CSS Primary Standard “Mathematics” 1 CSS Primary Standard Mathematics For Class 6 1 st term Syllabus Teacher’s Guide Fully Solved Exercises
CSS Primary Standard “Mathematics” 2 Table of Contents Sr. No. Description Page No. 1. Set 2. Whole numbers 3. Factors and multiples 4. Integers 5. Simplification 6. Ratio 7. Financial Arithmetic 8. Introduction Algebra 9. Linear equation 10. Geometry 11. Perimeter and Area 12. Three dimensional solid 13. Information Handling
CSS Primary Standard “Mathematics” 3 Division of Syllabus 1 st Term Week 1 Unit # 1 Sets Set Week 2 Types of Sets Week 3 Unit # 2 Whole Numbers Natural and Whole Numbers Addition and subtraction of whole numbers Multiplication and division of whole numbers Distributive laws of whole numbers Week 4 Week 5 Week 6 Revision and tests of Unit #1 and 2 Week 7 Unit # 3 Factors and Multiples Factors and Multiples Tests for divisibility Factorization HCF Week 8 Week 9 LCM Applications of HCF and LCM Week 10 Revision of Unit 3 Final Test 2 nd Term Week 1 Unit # 4 Integers (Exercise 4 a, b and c) Week 2 Exercise 4 d and e and Review Exercise 4 Week 3 Unit # 5 Simplification (Exercise 5a, b and c) Week 4 Exercise 5d and Review exercise Unit# 6 Ratio (Exercise 6a) Week 5 Exercise 6b and Review Exercise 6 Unit # 7 Finanacial Arithematic (Exercise7a) Week 6 Exercise 7b, c and d Week 7 Review Exercise 7 Unit # 8 Introduction of Algebra (Exercise 8a and b) Week 8 Exercise 8c, d and Review Exercise 8
CSS Primary Standard “Mathematics” 4 Week 9 Unit # 9 Linear Equation (Exercise 9a, b and c) Week 10 Review Exercise 9 Unit# 10 Geometry (Exercise 10a and b) Week 11 Exercise 10b, c and Review Exercise 10 Week 12 Revision Unit 4,5,6 Week 13 Revision Unit 7,8 Week 14 Revision of Unit 9, 10 ‘Detail Division of Syllabus’ Week 1 Unit– 1 Integers Day 1 Lesson: 1 Exercise 4a Q # 1,2 Day 2 Exercise 4a Q# 3 to Q# 6 Day 3 Lesson: 2 Addition of integers on number line Exercise 4b Q#1 to Q#3 Day 4 Exercise 4b Q# 4 to Q# 7 Day 5 Lesson: 3 Subtraction of Integers Exercise 4c Q# 1 (i–iii) Day 6 Exercise 4c Q# 1 (iv–vii) Week 2 Day 1 Lesson : 4 Multiplication of Integers Exercise 4d Q# 1 Day 2 Exercise 4d Q# 2, 3 Day 3 Lesson : 5 Division of integers Exercise 4e Q# 1,2 Day 4 Exercise 4e Q# 3, 4, 5 Day 5 Review Exercise 4 Q#1, 2, 3, 4 Day 6 Review Exercise 4 Q# 5, 6, 7, 8, 9 Week 3 Unit – 5: Simplification Day 1 Lesson 6: Kind of brackets BODMAS Rule Exercise 5a
CSS Primary Standard “Mathematics” 5 Day 2 Exercise 5a Q# 1 (v–vii) Day 3 Lesson 7: Mathematical Expression Involving Fraction Exercise 5b Day 4 Exercise 5b Q# 1 (v–ix) Day 5 Lesson 8: Mathematical Expression Involving Fraction Exercise 5c Day 6 Exercise 5c Q# 1 (iv–vii) Week 4 Day 1 Lesson 9: Real life problem Involving Fraction and Decimals Exercise 5d Day 2 Exercise 5d Q# 3, 4, 5, 6 Day 3 Review Exercise 5 Q# 1, 2, 3 Day 4 Review Exercise 5 Q# 4, 5, 6, 7, 8 Day 5 Unit – 6: Ratio Lesson 10: Ratio and Proportional: Ratio Exercise 6a Q# 1, 2, 3 Day 6 Exercis 6a Q# 4, 5, 6, 7, 8 Week 5 Day 1 Lesson 11: Exercise 6b Q# 1, 2, 3, 4 Day 2 Exercise 6b Q# 5, 6, 7, 8, 9, 10 Day 3 Review Exercise 6 Q# 1, 2, 3, 4 Day 4 Review Exercise 6 Q# 5, 6, 7, 8, 9 Day 5 Unit – 7: Financial Arithmetic Lesson 12: Financial Arithmetic Percentage Exercise 7a Day 6 Exercise 7a Q# 2
CSS Primary Standard “Mathematics” 6 Week 6 Day 1 Exercise 7b Q# 1 Day 2 Exercise 7b Q# 2 Day 3 Lesson 13: Real life problem involving percentage Exercise 7c Q# 1, 2, 3, 4 Day 4 Exercise 7c Q# 5, 6, 7, 8, 9, 10 Day 5 Lesson 14: Selling price and Cost Price, Price, Profit, Loss, Discount Exercise 7d Q# 1, 2, 3 Day 6 Exercise 7d Q# 4, 5, 6, 7 Week 7 Day 1 Review Exercise 7 Q# 1, 2, 3 Day 2 Review Exercise 7 Q# 4, 5, 6, 7 Day 3 Unit – 8: Introduction of Algebra Lesson 15: Algebra, Mathematical Statement Exercise 8a Q# 1 Day 4 Exercise 8a Q#2,3 Day 5 Lesson 16: Constant, Variable, Algebraic expression, Coefficient terms, Algebraic Sentences Exercise 8b Q#1 Day 6 Exercise 8b Q# 2, 3, 4 Week 8 Day 1 Lesson 17: Addition of like and unlike terms, simplification of algebraic expression, Exercise 8c Q# 1 Day 2 Exercis3 8c Q# 2, 3, 4 Day 3 Lesson 18: Evaluation and simplification of algebraic expression Exercise 8d Q# 1, 2 Day 4 Exercise 8d Q# 3,4 Day 5 Review Exercise 8 Q# 1, 2, 3 Day 6 Review Exercise 8 Q# 4, 5, 6
CSS Primary Standard “Mathematics” 7 Week 9 Unit – 9: Linear Equations Day 1 Lesson 19: Algebraic Equation Exercise 9a Q# 1 to Q# 3 Day 2 Lesson 20: Linear Equation Exercise 9b Q# 1 Day 3 Exercise 9c Q# 2 Day 4 Lesson 21: Linear equations involving fractional and decimal co-efficient Exercise 9c Q# 1, 2 Day 5 Exercise 9c Q# 3 to Q# 7 Day 6 Review Exercise 9 Q# 1, 2 Week 10 Day 1 Review Exercise 9 Q# 3, 7 Day 2 Unit – 10: Geometry Lesson 22: Geometry Exercise 10a Q#1, 2 Day 3 Exercise 10a Q#3, to Q# 7 Day 4 Exercise 10a Q#8, 9 Day 5 Lesson 23: Angle Exercise 10b Q#1, 2 Day 6 Exercise 10b Q#3, 4 Week 11 Day 1 Exercise 10b Q# 5, 6 Day 2 Lesson 24: Triangle Exercise 10c Q# 1 to Q# 3 Day 3 Exercise 10c Q#4, 5 Day 4 Review Exercise 10 Q#1 to Q# 4 Day 5 Review Exercise 10 Q# 5, 6 Day 6 Review Exercise 10 Q# 7 to Q# 11
CSS Primary Standard “Mathematics” 8 Week 12 Day 1 Revision Unit 4 Day 2 Revision Unit 4 Day 3 Revision Unit 5 Day 4 Revision Unit 5 Day 5 Revision Unit 6 Day 6 Revision Unit 6 Week 13 Day 1 Revision Unit 7 Day 2 Revision Unit 7 Day 3 Revision Unit 7 Day 4 Revision Unit 8 Day 5 Revision Unit 8 Day 6 Revision Unit 8 Week 14 Day 1 Revision Unit 9 Day 2 Revision Unit 9 Day 3 Revision Unit 9 Day 4 Revision Unit 10 Day 5 Revision Unit 10 Day 6 Revision Unit 10
