Math-4

1 CSS Primary Standard “Mathematics” CSS Primary Standard Mathematics For Class 4 Division of Syllabus into three terms Teacher’s Guide Fully Solved Exercises

2 CSS Primary Standard “Mathematics” Table of Contents Sr. No. Description Page No. 1. Division of Syllabus 3 2. Unit # 1 4 3. Unit # 2 (1st Half) 20 4. Model Paper # 1 25 5. Model Paper # 2 27 6. Model Paper # 3 29 7. Unit # 2 (2nd Half) 32 8. Unit # 3 47 9. Unit # 4 59 10. Unit # 5 69 11. Model Paper # 1 91 12. Model Paper # 2 93 13. Model Paper # 3 95 14. Unit # 6 98 15. Unit # 7 104 16. Model Paper # 1 108 17. Model Paper # 2 112 18. Model Paper # 3 116

3 CSS Primary Standard “Mathematics” Division of Syllabus 1 st Term Week 1 Unit # 1… Numbers and Arithmetic Operations Numbers Numbers up to one hundred millions Compare and Order Numbers up to 8-digits Addition Subtraction Multiplication Division Week 2 Week 3 Week 4 Week 5 Monthly Test / Revision of Unit # 1 Week 6 Unit # 2…Factors and Multiples Divisibility Test Prime and Composite Numbers + Revision Week 7 Week 8 2 nd Term Week 1 Unit # 2…Factors and Multiples Factors and Multiples Prime Factorization Highest Common Factor Least Common Multiple Week 2 Week 3 Unit # 3…Fraction Like and Unlike Fractions Types of Fractions Addition and Subtraction of Fractions Multiplication of Fractions Division of Fractions Week 4 Week 5 Week 6 Revision of Unit # 2 & 3 Week 7 Unit # 4…Decimal and Fractions Decimals Basic Operations on Decimal Unit # 5…Measurements Length Mass Capacity Time + Revision Week 8 Week 9 Week 10 3 rd Term Week 1 Unit # 6…Geometry

4 CSS Primary Standard “Mathematics” Week 2 Week 3 Unit # 7…Information Handling Week 4 Week 5 Complete Revision of 3rd Term Week 6 Complete Revision of 2nd Term 1 st Term Unit No. 1 Number and Arithmetic Operations Lesson # 1 Teaching Objectives: To revise large numbers. To revise 6 digit numbers. To introduce the Pakistan system of numbering. To introduce place value up to 8-digit numbers. To compare and order large numbers. To explain addition of large numbers and the properties of addition. To explain subtraction of large numbers and the properties of subtraction. To explain multiplication of large numbers and the multiplication properties. To explain division of large numbers and the properties of division. Learning Outcomes: The students will be able to: Compare the international place value names and the Pakistani system. Identify 9-digit numbers Add, subtract, multiply, and divide large numbers. Explain the properties of the binary operations listed above. Apply binary operations to real life situations. Teaching Materials: CSS Primary Standard Mathematics Book 4. Place value charts of both international and Pakistan systems. Writing Board. Marker. Eraser. Background: Step by step, 5-digit numbers were introduced in Book 3 based on the students' previous

5 CSS Primary Standard “Mathematics” knowledge of smaller numbers. Comparison of place value was done pictorially. It must be emphasized here that, if a student is working well with 4-digit numbers, going on to 5-or 6-digit numbers will be quite simple. The language used, the methodology and the techniques are the same. The same terminology should be used, as for the lessons for the houses of hundreds and thousands: terms include groups of 10, carry over, borrowing, and others. This is the first time the students will be introduced to the concept of the international system of writing numbers. It is a good idea to compare the same number in both writing styles. Take enough time to explain to the student that the same number may be written in 2 different styles. This does not change the value of the number. It is just 2 different ways of representing the same quantity. To begin with the fun activities is a good idea. Fun activities 1) Roll the Dice What You Need: 6 dice Several players Paper Pencil What You Do: 1. Decide who will go first. The first player should roll all 6 dice. Each player should add up the total from their roll and record it. 2. The player with the highest sum from round 1 earns 3 points. The player with the second highest sum earns 2 points. The rest of the players receive 1 point. 3. Play continues for 10 rounds, or decide on a time limit. 4. After the game is finished, have the players add up their scores. 5. The player with the highest sum wins. 2) Math Facts Secret Codes What You Need: Paper Pen Math fact "decoder" key Message What You Do: 1. Make up some addition problems for your child to solve. Make a decoding sheet to correspond with the answers, and write a letter for each answer to create a message! 2. Write your message on the decoder key, by making a small line for each letter of the alphabet in the message. Write out your message lines, and then let your child take a whack at the math facts to decode your words. The sum of each pair of numbers appears under each line of the message, and matches up with a letter. For a child who is making good progress on math facts, this is a fairly fast activity … but one that will bring a sense of accomplishment that lasts all day and beyond!

6 CSS Primary Standard “Mathematics” 3) Top of the Heap What You Need: Deck of playing cards 1 die Scratch paper, 1 per player Pencil, 1 per player What You Do: 1. Ask your child to shuffle the cards and place them face down in a pile in the center of the table. 2. Have her roll the die twice. The first roll determines the number of piles of cards she'll need to create. The second roll shows how many playing cards she'll need to place face down on each of the piles she creates. 3. After she makes the piles of cards based on the rolls, she should add up the total number of cards she placed in the piles. Ask her to try multiplying them in her head first, then count them aloud. 4. Ask her to write her score down on the scratch paper. 5. Repeat this process with each player. 6. Play for 10 rounds. Whoever ends up using the most cards wins! 4) Multiplication Tables Game What You Need: Deck of playing cards with the face cards (jacks, queens and kings) removed Photocopied black outlined map of the US, one per player. Colored pencils, or markers 2 or more players What You Do: 1. Ask one of the players to shuffle the deck and place it face down in the center of the table. Have another player pass out maps and either colored pencils or markers to the players. 2. Have the kids label each of the states with their correct state names. 3. Then, in each of the states, have the kids write in different products they'll encounter while multiplying the different cards in the deck together. 4. Have the players determine the value of the face cards. Tell them that for the purpose of the game aces = 1. 5. Choose one player to start. Ask her to draw two cards and place them face up so the other players can see. She must correctly state the product that results when the two cards are multiplied together. 6. If she answers correctly, she should find the state containing that product. 7. Before she can color it in, she must correctly identify the respective state's name.

7 CSS Primary Standard “Mathematics” 8. If she doesn't come up with the right product, and follow up with a correct state name, play moves on to the next player. 9. The player who's first to successfully color his map in completely is the winner. Helpful Tip: Make this game even more challenging by asking players to name the capital city of each state before coloring they're allowed to color it in. 5) Find the Math Fact Family What You Need: Pen 20-30 Strips of Paper Clock or timer What You Do: Step 1: To set up the game, you will write 4 numbers onto each strip of paper. 3 will be part of a fact family, and one will not be part of the fact family. A fact family is 3 numbers that are connected through multiplication and division. For instance, 2, 4 and 8 are a fact family because 2 × 4 = 8, 4 × 2 = 8, 8 ÷ 4 = 2 and 8 ÷ 2 = 4. Step 2: Explain the concept of the fact family to your child and give several examples, such as 3, 9 and 27. Ask your child to go through the multiplication and division relationships between the example you gave. Fact Family Examples: 2, 3, 6 6, 8, 48 4, 7, 28 5, 8, 40 3, 7, 21 8, 9, 72 Step 3: Explain to your child that she will select a strip of paper with 4 numbers on it. 3 numbers will be part of a fact family and one will not. She will need to tell you which one does not belong and then create a multiplication or division equation using the 3 numbers that are in the fact family. She will be given a group of four numbers, three that make up a fact family and one that doesn’t belong. She must correctly identify the number that doesn’t belong and then state a division fact using the numbers in the fact family. Step 4: Ask your child to start by choosing a strip of paper and trying to identify the number that does not belong. Step 5: Once she has done one for practice, set a timer for 2 minutes and tell her to go through as many as she can in 2 minutes. Step 6: After 2 minutes have passed, count the number of strips she completed. Now you can challenge her to try to beat her record and complete even more strips in 2 minutes this time. Challenge your child to beat her record. Play several rounds and see whether she is able to improve. It may be beneficial to return to the game several days later to see whether your child can get an even better time. Another version of this game is to compete against someone else. Show the strip of paper to two people at the same time, and the first person to call out the number that isn’t part of the fact family wins that strip and earns one point. The person with the most points at the end of the game wins.

