CSS Primary Standard “Mathematics” 1 CSS Primary Standard Mathematics For Class 5 Division of Syllabus into three terms Teacher‟s Guide Fully Solved Exercises Model Papers
CSS Primary Standard “Mathematics” 2 TABLE OF CONTENTS Division of Syllabus 3 Unit # 1 5 Unit # 2 22 Model Paper # 1 36 Model Paper # 2 38 Model Paper # 3 40 Unit # 3 43 Unit # 4 59 Unit # 5 72 Model Paper # 1 87 Model Paper # 2 90 Model Paper # 3 94 Unit # 6 98 Unit # 7 107 Unit # 8 108 Unit # 9 112 Model Paper # 1 120 Model Paper # 2 123 Model Paper # 3 127
CSS Primary Standard “Mathematics” 3 Division of Syllabus 1 st Term Week 1 Unit # 1… Numbers and Arithmetic Operations Numbers Numbers upto one billion Addition and Subtraction Multiplication and Division BODMAS Rule Week 2 Week 3 Week 4 Week 5 Monthly Test / Revision of Unit # 1 Week 6 Unit # 2…Factors and Multiples Highest Common Factor (HCF) Least Common Multiple (LCM) Week 7 Week 8 Week 9 Monthly Test / Revision of Unit # 2 Week 10 Final Test 2 nd Term Week 1 Unit # 3…Fractions Addition and Subtraction of Fractions. Multiplication of Fraction Division of Fraction The use of BODMAS Rule Week 2 Week 3 Week 4 Unit # 4…Decimals and Percentages Decimals Rounding Off Decimals Decimals and Percentages Week 5 Week 6 Monthly Test / Revision of Unit # 3 & 4 Week 7 Unit # 5…Distance Time and Temperature Length Time Temperature Week 8 Week 9 Week 10 Week 11 Monthly Test / Revision of Unit # 3 and 4 Week 12
CSS Primary Standard “Mathematics” 4 Week 13 Revision of Unit # 5 and 6 Week 14 Final Test 3 rd Term Week 1 Unit # 6…Unitary Method Week 2 Unit # 7…Geometry Week 3 Week 4 Unit # 8…Information Handling Unit # 7: Perimeter and Area Week 5 Week 6 Complete Revision of 3rd Term Week 7 Complete Revision of 2nd Term Week 8 Complete Revision of 1st Term
CSS Primary Standard “Mathematics” 5 Week 1, 2, 3 & 4 Number and Arithmetic Operations Lesson # 1 Teaching Objectives: ☻ To revise large numbers. ☻ To introduce the Pakistani system of place value. ☻ To introduce place value up to 10-digit numbers and introduces the concept of a billion. ☻ To compare and order numbers up to 10 digits. ☻ To revise properties of addition and introduce addition of large numbers. ☻ To revise properties of subtraction and introduce subtraction of large numbers. ☻ To demonstrate multiplication of large numbers and verify multiplication properties. ☻ To introduce division of large numbers. ☻ To introduce multiplication and division by 10, 100, 1000. ☻ To explain the order of number operations. ☻ To explain BODMAS rule. Learning outcomes: Students should be able to: ☻ Differentiate between the international place value system and the Pakistani system of notation. ☻ Identify numbers up to a billion, and 10-digit numbers. ☻ Add, subtract, multiply, and divide large numbers. ☻ Perform multi-operation simplification using BODMAS. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: Step by step, numbers up to a million have been introduced in Mathematics Book 4. The concept has been introduced based on the student's knowledge from previous years of place value of numbers. Comparison of place value has been done pictorially: visual and practical teaching enhances understanding and support learning. This is not the first time the students are introduced to the concept of the international system of writing numbers. However, it is important to compare the same number in both writing styles.
CSS Primary Standard “Mathematics” 6 Reinforce the fact that same number may be written in 2 different notations, dividing a large number into two different patterns of grouping. This does not change the value of the number. It is just two different ways of representing the same quantity. Simple examples: 30 years is the same as 3 decades. 60 apples is the same as 5 dozen apples. 900 years is the same as 9 centuries. 10 000 years is the same as 10 millennia. Answer any queries the students may have regarding the two styles. Show them how both styles of writing are used in real life. You may take newspapers of Pakistan and online international newspapers to show both styles of notation… crores and lakhs, versus billions, millions, and hundreds of thousands. The most important point to remember is that in the international system numbers are divided into ALL groups of 3: Units, Tens and Hundreds, as against the Pakistani system of notation. International System of Notation: H T O H T O H T O Hundred Tens Ones Billions Millions Thousands Units Pakistani System of Notations: T O T O T O Hundred Tens Ones Crores Lakhs Thousands Units You may want to conduct a small activity of comparing both the styles of notation. Divide the students into pairs. One student writes an 8-9 digit number in the international system of notation on a large sheet of paper and holds it up for the other student to see. The second student reads it out aloud, and writes the same number in crores and lakhs, and holds up his/her numbers. Then repeat the activity with the students taking opposite roles. Exercise 1a Q 1: Write the following numbers in words: i. 214, 629: 2 hundred thousands, 1 ten thousands, 4 thousands, 6 hundred, 2 tens, 0 units. ii. 46, 589, 533: 4 ten millions, 6 millions, 5 hundred thousands, 8 ten thousands, 9 thousands, 5 hundred, 3 tens, 3 units. iii. 59, 306, 588: 5 ten millions, 9 millions, 3 hundred thousands, 0 ten thousands, 6 thousands, 5 hundred, 8 tens, 8 units.
CSS Primary Standard “Mathematics” 7 iv. 22, 566, 621: 2 ten millions, 2 millions, 5 hundred thousands, 6 ten thousands, 6 thousands, 6 hundred, 2 tens, 1 units. v. 61, 216, 834: 6 ten millions, 1 millions, 2 hundred thousands, 1 ten thousands, 6 thousands, 8 hundred, 3 tens, 4 units. Q 2: What does each digit stands for in numbers given below: i. 568, 924, 126 = 500,000,000 + 60,000,000 + 8,000,000 + 900,000 + 20,000 + 4,000 + 100 + 20 + 6 ii. 256, 241, 609 = 200,000,000 + 50,000,000 + 6,000,000 + 200,000 + 40,000 + 1,000 + 600 + 00 + 9 Q 3: Write the following in numerals: i. Three hundred sixty four millions, two hundred three thousands, five hundred and ninety five. = 364, 203, 595 ii. Two hundred fifty six millions, three hundred twenty nine thousands, four hundred and fifty six. = 256, 329, 456 iii. Two hundred fifty five millions, four hundred twenty six thousands, nine hundred. = 255, 426, 900 iv. Two millions, five hundred three thousands, eight hundred and six. = 2, 503, 806 Q 4: Observe the commas carefully and write the values of the digits in pink boxes: i. 894, 385, 600 = 80,000 ii. 560, 849, 621 = 500,000,000 iii. 894, 381, 440 = 4,000,000 iv. 569, 431, 428 = 60,000,000 Number and Arithmetic Operations Lesson # 2 Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: The four number operations have been handled using 6- digit numbers in Mathematics Book 4. Handling larger numbers should not be difficult provided the students have understood their concepts in the previous years.