CSS Primary Standard “Mathematics” 9 Week 1 Unit: 1 Sets Lesson # 1 Teaching Objectives: ☻ To introduce sets and their notations. ☻ To introduce tabular, descriptive and set builder notations. ☻ To introduce and exemplify different types of sets. Learning outcomes: Students should be able to: ☻ Define sets. ☻Recognize notation of a set and its objects/ elements. ☻Describe tabular form of a set and demonstrate through examples. ☻Define the following sets and demonstrate through examples: finite and infinite sets, empty /void/null set, singleton equal and equivalent sets, subset and superset of a set, proper and improper subsets of a set, Teaching Materials: CSS Primary Standard Mathematics Book 6. Writing Board. Marker. Eraser. Classroom Activity: This is the first time students are being taught sets. So, detailed explanation and easy exemplification is necessary. Relate the concept of a set with daily life examples such as a set of apples and a set of oranges. Reinforce the fact that sets can be represented in three notation forms that is, tabular, descriptive and set builder notation. Give simple examples of each before proceeding to the exercise.
CSS Primary Standard “Mathematics” 10 Simple examples: A = {a, b, c, d} and B = {1, 2, 3, 4} are both different sets. Their elements are a b c d and 1 2 3 4. These elements are distinguishable entities. Here they are written in tabular form. In descriptive form they will be written as, A = set of first four letters in the English alphabet B = set of first four natural numbers In set builder notation, sets A and B will be written as, A = {x/x є first four English alphabets} B = {x/x є N Ѵ 1 ≤ x ≤ 4} Answer any queries the students may have regarding the three styles. Show them how they are important in different questions. Also, while explaining set builder notation, introduce the students with symbols used for specific sets such as N for natural numbers, W for whole numbers, Z for integers etc. Exercise 1a Q.1 Justify that the following statements form a set or not. i. The first 5 days of the week. Ans: First five days of the week are Monday, Tuesday, Wednesday, Thursday and Friday. All these days are well defined because Monday means Monday not Sunday and they are distinct because Friday has its own distinction from Tuesday, Thursday. Therefore first five of a week form a set. ii. All the cups in the tea set. Ans: All the cups in the tea set are well defined items but it a set because all the cups are similar and there is not distinction of one cup from another cup. iii. The first 5 letters of the English alphabet. Ans: The first five letters of english alphabet {a, b, c, d, e} form a set because all the letters are well defined and are distinct from each other. iv. Students in class-room. Ans: Students in a class form a set because each student is well defined and is distinct from another student. v. The first 4 odd numbers. Ans: The first 4 odd numbers {1, 3, 5, 7} form a set because each number is well defined and we know what 1 mean. We do not confuse it with 2. Secondly 1, 3, 5, 7 are distinct from each other because they are not similar.
CSS Primary Standard “Mathematics” 11 vi. Names of 4 students of class 6th of your school. Ans: Same as iv vii. All the glasses of a water set. Ans: Same as ii Exercise 1b Q 1: Write the following sets in tabular form. i. The set of vowels in English alphabet. Ans: {a, e, i, o, u} ii. The set of names of lunar months in a year. Ans: {Muharram, Safar, Rabi’ al-awal, Rabi’ al-thani, Jumada al-awal, Jumada al-thani, Rajab, Sha’aban, Ramadan, Shawwal, Duh al-Q’idah, Duh al-Hijjah iii. The set of colours in our flag. Ans: {Green, White} iv. The set of names of your subjects in grade 6. Ans: {English, Urdu, Maths, Science, History, Geography, Islamiyat, Computer science} v. The set of your family members. Ans: {Every student will have different} vi. The set of names of your friends in grade 6. Ans: {Every student will have different names} Q 2: Count the number of elements in the following sets. i. {0} Ans: One ii. {5, 7} Ans: Two iii. {5, 7, 9, 11} Ans: Four iv. {1, 3, ... 9} Ans: Five v. {1, 2, 3, ... , 10} Ans: Ten vi. {4, 6, 8, 10, 12} Ans: Five vii. {2, 4, 6, … 10} Ans: Five
CSS Primary Standard “Mathematics” 12 Q 3: Write the following in tabular form of the set. i. 9 and 13 A. Ans: A={9,13} ii. Ali and Amna X. Ans: X={Ali, Amna} iii. 1,2,3,4,5,6 F. Ans: F={1, 2, 3, 4, 5, 6} iv. First 10 even number Z. Ans: {0, 2, 4, 6, 8, 10, 12, 14, 16, 18} v. Hammad and Ammad W. Ans: W={Hammad, Ahmad} vi. 100,101,143 S. Ans: S={100, 101, 143} vii. The set natural numbers when even numbers Y. Ans: Y={1, 3, 5, .....} Week 2 Types of Sets Lesson # 2 Classroom Activity: Start the lesson on types of set with finite and infinite sets. By now the students will have an idea on what a set is and what are its elements and their properties. Finite and infinite sets will be easier to handle at such a point. Furthermore, advanced topics in the chapter such as subsets require this solid foundation. Again, give examples from real life, so the students are able to understand the idea behind finite and infinite sets. The textbook is of great help in this regard. Moving on to empty set, teaching the concept of a null or void set can be a bit difficult. As the frequently asked question is that, “Why an empty set called a set when it is empty?” Such a question is tackled by relating to the conventions developed in mathematics and sciences for our convenience in building a theory. For example, positive and negative for charges of protons and electrons and choice of carbon-12 Avogadro’s number (6.022x1022) for mole. Teaching the students about singleton sets should not be a difficult task once they will have walked the tricky roads of sets and empty set. However, at least three
CSS Primary Standard “Mathematics” 13 examples are necessary. While dealing with equal and equivalent sets, make sure that every student grasps the difference between equal and equivalent sets. Follow the book as well as improvise with some examples. Exercise 1c Q 1: Identify finite and infinite set. i. The set of natural numbers between 3 and 10. Ans: finite ii. {1, 2, 3, …, 23} Ans: finite iii. The set of natural numbers between O and1. Ans: finite iv. Cities in the world. Ans: finite v. The set of natural number divisible by 5. Ans: infinite vi. Stars in the sky. Ans: infinite vii. {2, 4, 6, 8, …} Ans: infinite viii. Points on a line. Ans: infinite ix. {10, 9, – 9, – 14, 6} Ans: finite x. {1, 3, 5, ..., 51} Ans: finite xi. The set of natural numbers greater than 10. Ans: infinite xii. The set of natural number not divisible by 2. Ans: finite xiii. The set of factors of 10. Ans: infinite Q 2: Pick out equal and equivalent signs for the following. i. {p, q, r}_____{P, Q, R} Ans: equivalent