8 CSS Primary Standard “Mathematics” Introduction: Encourage the students to tell you about the importance of numbers. Talk about the importance of addition, subtraction, multiplication and division. Invite them for book reading and solving questions. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Lesson # 2 Procedure: Divide the students into 2 groups. One group writes a 6-digit number using the international number system on a slate, and holds it up for the other group to see. The second group reads it out aloud. This group writes the same number using Pakistani system and holds it up for the first group to read out. Then the second group writes another 6-digit number using the international system and holds it up for the first group, who reads it out aloud, and writes it using the Pakistani system. Lesson # 3 Procedure: Explain terms such as 'sum', 'difference', 'product', and 'quotient' before starting on the problems. Revisit the associative, commutative, and distributive properties as you take them through the exercises. Remember, this topic requires a lot of practice. Team games are always an excellent way to present problems involving the large numbers in expanded form, ascending and descending orders, identifying number sequences, and skip counting. When you start this topic, it is a good idea to revise the place values of numbers up to a million. If students are working well with 7-digit numbers, going up to 8- or 9-digit numbers will be simple. Keep the language used, the methodology, and the techniques the same. Use

9 CSS Primary Standard “Mathematics” the same terminology: houses of tens, hundreds, thousands, carry over, grouping, borrowing, and so on and, there should be no problems with larger numbers. If some students wish to use their fingers to start with it is not a problem. Explain the pages # 3, 4, 5, 6, 7 and 8 to explain the given concepts. Don’t forget to assign homework for the reinforcement of the topic. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part I Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (1a) Q 1: a). 3 Ten Millions, 4 Millions, 0 hundred Thousands, 3 Ten Thousands, 5 Thousands, 3 Hundreds, 9 Tens, 6 Ones. Expanded Form: 30,000,000 + 4,000,000 + 30,000 + 5,000 + 300 + 90 + 6 Standard Form: 34, 035, 396 b). 3 Ten Millions, 3 Millions, 4 hundred Thousands, 6 Ten Thousands, 4 Thousands, 4 Hundreds, 3 Tens, 8 Ones. Expanded Form: 30,000,000 + 3,000,000 + 400,000 + 60,000 + 4,000 + 400 + 30 + 8 Standard Form: 33, 464, 438 Q 2: What does each digit stands for in the number? i. 35, 159, 805 ii. 61, 348, 259 iii. 84, 158, 693 iv. 14, 568 v. 3,351, 589 5 00 800 9000 50000 100000 5000000 30000000 9 50 200 8000 40000 300000 1000000 60000000 3 90 600 8000 50000 100000 4000000 80000000 8 60 500 4000 10000 9 80 500 1000 50000 300000 3000000

10 CSS Primary Standard “Mathematics” Q 3: What does each encircled digit stands for in the number? i. 38, 956, 259 = 900,000 ii. 81, 389, 564 = 500 iii. 34, 184, 609 = 30,000,000 iv. 584, 309 = 4,000 Q 4: Read loudly and write in words, the price of each of the following: i. 89, 564 = Eighty nine thousands, five hundred and sixty four. ii. 45, 658 = Forty five thousands, six hundred and fifty eight. iii. 35, 849, 911 = Thirty five millions, eight hundreds forty nine thousands, nine hundreds and eleven. Q 5: Read loudly and write in numerals: i. Sixty five thousands and two hundreds ninety four. 65, 294 ii. One hundred six thousands, nine hundred and fifty five. 106, 955 iii. Three millions, five hundreds, sixty four thousands, two hundreds and ninety four. 3, 564, 294 iv. Eight hundred thirty five thousands, nine hundred and twenty two. 835, 922 v. Three millions, five hundreds sixty four thousands. 3, 564, 000 vi. Twenty five millions and nine. 25, 000, 009 Q 6: Compare the numbers and write “>”, “=” or “<” in the boxes: i. 30,576,201 > 3,250,111 ii. 45,625,987 < 52,320,566 iii. 22,560,985 < 80,000,000 iv. 3,580,256 < 81,592,304 v. 98,650,000 > 20,540,928 vi. 34,851,612 = 34,851,612 Q 7: Arrange the following numbers in ascending order: i. 36,425 92,856 620,321 50,532,922 36,425 92,856 620,321 50,532,922 ii. 92,625 55,586 542,000 300,401 55,586 92,625 300,401 542,000 iii. 21, 250 80,000,300 25,022 200,000 21, 250 25,022 200,000 80,000,300 Q 8: Arrange the following numbers in descending order: i. 9,84,621 81,586,321 81,982,561 314,586 81,982,561 81,586,321 9,845,621 314,586 ii. 45,382,111 41,865,144 9,248,514 88,945,666 88,945,666 45,382,111 41,865,144 9,248,514

11 CSS Primary Standard “Mathematics” Exercise (1b) Q 1: Write vertically and add the following: i. 468,352 and 301,604 ii. 831,524 and 103,541 H.Th T.Th Th H T O H.Th T.Th Th H T O 4 6 8 3 5 2 8 3 1 5 2 4 + 3 0 1 6 0 4 +1 0 3 5 4 1 7 6 9 9 5 6 9 3 5 0 6 5 iii. 218,300 and 1,604 iv. 568,345 and 12,569 and 3,481 H.Th T.Th Th H T O H.Th T.Th Th H T O 2 1 8 3 0 0 5 6 8 3 4 5 + 1 6 0 4 1 2 5 6 9 + 3 4 8 1 2 1 9 9 0 4 5 8 4 3 9 5 v. 819,321 and 56,382 and 4,058 vi. 389,568 and 45,385 and 168,934 H.Th T.Th Th H T O H.Th T.Th Th H T O 8 1 9 3 2 1 3 8 9 5 6 8 + 5 6 4 3 0 8 5 2 8 + 1 4 6 5 8 3 9 8 3 5 4 8 7 9 7 6 1 6 0 3 8 8 7 Q 2: Mr. Ali donated in 2016 = 326, 000 Mr. Ali donated in 2017 = 525, 500 How much total amount he donated = ? H.Th T.Th Th H T O 3 2 6 0 0 0 + 5 2 5 5 0 0 8 5 1 5 0 0 Hence, total amount he donated = Rs. 851,500 Q 3: Annual bonus in 2016 = Rs. 197,253 Annual bonus in 2017 = Rs. 210,567 Total bonus in 2016 and 2017 = ? H.Th T.Th Th H T O 1 9 7 2 5 3 + 2 1 0 5 6 7 4 0 7 8 2 0 Total bonus in 2016 and 2017 = 407,820 Q 4: Residents in city A = 324,560 Residents in city B = 269,521

12 CSS Primary Standard “Mathematics” Total residents = ? H.Th T.Th Th H T O 3 2 4 5 6 0 + 2 6 9 5 2 1 5 9 4 0 8 1 Total residents = 594,081 residents Exercise (1c) Q 1: Subtract the following. i. 45896 and 16872 ii. 38412 and 4201 H.Th T.Th Th H T O H.Th T.Th Th H T O 3 4 15 5 8 9 6 3 8 4 1 2 – 1 6 8 7 2 – 4 2 0 1 2 9 0 2 4 3 4 2 1 1 iii. 89612 and 5340 iv. 64198 and 184 H.Th T.Th Th H T O H.Th T.Th Th H T O 8 9 5 6 11 1 2 6 4 1 9 8 – 5 3 4 0 – 1 8 4 8 4 2 7 2 6 4 0 1 4 v. 8431 and 38 H.Th T.Th Th H T O 8 3 4 12 3 11 1 – 3 8 8 3 9 3 Q 2: Find the difference between. i. 3489 and 65834 ii. 85692 and 568 H.Th T.Th Th H T O H.Th T.Th Th H T O 6 5 7 8 12 3 14 4 8 5 6 8 9 12 2 – 3 4 8 9 – 5 6 8 6 2 3 4 5 8 5 1 2 4 iii. 52146 and 12531 iv. 45693 and 58451 H.Th T.Th Th H T O H.Th T.Th Th H T O 4 5 11 2 11 1 4 6 5 7 8 13 4 14 5 11 1 – 1 2 5 3 1 – 4 5 6 9 3 3 9 6 1 5 1 2 7 5 8

13 CSS Primary Standard “Mathematics” v. 38613 and 48935 vi. 35695 and 124 H.Th T.Th Th H T O H.Th T.Th Th H T O 4 8 9 3 5 3 5 6 9 5 – 3 8 6 1 3 – 1 2 4 1 0 3 2 2 3 5 5 7 1 Q 3: Total population of the village = 53849 Number of men and women = 35641 Number of children = ? Number of children = Total population – number of men and women = 53849 – 35641 = 18208 children Q 4: Subtract the greatest 4-digit number from greatest 5-digits number. Greatest 4-digit number = 9,999 Greatest 5-digit number = 99,999 Difference = 99,999 – 9,999 = 90,000 Q 5: Toys produced in first two months of 2015 = 84568 Toys produced in first two months of 2016 = 76184 How many more toys produced = 84568 – 76184 = 8384 more toys Q 6: Farmer Aleem grow carrots in 2010 = 35,624 Farmer Aleem grow carrots in 2011 = 29,200 Difference in carrots = ? = 35, 624 – 29, 200 = 6, 424 carrots Exercise (1d) Q 1: Solve the following: i. 3456 × 5 ii. 4518 × 8 H.Th T.Th Th H T O H.Th T.Th Th H T O 3 4 5 6 4 5 1 8 × 5 × 8 1 7 2 8 0 3 6 1 4 4 iii. 9815 × 10 iv. 6584 × 30 H.Th T.Th Th H T O H.Th T.Th Th H T O 9 8 1 5 6 5 8 4 × 1 0 × 3 0 9 0 8 0 1 0 5 0 0 1 9 0 7 0 5 0 2 0 0 9 8 1 5 0 1 9 7 5 2 0