CSS Primary Standard “Mathematics” 8 Discuss the words 'sum', 'difference', 'product', and 'quotient', before they start working out problems. Exercise 1b Q 1: Add the following: i. 58, 964, 308 and 59, 420, 000 ii. 321, 624, 550 and 95, 384, 311 H T O H T O H T O H T O H T O H T O Millions Thousands Units Millions Thousands Units 5 8 9 6 4 3 0 8 3 2 1 6 2 4 5 5 0 + 5 9 4 2 0 0 0 0 + 9 5 3 8 4 3 1 1 1 1 8 3 8 4 3 0 8 4 1 7 0 0 8 8 6 1 iii. 28, 942, 420 and 61, 211, 692 iv. 294, 568, 334 and 321, 861, 321 H T O H T O H T O H T O H T O H T O Millions Thousands Units Millions Thousands Units 2 8 9 4 2 4 2 0 2 9 4 5 6 8 3 3 4 + 6 1 2 1 1 6 9 2 3 2 1 8 6 1 3 2 1 9 0 1 5 4 1 1 2 6 1 6 4 2 9 6 5 5 v. 246, 321, 413 and 111,050, 681 vi. 5,824, 386 & 6,892, 456 & 9,843, 321 & 4,561, 211 H T O H T O H T O H T O H T O H T O Millions Thousands Units Millions Thousands Units 2 4 6 3 2 1 4 1 3 5 8 2 4 3 8 6 1 1 1 0 5 0 6 8 1 6 8 9 2 4 5 6 3 5 7 3 7 2 0 9 4 9 8 4 3 3 2 1 + 4 5 6 1 2 1 1 2 7 1 2 1 3 7 4 Q 2: Subtract the following: i. 846, 295, 341 and 32, 599, 891 ii. 468, 321, 844 and 288, 321, 001 H T O H T O H T O H T O H T O H T O Millions Thousands Units Millions Thousands Units 11 18 14 12 14 3 16 8 4 5 2 9 5 3 4 1 4 6 8 3 2 1 8 4 4 - 3 2 5 9 9 8 9 1 2 8 8 3 2 1 0 0 1 8 1 2 6 9 5 4 5 0 1 8 0 0 0 0 8 4 3
CSS Primary Standard “Mathematics” 9 iii. 456, 982, 111 and 32, 841, 000 iv. 4, 560, 982 and 561, 302 H T O H T O H T O H T O H T O H T O Millions Thousands Units Millions Thousands Units 14 15 10 4 5 6 9 8 2 1 1 1 4 5 6 0 9 8 2 - 3 2 8 4 1 0 0 0 - 5 6 1 3 0 2 4 2 4 1 4 1 1 1 1 3 9 9 9 6 8 0 v. 682, 584, 100 and 298, 520, 000 vi. 384, 891, 621 and 104, 813, 321 H T O H T O H T O H T O H T O H T O Millions Thousands Units Millions Thousands Units 5 17 12 8 11 6 8 2 5 8 4 1 0 0 3 8 4 8 9 1 6 2 1 2 9 8 5 2 0 0 0 0 1 0 4 8 1 3 3 2 1 3 8 4 0 6 4 1 0 0 2 8 0 0 7 8 3 0 0 Q 3: Simplify the following: i. 849, 568, 332 – 2,156, 841 + 40, 985, 611 Solution: 849, 568, 332 – 2,156, 841 + 40, 985, 611 = 849, 568, 332 + 40, 985, 611 - 2,156, 841 = 890, 553, 943 - 2,156, 841 = 888, 397, 102 ii. 498, 321, 611 + 241 – 85,692, 581 + 41, 386 Solution: 498, 321, 611 + 241 – 85,692, 581 + 41, 386 = 498, 321, 611 + 241 – 85,692, 581 + 41, 386 = 498, 321, 611 + 241 + 41, 386 – 85,692, 581 = 498, 363, 238 – 85, 692, 581 = 412, 670, 657 Q 4: The total income of a private bank in 2008 was Rs. 962, 389, 210 and the expenditures were Rs. 238, 659, 000. Find the net profit of the bank. Solution: Total Income = 962, 389, 210 Total Expenditures = 238, 659, 200 Net Profit = Total Income – Expenditures = 962, 389, 210 – 238, 659, 200 = 723, 730, 010 Rupees H T O H T O H T O Millions Thousands Units 5 11 13 9 6 2 3 8 9 2 1 0 2 3 8 6 5 9 2 0 0 7 2 3 7 3 0 0 1 0
CSS Primary Standard “Mathematics” 10 Q 5: The total exports of a country for the year 2012 were 342, 846, 042 and for the year 2013 was 56, 845, 392. How much exports of the country altogether for both years? Solution: Exports in 2012 = 342, 846, 042 Exports in 2013 = 56, 845, 392 Total Exports = = Exports of 2012 + Exports of 2013 = 342, 846, 042 + 56, 845, 392 = 399, 691, 434 H T O H T O H T O Millions Thousands Units 3 4 2 8 4 6 0 4 2 + 5 6 8 4 5 3 9 2 3 9 9 6 9 1 4 3 4 Q 6: What is the difference between smallest ten digit number and largest 8 digit number? Solution: Smallest ten digit number = 1,000,000,000 Largest 8 digit number = 99,999,999 Difference = 1,000,000,000 – 99,999,999 = 900,000,001 Exercise 1c Q 1: Multiply i. 34, 692 x 7 ii. 895, 681 x 1 H T O H T O H T O H T O H T O H T O Millions Thousands Unit Millions Thousands Unit 3 4 6 9 2 8 9 5 6 8 1 x 7 x 1 2 4 2 8 4 4 8 9 5 6 8 1 iii. 34, 692 x 70 iv. 895, 681 x 10 H T O H T O H T O H T O H T O H T O Millions Thousands Unit Millions Thousands Unit 3 4 6 9 2 8 9 5 6 8 1 x 7 0 x 1 0 0 0 0 0 0 0 0 0 0 0 0 2 4 2 8 4 4 0 8 9 5 6 8 1 0 2 4 2 8 4 4 0 8 9 5 6 8 1 0
CSS Primary Standard “Mathematics” 11 v. 34, 692 x 700 vi. 895, 681 x 100 H T O H T O H T O H T O H T O H T O Millions Thousands Unit Millions Thousands Unit 3 4 6 9 2 8 9 5 6 8 1 x 7 0 0 x 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 2 8 4 4 0 0 8 9 5 6 8 1 0 0 2 4 2 8 4 4 0 0 8 9 5 6 8 1 0 0 vii. 34, 692 x 7000 viii. 895, 681 x 1000 H T O H T O H T O H T O H T O H T O Millions Thousands Unit Millions Thousands Unit 3 4 6 9 2 8 9 5 6 8 1 x 7 0 0 0 x 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 2 8 4 4 0 0 0 8 9 5 6 8 1 0 0 0 2 4 2 8 4 4 0 0 0 8 9 5 6 8 1 0 0 0 Q 2: Solve the following: i. 341, 298 x 23 ii. 684, 294 x 14 H T O H T O H T O H T O H T O H T O Millions Thousands Unit Millions Thousands Unit 3 4 1 2 9 8 6 8 4 2 9 4 x 2 3 x 1 4 1 0 2 3 8 9 4 2 1 3 7 1 7 6 6 8 2 5 9 6 0 6 8 4 2 9 4 0 7 8 4 9 8 5 4 8 9 8 0 1 1 6
CSS Primary Standard “Mathematics” 12 iii. 524, 390 x 184 iv. 489, 324 x 129 H T O H T O H T O H T O H T O H T O Millions Thousands Unit Millions Thousands Unit 1 8 1 8 2 2 3 5 2 4 3 9 0 4 8 9 3 2 4 x 1 8 4 x 1 2 9 2 0 9 7 5 6 0 4 4 0 3 9 1 6 4 1 9 5 1 2 0 0 9 7 8 6 4 8 0 5 2 4 3 9 0 0 0 4 8 9 3 2 4 0 0 9 6 4 8 7 7 6 0 6 3 1 2 2 7 9 6 iv. 241, 864 x 420 v. 884, 958 x 642 H T O H T O H T O H T O H T O H T O Millions Thousands Unit Millions Thousands Unit 3 1 1 1 2 4 1 8 6 4 8 8 4 9 5 8 x 4 2 0 x 6 4 2 0 0 0 0 0 0 1 7 6 9 9 1 6 4 8 3 7 2 8 0 3 5 3 9 8 3 2 0 9 6 7 4 5 6 0 0 5 3 0 9 7 4 8 0 0 1 0 1 5 8 2 8 8 0 5 6 8 1 4 3 0 3 6 Q 3: Solve the following: i. 12545 ÷ 5 ii. 187, 616 ÷ 143 iii. 313, 636 ÷ 184 iv. 833, 170 ÷ 845
CSS Primary Standard “Mathematics” 13 v. 175, 686 ÷ 329 vi. 326, 922 ÷ 529 Q 4: The price of a sugar bag is Rs. 6894. What will be the price of 312 such bags of sugar? Solution: Price of a Sugar Bag = Rs. 6894 Price of 312 sugar bags = 6894 x 312 = Rs. 2, 150, 928 H T O H T O H T O Millions Thousands Unit 6 8 9 4 x 3 1 2 1 3 7 8 8 6 8 9 4 0 2 0 6 8 2 0 0 2 1 5 0 9 2 8 Q 5: There are 295 sweets in a packet. How many sweets are there in 364 packets? Solution: Sweets in a packet = 295 Sweets in 364 packets = 295 x 364 = 107, 380 sweets H T O H T O H T O Millions Thousands Unit 2 9 5 x 3 6 4 1 8 2 0 3 2 7 6 0