CSS Primary Standard “Mathematics” 14 ii. {India, Srilanka, China}____{Pakistan, Iran, China} Ans: equal iii. {a, e, i, o, u}____{vowels of the alphabet} Ans: equal iv. {10, 11, 12}_____{11, 12, 10} Ans: equal v. {2, 4, 6, 8}____{1, 2, 3, 4,...} Ans: equal vi. {a, b, c, d, e}_____{e, b, c, a, d} Ans: equivalent vii. {1,2,3,4}____{4,1,2,3} Ans: equivalent viii. {Ali, Ahmed, Amna}_____{Ali, Amna, Haris} Ans: equivalent ix. {a, e, i, o, u}____{1,2,3,4,5} Ans: finite x. {tea, bread, egg}_____{shoes, socks, pants} Ans: finite xi. {Maths, English, Urdu}_____{Urdu, English, Maths} Ans: infinite xii. {Spring, Summer, Winter}_____[Autumn, Spring, Summer} Ans: finite Week 2 Subsets Lesson # 3 Classroom Activity: At the level of grade 6, Subsets is perhaps the most difficult topic for students to understand. Emphasize on clarification of the definition of a subset. Start with simpler examples such as examples related to box containing packets of chocolates and candies. Each packet will be a subset of the box which is a superset of the packets. Then move on to the examples dealing with numbers. For this purpose, follow the book and improvise.
CSS Primary Standard “Mathematics” 15 Once the concept of subsets is clear, move on to the classification of subsets, that is, proper and improper subset. Every concept must be related to real life examples that are easier for the students to understand such as, cars, planes, fruits, toys etc. Exercise 1d Q 1: If a set has 5 number of elements. Find the number of subset, proper subset and improper subset. Ans: Number of subsets = 32 Number of proper subsets = 31, Number of improper subsets = 1 Q 2: Find all the possible subsets of the following sets. i. A = {1,2} Ans: { }, {1}, {2}, {1, 2} ii. X = {a,b,c} Ans: { }, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c} iii. Y = {W,h,a,g} Ans: { }, {W}, {h}, {a}, {g}, {W, h}, {W, a}, {W, g}, {h, a}, {h, g}, {a, g}, {W, h, a}, {W, a, g}, {h, a, g}, {W, h, g}, {W, h, a, g} Q 3: Find the proper and improper subsets of the following. i. B = {x,y,z} Ans: proper subset = { }, {x}, {y}, {z}, {x, y}, {x, z}, {y, z} improper subset = {x, y, z} ii. C = {1,2,3} Ans: proper subset = { }, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3} improper subset = {1, 2, 3} Q 4: Which of the following sets are proper subset and which are improper subsets? Use the subset symbols in your answer. i. A = {7, 14, – 15, 23} B = {– 15, 23, 14, 7} Ans: A B ii. A = {e} B = {g, h, j, e} Ans: A B iii. A = {book, pen, car, ruler} B = {book, pen, ruler} Ans: B A iv. A = [1, 2, 3, 4} B = {4, 3, 2, 1} Ans: A B v. A = {2, 4, 6, 8, 10} B = {2, 4, 6, 8, 10, 12}
CSS Primary Standard “Mathematics” 16 Ans: A B Review Exercise 1 Q 1: Choose the correct answer and fill the circle: i. If A= { 3,6,9,12} and B= { 9,12,3,6} then: A is subset of B they are equal set they are equivalent set all of them ii. All the even numbers in whole number are: empty set finite set infinite set void set iii. 14 A means: 14 is proper subset of A 14 is a member of A 14 does not belongs to A all of these iv. A is set of factors of 12. Which one of the following is not a member of A? 3 4 5 6 v. X is set of multiples of 3, Y is the set of multiples of 6, Z is the set of multiples of 9. Which one is true: X Y X Z Z Y Z X vi. S = {a,b,c,d,e}, how many proper subset does the set S have? 15 31 32 33 vii. A = {a, b, c, d}, how many subset does the set A have? 4 6 16 64 viii. If A = {3,4,6,7,8}, which of them is not a subset of A: B = {3,6,7} C = { 3,4} {3,4,5} {7,8} ix. If A has 18 elements. How many subset A has: 2 10 2 18 2 18–1 2 18 –1 x. B = {3,4,6,7,8,9}, which one is superset of B: A = {1,3,4,6,7} C = {3,4,6,7,8,9,10} D = {4,6,7,8} E = {1,3,4,7,8,10,11}
CSS Primary Standard “Mathematics” 17 xi. If Z has 16 elements. How many proper subset z has: 2 16 2 16-2 2 14 none of them xii. If X = {88,84,98} and Y = {88,101,102} then: X Y X Y X Y X Y Q 2: Fill in the blanks with the symbol of subset. i. {a,b,c}____{a,b,c,d} Ans: {a, b, c} {a, b, c, d} ii. { }____{0,1,2} Ans: { } {0, 1, 2} iii. {1,2}____{1} Ans: {1, 2} {1} or {1} {1, 2} iv. {1,2,3}____{0,1,2...} Ans: {1, 2, 3} {0,1, 2,.......} Q 3: Name the following sets: i. {} Ans: singleton set ii. A = {a,b,c }, B = {c,b,a} Ans: equal sets iii. { } Ans: empty set iv. X = {1,2,3...} Ans: infinite set v. A = {1,2,3}, B = {a,b,c} Ans: equivalent sets vi. X = set of all positive integers which is a multiple of 2: Ans: Q 4: Which of the following sets are subsets of other sets? Use the symbols. A = {0,1,2}, B = {1,2,–1} C = {1,2,0}, D = {1,0,–1} E = {e, f, g} F = {e,f} G = { } H = {g, f,e} Ans: A C, F E, F H, E H, G A, B, C, D, E, F Q 5: Find the possible subsets of the following sets. i. A = {a}
CSS Primary Standard “Mathematics” 18 Ans: { }, {a} ii. B = {a,b} Ans: { }, {a}, {b}, {a, b} iii. C = {1,2,3,4,5} Ans: { }, {1}, {2}, {3}, {4}, {5}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {4, 5}, {3, 4}, {3, 5}, {1, 2, 3}, {2, 3, 4}, {3, 4, 5}, {4, 5, 1}, {1, 2, 5}, {1, 3, 5}, {2, 4, 5}, {1, 2, 4}, {1, 3, 4}, {2, 3, 5}, {1, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 1}, {4, 5, 1, 2}, {5, 1, 4, 3}, {1, 2, 3, 4, 5} Week 3 Unit: 2 Whole Numbers and Number Line Lesson # 1 Teaching Objectives: To revise the difference between natural and whole numbers. To revise equalities and inequalities of whole numbers. To revise mathematical operations on whole numbers (also using number line). To revise commutative, associative and distributive properties of whole numbers under addition and multiplication. Learning outcomes: Students should be able to: Differentiate between natural and whole numbers. Identify natural and whole numbers, and their notations. Represent a given list of whole numbers, whole numbers < (or >) a given whole number, whole numbers ≤ (or ≥ ) a given whole number, whole numbers > but < a given whole number, whole numbers ≤ but ≥ a given whole number, sum of two or more given whole numbers, on the number line. Add and subtract two given whole numbers.