14 CSS Primary Standard “Mathematics” v. 5679 × 70 vi. 5694 × 23 H.Th T.Th Th H T O H.Th T.Th Th H T O 5 6 7 9 5 6 9 4 × 7 0 × 2 3 3 9 0 7 0 5 0 3 0 0 1 1 1 7 3 0 8 8 8 2 0 3 9 7 5 3 0 1 3 0 9 6 2 vii. 3596 × 48 H.Th T.Th Th H T O 3 5 9 6 × 4 8 1 2 4 8 3 7 8 6 4 8 0 1 7 2 6 0 8 Q 2: Find the product of 3159 and 84. H.Th T.Th Th H T O 3 1 5 9 × 8 4 2 1 5 2 2 6 7 3 2 6 0 2 6 5 3 5 6 Q 3: Price of dress = Rs. 3758 Price of 3 dresses = Rs. 3758 × 3 H.Th T.Th Th H T O 3 7 5 8 × 3 1 1 2 7 4 Q 4: Find the product of 6854 and 38. H.Th T.Th Th H T O 6 8 5 4 × 3 8 2 5 0 4 5 8 6 3 2 2 0 2 6 0 4 5 2 Q 5: Cost of a mobile = Rs. 9584 Cost of 24 mobiles = ? H.Th T.Th Th H T O 9 5 8 4 × 2 4 1 3 9 8 1 3 6 3 8 6 0 2 3 0 0 1 6

15 CSS Primary Standard “Mathematics” Q 6: Namra’s school fee per month = Rs. 2840 Namra’s school fee for the whole year = ? Months in a year = 12 H.Th T.Th Th H T O 2 8 4 0 × 1 2 2 5 8 6 4 8 0 0 0 3 4 0 8 0 Q 7: Cost of a dinner set = Rs. 9502 Cost of 39 dinner sets = ? H.Th T.Th Th H T O 9 5 0 2 × 3 9 2 8 8 5 6 5 0 1 6 8 0 3 7 1 5 7 8 Q 8: Ali sold tickets = 8495 Waqar sold tickets = 8495 × 10 = 84950 Exercise (1e) Q 1: Solve the following: i. 321 ÷ 3 ii. 568 ÷ 8 iii. 3582 ÷ 6 iv. 7362 ÷ 9 v. 484 ÷ 11 vi. 672 ÷ 16

16 CSS Primary Standard “Mathematics” vii. 2970 ÷ 18 viii. 5635 ÷ 23 ix. 4563 ÷ 45 Q 2: Solve the following: i. 3869 ÷ 5 ii. 4868 ÷ 7 iii. 8469 ÷ 13 iv. 9839 ÷ 19 v. 6315 ÷ 24 vi. 2894 ÷ 66 Q 3: Alishaba baked muffins = 455 Muffins put in each box = 7 How many boxes of muffins = ? = 455 ÷ 7 = 65 boxes of muffins Q 4: Price of 22 ink pens = Rs. 5522 Price of an ink pen = ? = 5522 ÷ 22 = Rs. 251 65 –95

17 CSS Primary Standard “Mathematics” Q 5: Cost of 13 mobile phones = Rs. 128, 440 Cost of each mobile = ? = 128, 440 ÷ 13 = Rs. 9880 Q 6: Samiya has baby carrots = 5250 Number of boxes = 35 = 5250 ÷ 35 = 150 baby carrots Exercise (1f) Q 1: Use DMAS rule to solve the following: i. 6 + 5 – 3 = 11 – 3 = 8 ii. 16 – 5 + 15 = 16 + 15 – 5 = 31 – 5 = 26 iii. 13 + 5 – 16 + 2 = 13 + 5 + 2 – 16 = 20 – 16 = 4 iv. 25 – 5 + 6 – 2 = 25 + 6 – 5 – 2 = 31 – 7 = 24 v. 125 – 13 + 25 – 16 = 125 + 25 – 13 – 16 = 150 – 29 = 121 vi. 34 – 6 + 4 + 8 = 34 + 4 + 8 – 6 = 46 – 6 = 40 Q 2: Use DMAS rule to solve the following: i. 8 ÷ 2 × 6 = 4 × 6 = 24 ii. 15 ÷ 3 × 7 = 5 × 7 = 35 iii. 16 × 10 ÷ 2 = 16 × 5 = 80 iv. 38 × 16 ÷ 8 = 38 × 2 = 76 v. 32 ÷ 2 × 32 ÷ 16 = 16 × 2 = 32 vi. 92 ÷ 4 × 84 ÷ 4 = 23 × 21 = 483 Q 3: Use DMAS rule to solve the following: i. 6 × 21 ÷ 7 – 11 = 6 × 3 – 11 = 18 – 11 = 7 ii. 5 × 7 + 32 ÷ 4 = 5 × 7 + 8 = 35 + 8 = 43 iii. 35 ÷ 7 + 8 – 4 = 5 + 8 – 4 = 13 – 4 = 9 iv. 48 + 15 × 5 – 100 = 48 + 75 – 100 = 123 – 100 = 23 v. 95 ÷ 5 × 10 + 6 – 14 = 19 × 10 + 6 – 14 = 196 – 14 = 182 vi. 105 ÷ 5 + 8 × 11 – 14 = 21 + 8 × 11 – 14 = 21 + 88 – 14 = 109 – 14 = 95 Q 4: Sobia and Arslan bought books = 45 × 30 = 1350 Sobia and Arslan sold books = 10 × 24 = 240 Difference = 1350 – 240 = 1110 Q 5: Laiba has = Rs. 3650 Price of dress = Rs. 1560 Price of socks = 4 × 90 = Rs. 360 Cost of mirrors = 2 × 150 = Rs. 300 Amount left with Laiba now = 3650 – 1560 – 360 – 300 = Rs. 1430

18 CSS Primary Standard “Mathematics” Q 6: Waqas and Namra have pictures = 2450 Waqas has picture cards = 250 Namra has picture cards = 2450 – 250 = 2200 Q 7: Aleezay bought chairs = 19 × 1200 = Rs. 22800 Aleezay bought table = Rs. 7560 Aleezay spend altogether = 22800 + 7560 = 30360 Review Exercise Q 1: What does each digit stands for in the number 58,624,924. Solution: = 58,624,924 4 20 900 4000 20000 600000 8000000 50000000 Q 2: Read loudly and write the following number in words 89,438,486. Solution: Eighty nine millions, four hundreds thirty eight thousands, four hundreds and eighty six. Q 3: Read loudly and write the number in numerals. Forty six millions, two hundred thirty two thousands, four hundreds and eighty three. Solution: 46, 232, 483 Q 4: Compare the number and put the correct sign “>”, “<” or “=” in the given space. i. 84,685,924 > 4,685,924 ii. 24,984,682 = 24,984,682 iii. 658,392 < 21,658,392 Q 5: Solution: 3 ten millions, 2 million, 4 hundred thousands, 3 ten thousands, 5 thousands, 1 hundred, 3 tens, 8 ones. (32, 435, 138) Q 6: Solve the following questions: i. 642,382 + 531,489 ii. 456,321 + 1482 + 921,456 M H.Th T.Th Th H T O M H.Th T.Th Th H T O 6 4 2 3 8 2 4 5 6 3 2 1 + 5 3 1 4 8 9 + 9 2 1 1 4 4 8 5 2 6 1 1 7 3 8 7 1 1 3 7 9 2 5 9

19 CSS Primary Standard “Mathematics” iii. 856,892 – 31,421 iv. 859,248 – 169,159 M H.Th T.Th Th H T O M H.Th T.Th Th H T O 8 5 6 8 9 2 8 5 9 2 4 8 – 3 1 4 2 1 – 1 6 9 1 5 9 8 2 5 4 7 1 6 9 0 0 8 9 Q 7: Solve the following: i. 35624 × 56 ii. 4518 × 15 M H.Th T.Th Th H T O M H.Th T.Th Th H T O 3 5 6 2 4 4 5 1 8 × 5 6 × 1 5 2 1 3 7 4 4 4 4 6 2 4 0 1 7 8 1 2 0 0 8 9 2 4 8 0 1 9 9 4 9 4 4 1 3 3 8 7 2 0 Q 8: Solve the following and find the quotient and remainder: i. 3553 ÷ 19 ii. 8569 ÷ 37 Remainder = 0, Quotient = 187 Remainder = 22, Quotient = 231 Q 9: Solve by using DMAS rule: i. 3 – 8 + 5 × 4 = 3 – 8 + 20 = 3 + 20 – 8 = 23 – 8 = 15 ii. 18 ÷ 2 × 3 – 15 + 6 × 2 Solution: 18 ÷ 3 × 6 –14 + 13 = 6 × 6 – 14 + 13 = 36 – 14 + 13 = 36 + 13 – 14 = 49 – 14 = 35 iii. 84 ÷ 2 × 3 – 15 + 6 × 2 Solution: 84 ÷ 2 × 3 – 15 + 6 × 2 = 42 × 3 – 15 + 6 × 2 = 126 – 15 + 12 = 138 – 15 = 123 Q 10: Ali got the votes in 2013 = 154,815 Ayaz got the votes in 2013 = 100,880 They got the votes altogether = 154,815 + 100,880 = 255,695 votes Q 11: Price of two cars = Rs. 925,675 Price of one car = Rs. 300,750 Price of other car = ? Price of other car = 925,675 – 300,750 = 624,925 Rupees