CSS Primary Standard “Mathematics” 14 1 0 9 0 0 0 1 0 7 3 8 0 Q 6: Basic Salary of Ahmad = Rs. 25,000 Ahmad‟s salary for the last month = 227, 800 Commission amount = 227,800 - 25000 = 202, 800 Number of mobiles sold = 202,800 ÷ 325 = 624 Mobiles Number and Arithmetic Operations Lesson # 3 Teaching Objectives: ☻ To revise large numbers. ☻ To introduce the Pakistani system of place value. ☻ To introduce place value up to 10-digit numbers and introduces the concept of a billion. ☻ To compare and order numbers up to 10 digits. ☻ To revise properties of addition and introduce addition of large numbers. ☻ To revise properties of subtraction and introduce subtraction of large numbers. ☻ To demonstrate multiplication of large numbers and verify multiplication properties. ☻ To introduce division of large numbers. ☻ To introduce multiplication and division by 10, 100, 1000. ☻ To explain the order of number operations. ☻ To explain BODMAS rule. Learning outcomes: Students should be able to: ☻ Differentiate between the international place value system and the Pakistani system of notation. ☻ Identify numbers up to a billion, and 10-digit numbers. ☻ Add, subtract, multiply, and divide large numbers. ☻ Perform multi-operation simplification using BODMAS. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: The new concept that has been introduced in Maths Wise 5 is the order of operations in
CSS Primary Standard “Mathematics” 15 an expression, according to the commutative, associative, and distributive laws. It is important for students to understand why we need to fix an order in which operations have to be performed in a multi-operation simplification problem. Explain this idea with a real life problem: Example 1: Anoral has Rs 150 in her bag. She needs to buy a geometry box for Rs 300 and have some money left for donation to an orphanage. She looked through her savings and found Rs 250 in it. Once she buys the geometry box, how much money does she have left for the donation? This can be written as: 150 – 300 + 250 = 400 – 300 = 100 This can also be written as: 150 + 250 – 300 = 400 – 300 = 100 Anoral has Rs100 left for the donation. So, at this level, students need to ADD before they subtract. Example 2: Maher goes to a shop to buy some groceries with Rs 600. Maher buys 3 kg flour at Rs 50 per kg. If this is worked out as: 600 – 50 × 3 = 550 × 3 = 1650 × … This is incorrect. Therefore, rules were made which said: Work out Multiplication, before Subtraction. 600 – 50 × 3 = 500 – 150 = 450 this is correct. Or, use brackets: 600 – (50 × 3) = 500 – 150 = 450 Multiplication MUST BE DONE BEFORE addition or subtraction. The above operations need to be performed in the exact order as above. Alteration in the order will not only produce a completely different result, but will not be logically correct. With other similar examples, one can arrive at BODMAS, which gives the order of operations as follows: Brackets, Of (Multiplication before ×), Division, Multiplication, Addition, Subtraction Example 3: Zain goes to a shop to buy some groceries with Rs 500. He buys 2 kg sugar at Rs 45 per kg, 3 packets of biscuits at Rs 30 a packet, and a bottle of orange juice for Rs 125. The remaining money is distributed equally among 5 needy women. How much money did each woman get? 500 – 2 × 45 – 3 × 30 – 125 OR 500 – 2 × 45 – 3 × 30 – 125 = 500 – (2 × 45) – (3 × 30) – 125 = 500 – (2 × 45) – (3 × 30) – 125 = 500 – 90 – 90 – 125 = 500 – (90 + 90 + 125) = 410 – 90 – 125 = 500 – 305 = 320 – 125 = 195 = 195 The second format needs to be explained. Ali‟s wallet has Rs 300. Ali needs to take out from his
CSS Primary Standard “Mathematics” 16 savings box Rs 50 on the 1st day, Rs 25 the 2nd day, and Rs 60 on 3rd day: It is correct to write: Rs 300 – (50 + 25 + 60) = Rs 300 – Rs 135 = Rs 165 The concept of the use of brackets can only be explained by working this problem practically. Rs 300 in small notes in a wallet … take out Rs 50, Rs 25, and Rs 60 and place the money on the desk. What total amount of money has been taken out from the wallet, and given out to the shopkeeper? 300 – 50 – 25 – 60 = 300 – (50 + 25 + 60) = 300 – 135 = 165 Now getting back to example 3. Rs 195 is to be divided amongst 5 women: 195 5 = 39 Each woman gets Rs 39. The operations you need to perform are as follows: cost of 2 kg sugar = 2 × 45 = Rs 90 cost of 3 packets of biscuits = 3 × 30 = 90 total expenses = 90 + 90 + 125 (juice) = Rs 305 therefore, money left = 500 – 305 = Rs 195 therefore, each each women gets Rs 195/5 = Rs 39 To work out the entire problem, use brackets. Explain to the students the use of a bracket … a bracket tells you „Work the problem inside the brackets first‟. 500 – (2 × 45) – (3 × 30) – 125 = 500 – 90 – 90 – 125 = 500 – 350 = 195 Exercise 1d Q 1: Find the missing numbers: i. 7 x (5 + 2) = 7 x 5 + 7 x 2 ii. 3 x (8 + 4) = 3 x 8 + 3 x 4 iii. 9 x (6 + 15) = (9 x 6) + (9 x 15) iv. 8 x (6 + 7) = (8 x 6) + (8 x 7) Q 2: Rewrite the expression using distributive property of multiplication and then solve: i. 6 x (5 + 3) = (6 x 5) + (6 x 3) = 30 + 18 = 48 ii. 2 x (7 + 4) = (2 x 7) + (2 x 4) = 14 + 8 = 22 iii. 9 x (9 + 4) = (9 x 9) + (9 x 4) = 81 + 36 = 117
CSS Primary Standard “Mathematics” 17 iv. 2 x (6 + 2) = (2 x 6) + (2 x 2) = 12 + 4 = 16 Q 3: Calculate using BODMAS rule: i. 18 ÷ 6 x 8 + 10 = (18 ÷ 6) x 8 + 10 = 3 x 8 + 10 = 80 + 10 = 90 ii. 80 ÷ 16 - 16 + 4 = (80 ÷ 16) - 16 + 14 = 5 - 16 + 14 = 5 + 14 - 16 = 19 - 16 = 3 iii. 12 - 6 + 11 + 2 = 12 + 11 + 2 - 6 = 25 - 6 = 19 iv. 24 ÷ 6 - 3 + 11 = (24 ÷ 6) - 3 + 11 = 4 - 3 + 11 = 4 + 11 - 3 = 15 - 3 = 12 v. 9 + 16 - 16 ÷ 4 = 9 + 16 - (16 ÷ 4) = 9 + 16 - 4 = 25 - 4 = 21 vi. 3 x 24 ÷ 12 - 2 = 3 x (24 ÷ 12) - 2 = 3 x 2 - 2 = 6 - 2 = 4 Match the equal quantities using BODMAS rule: Review Exercise 1 Q 1: Choose the correct answer and fill the circle: 1. The smallest 10-digit number is .………... 1,000,000,000 9,999,999,999 1,111,111,111 1,999,999,999 2. The largest 10-digit number is …………. 1,000,000,000 9,999,999,999 1,111,111,111 1,999,999,999 3. One billion can be written as……. 100,000,000 1,000,000,000
CSS Primary Standard “Mathematics” 18 100,000,000,000 1,000,000 4. Four hundreds sixty nine million is in numeral form: 469,000,000,000 469,000,000 469,000 469,000,000,000,000 5. Addition of smallest and greatest three digit number is: 199 1099 1909 1000 6. The subtraction of smallest three digit number from greatest three digit number is: 899 8099 8990 1000 7. Dividing 610 by 10 is …. 6100 610 6.10 61 8. Which operation will be performed first? addition subtraction multiplication division 9. When we multiply 610 by 10 we get: 6100 610 6.10 61 10. 3 x 4 + 55 – 1: 12 13 14 66 Q 2: Write the following in words: i. 342, 841, 612 = Three hundred forty two millions, eight hundred forty one thousands, six hundred and twelve. ii. 92, 586, 401 = Ninety two millions, five hundred eighty six thousands, four hundred and one. iii. 851, 489, 341 = Eight hundred fifty one millions, four hundred eighty nine thousands, three hundred and fifty one. Write the following in numerals: i. Two hundreds ninety four millions, three hundred twenty five tousands, six hundreds and twenty five. = 294, 325, 625 ii. One hundred sixty five millions, two hundred thirty five thousands, nine hundred and twenty two. = 165, 235, 922 iii. Sixty five millions, two hundred ninety five thousands, six hundred and twenty nine.