CSS Primary Standard “Mathematics” 19 Verify commutative and associative law (under addition) of whole numbers. Recognize ‘0’ as additive identity. Multiply and divide two given whole numbers. Verify commutative and associative law (under multiplication) of whole numbers. Recognize ‘1’ as multiplication identity. Verify distributive law of multiplication over addition. Verify distributive law of multiplication over subtraction (with positive difference). Teaching Materials: CSS Primary Standard Mathematics Book 6. Writing Board. Marker. Eraser. Classroom Activity: The large numbers and arithmetic operations have been handled in Mathematics Book 5. Set of whole numbers has been introduced in chapter 1. Handling whole numbers should not be difficult provided the students have understood their concepts in the previous years. Discuss the difference between natural and whole numbers clearly. State clearly that natural numbers are ordinarily used counting numbers. Give examples from daily life. Follow the book in this regard. For comparisons and inequalities, go a step further and give numerical examples related to the formulae given in the book on page 16. For example, to explain x>a give an example that 5>2, here x = 5 and a = 2. Number line can be difficult to understand at first. Tell them that it is a pictorial representation of numbers. Give examples of other diagrammatical representations such as the world map, human body etc. to relate the concept. Exercise 2a Q 1: Fill in the blanks by using the symbol < or >. i. 21089346589 — 43586701 Ans: > ii. 415678910 — 483467890 Ans: < iii. 101023410 — 101022400 Ans: >
CSS Primary Standard “Mathematics” 20 iv. 1435861070 — 189345678 Ans: > v. 348964173 — 389814342 Ans: < vi. 4384642310 — 143210342 Ans: > vii. 1892341039 — 7189403479 Ans: < viii. 5678989610 — 437248910 Ans: > ix. 4132867180 — 63798543 Ans: > x. 4235115187 — 4237593480 Ans: < Q 2: Find the sum of the following whole numbers by using number line. i. 2 and 6 ii. 8 and 4 iii. 10 and 3 iv. 1 and 6 v. 24 and 6
CSS Primary Standard “Mathematics” 21 vi. 40 and 20 vii. 15 and 25 Q 3: Find the difference of the following whole number using number line. i. 2, 6 ii. 15, 20 iii. 9, 15 iv. 10, 6 v. 5, 9
CSS Primary Standard “Mathematics” 22 Q 4: Add more then two numbers on number line. i. 3, 6, 5 ii. 9, 12, 5 iii. 4, 8, 2 iv. 1, 4, 5 v. 3, 8, 12 vi. 4, 6, 10 Q 5: Find the difference on the number line and adjust the scale. i. 18 , 17 ii. 95 , 90
CSS Primary Standard “Mathematics” 23 iii. 75 , 55 iv. 170 , 70 v. 110 , 50 vi. 250 , 200 vii. 350 , 150 viii. 850 , 50 ix. 475 , 200 x. 1700 , 300 Q 6: Which of the following statements are true or false. i. 14387234 > 14381123
CSS Primary Standard “Mathematics” 24 Ans: true ii. 51432734 > 431411734 Ans: false iii. 411157832 > 21114321 Ans: false iv. 243789243 < 24534890 Ans: true v. 73429143 < 73429014 Ans: true vi. 73849672 < 83481432 Ans: true vii. 67892432 > 1143200 Ans: false viii. 805898724 > 984345670 Ans: false Q 7: Write all the natural numbers less then 15. Ans: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 Q 8: Write all the whole numbers less than 12 Ans: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 Q 9: Represent on number line. i. Whole numbers < 60. ii. Whole numbers > 6. iii. Whole numbers 700. iv. Whole numbers 7. v. Whole numbers > 4 but <10. vi. Whole numbers 4 but 10. vii. Whole numbers greater than 5.
