square covers space with area of 1 cm2. If an ant walks around the 4 sides, it will cover a distance of 4 cm. This is the perimeter of the square. ☻ Use the explanation as given on pages # 109, 110, 111, 112, 113 and 114 to explain the concepts of Perimeter and Area. Exercise 8a Q 1: Find the perimeter of the following figures: i. 2cm + 2cm + 2cm + 2cm = 8cm ii. 2cm + 4cm + 2cm + 4cm = 12cm iii. 2.6cm + 2.6cm + 2.6cm + 2.6cm = 10.4 cm iv. 6cm + 6cm + 6cm + 6cm = 24 cm v. 2.5 cm + 4.5 cm + 2.5 cm + 4.5 cm = 14 cm Q 2: Find the area of each pat of question (1): i. 2cm x 2cm = 4cm 2 ii. 2cm x 4cm = 8cm 2 iii. 2.6cm x 2.6cm = 6.76 cm2
CSS Primary Standard “Mathematics” 110 iv. 6cm x 6cm = 36 cm2 v. 2.5 cm x 4.5 cm = 11.25 cm2 Q 3: Find the area and perimeter of the squares having length of a side are given below: i. 2.5 cm Perimeter = 2.5cm + 2.5cm + 2.5cm + 2.5 cm = 10 cm Area = 2.5 x 2.5 = 6.25 cm2 ii. 6 cm Perimeter = 6cm + 6cm + 6cm + 6 cm = 24 cm Area = 6 x 6 = 36 cm2 iii. 8.5 cm Perimeter = 8.5cm + 8.5cm + 8.5cm + 8.5 cm = 34 cm Area = 8.5 x 8.5 = 72.25 cm2 iv. 9.1 Perimeter = 9.1cm + 9.1cm + 9.1cm + 9.1 cm = 36.4 cm Area = 9.1 x 9.1 = 82.81 cm 2 v. 15 cm Perimeter = 15cm + 15cm + 15cm + 15 cm = 60 cm Area = 15 x 15 = 225 cm2 Q 4: Find the area and perimeter of the rectangles having lengths and breadth as given below: i. Length = 5 cm , Breadth = 2.5 cm Perimeter = 2(L + B) = 2(5 + 2.5) = 2 (7.5)= 15 cm Area = L x B = 5 x 2.5 = 12.5 cm2 ii. Length = 6.5 cm, Breadth = 3.8 cm Perimeter = 2(L + B) = 2(6.5 + 3.8) = 2 (10.3) = 20.6 cm Area = L x B = 6.5 x 3.8 = 24.7 cm2 iii. Length = 9.8 cm, Breadth = 4.5 cm Perimeter = 2(L + B) = 2(9.8 + 4.5) = 2 (14.3) = 28.6 cm Area = L x B = 9.8 x 4.5 = 44.1 cm2 iv. Length = 9.8 cm, Breadth = 4.5 cm Perimeter = 2(L + B) = 2(8.6 + 6.2) = 2 (14.8) = 29.6 cm Area = L x B = 8.6 x 6.2 = 53.32 cm2 Q 5: Length of the water tank = 15 m Width of the water tank = 13 m Area = 15 x 13 = 195 m2 Q 6: Length of the park = 75 m Width of the park = 50 m Area of the park = 75 x 50 = 3750 m2 Perimeter = 75 + 50 + 75 + 50 = 250 m
CSS Primary Standard “Mathematics” 111 Q 7: Length of the squared card board = 50 cm Area = ? Area = 50 x 50 = 2500 cm2 Q 8: Length of the wall = 18m Width of the wall = 12 m Area of the wall = 18m x 12 m = 216 m2 Rate of painting = Rs. 200 Cost of painting the full wall = 216 x 200 = 43200 Review Exercise 8 Q 1: Choose the correct answer and fill the circle: 1. Area of square is .………... if the length of a side is 1: 1 2 3 4 2. perimeter of square is …… if length of the side is of square is 1 1 2 4 4 3. A figure having same starting and ending point is called……….. open figure closed figure point figure curve 4. Sum of all sides of a two dimension figure is called…….. area perimeter circumference volume 5. Space occupied by the close figure is called …………. area perimeter circumference volume 6. If the length of the rectangle is 10 cm and width is 5 cm, then the area of the rectangle is……. 30 50 60 40 7. If the length of the rectangle is 10 cm and width is 5 cm, then the perimeter of the rectangle is……. 30 50 60 40 8. The area of square is ………., if the length of a side of square is 10 cm. 10 1000 10000 100 Q 2: Perimeter = 13 cm + 13 cm + 13cm + 13 cm = 52 cm Area = 13 cm x 13 cm = 169 cm2