CSS Primary Standard “Mathematics” 19 = 65, 295, 629 Q 4: What does each circled digit stands for? i. 586, 348, 986 = 6,000,000 ii. 389, 458, 600 = 300,000,000 iii. 925, 145, 600 = 45,000 Q 5: Put commas in the correct place: i. 321526859 = 321, 526, 859 ii. 21692143 = 21, 692, 143 iii. 841321614 = 841, 321, 614 Q 6: Do the following Sums: i. 925, 128, 601 + 285, 381, 416 + 125, 328 ii. 924, 843, 684 – 841, 894 H T O H T O H T O H T O H T O H T O Millions Thousands Units Millions Thousands Units 2 15 18 9 2 5 1 2 8 6 0 1 9 2 4 8 4 3 6 8 4 2 8 5 3 8 1 4 1 6 0 0 0 8 4 1 8 9 4 + 1 2 5 3 2 8 9 2 4 0 0 1 7 9 0 12 1 0 6 3 5 3 4 5 iii. 62, 859, 458 + 681, 452, 341 + 205 iv. 856, 324, 581 – 2,113, 470 H T O H T O H T O H T O H T O H T O Millions Thousands Units Millions Thousands Units 6 2 8 5 9 4 5 8 8 5 6 3 2 4 5 8 1 6 8 1 4 5 2 3 4 1 0 0 2 1 1 3 4 7 0 + 2 0 5 8 5 4 2 0 1 1 1 1 7 4 4 3 1 2 0 0 4 Q 7: Solve: i. 481, 382 x 10 ii. 481, 382 x 100 H T O H T O H T O H T O H T O H T Millions Thousands Unit Millions Thousands Unit 4 8 1 3 8 2 4 8 1 3 8 2 x 1 0 x 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 8 1 3 8 2 0 0 0 0 0 0 0 0 4 8 1 3 8 2 0 4 8 1 3 8 2 0 0 4 8 1 3 8 2 0 0
CSS Primary Standard “Mathematics” 20 iii. 481, 382 x 1000 iv. 924, 621 x 5 H T O H T O H T O H T O H T O H T O Millions Thousands Unit 1 2 3 1 4 8 1 3 8 2 9 2 4 6 2 1 x 1 0 0 0 x 5 0 0 0 0 0 0 4 6 2 3 1 0 5 0 0 0 0 0 0 0 4 8 1 3 8 2 0 0 4 8 1 3 8 2 0 0 v. 586, 589 x 421 iv. 732, 859 x 39 H T O H T O H T O H T O H T O H T O Millions Thousands Unit 5 8 6 5 8 9 7 3 2 8 5 9 x 4 2 1 x 3 9 5 8 6 5 8 9 6 5 9 5 7 3 1 1 1 7 3 1 7 8 0 2 1 9 8 5 7 7 0 2 3 4 6 3 5 6 0 0 2 8 5 8 1 5 0 1 2 4 6 9 5 3 9 6 9 Q 8: Divide: 186, 329 by 13 859, 329 by 132 280, 000 by 280
CSS Primary Standard “Mathematics” 21 Q 9: Do the following sums: i. 684 ÷ 2 x 5 - 921 + 18 - (35 - 12 x 2) = 684 ÷ 2 x 5 - 921 + 18 - (35 - 24) = 684 ÷ 2 x 5 - 921 + 18 - (11) = (684 ÷ 2) x 5 - 921 + 18 - 11 = 342 x 5 - 921 + 18 - 11 = 1710 - 921 + 18 - 11 = 1710 + 18 - 921 - 11 = 1728 - 932 = 796 ii. 921 ÷ 3 x 3 + 6 - 200 + (51 ÷ 17 x 3) = 921 ÷ 3 x 3 + 6 - 200 + (51 ÷ 17 x 3) = 921 ÷ 3 x 3 + 6 - 200 + (3 x 3) = 921 ÷ 3 x 3 + 6 - 200 + 9 = (921 ÷ 3) x 3 + 6 - 200 + 9 = 307 x 3 + 6 - 200 + 9 = 921 + 6 + 9 - 200 = 936 - 200 = 736 Q 10: Check the distributive property satisfy or not? i. 9 x (2 + 6) = (3 + 9) x 6 Solution: L.H.S 9 x (2 + 6) = (9 x 2) + (9 x 6) = 18 + 54 = 72 ……i R.H.S (3 + 9) x 6 = (3 x 6) + (9 x 6) = 18 + 54 = 72 …….ii From (i) and (ii) L.H.S = R.H.S Distributive property holds. ii. 18 x (16 + 15) = (18 x 16) + (18 x 15) Solution: L.H.S
CSS Primary Standard “Mathematics” 22 18 x (16 + 15) = (18 x 16) + (18 x 15) = 288 + 270 = 558…….i R.H.S (18 x 16) + (18 x 15) = (18 x 16) + (18 x 15) = 288 + 270 = 558…….ii From (i) and (ii) L.H.S = R.H.S Distributive property holds. Week 5 Monthly Test / Revision of Unit # 1 Week 6, 7, & 8 Factors and Multiples Lesson # 1 Teaching Objectives: ☻ To revise factors and multiples. ☻ To recap prime and composite numbers. ☻ To reinforce divisibility tests. ☻ To introduce prime factorization using the division and long division method. ☻ To introduce HCF using prime factorization, and long division. ☻ To find the LCM by listing common multiples, prime factorization, and short division of 3 numbers. Learning outcomes: Students should be able to: ☻ Use divisibility rules when dividing given numbers. ☻ Differentiate between prime and composite numbers. ☻ Identify and find factors and multiples of a number. ☻ Find the HCF using short division, and long division. ☻ Find the LCM of 3 numbers by prime factorization and the short division method. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker.
CSS Primary Standard “Mathematics” 23 Eraser. Classroom Activity: In class 4 students were introduced to the concept of HCF and LCM. As always, start the lesson with a revision of the basic concepts. You could conduct a quiz or have a class discussion or carry out some of the suggested activities during revision. Why do we need to find LCM of numbers? Addition of fractions cannot be done accurately without finding the LCM of denominators. LCM is important in everyday life for time and speed, and time and work problems, different people running around circular race tracks, timing of bells and flashing lights, such as from a lighthouse. HCF is important to find the largest size of tiles that may fit into rooms, while constructing a building. Any such activity is not merely useful in its mathematical field, but increases the power of reasoning and thinking. Introduce Prime Numbers: 2, 3, 5, 7, 11, 13, and so on. A prime number is a natural number greater than 1 that can be divided ONLY by the number itself and 1. All other numbers are composite numbers. 17 is a prime number because it has no factors other than 1 and itself. 17 ÷ 1 = 17 and 17 ÷ 17 = 1 Prime Numbers: 2, 3, 5, 7, 9, 11, 13, 15, 17 Composite Numbers: 4, 6, 8, 10, 12, 14, 16, 18 Prime and composite numbers can be placed in groups as shown below A composite number can be placed in rectangular formats. A prime number cannot be placed in rectangular formats like above. Here are the prime numbers below 100, which can be shown on the 1 to 100 number charts. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Prime and Composite Numbers: Discuss the meaning of prime and composite numbers and the importance of prime numbers. Then perform the Eratosthenes sieve test for prime numbers and list out the first 20 prime numbers. Explain the positioning of the prime and composite numbers in a 1 to 100 number square. The following information is important for you: ☻ No two prime numbers, other than 2 and 3, are consecutive. ☻ No prime number, other than 2, has an even number in its unit digit. ☻ No prime number, other than 5, has 5 or 0 in its unit digit. ☻ No prime number has the sum of its digits which is divisible by 3 or multiples of 3. ☻ No prime number has difference between the sums of alternate digits as 11, or a multiple of 11. ☻ The smallest prime number is 2. ☻ The smallest composite number is 4.