20 CSS Primary Standard “Mathematics” Q 12: Distance covered in one hour = 238 km Distance covered in 26 hours = ? Distance covered in 26 hours = 238 × 26 = 6188 kilometers Q 13: Number of total books = 8288 books Number of libraries = 16 Books for each library = ? Books for each library = 8288 ÷ 16 = 518 books Q 14: The price of 8 dozen oranges = Rs. 1080 Price of 1 dozen of orange = 1080 ÷ 8 = Rs. 135 The price of 11 dozen of oranges = Rs. 1650 Price of 1 dozen of oranges = 1650 ÷ 11 = Rs. 150 Price of each dozen of oranges = Rs. 135 + Rs. 150 = Rs. 285 Unit No. 2 Factors and Multiples Lesson # 1 Teaching Objectives: To introduce the use of divisibility tests with different numbers. To explain prime and composite numbers. To explain the concept of factors of numbers. To explain the concept of multiples of numbers. To explain prime factorization of numbers, using the listing method, tree method and short division. To explain how to find the HCF by Venn diagram. To explain how to the find the LCM of 2 or more numbers by listing common multiples, prime factorization and short division. Learning Outcomes: The students will be able to: Use the rules of divisibility for different numbers. Differentiate between prime and composite numbers, using their properties. Identify the factors and multiples of a number. Calculate the factor and multiple of any given number. Apply the above concepts to real life situations. Teaching Materials: CSS Primary Standard Mathematics Book 4. Writing Board. Marker. Eraser. Procedure: Greet students and ask them what is division. Ask them to look the following examples. 6 ÷ 2 = 3, and 6 ÷ 3 = 2 (All numbers are

21 CSS Primary Standard “Mathematics” divisible by 1, 6 is divisible by 1, 2, and 3). 15 ÷ 3 = 5 and 15 ÷ 5 = 3 (This shows that 15 is divisible by 5 and 3.) Work with other numbers such as 10, 12, and 15. The factors will be quite obvious, and the concept of divisibility will become clear. Share divisibility rules: Despite the use of calculators and mobile calculators, it is very important for the students to know their tables and work out multiplication, division, and factorization mentally as far as possible. Mental arithmetic adds to mental discipline and flexibility in reasoning. Tell them that divisibility rules are important concepts that will be very useful in carrying out the LCM and factorization. What might seem minor steps in comparison to the speed of computers are actually useful in the later stages of learning. Understanding of factorization and divisibility will add to the learning capability towards a higher level. Therefore, it is advisable to spend sufficient time on every new concept, mentioned in this chapter (and later). Go through pages # 23, 24, 25 and 26 of the book. FUN ACTIVITIES

22 CSS Primary Standard “Mathematics” Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom.

23 CSS Primary Standard “Mathematics” Lesson # 2 Procedure: Ask students about Prime Numbers. Introduce Prime Numbers: 2, 3, 5, 7, 11, 13, and so on. Tell them that a Prime Number is a natural number greater than 1 that can be divisible 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, 11, 13, 15, 17 Composite Numbers: 4, 6, 8, 10, 12, 14, 16, 18 Tell them that 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. Tell them that these 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: 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. 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. Tell them that there is no biggest prime number or composite number. Numbers go to 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? 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. Go through page # 26, 27 and 28 to explain Prime and Composite Numbers to the students. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by

24 CSS Primary Standard “Mathematics” yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part I Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (2a) Q 1: Encircle the numbers which are divisible by 2: i. 32, 800 ii. 85, 901 iii. 86, 308 iv. 54,004 v. 34, 568 vi. 98, 311 vii. 35 Q 2: Identify and encircle the number which are divisible by 3, also write the rule to check the given numbers: Rule: If the sum of all the digits of a number is divisible by 3, then the number is divisible by 3. i. 48, 609 ii. 34, 200 iii. 48, 456 iv. 99,999 v. 66, 000 Q 3: Identify the numbers which are divisible by 5. i. 94,560 ii. 84, 300 iii. 42, 309 iv. 98,632 v. 45,685 vi. 84,965 Q 4: Identify the numbers which are divisible by 10. i. 98,400 ii. 44, 844 iii. 38,495 iv. 39,050 v. 50,000 vi. 34,215 Q 5: Identify the prime numbers from the list given below: 2, 5, 7, 23, 59, 19 Q 6: Identify the composite numbers from the list given below: 16, 6, 4, 18, 56, 42

25 CSS Primary Standard “Mathematics” 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. Section A Time Allowed: 45 Minutes (Objective Type) Total Marks: 30 Q.1: Fill the circle of correct answer. (10 Marks) 1. Count the number of digits first. If a number has ……….. number of digits than other, the number will be greater number. more less equal 2. The number from which another number is subtracted is called ………... difference minuend divisor 3. The answer of the subtraction is called ………... difference minuend divisor 4. The number which is multiplied is called ………... difference multiplicand divisor 5. The result of the multiplication is called ………... product multiplicand divisor 6. For division, we use table of ………... product multiplicand divisor 7. ……….. is an abbreviation of Latin Phrase. It stands for id est, meaning that is i.e. e.g. etc. 8. The numbers which have only two distinct factors are called ……….. numbers. prime composite both 9. If the sum of all the digits of a number is divisible by “………..”, then the number is divisible by “3”. 3 5 10 10. If any number which has “0” at once place, it will be divisible by “………..”. 3 5 10 B: Fill in the blanks: (10 Marks) 1. Ascending means from ………. to the greatest. 2. The number which is subtracted from ………. is called subtrahend. 3. To find the product, we ………. the number. 4. The number by which ………. is multiplied is called multiplier.

26 CSS Primary Standard “Mathematics” 5. Always do addition and then do ……….. 6. We use ………. rule, in case the expression involves addition, subtraction, multiplication and division. 7. ………. is neither a prime nor a composite number. 8. Those numbers which have more than two different factors are called ………. numbers. 9. A number which has “0” or “5” at once place, it is divisible by ……….. 10. 2,3,5,7 and ………. are all prime numbers. C: Mark as “True” or “False”: (10 Marks) 1. Ascending means from smallest to the greatest. True / False 2. The number which is subtracted from minuend is called subtrahend. True / False 3. The answer of the subtraction is called difference. True / False 4. To find the product, we add the number. True / False 5. The number by which multiplicand is multiplied is called multiplier. True / False 6. The result of the multiplication is called sum. True / False 7. e.g. is an abbreviation of Latin Phrase. It stands for id est, meaning that is True / False 8. “2” is neither a prime nor a composite number. True / False 9. A number which has “0” or “5” at once place, it is divisible by “3”. True / False 10. 2,3,5,7 and 11 are all composite numbers. True / False Section B Time Allowed: 75 Minutes (Subjective Type) Total Marks: 45 Note: Attempt all questions. All questions carry equal (3) Marks. 1. Which one is smaller 42, 568, 924 or 32, 586, 900? 2. Read loudly and write in numerals. i. Sixty five thousands and two hundreds ninety four. ii. One hundred, six thousands, nine hundred and fifty. iii. Three million, five hundred, sixty four thousands, two hundreds and ninety four. 3. Arrange the following numbers in ascending order. i. 36, 425 92, 856 620,321 50, 532, 922 ii. 92, 625 55, 586 542,000 300, 401 iii. 21, 250 80, 000,300 25, 022 200,000 4. Mr. Ali donates Rs. 326,000 to Shaukat Khanum Memorial Cancer Hospital in 2016 and Rs. 525,500 in 2017. How much total amount he donates in two years? 5. Write vertically and add the following: i. 468,352 and 301,604 ii. 831,524 and 103,541 6. Subtract the following and identify minuend, subtrahend and difference. i. 45896 and 16872 ii. 8431 and 38 7. Subtract the greatest 4-digit number from the greatest 5-digit number.