CSS Primary Standard “Mathematics” 112 Q 3: Length = 20 cm Breadth = 12 cm Perimeter = 2(L + B) = 2 (20 + 12) = 2(32) = 64 cm Area = L x B = 20 x 12 = 240 cm2 Q 4: Length of the square park = 330 m Perimeter = 330m + 330m + 330m + 330 = 1320 m Cost of wire per meter = Rs. 450 Total cost = 1320 x 450 = Rs. 594000 Week 4 & 5 Information Handling Lesson # 1 Teaching Objectives: To draw and interpret a bar graph/column graph. To draw and interpret a pie chart. To introduce averages. Learning Outcomes: Students should be able to: ☻ identify a graphical representation of data • draw a bar graph, a column graph, or a pie chart from given data • draw conclusions from a bar chart, a column graph, and a pie chart • calculate averages ☻Find the areas and perimeters of irregular shapes using a square grid and approximation. Teaching Materials: CSS Primary Standard Mathematics Book 5. Geometry box. Ruler. Set-squares. Clock with moveable hands. Board and markers/chalk. Sample graphs from newspapers, the Internet, or magazines. Charts. Excel sheets Classroom Activity: ☻ Introduce the concept of average as „normal‟ or „something that is in the middle of a range‟. It involves flattening out a range of numbers. Tahira‟s mother bought 100 sweets
CSS Primary Standard “Mathematics” 113 for her birthday party. Fifty were given to the children of the domestic staff. She packed the remaining 50 into 10 gift packets for Tahira‟s friends. But, the packets did not all contain the same number of sweets. She put 6 or 7 in each packet and realized that she was running out of sweets, so she started putting 3, 4, or 5 in the remaining packets. Tahira picked the largest one containing 8 sweets; Rahman‟s packet held 6, Mehru‟s 6, Syeeda‟s 6, Kishwer‟s 5, Alia‟s 5, Charu‟s 4, Lara‟s 4, Hameed‟s 3, and Neera‟s 3. What was the average number of sweets each child received? The average is calculated by dividing the total number of sweets by the number of children at the party. 50 /10 = 5. ☻ Use the explanation as given on pages # 117 and 118 to explain the concepts of Average. Exercise 9a Q 1: Find the average (arithmetic mean) of the following numbers: i. 1,2,3,4,5,6 Solution: Sum of values = 1 + 2 + 3 + 4 + 5 + 6 = 21 Number of values = 6 Average = Sum of values / number of values = 21/6 = 3.5 ii. 22cm, 13 cm, 14cm, 20cm, 25cm Solution: Sum of values = 22 + 13 + 14 + 20 + 25 = 94 Number of values = 5 Average = Sum of values / number of values = 94 / 5 = 18.8 cm iii. 3.2, 4.8, 5.5, 5.6 Solution: Sum of values = 3.2 + 4.8 + 5.5 + 5.6 = 19.1 m Number of values = 4 Average = 19.1/4 = 4.775 m iv. 430, 420, 320, 520, 680 Solution: Sum of values = 430 + 420 + 320 + 520 + 680 = 2370 Number of values = 5 Average = 474 v. 56km, 14km, 64km, 24km, 19km, 18km Solution: Sum of values = 56 + 14 + 64 + 24 + 19 + 18 = 195 Number of values = 6 Average = 195/6 = 32.5 km Q 2: Weight of four children:
CSS Primary Standard “Mathematics” 114 Zaheer’s weight = 32.2 kg Shahbaz’s weight = 37.2 kg Shahid’s weight = 41.5 kg Yaqoob’s weight = 38.9 kg Average weight = Sum of the weight Number of students = 32.2 + 37.2 + 41.5 + 38.9 = 150.1 = 37.525 4 4 How many children have weight more than average = 2 children Q 3: Duration of sunshine in Lahore = 12:13, 12:19, 12:10, 12:00, 12:15, 12:22 Average duration of sunshine = ? Average duration of sunshine = Sum of duration of sunshine / number of sunshine = 12.13 + 12.19 + 12.10 + 12.00 + 12.15 + 12.22 / 6 = 72.79 / 6 = 12.13 Q 4: Marks obtained by students inn class 5 are = 35, 39, 45, 38, 50 and 16 Average marks = ? Average marks = Sum of marks obtained / number of students = 35 + 39 + 45 + 38 + 50 + 16 / 6 = 223 / 6 = 