CSS Primary Standard “Mathematics” 24 There is no biggest prime number or composite number. Numbers go into infinity > > > > Discuss the answers to the following questions: ☻ Which is an even prime number? ☻ Why is it the only even prime? ☻ What are the number 0 and 1 called? ☻ Why? ☻ What are composite numbers? ☻ What are the differences between prime and composite numbers? ☻ No prime number greater than 5 ends in 5. Why? ☻ Which is the greatest/smallest prime number? ☻ How many prime numbers are there? Put the chart of prime numbers between 1 and 1000 in class. Week 6, 7, & 8 Factors and Multiples Lesson # 2 Teaching Objectives: ☻ To revise factors and multiples. ☻ To recap prime and composite numbers. ☻ To reinforce divisibility tests. ☻ To introduce prime factorization using the division and long division method. ☻ To introduce HCF using prime factorization, and long division. ☻ To find the LCM by listing common multiples, prime factorization, and short division of 3 numbers. Learning outcomes: Students should be able to: ☻ Use divisibility rules when dividing given numbers. ☻ Differentiate between prime and composite numbers. ☻ Identify and find factors and multiples of a number. ☻ Find the HCF using short division, and long division. ☻ Find the LCM of 3 numbers by prime factorization and the short division method. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity:
CSS Primary Standard “Mathematics” 25 ☻ Use the explanation as given on pages # 23, 24, 25 and 26 to calculate the H.C.F of two or more than two, 2-digits number. ☻ Explain the Prime Factorization method to find the H.C.F of given numbers as explained on page # 24. ☻ Explain the Division method to find the H.C.F of given numbers as explained on page # 25. ☻ Explain the Long Division method to find the H.C.F of given numbers as explained on page # 25 and 26. Exercise 2a Q 1: Find H.C.F using the prime factorization: i. 12, 18, 20 2 12 2 18 2 20 2 6 3 9 2 10 3 3 3 3 5 5 1 1 1 Prime Factors of 12 = 2 x 2 x 3 Prime Factors of 18 = 2 x 3 x 3 Prime Factors of 20 = 2 x 2 x 5 Common Factor = 2 Therefore Highest Common Factor = 2 ii. 11, 22, 33 11 11 2 22 3 33 1 11 11 11 11 1 1 Prime Factors of 11 = 11 x 1 Prime Factors of 22 = 11 x 2 Prime Factors of 33 = 11 x 3 Common Factor = 11 Therefore Highest Common Factor = 11 iii. 40, 80 2 40 2 80 2 20 2 40 2 10 2 20 5 5 2 10 1 5 5 1 Prime Factors of 40 = 2 x 2 x 2 x 5 Prime Factors of 80 = 2 x 2 x 2 x 2 x 5
CSS Primary Standard “Mathematics” 26 Common Factor = 2 x 2 x 2 x 5 = 40 Therefore Highest Common Factor = 40 iv. 25, 30, 50 5 25 2 30 2 50 5 5 3 15 5 25 1 1 5 5 5 5 1 1 1 Prime Factors of 25 = 1 x 5 x 5 Prime Factors of 30 = 2 x 3 x 5 Prime Factors of 50 = 2 x 5 x 5 Common Factor = 5 Therefore Highest Common Factor = 5 Q 2: Find H.C.F using division method: i. 12, 16, 40 2 12, 16, 40 2 6, 8, 20 1 3, 4, 10 1 H.C.F of 12, 16 and 40 is = 2 x 2 = 4 ii. 13, 26, 60 13 13, 26, 65 1 1, 2, 5 1, 2, 6 H.C.F of 13, 26 and 65 is = 13 x 1 = 13 iii. 15, 18, 21 3 15, 18, 21 1 5, 6, 7 5, 6, 7 H.C.F of 15, 18 and 21 is = 3 x 1 = 3 iv. 88, 92, 98 2 88, 92, 98 1 44, 46, 49 1 H.C.F of 12, 16 and 40 is = 2 x 1 = 2 v. 35, 55, 95 5 35, 55, 95 1 5, 11, 19 5, 11, 19 H.C.F of 12, 16 and 40 is = 5 x 1 = 5 vi. 17, 51, 85
CSS Primary Standard “Mathematics” 27 17 17, 51, 85 1 1, 3, 5 1, 3, 5 H.C.F of 12, 16 and 40 is = 17 x 1 = 17 Q 3: Find H.C.F using long division method: i. 19, 57 ii. 55, 77, 99 iii. 15, 45, 90
CSS Primary Standard “Mathematics” 28 iv. 15, 25, 30 v. 19, 38, 76 vi. 21, 36, 42 Q 4: The length of three wires is 75m, 85m and 95m. Find the length of the rod that can be used to measure exactly. Solution: 5 75, 85, 95 1 15, 17, 19 15, 17, 19 So the H.C.F would be = 5 x 1 = 5 So, 5m would be the length of the rod that can be used to measure exactly. Q 5: Find the greatest number which exactly divides 39 and 169.
CSS Primary Standard “Mathematics” 29 Solution: 3 39, 169 1 13, 55 13, 55 So, the greatest number which exactly divides 39 and 169 would be 3. Q 6: Find the highest number which exactly divided 14, 21 and 42. Solution: 7 14, 21, 42 1 2, 3, 6 2, 3, 6 Therefore 7 is the highest number which exactly divide 14, 21 and 42. Week 6, 7, & 8 Factors and Multiples Lesson # 3 Teaching Objectives: ☻ To revise factors and multiples. ☻ To recap prime and composite numbers. ☻ To reinforce divisibility tests. ☻ To introduce prime factorization using the division and long division method. ☻ To introduce HCF using prime factorization, and long division. ☻ To find the LCM by listing common multiples, prime factorization, and short division of 3 numbers. Learning outcomes: Students should be able to: ☻ Use divisibility rules when dividing given numbers. ☻ Differentiate between prime and composite numbers. ☻ Identify and find factors and multiples of a number. ☻ Find the HCF using short division, and long division. ☻ Find the LCM of 3 numbers by prime factorization and the short division method. Teaching Materials: CSS Primary Standard Mathematics Book 5. Writing Board. Marker. Eraser. Classroom Activity: ☻ Use the explanation as given on pages # 27 and 28 to calculate the L.C.M of two or more
CSS Primary Standard “Mathematics” 30 than two, 2-digits number. ☻ Explain the Prime Factorization method to find the L.C.M of given numbers as explained on page # 27. ☻ Explain the Division method to find the L.C.M of given numbers as explained on page # 27 & 28. Exercise 2b Q 1: Find L.C.M using the prime factorization: i. 15, 18 3 15 2 18 5 5 3 9 1 3 3 1 Prime Factors of 15 = 3 x 5 Prime Factors of 18 = 2 x 3 x 3 Therefore Highest Common Factor = 3 Non common factors = 5 x 2 x 3 = 30 L.C.M = H.C.F x Non common factors = 3 x 30 = 90 ii. 12, 16, 22 2 12 2 16 2 22 2 6 2 8 11 11 3 3 2 4 1 1 2 2 1 Prime Factors of 12 = 2 x 2 x 3 Prime Factors of 18 = 2 x 2 x 2 x 2 Prime Factors of 22 = 2 x 11 Therefore Highest Common Factor = 2 Non common factors = 2 x 3 x 2 x 2 x 2 x 11 = 264 L.C.M = H.C.F x Non common factors = 2 x 264 = 528 ii. 7, 8, 56 1 7 2 8 2 14 7 2 4 7 7 2 2 1 1
CSS Primary Standard “Mathematics” 31 Prime Factors of 7 = 7 x 1 Prime Factors of 8 = 2 x 2 x 2 Prime Factors of 22 = 2 x 7 Common factor = 1 Non common factor = 7 x 2 x 2 x 2 = 56 Q 2: Find L.C.M of the following using division method: i. 3, 6 3 3, 6 2 1, 2 1,1 L.C.M= 3 x 2 = 6 ii. 2, 6, 8 2 2, 6, 8 3 1, 3, 4 2 1,1, 4 2 1, 1, 2 1, 1, 1 L.C.M= 2 x 3 x 2 x 2 = 24 iii. 54, 87, 97 3 54, 87, 96 2 18, 29, 32 9 9, 29, 16 29 1, 29, 16 16 1, 1, 16 1, 1, 1 L.C.M= 3 x 2 x 9 x 29 x 16 = 25056 iv. 24, 60, 78, 90 2 24, 60, 78, 90 3 12, 30, 39, 45 2 4, 10, 13, 15 2 2, 5, 13, 15 5 1, 5, 13, 15 3 1, 1, 13, 3 13 1, 1, 13, 1 1, 1, 1, 1 L.C.M= 2x3x2x2x5x3x13 = 4680 v. 14, 21, 28, 42 7 14, 21, 28, 42 2 2, 3, 4, 6 2 1, 3, 2, 6
CSS Primary Standard “Mathematics” 32 3 1, 3, 1, 3 1, 1, 1, 1 L.C.M= 7x2x2x3 = 84 vi. 55, 58, 70, 80 2 55, 58, 70, 80 5 55, 29, 35, 40 11 11, 29, 7, 8 29 1, 29, 7, 8 7 1, 1, 7, 8 8 1, 1, 1, 8 1, 1, 1, 1 L.C.M= 2x5x11x29x7x8 = 178640 Q 3: Find the minimum length of the rope that can be cut into 15, 18 and 20 meters. Solution: 2 15, 18, 20 3 15, 9, 10 2 5, 3, 10 5 5, 3, 5 3 1, 3, 1 1, 1, 1 Minimum length of the rope that can be cut into 15, 18 and 20 meters is = 2x3x2x5x3 = 180 meters Q 4: Maria wear a jacket every 4 days and her hat every 5 days. If she wears her jacket and hat on 20th December, what is the next day she will wear both her jacket and hat? Solution: 2 4,5 2 2, 5 5 1,5 1,1 L.C.M of 4 and 5 = 2x2x5 = 20 days Add 20 days to 20th December = 20 + 20 = 9 th January Q 5: Find the smallest number that is exactly divisible by 52, 62 and 72. Solution: 2 52, 62, 72 2 26, 31, 36 2 13, 31, 18 3 13, 31, 9