CSS Primary Standard “Mathematics” 25 viii. Even whole numbers greater than or equal to 6 but less than 15. Week 4 Addition and Subtraction of Whole Numbers Lesson 2 Classroom Activity: Before moving on to addition and subtraction of very large numbers in the book, make the students recall the processes of these mathematical operations. A brainstorming session could be very helpful for this purpose. Simple demonstrative examples are necessary to clarify the commutative and associative properties. For example, take identical tennis balls and add two of them by placing one by one on the table to in reverse orders to show the commutative property with respect to addition. Before jumping to additive identity, explain the mathematical meaning of an identity that is, “a number is an identity when it leaves another number unchanged under some operation.” Now relate this concept with zero in case of addition and tell them that zero is called “additive” identity because it leaves any number unchanged when it is added to it. Exercise 2b Q 1: Fill in the blanks with correct statements. i. 100013601 + ______ = 100013601 Ans: 0 ii. 134134180 + 4281517 = ______ + 134134180 Ans: 4281517 iii. 710415 + (63 + 72) = (710415 + ______) + 72 Ans: 63 iv. ______ × 134712118123 = 0 Ans: 0
CSS Primary Standard “Mathematics” 26 v. ______ + 0 = 0 + 1143 Ans: 1143 vi. ______ + 0 = 1110 Ans: 1110 vii. ______ ÷ 1101 = 0 Ans: 0 viii. 1231014 + ______ = 1231014 Ans: 0 Q 2: Draw first 100 even numbers on number line with the difference of 10. Q 3: Find the sum of smallest five digit number and largest four digit number. Ans: 19999 Q 4: Add the following. i. 32,963,508 and 59,300,456 Ans: 92263964 ii. 284,492,334 and 321,211,692 Ans: 605704026 iii. 256,321,413 and 222,111,681 Ans: 478433094 Q 5: Subtract the following. i. 4,690,882 and 1,51,302 Ans: 4539580 ii. 284,591,621 and 103,381,111 Ans: 181210510 iii. 4,580,198 and 541,698 Ans: 4038500 Q 6: Prove the commutative law and associative law w.r.t to addition in the following questions. i. 349, 7895 Ans: Proved ii. 10050, 35965 Ans: Proved iii. 285, 920, 1089 Ans: Proved
CSS Primary Standard “Mathematics” 27 iv. 2132, 8931, 6754 Ans: Proved v. 7825, 8123, 9250 Ans: Proved Q 7: Find the total expenditures of a publishing company per annum. If the salaries of the labour is Rs. 7,950,438 per annum and the cost of maintance of the press is Rs. 380,540 per annum. Ans: Rs. 8330978 Q 8: Find is the increase in the population of Pakistan during 1998.census and 2017 census. The population of Pakistan in 1998 was 132352279 and in 2017 was 207774550. Ans: 75422271 Week 5 Multiplication and division of Whole Numbers Lesson 3 Classroom Activity: Addition, subtraction and division can be easily comprehended by senses. But multiplication is difficult. Addition and subtraction and their properties can easily be proved by identical objects such as tennis balls. Division is also easily exemplified by dividing candies among children but multiplication is a bit difficult to demonstrate with ordinary objects. This difficulty can be surpassed by the following classroom activity: Ask one of the students to count the numbers of rows and columns in which they are seated (say 6 and 4). Ask him to write the numbers on the board. Now ask another student to count the total number of the students in the classroom. Finally write the equation 6 x 4 = 24 Exercise 2c Q 1: Fill in the blanks with suitable words. i. 14 × (5 × 60) = (14 × ______) × 60 Ans: 5 ii. ______ × (300 + 4) = ( _____ × 300) + (5 × 4)
CSS Primary Standard “Mathematics” 28 Ans: 5, 5 iii. 30 × (40 + 10) = (30 × 40) + ______ Ans: (30x10) iv. 115 × (7 + 21) = (115 × _____) + (115 × 21) Ans: 7 v. 13 × (50 + 30) = (---_____) + (13 x 30) Ans: (13x50) Q.2 Multiply the following. i. 44 × 173 Ans: 1 7 3 × 4 4 ① ① 6 9 2 (173×4) 6 9 2 0 (173×40) 7 6 1 2 ii. 1842× 22 Ans: 1 8 4 2 × 2 2 ① ① ① 3 6 8 4 (1842×2) 3 6 8 4 0 (1842×20) 4 0 5 2 4 iii. 17432× 100 Ans: 1 7 4 3 2 × 1 0 0 0 0 0 0 0 (17432×0) 1 7 4 3 2 0 0 (17432×100) 1 7 4 3 2 0 0 iv. 1872× 110×2 Ans: Step (i) 1 1 0
CSS Primary Standard “Mathematics” 29 × 2 2 2 0 Step (ii) 1870×220 1 8 7 0 × 2 2 0 0 0 0 0 (1870×2) 3 7 4 0 0 (1870×20) 3 7 4 0 0 0 4 1 1 4 0 0 (1870×200) So 1870×110×2 = 411400 v. 3432 × 4440 × 110 Ans: Step (i) 4440 × 110 4 4 4 0 × 1 1 0 0 0 0 0 (4440×0) 4 4 4 0 0 (4440×10) 4 4 4 0 0 0 (4440×100) 4 8 8 4 0 0 Step (ii) 3432 × 488400 4 8 8 4 0 0 × 3 4 3 2 9 7 6 8 0 0 (488400×2) 1 4 6 5 2 0 0 0 (488400×30) 1 9 5 3 6 0 0 0 0 (488400×400) 1 4 6 5 2 0 0 0 0 0 (488400×3000) 1 6 7 6 1 8 8 8 0 0 So 3432 × 4440 × 110 = 1676188800 vi. 1110043 × 4320 Ans: 1 1 1 0 0 4 3 × 4 3 2 0
CSS Primary Standard “Mathematics” 30 0 0 0 0 0 0 0 (1110043×0) 2 2 2 0 0 8 6 0 (1110043×20) 3 3 3 0 1 2 9 0 0 (1110043×300) 4 4 4 0 1 7 2 0 0 0 (1110043×4000) 4 7 9 5 3 8 5 7 6 0 vii. 8432 × 10 × 230 Ans: Step (i) 10 × 230 2 3 0 × 1 0 0 0 0 (230×0) 2 3 0 0 (230×10) 2 3 0 0 Step (ii) 8432 × 2300 8 4 3 2 × 2 3 0 0 0 0 0 0 (8432×0) 0 0 0 0 0 (8432×00) 2 5 2 9 6 0 0 (8432×300) 1 6 8 6 4 0 0 0 (8432×2000) 1 9 3 9 3 6 0 0 So 8432 × 10 × 230 = 19393600 Q.3 Solve the following. i. 15,545 ÷ 5 Ans: 3109 5 15545 15 545 50 45 45 0 0 Remainder Hence, 15545 ÷ 5 = 3109 Quotient
CSS Primary Standard “Mathematics” 31 ii. 387616 ÷ 16 Ans: 24226 16 387616 32 67616 64616 3616 32 416 32 96 96 0 Hence, 387616 ÷ 16 = 24226 Quotient iii. 695450 ÷ 350 Ans: 695450 1987 350 350 345450 3150 30450 2800 2450 2460 0 Hence, 695450 ÷ 350 = 1987 Quotient iv. 133427 ÷ 389 Ans: 133427 343 389 1167 16727 1556 1167 1167 0 Hence, 133427 ÷ 389 = 343 Quotient