37.16 Q 5: Given number = 2,3,5,7,11 Average = Sum of the given numbers / total numbers = 2 + 3 + 5 + 7 + 11/5 = 28/5 = 5.6 Q 6: Given heights of six runners = 160 cm, 137 cm, 153 cm, 155 cm, 149 cm, 152 cm Average height per runner = Sum of heights / number of height = 160 + 137 + 153 + 155 + 149 + 152/6 = 906/6 = 151 cm Q 7: Given numbers = first six multiples of 3 = 3,6,9,12,15,18 Average = Sum of numbers / total numbers = 3 + 6 + 9 + 12 + 15 + 18 / 6 = 63/6 = 10.5 Q 8: Total sale = Rs. 27874 Number of days = 7 Average = 27874/7 = Rs. 3982 Q 9: Distance covered in 3 hours = 42 km Distance covered in 4 hours = 56 km
CSS Primary Standard “Mathematics” 115 Average distance covered per hour = Total distance / total time = 56 + 42 / 4 + 3 = 98/7 = 14 km/hr Week 4 & 5 Information Handling Lesson # 2 Teaching Objectives: To draw and interpret a bar graph/column graph. To draw and interpret a pie chart. To introduce averages. Learning Outcomes: Students should be able to: ☻ identify a graphical representation of data • draw a bar graph, a column graph, or a pie chart from given data • draw conclusions from a bar chart, a column graph, and a pie chart • calculate averages ☻Find the areas and perimeters of irregular shapes using a square grid and approximation. Teaching Materials: CSS Primary Standard Mathematics Book 5. Geometry box. Ruler. Set-squares. Clock with moveable hands. Board and markers/chalk. Sample graphs from newspapers, the Internet, or magazines. Charts. Excel sheets Classroom Activity: ☻ Use the explanation as given on pages # 120, 121, 122, 123, 124 and 125 to explain the concepts of graphs. Exercise 9b
CSS Primary Standard “Mathematics” 116 Q 1: Q 2:
CSS Primary Standard “Mathematics” 117 Q 3: Q 4: i. Electronics ii. Items Shopping Education Car Petrol Home Furniture Food Electronics Monthly ‘Expenditures 1000 7000 5000 6000 3500 8000 Q 5: Class Interval Marks of the Students Tally Number of Students 305-324 305 I 1 325-344 345-364 350 I 1 365-384 365, 375, 377, 377, 381, 382, 383 IIII II 7 385-404 385, 387, 388, 389, 390, 391, 395, 395, 397, 399, 400 IIII IIII III 11 405-424 405, 405, 407, 408, 409, 412, 412, 413, 418, 421, 422, 422, 422 IIII IIII IIII I 13 425-444 428 I 1 445-464 448, 450, 452, 455, 455, 455, 455 IIII II 7 465-484 465, 481, 482, 477, 477 IIII 5 Review Exercise 6 Q 1: Choose the correct answer and fill the circle:
CSS Primary Standard “Mathematics” 118 1. Average is also known as: Arithmetic mean Medium Mode none of these 2. The average of 1,2,3 is: -1 -3 2 4 3. The average of 2,4,6,8 is: -3 5 -1 7 4. The arithmetic means of 1,3,5,7 is: -2 4 -6 8 5. Sum of Values / Number of Values = ……………….. Arithmetic mean Medium Mode none of these 6. Column graph is also known as……. 30 bar graph pie chart pictograph 7. Data is any information boy animal girl 8. On the graph, the vertical line is called. x-axis y-axis both a and b none of these 9. The horizontal line on the graph is called: x-axis y-axis both a and b none of these 10. The number of time a value occur in the data is called …………… frequency data average graph Q 2: Given number = 300, 315, 284, 246, 316 Sum of the numbers = 300 + 315 + 284 + 246 + 316 = 1461 Numbers = 5 Average = Sum of numbers / numbers = 1461/5 = 292.2 Q 3: Cost of toys = 205, 308, 415, 150, 137 and 200 Sum of the cost of toys = 205 + 308 + 415 + 150 + 137 + 200 = 1415