CSS Primary Standard “Mathematics” 33 3 13, 31, 3 13 13, 31, 1 31 1, 31, 1 1, 1, 1 The smallest number that is exactly divisible by 52, 62 and 72 is = 2x2x2x3x3x13x31 = 29016 Review Exercise 2 Q 1: Choose the correct answer and fill the circle: 1. H.C.F stands for.………... Highest Common Factor Heaviest Common Factor Highest Colon Factor None of these 2. If the H.C.F of two or more numbers is “1” then the numbers are called …………. same numbers prime numbers different number composite number 3. Product of all the prime factors gives the ……. different number prime numbers composite number same number 4. H.C.F is also called: L.C.D G.C.D D.V.D D.C.D 5. A number which is divisible by “1” and a number itself is called: Composite Number Prime Number Even Number Odd Number 6. A number which have more than two factors is called: Composite Number Prime Number Rational Number Even Number 7. L.C.M of two prime number is their. difference sum quotient product 8. 342 is divisible by: 2 5 3 both a and c 9. H.C.F of 5 and 15 is: 5 10 3 15 10. L.C.M of 5 and 15 is: 3 5 10 15 Q 2: Find H.C.F and L.C.M of given numbers:
CSS Primary Standard “Mathematics” 34 i. 92, 94, 98 2 92 2 94 2 98 2 46 47 47 7 49 23 23 1 7 7 1 1 Prime Factor of 92: 2 x 2 x 23 Prime Factor of 94: 2 x 47 Prime Factor of 98: 2 x 7 x 7 Common Factor = 2 = Highest Common Factor To calculate L.C.M: 2 92, 94, 98 2 46, 47, 49 7 23, 47, 49 7 23, 47, 7 23 23, 47, 1 47 1, 47, 1 1, 1, 1 So L.C.M is = 2x2x7x7x23x47 = 211876 ii. 19, 38, 57, 95 19 19 2 38 3 57 5 95 1 19 19 19 19 19 19 1 1 1 Prime Factor of 19: 19 x 1 Prime Factor of 38: 19 x 2 Prime Factor of 57: 19 x 3 Prime Factor of 95: 19 x 5 Common Factor = 19 = Highest Common Factor To calculate L.C.M: 19 19, 38, 57, 95 2 1, 2, 3, 5 3 1, 1, 3, 5 5 1, 1, 1, 5 1, 1, 1, 1 So L.C.M is = 19x2x3x5 = 570 ii. 16, 18, 20, 32 2 16 2 18 2 20 2 32 2 8 3 9 2 10 2 16
CSS Primary Standard “Mathematics” 35 2 4 3 3 5 5 2 8 2 2 1 1 2 4 1 2 2 1 Prime Factor of 16: 2 x 2 x 2 x 2 Prime Factor of 18: 2 x 3 x 3 Prime Factor of 20: 2 x 2 x 5 Prime Factor of 32: 2 x 2 x 2 x 2 x 2 Common Factor = 2 = Highest Common Factor To calculate L.C.M: 2 16, 18, 20, 32 2 8, 9, 10, 16 2 4, 9, 5, 8 2 2, 9, 5, 4 2 1, 9, 5, 2 3 1, 9, 5, 1 3 1, 3, 5, 1 5 1, 1, 5, 1 1, 1, 1, 1 So L.C.M is = 2x2x2x2x2x3x3x5 = 1440 Q 3: Naeem is thinking of a number that is divisible both by 18 and 27. What is the smallest possible number that Naeem could be thinking of? Solution: To calculate L.C.M: 3 18, 27 3 6, 9 3 2, 3 2 2, 1 1, 1 So the smallest possible number that Naeem could be thinking of is = 3x3x3x2 = 54 Q 4: Rabia is making the flower arrangements. She has 14 roses and 21 daisies. If she wants to make all the arrangements identical and have no flower left over, what is the greatest number of flower arrangement that she can make? Solution: 2 14 3 21 7 7 7 7
CSS Primary Standard “Mathematics” 36 1 1 Prime factors of 14: 2 x 7 Prime factors of 21: 3 x 7 The greatest number of flowers arrangements that she can make is = 7 Week 9 Monthly Test / Revision of Unit # 2 Week 10 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. 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.
CSS Primary Standard “Mathematics” 37 BODMAS PEDMAS MASMAS BITMAS 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 B: Fill in the blanks: (10 Marks) 1. ………..stands for Highest Common Factor. 2. ………..stands for Least Common Multiple. 3. The numbers are said to be ………..if their only common factor is 1. 4. Zero is neither a ……….. nor a composite number. 5. L.C.M is a number which is completely ……….. by the given number. 6. We can find H.C.F of three numbers, up to ……….., using Division method. 7. We can find H.C.F of three numbers, up to 2-digits, using Prime ……….. method. 8. We can find ……….. of four numbers, up to 2-digits, using Division method. 9. We can find L.C.M of ……….. numbers, up to 2-digits, using Prime Factorization method. 10.In some countries the word BODMAS is used as PEDMAS or ………... C: Mark as “True” or “False”: (10 Marks) 1. H.C.F stands for Highest Common Friend. 2. L.C.M stands for Least Common Multiple. 3. The numbers are said to be co-prime if their only common factor is 0. 4. Zero is neither a prime nor a composite number. 5. L.C.M is a number which is completely divisible by the given number. 6. We can find H.C.F of 3 numbers, up to 2-digits, using Division method. 7. We can find H.C.F of 2 numbers, up to 2-digits, using Prime Factorization method. 8. We can find L.C.M of 3 numbers, up to 2-digits, using Division method. 9. We can find L.C.M of 2 numbers, up to 2-digits, using Prime Factorization method. 10.In some countries the word BODMAS is used as PEDMAS or BEDMAS. Part B Time Allowed: 75 Minutes Total Marks: 45
CSS Primary Standard “Mathematics” 38 Note:Attempt All questions. All questions carry equal (3) Marks. 1. 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? 2. The total income of a private bank in 2008 was Rs. 962, 389, 210 and the expenditures were Rs. 238, 659, 200. Find the net profit of the bank. 3. The price of a square field is Rs. 856, 945. What will be the price of 7 such square fields? 4. The price of a mobile is Rs. 103, 841. What will be the price of 324 sets of mobiles? 5. The cost of a hen is Rs. 215. How many hens can be bought in Rs. 853, 550? 6. The Price of a Sugar bag is Rs. 6894. What will be the price of 312 such bags of Sugar? 7. Solve the following: i. 34,692 x 700 ii. 895, 681 x 100 8. Solve the following: i. 833, 170 ÷ 845 ii. 326, 922 ÷ 529 9. Satisfy the distributive property: 2 x (3 + 8) = (2 x 3) + (2 x 8) 10.What does each circled digit stand for: i. 586, 348, 986 ii. 92, 145, 600 11.Find H.C.F of 6, 9 and 18 using Prime Factorization Method. 12.Find H.C.F of 4, 10 and 12 by using division method. 13.Find L.C.M of 9, 15 and 12 using Prime Factorization Method. 14.Find H.C.F of 9, 27 and 54 by using division method. 15.Maria wear a jacket every four days and her hat every 5 days. If she wears her jacket and hat on 20th December. What is the next day she will wear both jacket and hat? 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) 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
CSS Primary Standard “Mathematics” 39 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 B: Fill in the blanks: (10 Marks) 1. H.C.F stands for …………… Common Factor. 2. L.C.M stands for Least Common ……………. 3. The numbers are said to be co-prime if their only common factor is ……………. 4. Zero is neither a prime nor a …………… number. 5. …………… is a number which is completely divisible by the given number. 6. We can find …………… of three numbers, up to 2-digits, using Division method. 7. We can find H.C.F of three numbers, up to 2-digits, using ……… Factorization Method. 8. We can find …………… of four numbers, up to 2-digits, using Division method. 9. We can find L.C.M of four numbers, up to 2-digits, using Prime …………… method. 10.In some countries the word BODMAS is used as …………… or BIDMAS. C: Mark as “True” or “False”: (10 Marks) 1. H.C.F stands for His Common Friend. 2. L.C.M stands for Least Common Mode. 3. The numbers are said to be co-prime if their only common factor is 1.