27 CSS Primary Standard “Mathematics” 8. A toy factory produced 84568 toys in first two months of the year 2015. The factory produced 76184 toys in first two months of the year 2016. How many more toys did the factory produce in first two months of year 2015 than 2016? 9. Ali went to a furniture store to buy some coffee tables for his coffee shop. He selected a glass table costing Rs. 4232. How much would it cost him to buy 4 such tables? 10. Find the product of 6854 and 38. 11. On the National days of Pakistan, Alishba and Eman baked 455 muffins. They prepared boxes of muffins and put 7 muffins in each box. How many boxes of muffins they prepared in all? 12. Samiya has 5250 baby carrots. She put the carrots in 35 boxes equally. How many baby carrots did she put in each box? 13. Sobia and Arslan bought 45 books for Rs. 30 each and sold 10 of them at the rate of Rs. 24. Find the difference between the money spends and returned. 14. Define Prime and Composite numbers. 15. Encircle the numbers which are divisible by “10”. i. 98,400 ii. 44,844 iii. 39,050 Model Paper # 2 Instructions: 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. Section A Time Allowed: 45 Minutes (Objective Type) Total Marks: 30 Q.1: Fill the circle of correct answer. (10 Marks) 1. Ascending means from smallest to the greatest. smallest greatest equal 2. The number which is subtracted from minuend is called subtrahend. subtracted added divided 3. To find the product, we multiply the number. subtract add multiply 4. The number by which multiplicand is multiplied is called multiplier. subtracted multiplied divided 5. Always do addition and then do subtraction. subtraction addition division

28 CSS Primary Standard “Mathematics” 6. We use DMAS rule, in case the expression involves addition, subtraction, multiplication and division. MAS MMS DMAS 7. “1” is neither a prime nor a composite number. 0 1 2 8. Those numbers which have more than two different factors are called composite numbers. Prime Composite both 9. A number which has “0” or “5” at once place, it is divisible by “5”. 0 1 2 10. 2,3,5,7 and 11 are all prime numbers. Prime Composite both B: Fill in the blanks: (10 Marks) 1. The number from which another number is subtracted is called ……….. 2. The answer of the subtraction is called ……….. 3. The number which is ………. is called multiplicand. 4. The result of the ………. is called product. 5. For division, we use table of ……….. 6. “1” is neither a prime nor a ………. number. 7. The numbers which have only ………. distinct factors are called prime numbers. 8. Those numbers which have more than two different factors are called ………. numbers. 9. A number which has “0” or “……….” at once place, it is divisible by “5”. 10. 2,3,5, ………. and 11 are all prime numbers. C: Mark as “True” or “False”: (10 Marks) 1. Descending means from smallest to the greatest. True / False 2. The number which is subtracted from minuend is called difference. True / False 3. The answer of the subtraction is called difference. True / False 4. To find the product, we multiply the number. True / False 5. The number by which multiplicand is added is called multiplier. True / False 6. The result of the multiplication is called difference. True / False 7. i.e. is an abbreviation of Latin Phrase. It stands for id est, meaning that is True / False 8. “1” is neither a prime nor a composite number. True / False 9. A number which has “0” or “5” at once place, it is divisible by “5”. True / False 10. 2,3,5,7 and 11 are all prime numbers. True / False Section B Time Allowed: 75 Minutes (Subjective Type) Total Marks: 45 Note: Attempt all questions. All questions carry equal (3) Marks. 1. Which one is smaller 53, 578, 924 or 53, 656, 650?

29 CSS Primary Standard “Mathematics” 2. Read loudly and write in numerals. i. Fifty five thousands and three hundreds ninety six. ii. Two hundred, five thousands, six hundred and forty. iii. Four million, five hundred, forty four thousands, two hundreds and ninety four. 3. Arrange the following numbers in descending order. i. 36, 425 92, 856 620,321 50, 532, 922 ii. 92, 625 55, 586 542,000 300, 401 iii. 21, 250 80, 000, 300 25, 022 200,000 4. Mr. Saif is working in a company. He got Rs. 197, 253 as an annual bonus in 2016 and Rs. 210, 567 in 2017. What is the total bonus in two years? 5. Write vertically and add the following: i. 577,443 and 410,715 ii. 932,564 and 173,571 6. Subtract the following and identify minuend, subtrahend and difference. i. 56907 and 27983 ii. 9542 and 69 7. Subtract the greatest 5-digit number from the greatest 6-digit number. 8. Farmer Aleem grew35, 624 carrots in 2010. In 2011 he grew 29, 200 carrots. How many more carrots did he grew in 2010? 9. The cost of mobile is Rs. 9584. Find the cost of 24 such mobile. 10. Find the product of 3159 and 84. 11. If the price of 22 ink pens is Rs. 5522. What will be the price of an ink pen? 12. The total cost of 13 mobile phones is Rs. 128, 440. What is the price of each mobile? 13. Waqas and Namra have 2450 picture cards altogether. Waqas has 250 cards. How many cards does Namra have? 14. What does the each digit stands for in the number 58, 624, 924. 15. Encircle the numbers which are divisible by “5”. i. 94,560 ii. 42,309 iii. 45,685 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. Section A Time Allowed: 45 Minutes (Objective Type) Total Marks: 30 Q.1: Fill the circle of correct answer. (10 Marks)

30 CSS Primary Standard “Mathematics” 1. Count the number of digits first. If a number has ……….. number of digits than other, the number will be greater number. more less equal 2. The number from which another number is subtracted is called ………... difference minuend divisor 3. The answer of the subtraction is called ………... difference minuend divisor 4. The number which is multiplied is called ………... difference multiplicand divisor 5. The result of the multiplication is called ………... product multiplicand divisor 6. We use DMAS rule, in case the expression involves addition, subtraction, multiplication and division. MAS MMS DMAS 7. “1” is neither a prime nor a composite number. 0 1 2 8. Those numbers which have more than two different factors are called composite numbers. Prime Composite both 9. A number which has “0” or “5” at once place, it is divisible by “5”. 0 1 2 10. 2,3,5,7 and 11 are all prime numbers. Prime Composite both B: Fill in the blanks: (10 Marks) 1. The number from which another number is subtracted is called ……….. 2. The answer of the subtraction is called ……….. 3. The number which is ………. is called multiplicand. 4. The result of the ………. is called product. 5. For division, we use table of ……….. 6. We use ………. rule, in case the expression involves addition, subtraction, multiplication and division. 7. ………. is neither a prime nor a composite number. 8. Those numbers which have more than two different factors are called ………. numbers. 9. A number which has “0” or “5” at once place, it is divisible by ……….. 10. 2,3,5,7 and ………. are all prime numbers. C: Mark as “True” or “False”: (10 Marks) 1. Ascending means from smallest to the greatest. True / False 2. The number which is subtracted from minuend is called subtrahend. True / False 3. The answer of the subtraction is called difference. True / False

31 CSS Primary Standard “Mathematics” 4. To find the product, we add the number. True / False 5. The number by which multiplicand is multiplied is called multiplier. True / False 6. The result of the multiplication is called difference. True / False 7. i.e. is an abbreviation of Latin Phrase. It stands for id est, meaning that is True / False 8. “1” is neither a prime nor a composite number. True / False 9. A number which has “0” or “5” at once place, it is divisible by “5”. True / False 10. 2,3,5,7 and 11 are all prime numbers. True / False Section B Time Allowed: 75 Minutes (Subjective Type) Total Marks: 45 Note: Attempt all questions. All questions carry equal (3) Marks. 1. Which one is smaller 42, 568, 924 or 32, 586, 900? 2. Read loudly and write in numerals. i. Sixty five thousands and two hundreds ninety four. ii. One hundred, six thousands, nine hundred and fifty. iii. Three million, five hundred, sixty four thousands, two hundreds and ninety four. 3. Arrange the following numbers in ascending order. i. 36, 425 92, 856 620,321 50, 532, 922 ii. 92, 625 55, 586 542,000 300, 401 iii. 21, 250 80, 000, 300 25, 022 200,000 4. Mr. Ali donates Rs. 326,000 to Shaukat Khanum Memorial Cancer Hospital in 2016 and Rs. 525,500 in 2017. How much total amount he donates in two years? 5. Write vertically and add the following: i. 468,352 and 301,604 ii. 831,524 and 103,541 6. Subtract the following and identify minuend, subtrahend and difference. i. 56907 and 27983 ii. 9542 and 69 7. Subtract the greatest 5-digit number from the greatest 6-digit number. 8. Farmer Aleem grew35, 624 carrots in 2010. In 2011 he grew 29, 200 carrots. How many more carrots did he grow in 2010? 9. The cost of mobile is Rs. 9584. Find the cost of 24 such mobile. 10. Find the product of 3159 and 84. 11. If the price of 22 ink pens is Rs. 5522. What will be the price of an ink pen? 12. The total cost of 13 mobile phones is Rs. 128, 440. What is the price of each mobile? 13. Sobia and Arslan bought 45 books for Rs. 30 each and sold 10 of them at the rate of Rs. 24. Find the difference between the money spends and returned. 14. Define Prime and Composite numbers. 15. Encircle the numbers which are divisible by “10”. i. 98,400 ii. 44,844 iii. 39,050

32 CSS Primary Standard “Mathematics” Lesson # 3 Teaching Objectives: To introduce the use of divisibility tests with different numbers. To explain prime and composite numbers. To explain the concept of factors of numbers. To explain the concept of multiples of numbers. To explain prime factorization of numbers, using the listing method, tree method and short division. To explain how to find the HCF by Venn diagram. To explain how to the find the LCM of 2 or more numbers by listing common multiples, prime factorization and short division. Learning Outcomes: The students will be able to: Use the rules of divisibility for different numbers. Differentiate between prime and composite numbers, using their properties. Identify the factors and multiples of a number. Calculate the factor and multiple of any given number. Apply the above concepts to real life situations. Teaching Materials: CSS Primary Standard Mathematics Book 4. Writing Board. Marker. Eraser. Procedure: Greet students and ask them to recite 2, 3, 4, 6, and 10 times tables. Ask them in which tables do you see 6, 12, and 18? (Ans: 2, 3, and 6, this means the common multiples of 2, 3, and 6 are 6, 12, and 18. The lowest common multiple of 2, 3, and 6 is 6.) Ask them in which tables do you see 12, 24, and 36? (Ans: 2 , 3, 4, and 6, the lowest common multiple of 2, 3, 4 and 6 is 12.) Tell them that factors of 12 are 2, 3, 4, and 6; Factors of 8 are 2 and 4 Common factors of 12 and 8 are 2 and 4. The highest common factor of 12 and 8 is 4. Factors of 24 are 2, 3, 4, 6, 8, 12 and 24 Factors of 18 are 2, 3, 6, and 9 Common factors of 24 and 18 are 2, 3, 6. Highest Common Factor of 24 and 18 is 6. Ask the students to note the similarities between the multiples in the tables. Then explain the rules of divisibility, one rule at a time. Consolidate the concept through a great deal of board work and oral activity. Go through pages # 29, 30 31 and 32 to explain the factors and multiples to the students and the concept of Highest Common Factor by Prime Factorization Method and Van Diagram Method to the students. Use explanation as given on pages # 34 and 35 to explain the concept of Least Common Multiples to the students.