CSS Primary Standard “Mathematics” 32 Q.4 Prove the Commutative law under multiplication for the pair of whole number given below. i. a = 1777,b = 65 Ans: a × b = 1777 × 65 = 115505 b × a = 65 × 1777 = 115505 Hence, a × b = b × a ii. a = 6767, b = 12 Ans: a × b = 6767 × 12 = 80724 b × a = 12 × 6767 = 80724 Hence, a × b = b × a iii. a = 7777, b = 234 Ans: a × b = 7777 × 234 = 1819818 b × a = 234 × 7777 = 1819818 Hence, a × b = b × a iv. 2505,19423 Ans: 2505 × 19423 = 48654615 19423 × 2505 = 48654615 Hence, 2505 × 19423 = 19423 × 2505 v. 8320,4302 Ans: 8320 × 4302 = 35792640 4302 × 8320 = 35792640 Hence, 8320 × 4302 = 4302 × 8320 Q.5 Verify associative law under multiplication in the following whole numbers. i. 110,160,300 Ans: 110 × (160 × 300) = 5280000 (110 × 160) × 300 = 5280000 Hence, 110 × (160 × 300) = (110 × 160) × 300 ii. 141,213,10 Ans: 141 × (213 × 10) = 300330 (141 × 213) × 10 = 300330
CSS Primary Standard “Mathematics” 33 Hence, 141 × (213 × 10) = (141 × 213) × 10 iii. 21,2300, 404 Ans: 21 × (2300 × 404) = 19513200 (21 × 2300) × 404 = 19513200 Hence, 21 × (2300 × 404) = (21 × 2300) × 404 iv. 191, 166, 511 Ans: 191 × (166 × 511) = 16201766 (191 × 166) × 511 = 16201766 Hence, 191 × (166 × 511) = (191 × 166) × 511 v. 155,1341,40 Ans: 155× (1341 × 40) = 8314200 (155 × 1341) × 40 = 8314200 Hence, 155× (1341 × 40) = (155 × 1341) × 40 vi. 2011, 800, 244 Ans: 2011 × (800 × 244) = 392547200 (2011 × 800) × 244 = 392547200 Hence, 2011 × (800 × 244) = (2011 × 800) × 244 Q.6 Prove the distributive law of multiplication over addition in the following: i. 24, 17, 10 Ans: 24 (17 + 10) = 24 (27) = 648 24 (17) + 24 (10) = 408 + 240 = 648 Hence, 24 (17 + 10) = 24 (17) + 24 (10) ii. 35, 42, 70 Ans: 35 (42 + 70) = 35 (112) = 3920 35 (42) + 35 (70) = 1470 + 2450 = 3920 Hence, 35 (42 + 70) = 35 (42) + 35 (70) iii. 74, 100, 400 Ans: 74 (100 + 400) = 74 (500) = 37000 74 (100) + 74 (400) = 7400 + 29600 = 37000 Hence, 74 (100 + 400) = 74 (100) + 74 (400)
CSS Primary Standard “Mathematics” 34 iv. 555, 621, 843 Ans: 555 (621 + 843) = 555 (1464) = 812520 555 (621) + 555 (843) = 344655 + 467865 = 812520 Hence, 555 (621 + 843) = 555 (621) + 555 (843) v. 423, 700, 100 Ans: 423 (700 + 100) = 423 (800) = 338400 423 (700) + 423 (100) = 296100 + 42300 = 338400 Hence, 423 (700 + 100) = 423 (700) + 423 (100) vi. 810, 7341, 100 Ans: 810 (7341 + 100) = 810 (7441) = 6027210 810 (7341) + 810 (100) = 5946210 + 81000 = 6027210 Hence, 810 (7341 + 100) = 810 (7341) + 810 (100) Q.7 Prove the distribution law of multiplication over subtraction in the following. i. 15, 13, 11 Ans: 15 (13 – 11) = 15 (2) = 30 15 (13) + 15 (11) = 195 – 165 = 30 Hence, 15 (13 – 11) = 15 (13) + 15 (11) ii. 74, 44, 33 Ans: 74 (44 – 33) = 74 (11) = 814 74 (44) – 74 (33) = 3256 – 2442 = 814 Hence, 74 (44 – 33) = 74 (44) – 74 (33) iii. 100, 80, 17 Ans: 100 (80 – 17) = 100 (63) = 6300 100 (80) – 100 (17) = 8000 – 1700 = 6300 Hence, 100 (80 – 17) = 100 (80) – 100 (17) iv. 378, 112, 100 Ans: 378 (112 – 100) = 378 (12) = 4536 378 (112) – 378 (100) = 42336 – 37800 = 4536 Hence, 378 (112 – 100) = 378 (112) – 378 (100) v. 500, 675, 555
CSS Primary Standard “Mathematics” 35 Ans: 500 (675 – 555) = 500 (120) = 60000 500 (675) – 500 (555) = 337500 – 277500 = 60000 Hence, 500 (675 – 555) = 500 (675) – 500 (555) vi. 7341, 2340, 1132 Ans: 7341 (2340 – 1132) = 7341 (1208) = 8867928 7341 (2340) – 7341 (1132) = 17177940 – 8310012 = 8867928 Hence, 7341 (2340 – 1132) = 7341 (2340) – 7341 (1132) Q.8 The price of a mobile set is Rs. 92,500. What is the price of 312 such set of mobiles? Ans: Price of 1 mobile set = Rs. 92500/- Price of 312 mobile sets = 312 × 92500 = Rs. 28860000/- Q.9 The price of 380 bags of rice’s is Rs. 570,000. Find the price of one bag of rice. Ans: Price of 380 bags of rice = Rs. 570000/- Price of 312 mobile sets = 570000 380 = Rs. 1500/- Review Exercise 2 Q 1: Choose the correct answer and fill the circle: i. If 20 ÷ 10 then the quotient is: zero 10 2 1 ii. “1” in whole numbers is called: additive identity inverse identity multiplicative identity subtraction iii. “0” in whole number is called: additive identity multiplicative identity inverse identity none of them iv. Name of property 4 + 3 = 3 + 4 is: commutative property of addition distributive property of addition
CSS Primary Standard “Mathematics” 36 associative property of addition none of these v. 311420 × 1 = ________: 311420 1 0 22 vi. 27070 + 0 = ________: 0 35 27070 1 vii. 10010 – 10000 = ________: 0 1 7 10 viii. “0” is a/an _______ number: natural numbers whole number odd numbers none of them ix. Natural numbers start with _________: 0 –1 1 000 Q 2: Complete the following. i. 6 × (5 – 2) = (___ × ___) – (6 × 2) Ans: 6, 5 ii. 27 + 330 = ____ Ans: 357 iii. 1 ×0 = _____ 100 Ans: 0 iv. 88 × 10 =____ Ans: 880 v. (15 × 31) × 4 = 15 × (___ × ___) Ans: 31, 4 vi. 100 + 0 = ____ Ans: 100 vii. 11 × (70 + 41) = (11 × ____) + (___ × ___) Ans: 70, 11, 41 viii. 44701 + (3424 + 2340) =____ Ans: 50465 ix. 150 × ____ = 150 Ans: 1
CSS Primary Standard “Mathematics” 37 x. 150 = 150 Ans: 1 Q 3: Name and satisfy the following properties. i. (15 × 13) × 14 = 15 × ( 13 × 14 ) = ____________________ Ans: Associative property of multiplication ii. 27 × 33 = 33 × 27 = __________________ Ans: Commutative property of multiplication iii. 11 + (70 + 41 ) = ( 11 + 70 ) + 41 = ______________________ Ans: Associative property of addition Q 4: Write “T” for true and “F” for false in the following statements. i. 17 × 44 = 748 Ans: T ii. 14 + 81 + 31 = 125 Ans: F iii. 177 – 44 – 22 = 222 Ans: F iv. 4840 = 4840 1 Ans: T v. 44 – 0 = 44 Ans: T vi. 44,55,66,are all even numbers Ans: F Q 5: Do that following sums. i. 935, 695, 321 + 295, 481, 416 + 125, 328 Ans: Billion H-M TM Million H-T T-T Thousands Hundreds Tens Ones 9 3 5 6 9 5 3 2 1 2 9 5 4 8 1 4 1 6 1 2 5 3 2 8 1 2 3 1 3 0 2 0 6 5 935, 695, 321 + 295, 481, 416 + 125, 328 = 1, 231, 302, 065