CSS Primary Standard “Mathematics” 40 4. “1” is neither a prime nor a composite number. 5. L.C.M is a number which is completely divisible by the given number. 6. We can find H.C.F of 1 numbers, up to 2-digits, using Division method. 7. We can find H.C.F of 4 numbers, up to 2-digits, using Prime Factorization method. 8. We can find L.C.M of 3 numbers, up to 2-digits, using Division method. 9. We can find L.C.M of 3 numbers, up to 2-digits, using Prime Factorization method. 10.In some countries the word BODMAS is used as PEDMAS or BEDMAS. Part B Time Allowed: 75 Minutes Total Marks: 45 Note:Attempt All questions. All questions carry equal (3) Marks. 1. The total exports of a country for the year 2012 was 324,, 846, 042 and for the year 2013 was 56, 845, 392. How much exports of the country altogether for both years? 2. What is the difference between smallest ten digits and largest 8-digit number? 3. There are 295 sweets in a packet. How many sweets are there in 364 packets? 4. The price of a ball is Rs. 92. How many balls can be bought in Rs. 35, 604? 5. The cost of a hen is Rs. 215. How many hens can be bought in Rs. 853, 550? 6. 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? 7. Solve the following: i. 341,298 x 23 ii. 326,922 x 100 8. Solve the following: i. 187,616 ÷ 329 ii. 175,686 ÷ 329 9. Satisfy the distributive property: 5 x (6 + 9) = (5 x 6) + (5 x 9) 10.What does each circled digit stand for: i. 686, 548, 986 ii. 82, 145, 598 11.Find H.C.F of 12, 18 and 20 using Prime Factorization Method. 12.Find H.C.F of 13, 26 and 65 by using division method. 13.Find L.C.M of 9, 27 and 54 using Prime Factorization Method. 14.Find H.C.F of 54, 87 and 96 by using division method. 15.Naeem is thinking of a number that is divisible by both 18 and 27. What is the smallest possible number that Naeem could be thinking of? 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.
CSS Primary Standard “Mathematics” 41 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. 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 B: Fill in the blanks: (10 Marks) 1. ………..stands for Highest Common Factor. 2. ………..stands for Least Common Multiple. 3. The numbers are said to be ………..if their only common factor is 1.
CSS Primary Standard “Mathematics” 42 4. Zero is neither a ……….. nor a composite number. 5. L.C.M is a number which is completely ……….. by the given number. 6. We can find …………… of three numbers, up to 2-digits, using Division method. 7. We can find H.C.F of three numbers, up to 2-digits, using ……… Factorization Method. 8. We can find …………… of four numbers, up to 2-digits, using Division method. 9. We can find L.C.M of four numbers, up to 2-digits, using Prime …………… method. 10.In some countries the word BODMAS is used as …………… or BIDMAS. C: Mark as “True” or “False”: (10 Marks) 1. H.C.F stands for Highest Common Friend. 2. L.C.M stands for Least Common Multiple. 3. The numbers are said to be co-prime if their only common factor is 0. 4. Zero is neither a prime nor a composite number. 5. L.C.M is a number which is completely divisible by the given number. 6. We can find H.C.F of 1 numbers, up to 2-digits, using Division method. 7. We can find H.C.F of 4 numbers, up to 2-digits, using Prime Factorization method. 8. We can find L.C.M of 3 numbers, up to 2-digits, using Division method. 9. We can find L.C.M of 3 numbers, up to 2-digits, using Prime Factorization method. 10.In some countries the word BODMAS is used as PEDMAS or BEDMAS. Part B Time Allowed: 75 Minutes Total Marks: 45 Note:Attempt All questions. All questions carry equal (3) Marks. 1. 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? 2. The total income of a private bank in 2008 was Rs. 962, 389, 210 and the expenditures were Rs. 238, 659, 200. Find the net profit of the bank. 3. The price of a square field is Rs. 856, 945. What will be the price of 7 such square fields? 4. The price of a mobile is Rs. 103, 841. What will be the price of 324 sets of mobiles? 5. The cost of a hen is Rs. 215. How many hens can be bought in Rs. 853, 550? 6. The Price of a Sugar bag is Rs. 6894. What will be the price of 312 such bags of Sugar? 7. Solve the following: i. 34,692 x 700 ii. 895, 681 x 100 8. Solve the following: i. 833, 170 ÷ 845 ii. 326, 922 ÷ 529 9. Satisfy the distributive property: 5 x (6 + 9) = (5 x 6) + (5 x 9) 10.What does each circled digit stand for: i. 686, 548, 986 ii. 82, 145, 598 11.Find H.C.F of 12, 18 and 20 using Prime Factorization Method. 12.Find H.C.F of 13, 26 and 65 by using division method. 13.Find L.C.M of 9, 27 and 54 using Prime Factorization Method. 14.Find H.C.F of 54, 87 and 96 by using division method.