33 CSS Primary Standard “Mathematics” Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (2b) Q 1: Find the factors of the following numbers: i. 25 1 × 25 = 25 5 × 5 = 25 So factors of 25 are = 1, 5 and 25 ii. 48 1 × 48 = 48 2 × 24 = 48 3 × 16 = 48 4 × 12 = 48 6 × 8 = 48 So the factors of 48 are = 1, 2, 3,4,6,8,12,16,24 and 48. iii. 18 1 × 18 = 18 2 × 9 = 18 3 × 6 = 18 So the factors of 18 are = 1, 2,3,6,9 and 18. iv. 28 1 × 28 = 28 2 × 14 = 28 4 × 7 = 28 So the factors of 28 are = 1, 2, 4,7,14 and 28. v. 125 1 × 125 = 125 5 × 25 = 125 So the factors of 125 are = 1,5,25 and 125. vi. 136 1 × 136 = 136 2 × 68 = 136 4 × 34 = 136 8 × 17 = 136 So the factors of 136 are 1,2,4,8,17,34,68 and 136. Q 2: Find first five multiples of numbers as given below: i. 13 = 13, 26, 39, 52, 65 ii. 29 = 29, 58, 87, 116, 145 iii. 35 = 35, 70, 105, 140, 175 iv. 43 = 43, 86, 129, 172, 215 v. 15 = 15, 30, 45, 60, 75 vi. 11 = 11, 22, 33, 44, 55 vii. 12 = 12, 24, 36, 48, 60

34 CSS Primary Standard “Mathematics” Exercise (2c) Q 1: Find H.C.F using prime factorization method: i. 6, 9 2 6 3 9 3 3 3 3 1 1 Prime Factors of 6 = 1 × 2 × 3 Prime Factors of 9 = 1 × 3 × 3 Common Factor = 3 Therefore Highest Common Factor = 3 ii. 24, 39 2 24 3 39 2 12 13 13 2 6 1 3 3 1 Prime Factors of 24 = 2 × 2 × 2 × 3 Prime Factors of 39 = 1 × 13 × 3 Common Factor = 3 Therefore Highest Common Factor = 3 iii. 22, 32, 60 2 22 2 32 2 60 11 11 2 16 2 30 1 2 8 3 15 2 4 5 5 2 2 1 1 Prime Factors of 22 = 2 × 11 Prime Factors of 32 = 2 × 2 × 2 × 2 × 2 Prime Factors of 60 = 2 × 2 × 3 × 5 Common Factor = 2 Therefore Highest Common Factor = 2 iv. 15, 95, 35 3 15 5 95 5 35 5 5 19 19 7 7 1 1 1 Prime Factors of 15 = 5 × 3 Prime Factors of 95 = 5 × 19 Prime Factors of 35 = 5 × 7 Common Factor = 5 Therefore Highest Common Factor = 5

35 CSS Primary Standard “Mathematics” v. 21, 27, 35 3 21 3 27 5 35 7 7 3 9 7 7 1 3 3 1 1 Prime Factors of 21 = 1 × 3 × 7 Prime Factors of 27 = 1 × 3 × 3 × 3 Prime Factors of 35 = 1 × 7 × 5 Common Factor = 1 Therefore Highest Common Factor = 1 vi. 36, 48 2 36 2 48 2 18 2 24 3 9 2 12 3 3 2 6 1 3 3 1 Prime Factors of 36 = 1 × 3 × 3 × 2 × 2 Prime Factors of 48 = 1 × 3 × 2 × 2 × 2 × 2 Common Factor = 1,2,3,12 Therefore Highest Common Factor = 12 vii. 24, 36 2 36 2 24 2 18 2 12 3 9 2 6 3 3 3 3 1 1 Prime Factors of 36 = 1 × 3 × 3 × 2 × 2 Prime Factors of 24 = 1 × 3 × 2 × 2 × 2 Common Factor = 1,2,3,12 Therefore Highest Common Factor = 12 viii. 9, 15, 21 3 9 3 15 3 21 3 3 5 5 7 7 1 1 1 Prime Factors of 9 = 1 × 3 × 3 Prime Factors of 15 = 1 × 3 × 5 Prime Factors of 21 = 1 × 3 × 7 Common Factor = 1,3 Therefore Highest Common Factor = 3

36 CSS Primary Standard “Mathematics” Q 2: Find the H.C.F using Van Diagram method: i. 72, 30 2 72 2 30 2 36 3 15 2 18 5 5 3 9 1 3 3 1 ii. 50, 80 2 50 2 80 5 25 2 40 5 5 2 20 1 2 10 5 5 1 iii. 48, 84 2 48 2 84 2 24 2 42 2 12 3 21 2 6 7 7 3 3 1 1

37 CSS Primary Standard “Mathematics” Q 3: Capacity of three drums = 36 liters, 48 liters and 72 liters Biggest measure = ? 2 36 2 48 2 72 2 18 2 24 2 36 3 9 2 12 2 18 3 3 2 6 3 9 1 3 3 3 3 1 1 Prime Factors of 36 = 2 × 2 × 3 × 3 Prime Factors of 48 = 2 × 2 × 2 × 2 × 3 Prime Factors of 72 = 2 × 2 × 2 × 3 × 3 Biggest measure = 2 × 2 × 3 = 12 liters Q 4: Length of three tracks = 44m, 88m and 114m Highest length of each track = ? 2 44 2 88 2 114 2 22 2 44 3 57 11 11 2 22 19 19 1 11 11 1 1 Prime factor of 44 = 2 × 2 × 11 × 1 Prime factor of 88 = 2 × 2 × 2 × 11 × 1 Prime factor of 114 = 2 × 3 × 19 Highest length of each track = 2m Q 5: Given numbers = 50, 60 and 86 Highest number = ? 2 50 2 60 2 86 5 25 2 30 43 43 5 5 3 15 1 1 5 5 1 Prime factor of 50 = 2 × 5 × 5 Prime factor of 60 = 2 × 2 × 3 × 5 Prime factor of 114 = 2 × 43 Highest Number = 2 Q 5: Length of different strings = 22cm and 40cm Greatest possible string = ?

38 CSS Primary Standard “Mathematics” 2 22 2 40 11 11 2 20 1 2 10 5 5 1 Prime factor of 22 = 2 × 11 Prime factor of 40 = 2 × 2 × 2 × 5 Greatest possible string = 2 cm Exercise (2d) Q 1: Find L.C.M numbers given below by using prime factorization: i. 18, 26 2 18 2 26 3 9 13 13 3 3 1 1 Factors of 18 = 2 × 3 × 3 Factors of 26 = 2 × 13 Common factors = 2 Non common factors = 3 × 3 × 13 = 117 L.C.M = (common factors)x(non-common factors) = 2 × 117 = 234 ii. 6, 39 2 6 3 39 3 3 13 13 1 1 Factors of 6 = 2 × 3 Factors of 39 = 3 × 13 Common factors = 3 Non common factors = 2 × 13 = 26 L.C.M = (common factors) × (non-common factors) = 3 × 13 × 2 = 78 iii. 75, 90, 95 3 75 2 90 5 95 5 25 3 45 19 19 5 5 3 15 1 1 5 5 Factors of 75 = 3 × 5 × 5

39 CSS Primary Standard “Mathematics” Factors of 90 = 2 × 3 × 3 × 5 × 5 Factors of 95 = 5 × 19 Common factors = 5 Non common factors = 5 × 2× 3 × 3 × 19 = 1710 L.C.M = (common factors) × (non-common factors) = 5 × 1710 = 8550 iv. 36, 48, 60 2 36 2 48 2 60 2 18 2 24 2 30 3 9 2 12 3 15 3 3 2 6 5 5 1 3 3 1 1 Factors of 36 = 2 × 2 × 3 x 3 Factors of 48 = 2 × 2 × 2 × 2 × 3 Factors of 60 = 2 × 2 × 3 × 5 Common factors = 2 × 2 × 3 = 12 Non common factors = 5 × 3 × 2 ×2 = 60 L.C.M = (common factors) × (non-common factors) = 12 × 60 = 720 v. 15, 75, 95 3 75 3 15 5 95 5 25 5 5 19 19 5 5 1 1 1 Factors of 75 = 3 × 5 × 5 Factors of 15 = 3 × 5 Factors of 95 = 5 × 19 Common factors = 5 Non common factors = 5 × 3 × 19 = 285 L.C.M = (common factors) × (non-common factors) = 5 × 285 = 1425 v. 42, 66, 64 2 42 2 66 2 64 3 21 3 33 2 32 7 7 11 11 2 16 1 1 2 8 2 4 2 2 1 Factors of 42 = 2 × 3 × 7

40 CSS Primary Standard “Mathematics” Factors of 66 = 2 × 3 × 11 Factors of 64 = 2 × 2 × 2 × 2 × 2 × 2 Common factors = 2 Non common factors = 3 × 7 × 11 × 2 × 2 × 2 × 2 × 2 = 7392 L.C.M = (common factors) × (non-common factors) = 2 × 7392 = 14784 vi. 22, 33, 44 2 22 3 33 2 44 11 11 11 11 2 22 1 1 11 11 1 Factors of 22 = 2 × 11 Factors of 33 = 3 × 11 Factors of 44 = 2 × 2 × 11 Common factors = 11 Non common factors = 2 × 3 × 4 = 24 L.C.M = (common factors) × (non-common factors) = 11 x 24 = 264 vi. 8, 14, 22 2 8 2 14 2 22 2 4 7 7 11 11 2 2 1 1 1 Factors of 8 = 2 × 2 × 2 Factors of 14 = 2 ×7 Factors of 22 = 2×11 Common factors = 2 Non common factors = 2 × 2 ×7 × 11 = 308 L.C.M = (common factors) × (non-common factors) = 2 × 308 = 616 Q 2: Find L.C.M by common multiple method: i. 15, 45, 60 Multiple of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180… Multiple of 45 = 45, 90, 135, 180, 225, 270… Multiple of 60 = 60, 120, 180, 240… Least Common Multiple = 180

41 CSS Primary Standard “Mathematics” ii. 8, 32, 64 Multiple of 8 = 8, 16, 24, 32, 40, 48, 56, 64… Multiple of 32 = 32, 64, 96… Multiple of 64 = 64… Least Common Multiple = 64 ii. 13, 20, 91 Multiple of 13 = 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390, 403, 416, 429, 442, 455, 468, 481, 494, 507, 520, 533, 546, 559, 572, 585, 598, 611, 624, 637, 650, 663, 676, 689, 702, 715, 728, 741, 754, 767, 780, 793, 806, 819, 832, 845, 858, 871, 884, 897, 910, 923, 936, 949, 962, 975, 988, 1001, 1014, 1027, 1040, 1053, 1066, 1079, 1092, 1105, 1118, 1131, 1144, 1157, 1170, 1183, 1196, 1209, 1222, 1235, 1248, 1261, 1274, 1287, 1300, 1313, 1326, 1339, 1352, 1365, 1378, 1391, 1404, 1417, 1430, 1443, 1456, 1469, 1482, 1495, 1508, 1521, 1534, 1547, 1560, 1573, 1586, 1599, 1612, 1625, 1638, 1651, 1664, 1677, 1690, 1703, 1716, 1729, 1742, 1755, 1768, 1781, 1794, 1807, 1820. .. Multiple of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400, 420, 440, 460, 480, 500, 520, 540, 560, 580, 600, 620, 640, 660, 680, 700, 720, 740, 760, 780, 800, 820, 840, 860, 880, 900, 920, 940, 960, 980, 1000, 1020, 1040, 1060, 1080, 1100, 1120, 1140, 1160, 1180, 1200, 1220, 1240, 1260, 1280, 1300, 1320, 1340, 1360, 1380, 1400, 1420, 1440, 1460, 1480, 1500, 1520, 1540, 1560, 1580, 1600, 1620, 1640, 1660, 1680, 1700, 1720, 1740, 1760, 1780, 1800, 1820… Multiple of 91 = 91, 182, 273, 364, 455, 546, 637, 728, 819, 910, 1001, 1092, 1183, 1274, 1365, 1456, 1547, 1638, 1729, 1820, 1911… Least Common Multiple = 1820 iv. 18, 54, 72 Multiple of 8 = 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252… Multiple of 54 = 54, 108, 162, 216, 270, 314 … Multiple of 72 = 72, 144, 216, 288… Least Common Multiple = 216 v. 5, 15, 25 Multiple of 5 = 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75… Multiple of 15 = 15,30,45,60, 75 … Multiple of 25 = 25,50,75… Least Common Multiple = 75

42 CSS Primary Standard “Mathematics” vi. 42, 66, 64 Multiples of 42 = 42, 84, 126,168, ……..14784 Multiples of 66 = 66, 132, 198, 264, 330, 396, 462, 528, 594,…………14784 Multiples of 64 = 64, 128, 192, ……..14784 LCM = 14784 Ans. vii. 11, 22, 33 Multiple of 11 = 11,22,33,44,55,66,77,88,99… Multiple of 22 = 22,44,66,88,110, Multiple of 33 = 33,66,99,132 … Least Common Multiple = 66 viii. 9, 27, 36 Multiple of 9 = 9,18,27,36,45,54,63,72,81,90,99,108,117,126… Multiple of 27 = 27,54,81,108,135 … Multiple of 36 = 36,72, 108, 180 … Least Common Multiple = 108 Q 3: Given numbers = 36, 64, 74 2 36 2 64 2 74 2 18 2 32 37 37 3 9 2 16 1 3 3 2 8 1 2 4 2 2 1 Prime Factors of 36 = 2 × 2 × 3 × 3 Prime Factors of 64 = 2 × 2 × 2 × 2 × 2 × 2 Prime Factors of 74 = 2 × 37 Common factors = 2 Non common factors = 2 × 3 × 3 × 2 × 2 × 2 × 2 × 37 = 10656 L.C.M = 2 × 10656 = 21312 Q 4: Given numbers = 24, 42, 52 2 24 2 42 2 52 2 12 3 21 2 26 2 6 7 7 13 13 3 3 1 1 1 Prime Factors of 24 = 2 × 2 × 2 × 3 Prime Factors of 42 = 2 × 3 × 7

43 CSS Primary Standard “Mathematics” Prime Factors of 52 = 2 × 2 × 13 Common factors = 2 Non common factors = 2 × 2 × 3 × 7 × 13 = 1092 L.C.M = 2 × 1092 = 2184 Q 5: Given numbers = 16 and 24 2 24 2 16 2 12 2 8 2 6 2 4 3 3 2 2 1 1 Prime Factors of 24 = 2 × 2 × 2 × 3 Prime Factors of 16 = 2 × 2 × 2 × 2 Common factors = 8 Non common factors = 2 × 3 = 6 L.C.M = 8 × 6 = 48 Review Exercise 2 Q 1: Which of the following numbers are divisible by 2, 3, 5 and 10 respectively? i. 58 Divisible by 2 ii. 324 Divisible by 2 and 3 iii. 225 Divisible by 3 and 5 iv. 830 Divisible by 2, 5 and 10 v. 125,126 Divisible by 2 vi. 38,942 Divisible by 2 vii. 1562 Divisible by 2 viii. 2489 Not divisible by any one of given divisors. ix. 5000 Divisible by 2, 5 and 10 x. 625 Divisible by 5 xi. 925 Divisible by 5 xii. 339 Divisible by 3 Q 2: Find the H.C.F of the following: i. 9, 45, 60 3 9 3 45 2 60 3 3 3 15 2 30 1 5 5 3 15 1 5 5 1

44 CSS Primary Standard “Mathematics” Prime factors of 9 = 3 × 3 Prime factors of 45 = 3 × 3 × 5 Prime factors of 22 = 2 × 2 × 3 × 5 Highest Common factors = 3 ii. 8, 18, 28 2 8 2 18 2 28 2 4 3 9 2 14 2 2 3 3 7 7 1 1 1 Prime factors of 8 = 2 × 3 × 2 Prime factors of 18 = 2 × 3 × 3 Prime factors of 28 = 2 × 2 × 7 Highest Common factors = 2 iii. 36, 72, 96 2 36 2 72 2 96 2 18 2 36 2 48 3 9 2 18 2 24 3 3 3 9 2 12 1 3 3 2 6 1 3 3 1 Prime factors of 36 = 2 × 2 × 3 × 3 Prime factors of 72 = 2 × 2 × 2 × 3 × 3 Prime factors of 96 = 2 × 2 × 2 × 2 × 2 × 3 Highest Common factors = 12 iv. 35, 49, 56 5 35 7 49 2 56 7 7 7 7 2 28 1 1 2 14 7 7 1 Prime factors of 35 = 5 × 7 Prime factors of 49 = 7 × 7 Prime factors of 56 = 2 × 2 × 2 × 7 Highest Common factors = 7 Q 3: Find the L.C.M of the following: i. 9, 45, 60