CSS Primary Standard “Mathematics” 119 Number of toys = 6 Average = 1415/6 = 235.83 Q 4: Q 5: Q 6: Frequency Distribution Table: Class Interval Marks of the Students Tally Number of Students 15-24 15, 17, 20, 21, 24 IIII 5 25-34 27, 27, 27, 29, 31, 32, 32 IIII II 7 35-44 35, 35, 35, 35, 38, 40,40, 41 IIII III 8 45-54 45, 48, 49, 50, 50, 54 IIII I 6 55-64 55, 57, 57, 60, 61 IIII 5 65-74 65, 65, 67, 68, 70 IIII 5
CSS Primary Standard “Mathematics” 120 Week 6 Complete Revision of 3rd Term Week 7 Complete Revision of 2nd Term Week 8 Complete Revision of 1st Term 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. The short form of Least Common Multiple is .………... LEM LCM LM LC 2. The number from which another number is subtracted is called ………... difference minuend divisor none of them 3. The answer of the subtraction is called ………... difference minuend divisor divider 4. The number which is multiplied is called ………... difference multiplicand divisor multiple 5. The result of the multiplication is called ………... product multiplicand divisor answer 6. For division, we use table of ………... product multiplicand divisor calculator 7. In some countries the word BODMAS is used as PEDMAS or BIDMAS. BODMAS PEDMAS MASMAS BITMAS
CSS Primary Standard “Mathematics” 121 8. When we write 10 digit numbers, we put (,) comma between billions, ………..., thousands and hundreds digits. billions millions trillions hundred 9. ………... stands for Bracket first, Order, Division, Multiplication, Addition and Subtraction. BODMAS BODMAD BODAAS PODMAS 10. The short form of Highest Common Factor is “………..”. HCF HF LCM HCCF 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
CSS Primary Standard “Mathematics” 122 19. 4.5 ÷ 1000 : 0.0045 0.45 0.00045 0.045 20. 4.5 x 1000 : 0.0045 0.45 0.00045 4500 21. The composition between .………... quantities of the same kind is called ratio. two one four three 22. If the price of a bubble is 5 rupees, then the price of 5 such bubbles will be…… 15 20 25 30 23. Farah travels with the constant speed. She covers 2 km in one hour. She will cover 8 km in……….. 1 4 2 3 24. Proportion is equality between two…….. quantities ratios variables proportions 25. Area of square is .………... if the length of a side is 1: 1 2 3 4 26. perimeter of square is …… if length of the side is of square is 1 1 2 4 4 27. A figure having same starting and ending point is called……….. open figure closed figure point figure curve 28. Average is also known as: Arithmetic mean Medium Mode none of these 29. The average of 1,2,3 is: -1 -3 2 4 30. The average of 2,4,6,8 is: -3 5 -1 7 Part B Time Allowed: 75 Minutes Total Marks: 45
CSS Primary Standard “Mathematics” 123 Note: Attempt All questions. All questions carry equal (3) Marks. 31.According to the Survey, the population of Turkey is 70, 536, 875 and the population of Iran is 85, 348, 390. How much population of both the countries altogether? 32.The price of a mobile is Rs. 103, 841. What will be the price of 324 sets of mobiles? 33.Solve the following: i. 34,692 x 700 ii. 895, 681 x 100 34.What does each circled digit stand for: i. 586, 348, 986 ii. 92, 145, 600 35.What number must be subtracted from 7/18 to get the difference of 1/9? 36.Zaid ate 11 /2 of pizza on dinner time and his friends are 21 /3 of pizza. How much pizza did they eat altogether? 37.The cost of an egg is Rs. 9.75. Find the cost of half dozen of eggs. 38.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? 39.The temperature yesterday was -4 o F in the morning and 13oF inn the evening. How much degrees did temperature rise? 40.