CSS Primary Standard “Mathematics” 43 15.Naeem is thinking of a number that is divisible by both 18 and 27. What is the smallest possible number that Naeem could be thinking of? Second Term Week 1, 2, & 3 Fractions Lesson # 1 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. ☻ 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 # 30, 31 and 32 to add and subtract the fractions. Exercise 3a Q 1: Add the following fractions and write your answer in simplest form: i. 5/3 + 2/3 Solution: 5/3 + 2/3 = 5 + 2/3 = 7/3 ii. 13/54 + 5/18
CSS Primary Standard “Mathematics” 44 Solution: 13/54 + 5/18 = 13 + 15/54 = 28/54 iii. 9/29 + 4 Solution: 9/29 + 4 = 9/29 + 4/1 = 9 + 116/29 = 125/29 iv. 51/94 + 121/188 Solution: 51/94 + 121/188 = 102 + 121 / 188 = 223 / 188 v. 13/16 + 14/32 +11 /8 Solution: 13/16 + 14/32 +11 /8 = 13/16 + 14/32 + 9/8 = 26 + 14 + 36 / 32 = 76/32 = 38/16 = 19/8 vi. 9 4 /129 + 1/258 Solution: 9 4 /129 + 1/258 = 1165/129 + 1/258 = 2330 + 1/258 = 2331/258 vii. 138 /158 + 25 /79 Solution: 138 /158 + 25 /79 = 2062/158 + 163/79 = 2062 + 326/158 = 2388/158 = 1194/79 viii. 8 5 /651 + 32 /651 Solution: 8 5 /651 + 32 /651 = 5213/651 + 1955/651 = 7168/651 = 1024/93 Q 2: Subtract the following fractions and write your answer in simplest form: i. 13/14 - 2/7 Solution: 13/14 - 2/7 = 13 – 4/7 = 9/7 ii. 14/17 – 8/17 Solution: 14/17 – 8/17 = 14 – 8 / 17 = 6/17 iii. 16/58 – 5/58 Solution: 16/58 – 5/58 = 16 – 5/58 = 11/58 iv. 2 – 5/6 Solution: 2 – 5/6 = 2/1 – 5/6 = 12 – 5/6 = 7/6
CSS Primary Standard “Mathematics” 45 v. 8 – 6/12 Solution: 8 – 6/12 = 8/1 – 6/12 = 96 – 6 / 12 = 90 / 12 = 30/4 = 15/2 vi. 2 – 5/8 – 2/8 Solution 2 – 5/8 – 2/8 = 2/1 – 5/8 – 2/8 = 16 – 5 – 2/8 = 9/8 vii. 130 – 5/12 Solution: 130 – 5/12 = 130/1 – 5/12 = 1560 – 5/12 = 1555/12 viii. 294 – 2/3 Solution: 294 – 2/3 = 294/1 – 2/3 = 882 – 2/3 = 880/3 ix. 14 – 18/39 -81/13 Solution: 14 – 18/39 -8 1 /13 = 14/1 – 18/39 – 105/13 = 546 – 18 – 315/39 = 213/39 = 71/13 Q 3: Solution: Abbas bought petrol = 3 2 /5 liters = 17/5 liters Ali bought petrol = 8 3 /10 liters = 83/10 liters a) How much petrol did they buy altogether? Solution: 13/5 + 83/10 = (17 x 2) + 83 / 10 = 34 + 83/10 = 117/10 b) How much more petrol did Ali bought than Abbas? 83/10 – 17/5 = 83 – (17 x 2)/10 = 83 – 34 / 10 = 49/10 Q 4: What number must be subtracted from 7/18 to get the difference of 1/9? Solution: Let x be the given number 7/18 - x = 1/9 7/18 - x = 2/18 -x = 2/18 - 7/18 = 2 - 7/18 -x = -5/18 => x = 5/18
CSS Primary Standard “Mathematics” 46 Q 5: Solution: Vote for party A = 41/100 Vote for party B = 39/100 Total vote for party A and B = 41/100 + 39/100 = 80/100 = 8/10 = 4/5 Undecided votes = 1 – 4/5 = 5 – 4 / 5 = 1/5 Week 1, 2, & 3 Fractions Lesson # 2 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. ☻ 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 # 33, 34, 35, 36 and 37 to multiply the fractions. Exercise 3b Q 1: Multiply: i. 5 x 1/3
CSS Primary Standard “Mathematics” 47 Solution: 5 x 1/3 = (5 x 1)/3 = 5/3 ii. 19 x 5/9 Solution: 19 x 5/9 = (19 x 5)/9 = 95/9 iii. 0 x 3/8 Solution 0 x 3/8 = 0 iv. 16 x 9/17 Solution 16 x 9/17 = (16 x 9)/17 = 144/17 v. 11/2 x 15 Solution: 1 1 /2 x 15 = 3/2 x 15 = (3 x 15)/2 = 45/2 vi. 13 x 1/5 Solution: 13 x 1/5 = (13 x 1)/5 = 13/5 Q 2: Multiply: i. 3/19 x 13/8 Solution: 3/19 x 13 /8 = 3/19 x 11/8 = (3 x 11) / (19 x 8) = 33/152 ii. 29/11 x 63/11 Solution: 2 9 /11 x 63 /11 = 31/11 x 69/11 = (31 x 69) / (11 x 11) = 2139 / 121 iii. 1656/9 x 0 x 153/18 Solution: 1656 /9 x 0 x 153 /18 = 1491/9 x 0 x 273/18 = 0 iv. 181/15 x 0 x 18 x 16/19 Solution: 181 /15 x 0 x 18 x 16/19 = 271/15 x 0 x 18 x 16/19 = 0 v. 352/5 x 1/8 x 163/8 Solution: 352 /5 x 1/8 x 163 /8 = 177/5 x 1/8 x 131/8 = (177 x 1 x 131)/(5 x 8 x 8) = 23187/320 vi. 18/19 x 11/2 x 5
CSS Primary Standard “Mathematics” 48 Solution: 18/19 x 11 /2 x 5 = 18/19 x 3/2 x 5 = (18 x 3 x 5) / (19 x 2 x 1) = 270/38 = 135/19 Q 3: Verify the Distributive Law: i. 1/5 x (8/9 + 6/7) = (1/5 x 8/9) + (1/5 x 6/7) Solution: L.H.S 1/5 x (8/9 + 6/7) = (1/5 x 8/9) + (1/5 x 6/7) = 8/45 + 6/35…….i R.H.S (1/5 x 8/9) + (1/5 x 6/7) = (1/5 x 8/9) + (1/5 x 6/7) = 8/45 + 6/35…….ii From (i) and (ii)… L.H.S = R.H.S ii. 1 1 /2 x (12 /9 + 23 /13) = (11 /2 x 12 /9) + (11 /2 x 23 /13) Solution: ii. 1 1 /2 x (12 /9 + 23 /13) = (11 /2 x 12 /9) + (11 /2 x 23 /13) L.H.S 1 1 /2 x (12 /9 + 23 /13) = (11 /2 x 12 /9) + (11 /2 x 23 /13)……i R.H.S (11 /2 x 12 /9) + (11 /2 x 23 /13)……ii From (i) and (ii) L.H.S = R.H.S iii. 15/17 x (83 /16 + 21 /5) = (15/17 x 83 /16) + (15/17 x 21 /5) Solution: L.H.S 15/17 x (83 /16 + 21 /5) = (15/17 x 83 /16) + (15/17 x 21 /5)…..i R.H.S (15/17 x 83 /16) + (15/17 x 21 /5)…..ii From (i) and (ii) L.H.S = R.H.S Q 4: Naeem ate pizza on Saturday = 1 – 5/12 = (12 – 5)/12 = 7/12 of pizza Naeem ate pizza on Sunday = 2/6 of 5/12 = 2/6 x 5/12 = 1/3 x 5/12 = 5/36 of pizza
CSS Primary Standard “Mathematics” 49 Q 5: Shazia lemon cookie recipe calls for = 5/20 of cup of Sugar = 5/20 = ¼ Batch of cookies = 2/8 = ¼ Sugar needed = ¼ x ¼ = 1/16 Q 6: Anarol picked = 1 1 /3 of strawberries Alishaba ate = ½ of Anarol picked strawberries = 4/3 x ½ = 4/6 = 2/3 part Q 7: Saima spends in school = 3/10 of the whole day Saima learns and practice Mathematics = 3/10 x 3/7 = (3 x 3)/(10 x 7) = 9/70 Week 1, 2, & 3 Fractions Lesson # 3 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. ☻ 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 # 39 and 40 to divide the fractions.
CSS Primary Standard “Mathematics” 50 Exercise 3c Q 1: Divide and write the answer in simplest form: i. 3/5 ÷ 3 Solution: 3/5 ÷ 3 => 3/5 x 1/3 => 3/15 => 1/5 ii. 25/37 ÷ 15 Solution: 25/37 ÷ 15 => 25/37 x 1/15 => (25 x 1)/(37 x 15) => 5/(37 x 3) = 5/111 iii. 1 2 /9 ÷ 15 Solution: 1 2 /9 ÷ 15 => 11/9 x 1/15 => 11/(15 x 9) => 11/135 iv. 85/89 ÷ 25 Solution: 85/89 ÷ 25 = 85 / 89 x 1/25 => (85 x 1) / 89 x 25) 85 / 2225 => 17/445 v. 115 /11 ÷ 121 Solution: 115 /11 ÷ 121 => 126 / 11 x 1/121 => (126 x 1) / (11 x 121) 126/1331 vi. 1 15/19 ÷ 5 Solution: 1 15/19 ÷ 5 => 34 / 19 x 1/5 => (34 x 1) / (19 x 5) = 34/95 Q 2: Divide and write the answer in simplest form: i. 6/7 ÷ 14/32 Solution: 6/7 ÷ 14/32 => 6/7 x 32/14 => (6 x 32) / (7 x 14) => 192/98 => 96/49 ii. 1 5 /6 ÷ 2 3 /9 Solution: 1 5 /6 ÷ 2 3 /9 => 11/6 x 9/21 => (11 x 9) / (6 x 21) => 99/126 => 11/14 iii. 4 1 /5 ÷ 9 3 /4 Solution: 4 1 /5 ÷ 9 3 /4 = 21/5 x 4/39 => (21 x 4) / (5 x 39) 84/ 195 => 28/65