45 CSS Primary Standard “Mathematics” 3 9 3 45 2 60 3 3 3 15 2 30 1 5 5 3 15 1 5 5 1 Factors of 9 = 3 × 3 Factors of 45 = 3 × 3 × 5 Factors of 60 = 2 × 2 × 3 × 5 Common factors = 3 Non common factors = 3 × 5 × 2 × 2 = 60 L.C.M = 3 × 60 = 180 ii. 12, 36, 48 2 12 2 36 2 48 2 6 2 18 2 24 3 3 3 9 2 12 1 3 3 2 6 1 3 3 1 Factors of 12 = 2 × 2 × 3 Factors of 36 = 2 × 2 × 3 × 3 Factors of 48 = 2 × 2 × 2 × 2 × 3 Common factors = 12 Non common factors = 2 × 2 × 3 = 12 L.C.M = 12 × 12 = 144 iii. 8, 12, 24 2 8 2 12 2 24 2 4 2 6 2 12 2 2 3 3 2 6 1 1 3 3 1 Factors of 8 = 2 × 2 × 2 Factors of 12 = 2 × 2 × 3 Factors of 24 = 2 × 2 × 2 × 3 Common factors = 4 Non common factors = 2 × 3 = 6 L.C.M = 4 × 6 = 24

46 CSS Primary Standard “Mathematics” iv. 16, 24, 42 2 16 2 24 2 42 2 8 2 12 3 21 2 4 2 6 7 7 2 2 3 3 1 1 1 Factors of 16 = 2 × 2 × 2 × 2 Factors of 24 = 2 × 2 × 2 × 3 Factors of 42 = 2 × 3 × 7 Common factors = 2 Non common factors = 2 × 2 × 2 × 3 × 7 = 168 L.C.M = 4 × 168 = 336 Q 4: Number of bandages = 12, 18 Greatest number of bandage kits = ? 2 12 2 18 2 6 3 9 3 3 3 3 1 1 Prime factors of 12 = 2 × 2 × 3 Prime factors of 18 = 2 × 3 × 3 H.C.F = 6 kits Q 5: Given numbers = 12, 18, 24 Greatest number = ? 2 12 2 24 2 18 2 6 2 12 3 9 3 3 2 6 3 3 1 3 3 1 1 Prime factors of 12 = 2 × 2 × 3 Prime factors of 18 = 2 × 3 × 3 Prime factors of 24 = 2 × 2 × 3 × 2 H.C.F = 6 Q 6: Given numbers = 16, 8, 20 Greatest number of pieces = ? 2 16 2 8 2 20 2 8 2 4 2 10 2 4 2 2 5 5 2 2 1 1 1 Prime factors of 16 = 2 × 2 × 2 × 2 Prime factors of 8 = 2 × 2 × 2 Prime factors of 20 = 2 × 2 × 5 Greatest number of pieces = 4

47 CSS Primary Standard “Mathematics” Unit No. 3 Fractions Lesson # 1 Teaching Objectives: To introduce the use of divisibility tests with different numbers. To introduce proper, improper, and mixed fraction. To introduce equivalent fractions. To compare fractions. To introduce addition, subtraction, multiplication, and division of fractions. Learning Outcomes: The students will be able to: Identify correctly the different types of fractions. Generate a series of equivalent fractions. Compare and arrange fractions in order. Perform number operations using fractions. Teaching Materials: CSS Primary Standard Mathematics Book 4. Writing Board. Marker. Eraser. Procedure: Ask students what they know about fractions. Use the explanation was given on pages # 37, 38, 39 and 40 to explain the concepts of like and unlike fractions, comparison of fractions, ascending and descending order of the fraction and simplification of the fraction. Fun activities Dividing by Fractions ... with Crackers What You Need: Crackers (whole can be divided into 2 parts) Lined paper Pencil What You Do: 1. First, have your child predict what he thinks 1 divided by 1/2 is. With a little help from a graham cracker, invite him to find out if he's correct. 2. Hand over a whole graham cracker to your child. Explain that this is one graham cracker, so it represents the number 1. 3. Then, have him divide the graham cracker in half by bending it down the middle. After it splits, ask him to count how many graham cracker pieces there now are. 4. After he responds that there are two, say “That's correct. 1 divided by ½ is 2.” He may looked puzzled, since most division problem answers or quotients are usually smaller than the dividend, which in this case was 1.

48 CSS Primary Standard “Mathematics” 5. Now, ask your child to predict what 2 divided by 1/2 is. 6. After your child responds, have him set the broken graham cracker aside and hand him two more. Explain that now he has two graham crackers, representing the number 2. 7. Then, have him divide the graham crackers in half by bending them and splitting them down the middle. After they split, ask your child how many pieces there are. 8. After he responds that there are 4 pieces, say, “That's correct. 2 divided by 1/2 equals 4.” 9. Next, explain how to divide whole numbers by fractions without using graham crackers. Multiply the whole number by the fraction that has been reversed. 1 divided by 1/2; 1 × 2/1 = 2, or 1/1 × 2/1 = 2/1, which equals 2. Remind him that any whole number is equivalent to that number, over 1. 10. Have your child try a few problems on lined paper. For example, 3 divided by 1/4 is 3 × 4 = 12. 4 divided by 1/4; 4 × 4 = 16, 5 divided by 1/3; 5 × 3 =15. Finally, celebrate your child's new math concept with a yummy snack of sweet graham crackers! Try practicing some more math during snack time. Assign fraction puzzle as given below. Invite the students for solving questions. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be: Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise 3a Q 1: Identify the like fractions from the given fractions: i. 3 5 6 2 , , , 2 2 2 2 = Like fractions iii. 29 54 35 18 , , , 61 61 61 61 = Like fractions

49 CSS Primary Standard “Mathematics” vi. 5 3 7 1 , , , 11 11 11 11 = Like fractions Q 2: Identify the unlike fractions from the given fractions: i. 5 3 6 , , 12 12 14 = Unlike fraction ii. 4 3 6 2 , , , 9 13 15 16 = Unlike fraction iv. 5 3 4 8 , , , 6 8 15 16 = Unlike fraction vi. 8 1 6 3 , , , 13 5 19 17 = Unlike fraction Q 3: Arrange the fractions given below in descending order: i. 5 3 6 9 , , , 11 11 11 11 9 6 5 3 , , , 11 11 11 11 ii. 8 3 15 17 4 , , , , 19 19 19 19 19 17 15 8 4 3 , , , , 19 19 19 19 19 iii. 2 5 3 6 , , , 4 4 4 4 17 7 5 3 , , , 18 18 18 18 iv. 4 21 5 8 , , , 61 61 61 61 21 8 5 4 , , , 61 61 61 61 v. 3 1 5 3 , , , 8 2 8 4 3 5 1 3 , , , 4 8 2 8 vi. 8 3 5 5 , , , 9 18 6 9 8 5 5 3 , , , 9 6 9 18 Q 4: Arrange the fractions given below in ascending order: i. 7 8 6 3 , , , 12 12 12 12 3 6 8 7 , , , 12 12 12 12 ii. 2 3 5 2 , , , 5 8 10 8 2 3 2 5 , , , 8 8 5 10 iii. 18 5 15 21 , , , 19 19 19 19 5 15 18 21 , , , 19 19 19 19 iv. 4 8 3 3 , , , 7 21 21 7 3 8 3 4 , , , 21 21 7 7 v. 6 2 11 9 , , , 13 13 13 13 2 6 9 11 , , , 13 13 13 13 vi. 6 5 9 2 , , , 11 11 11 11 2 5 6 9 , , , 11 11 11 11 Q 5: Simplify the given fractions to its lowest form: i. 16 8 4 2 1 32 16 8 4 2 ii. 24 12 4 42 21 7 iii. 18 9 3 1 54 27 9 3 iv. 5 1 20 4 v. 16 8 4 36 18 9 Lesson # 2 Procedure: Use the explanation as given on pages # 41 and 42 to explain the concepts of Unit, Proper, Improper and Mixed Fractions to the kids. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by yourself. Then encourage students to solve other questions there. For notebooks work, begin by pair work and finally ending with individual work. Suppose you have an exercise consisting of 5 questions. Each question further consists of 5 parts then your strategy should be:

50 CSS Primary Standard “Mathematics” Question No. Done by the teacher Board practice by the students Pair work Individual work Home work 1 Part i Part ii Part iii Part iv Part v Focus on the definitions and ask students to learn the definitions with understanding. Once in a week, homework can be assigned based on the definition given in the chapter / lesson / unit going on in the classroom. Exercise (3b) Q 1: Express the following as mixed number and then as an improper fraction. First one is done for you i. 23 5 = 3 4 5 ii. 39 14 = 11 2 14 iii. 41 12 = 5 3 12 Q 2: Represent each of the following fractions in diagrams. (Hint: Use circular or square boxes). Q 3: Express each improper fraction in mixed numbers / fractions. i. 13 3 = 1 4 3 ii. 12 5 = 2 2 5 iii. 15 4 = 3 3 4 iv. 19 3 = 1 6 3 v. 21 4 = 1 5 4 Q 4: Express each mixed fraction into improper fractions: i. 2 3 5 = 17 5 ii. 4 2 5 = 14 5 iii. 11 5 13 = 76 13 iv. 1 2 3 = 7 3 v. 1 7 2 = 15 2 Q 5: Express the following into lowest form: i. 13 26 = 1 2 ii. 18 12 = 3 2 1 1 2 iii. 27 12 = 9 4 1 2 4 iv. 10 8 25 = 210 25 42 5 2 8 5 v. 9 3 12 = 45 12 3 3 4 Lesson # 3 Procedure: Use the explanation as given on pages # 44, 45 and 46 to explain the concepts of Addition and Subtraction of fractions to the students. Note for the teacher: Focus on all examples given in the book. Always solve few questions on the board by