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? 41.The price of mangoes and apples are Rs. 120 per kg and Rs. 160 per kg respectively. Find the ratio of the price of apple. Also find the total price of 5 kg of apples and 3 kgs of mangoes. 42.Construct a square LMNO having length of a side is 4cm. 43.Use compass and straightedge / ruler to construct a triangle ABC having measures mAB = 3cm, mBC = 4cm and mAC = 5cm. 44.Find the area of a rectangle having length of 7cm and breadth of 4 cm. 45.The below table shows the number of students of class-5 passed in a school. Years 2010 2011 2012 2013 2014 2015 Students 100 80 130 140 70 170 Represent the data in column or bar graph. Model Paper # 2 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)
CSS Primary Standard “Mathematics” 124 Section A Time Allowed: 45 Minutes Total Marks: 30 1. The smallest 10-digit number is .………... 1,000,000, 000 9,999,999,999 1,111,111,111 1,999,999,999 1. The largest 10-digit number is .………... 1,000,000, 000 9,999,999,999 1,111,111,111 1,999,999,999 3. Addition of smallest and greatest 3-digit number is ………... 199 1099 1000 1909 4. The subtraction of smallest 3-digit number from greatest three digit number is ………... 899 8099 8990 1000 5. When we multiply 610 by 10, we get ………... 610 6100 61 6.10 6. L.C.M of two prime number is their ………... product quotient sum difference 7. L.C.M of 5 and 15 is…….. 3 5 10 15 8. H.C.F is also called…... L.C.D G.C.D D.C.D D.V.D 9. BODMAS stands for Bracket first, Order, Division, Multiplication, Addition and …...….... sum subtraction all three addition 10. The short form of Least Common Multiple is “………..”. HCF HF LCM HCCF 11. 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
CSS Primary Standard “Mathematics” 125 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. Proportion is equality between two…….. quantities ratios variables proportions 22. 33 : 22 = …………. 11:12 3:2 9:15 4:5 23. The ratio of boys to the girls in the class is 3:4. If there are 27 boys, then the girls will be……. 12 36 45 40 24. The unit of ratio is…….
CSS Primary Standard “Mathematics” 126 m km cm no unit 25. Sum of all sides of a two dimension figure is called…….. area perimeter circumference volume 26. Space occupied by the close figure is called …………. area perimeter circumference volume 27. If the length of the rectangle is 10 cm and width is 5 cm, then the area of the rectangle is……. 30 50 60 40 28. The arithmetic means of 1,3,5,7 is: -2 4 -6 8 29. Sum of Values / Number of Values = ……………….. Arithmetic mean Medium Mode none of these 30. Column graph is also known as……. 30 bar graph pie chart pictograph Part B Time Allowed: 75 Minutes Total Marks: 45 Note: Attempt All questions. All questions carry equal (3) Marks. 31.There are 295 sweets in a packet. How many sweets are there in 364 packets? 32.Mr. Ali is a sales manager at mobile company. His salary includes commission and basic salary. His basic salary is Rs. 25000 per month and he is given Rs. 325 for the sale of each mobile. If his total salary for last month was Rs. 227, 800. How many mobiles did he sell last month? 33.Satisfy the distributive property: 5 x (6 + 9) = (5 x 6) + (5 x 9) 34.Find H.C.F of 13, 26 and 65 by using division method. 35.Abbas bought 32 /5 liters of petrol and Ali bought 83 /10 liters of petrol. e. How much petrol did they buy altogether? f. How much more petrol did Ali bought than Abbas? 36.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?
CSS Primary Standard “Mathematics” 127 37.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? 38.Zoya travelled 38km 586m by bus and 82km 324 m by car. Find the total distance she travelled. 39.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? 40.During the week, the temperature each day at noon was 26oC, 23oC and 21oC. Find each temperature at Fahrenheit scale? 41. 7 people can fill a water tank in 5 hours. How many hours will it take to complete the work if 3 persons leave the work? 42.Construct a triangle LMN having measures are mLM = 5cm, m˂M = m˂L. Find the length of other two sides. 43.Find the expenditures of painting a rectangular wall of length 18m and width 12m. The rate of painting per square meter is Rs. 200. 44.The total sale in coffee shop for a week is Rs. 27874. Find the average sale in each day. 45.Draw the frequency distribution table of the following set of 36 numbers using interval size of 10. 35, 32, 15, 27, 57, 50, 45, 35, 70, 65, 35, 32, 31, 40, 48, 50, 57, 55, 27, 60, 65, 68, 49, 24, 20, 17, 21, 27, 29, 35, 38, 40, 41, 54, 61, 67. 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. The short form of Least Common Multiple is .………... LEM LCM LM LC 2. The number from which another number is subtracted is called ………... difference minuend divisor none of them 3. The answer of the subtraction is called ………... difference minuend
CSS Primary Standard “Mathematics” 128 divisor divider 4. The number which is multiplied is called ………... difference multiplicand divisor multiple 5. The result of the multiplication is called ………... product multiplicand divisor answer 6. L.C.M of two prime number is their ………... product quotient sum difference 7. L.C.M of 5 and 15 is…….. 3 5 10 15 8. H.C.F is also called…... L.C.D G.C.D D.C.D D.V.D 9. BODMAS stands for Bracket first, Order, Division, Multiplication, Addition and …...….... sum subtraction all three addition 10. The short form of Least Common Multiple is “………..”. HCF HF LCM HCCF 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
CSS Primary Standard “Mathematics” 129 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. The unit of ratio is……. m km cm no unit 22. The increase / decrease in quantity because of increase/decrease in other quantity is called ……….proportion. continued indirect none of these direct 23. The increase / decrease in quantity because of decrease/ increase in other quantity is called ……….proportion. continued indirect none of these direct 24. The value of one toy is Rs. 84, the value of 3 toys of same kind is Rs. …… 252 162 182 172 25. If the length of the rectangle is 10 cm and width is 5 cm, then the perimeter of the rectangle is……. 30 50 60 40 26. The area of square is ………., if the length of a side of square is 10 cm. 10 1000 10000 100 27. Data is any information boy
CSS Primary Standard “Mathematics” 130 animal girl 28. On the graph, the vertical line is called. x-axis y-axis both a and b none of these 29. The horizontal line on the graph is called: x-axis y-axis both a and b none of these 30. The number of time a value occur in the data is called …………… frequency data average graph Part B Time Allowed: 75 Minutes Total Marks: 45 Note: Attempt All questions. All questions carry equal (3) Marks. 1. There are 295 sweets in a packet. How many sweets are there in 364 packets? 2. Mr. Ali is a sales manager at mobile company. His salary includes commission and basic salary. His basic salary is Rs. 25000 per month and he is given Rs. 325 for the sale of each mobile. If his total salary for last month was Rs. 227, 800. How many mobiles did he sell last month? 3. Satisfy the distributive property: 5 x (6 + 9) = (5 x 6) + (5 x 9) 4. Find H.C.F of 13, 26 and 65 by using division method. 5. Abbas bought 32 /5 liters of petrol and Ali bought 83 /10 liters of petrol. g. How much petrol did they buy altogether? h. How much more petrol did Ali bought than Abbas? 6. 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? 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. Zoya travelled 38km 586m by bus and 82km 324 m by car. Find the total distance she travelled. 9. The temperature yesterday was -4 o F in the morning and 13oF inn the evening. How much degrees did temperature rise? 10.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?
CSS Primary Standard “Mathematics” 131 11.The price of mangoes and apples are Rs. 120 per kg and Rs. 160 per kg respectively. Find the ratio of the price of apple. Also find the total price of 5 kg of apples and 3 kgs of mangoes. 12.Construct a square LMNO having length of a side is 4cm. 13.Use compass and straightedge / ruler to construct a triangle ABC having measures mAB = 3cm, mBC = 4cm and mAC = 5cm. 14.Find the area of a rectangle having length of 7cm and breadth of 4 cm. 15.The below table shows the number of students of class-5 passed in a school. Years 2010 2011 2012 2013 2014 2015 Students 100 80 130 140 70 170 Represent the data in column or bar graph.