CSS Primary Standard “Mathematics” 38 ii. 956, 442, 530 – 879, 532, 200 Ans: H-M T-M Million H-T T-T Thousands Hundreds Tens Ones 9 5 6 4 4 2 5 3 0 8 7 9 5 3 2 2 0 0 7 6 9 1 0 0 3 0 956, 442, 530 – 879, 532, 200 = 76, 910, 330 Q.6 Solve the following. i. Ans: 3 8 2, 5 9 5 × 5 4 1 5 3 0 3 8 0 (382595×4) 1 9 1 2 9 7 5 0 (382595×50) 2 0 6 6 0 1 3 0 So, 382595 × 54 = 20660130 ii. Ans: 1 2 2, 5 0 0 × 1 2 5 6 1 2 5 0 0 (122500×5) 2 4 5 0 0 0 0 (122500×20) 1 2 2 5 0 0 0 0 (122500×100) 1 5 3 1 2 5 0 0 So, 122500 × 125 = 15312500 Q.7 Solve the following. i. 36384 ÷ 96 Ans: 379 96 36384 288 7584 672 864 864 0
CSS Primary Standard “Mathematics” 39 Hence, 36384 ÷ 96 = 379 Quotient ii. 1769768 ÷ 364 Ans: 0 4862 364 1769768 1456 313768 2912 22568 2184 728 728 Hence, 1769768 ÷ 364 = 4862 Quotient Q.8 Public library has 73000 books in it .Due to some weather disaster 18340 books were damaged in the library and 2300 were shifted to other branch of the library. How many books left in public library? Ans: Number of public library books = 73000 = T Number of damage books = 18340 = D Number of books left in the library = ? = L L = T – D – S = 73000 – 18340 – 2300 = 52360 Q.9 If the cost of a paint bucket is Rs. 700. For a house we need 300 bucket of paint. How much it will cost to paint the house? Ans: Cost of 1 bucket of paint = Rs. 700 = C Total cost of 300 buckets of paint = 300 × Rs. 700 Number of books left in the library = Rs. 21000/- Q.10 Anoral, Ibrahim and Alishaba got Rs. 18,000. They have to distribute it equally, what will be the share of Anoral? Ans: Total Amount = Rs. 18000
CSS Primary Standard “Mathematics” 40 Anoral’s share = 18000 3 = Rs. 6000/- Week 7 Unit:3 Factors and Multiples Lesson 1 Teaching Objectives: ☻ To revise the concept of factor and its definition. ☻ To revise the concept of multiple and its definition. ☻ To distinguish between even and odd numbers. ☻ To distinguish between prime and composite numbers. ☻ To revise that 1 is neither prime nor composite but a factor of every number and 2 is the only even prime number. ☻ To revise the divisibility tests for factors from 2 to 25. ☻ To revise prime factorization method and index notation. ☻ To revise the concept of HCF and methods to find it. ☻ To revise the concept of LCM and methods to find it. ☻ To create examples from daily life that describe the applications of HCF and LCM. Learning outcomes: Students should be able to: ☻ Define a factor as a number which divides the dividend completely leaving no reminder. ☻ Define a multiple as a dividend into which a factor can divide. ☻ Define even numbers as the numbers which are multiples of 2. ☻ Define odd numbers as the numbers which are not multiples of 2. ☻ Define prime numbers as numbers which have only two Factors (i.e., 1 and itself) ☻ Define composite numbers as numbers which have more than two factors. ☻ Know that 1 is neither prime nor composite as it has only one factor which is 1 itself. ☻ Know that 1 is a factor of every number. ☻ Know that 2 is the only even prime number where as all other prime number are odd. ☻ Tests by inspection whether the number 2, 3, 4, 5, 6,8, 9, 10, 11, 12, 15, and 25 can divide a given number.
CSS Primary Standard “Mathematics” 41 ☻ Define prime factorization as the process of factorizing a number into its prime factors. ☻ Recognize index notation. ☻ Factorize a given number and express its factor in the index notation. ☻ Define HCF as the greatest number which is a common factor of two or more numbers. ☻ Find HCF of two or more than two numbers by prime factorization long division method ☻ Define LCM as the smallest number which is a common multiple of two or more numbers. ☻ Find LCM of two or more numbers by prime factorization division method ☻ Solve real life problems related to HCF and LCM. Teaching Materials: CSS Primary Standard Mathematics Book 6. Writing Board. Marker. Eraser. Classroom Activity: ☻ 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: Factor and Multiple In class 5 students were discussed the concept of factor, multiple, even number odd number prime and composite number, HCF and LCM, now in this unit we will discuss all above topic in detail. At the start of lesson revise all basic concept
CSS Primary Standard “Mathematics” 42 by conducting a quiz or have a class discussion or carry out some of the suggested activities. Factor is a number which divides the dividend completely having no remainder. For example the Factors of 18 are 1, 2, 3, 6, and 18. Assign some number to students to find their factors. Multiple is the product of a number with the natural numbers 1, 2, 3, ….. For example the multiple of 8 are 8, 16, 24, 32,…..Bring some pencil and asked the student to make them the multiple of 15. Even and Odd Numbers The number which is multiple of 2 is called even number while the number which is not multiple of 2 is called odd number. List the numbers from 1 to 100 and ask the students to separate the even and odd numbers. Even Numbers: 2, 4, 6, 8, 10, … Odd Numbers: 1, 3, 5, 7, 9, … Check wether the given number are even or odd by method explained on page# 31. Prime and Composite Numbers 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.
CSS Primary Standard “Mathematics” 43 ☻ 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. Exercise 3a Q 1: Put all the prime numbers in a square and all the composite number in a circle. i. 11 190 37 6 9342 8810 420 3301 15123 5 6140 49734 173 17 107 23 7 250 139 197 Q 2: Write the factors of the following numbers. i. 4 Ans: 1, 2, 4 ii. 17 Ans: 1, 17
CSS Primary Standard “Mathematics” 44 iii. 39 Ans: 1, 3, 13, 39 iv. 12 Ans: 1, 2, 3, 4, 6, 12 v. 15 Ans: 1, 3, 5, 15 vi. 18 Ans: 1, 2, 3, 6, 9, 18 vii. 24 Ans: 1, 2, 3, 4, 6, 8, 12, 24 viii. 48 Ans: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 ix. 100 Ans: 1, 2, 4, 5, 10, 20, 25, 50, 100 x. 120 Ans: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 xi. 146 Ans: 1, 2, 73, 146 xii. 250 Ans: 1, 2, 5, 10, 25, 50, 125, 250 xiii. 400 Ans: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400 xiv. 550 Ans: 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, 550 Q 3: Write the first five multiple for each number. i. 14 Ans: 14, 28, 42, 56, 70 ii. 22 Ans: 22, 44, 66, 88, 110 iii. 43 Ans: 43, 86, 129, 172, 215 iv. 82 Ans: 82, 164, 246, 328, 410 v. 10 Ans: 10, 20, 30, 40, 50 vi. 38 Ans: 38, 76, 114, 152, 190
CSS Primary Standard “Mathematics” 45 vii. 93 Ans: 93, 186, 279, 372, 465 viii. 73 Ans: 73, 146, 219, 292, 365 Q 4: Write all the even and odd numbers separately. i. 13 Ans: odd ii. 76 Ans: even iii. 135 Ans: odd iv. 97 Ans: odd v. 400 Ans: even vi. 340 Ans: even vii. 700 Ans: even viii. 1057 Ans: odd ix. 3230 Ans: even x. 137843 Ans: odd Q 5: Write even numbers between 10 and 100. Ans: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100. Q 6: Write odd numbers between 1400 and 1500. Ans: 1401, 1403, 1405, 1407, 1409, 1411, 1413, 1415, 1417, 1419, 1421, 1423, 1425, 1427, 1429, 1431, 1433, 1435, 1437, 1439, 1441, 1443, 1445, 1447, 1449, 1451, 1453, 1455, 1457, 1459, 1461, 1463, 1465, 1467, 1469, 1471, 1473, 1475, 1477, 1479, 1481, 1483, 1485, 1487, 1489, 1491, 1493, 1495, 1497, 1499. Q 7: Write prime numbers between 1 and 50. Ans: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 Q 8: Why 1 is neither prime nor composite?
CSS Primary Standard “Mathematics” 46 Ans: A natural number (i-e 1, 2, 3, 4, 5, etc.) is called a prime number (or a prime) if it has exactly two positive factors, 1 and the number itself. Natural numbers that have more than two positive factors are called composite. 1 has only one positive factor i-e. 1 only. Hence, 1 is neither prime nor composite. Q 9: Write composite numbers between 1 and 75. Ans: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75. Week 7 Test for divisibility Lesson # 2 Classroom Activity: There are some rules by which we can check that the given numbers are divisible by 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, and 25. These rules are called test for divisibility. Put the chart of natural numbers between 1 and 1000 in class and use the explanation as given about the method of test for divisibility by 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, and 25 on page# 39, 40, 41, 42, 43, 44, and 45 to check their divisibility. Exercise 3b Q 1: Which of the following numbers are divisible by 2,3,4,5 using divisibility test. i. 786010 Ans: Number 786010 is divisible by 2 and 5 only. ii. 154262 Ans: Number 154262 is divisible by 2 only. iii. 104800 Ans: Number 104800 is divisible by 2, 4 and 5 only. iv. 960734 Ans: Number 960734 is divisible by 2 only. v. 777080
CSS Primary Standard “Mathematics” 47 Ans: Number 777080 is divisible by 2, 4 and 5 only. vi. 542175 Ans: Number 542175 is divisible by 3 and 5 only. vii. 1296010 Ans: Number 1296010 is divisible by 2 and 5 only. viii. 477333 Ans: Number 477333 is divisible by 3 only. Q 2: Using the divisibility test, find out which of the following numbers are divisible by 6, 8, 9 and 10. i. 540 Ans: Number 540 is divisible by 6, 9 and 10 only. ii. 2340 Ans: Number 2340 is divisible by 6, 9 and 10 only. iii. 3040 Ans: Number 3040 is divisible by 8 and 10 only. iv. 7896 Ans: Number 7896 is divisible by 6 and 8 only. v. 17460 Ans: Number 17460 is divisible by 6, 9 and 10 only. vi. 15008 Ans: Number 15008 is divisible by 8 only. vii. 9370 Ans: Number 9370 is divisible by 10 only. viii. 55008 Ans: Number 55008 is divisible by 6, 8 and 9 only. ix. 104800 Ans: Number 104800 is divisible by 8 and 10 only. x. 13830 Ans: Number 13830 is divisible by 6 and 10 only. xi. 414 Ans: Number 414 is divisible by 6 and 9 only. Q 3: Using the tests of divisibility, find out which of the following numbers are divisible by 11,12,15,25. i. 478300 Ans: Number 478300 is divisible by 25 only. ii. 384730 Ans: Number 384730 is divisible by none.
CSS Primary Standard “Mathematics” 48 iii. 709500 Ans: Number 709500 is divisible by all (11, 12, 15, 25). iv. 3107556 Ans: Number 3107556 is divisible by 12 only. v. 32820 Ans: Number 32820 is divisible by 12 and 15 only. vi. 406857 Ans: Number 406857 is divisible by 11 only. vii. 5293440 Ans: Number 5293440 is divisible by 12 and 15 only. viii. 100010 Ans: Number 100010 is divisible by none. ix. 252525 Ans: Number 252525 is divisible by 15 and 25 only. x. 2838 Ans: Number 2838 is divisible by 11 only. xi. 3104316 Ans: Number 3104316 is divisible by 12 only. xii. 450000 Ans: Number 450000 is divisible by 12, 15 and 25 only. Q 4: Using the test of divisibility answer with statement is true or false. i. Is 8775 divisible by 15? Ans: True ii. Is 1300010 divisible by 10? Ans: True iii. Is 4128 divisible by 12? Ans: True iv. Is 8235 divisible by 8? Ans: False v. Is 97250 divisible by 25? Ans: True vi. Is 155376 divisible by 6? Ans: True vii. Is 8884351 divisible by 10? Ans: False viii. Is 25896 divisible by 3? Ans: True
CSS Primary Standard “Mathematics” 49 ix. Is 29520 divisible by 3? Ans: True x. Is 2536987 divisible by 2? Ans: False Week 8 Factorization and Index Notation Lesson # 3 Classroom Activity: Explain the Prime Factorization method to find the given number by factor tree and repeated division method. Express the prime factorization in the index notation as explained on page # 46, 47, and 48 Twin primes are the prime numbers differ by 2 for example 3 and 5, 5 and 7 etc. List the Twin number between 50 to 80. Exercise 3c Q.1 Write prime factorization of given numbers with factor tree. i. 60 Ans: 60 2 30 2 2 15 2 2 3 5 So, prime factors are 2,2,3,5 ii. 400 Ans: 400 2 200 2 2 100
CSS Primary Standard “Mathematics” 50 2 2 2 50 2 2 2 2 25 2 2 2 2 5 5 So, prime factors are 2, 2, 2, 2, 5, 5 iii. 750 Ans: 750 2 375 2 5 75 2 5 5 15 2 5 5 5 3 So, prime factors are 2, 5, 5, 5, 3 iv. 800 Ans: 800 2 400 2 2 200 2 100 2 25 2 2 2 2 5 5 So, prime factors are 2, 2, 2, 2, 5, 5 v. 3423 Ans: