CO MPASS SERIES mathematics WORKBOOK part -1 3 Name: Learn@Home Sec�on: Roll No.: School:
Preface ClassKlap partners with schools, supporting them with learning materials and processes that are all crafted to work together as an interconnected system to drive learning. Our books strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. ClassKlap presents the Compass series, designed specifically to meet the requirements of the new curriculum released in November 2016 by the Council for the Indian School Certificate Examinations (CISCE). Guiding principles: The 2016 CISCE curriculum states the following as a few of its guiding principles for Mathematics teaching: D evelop mathematical thinking and problem-solving skills and apply these skills to formulate and solve problems. A cquire the necessary mathematical concepts and skills for everyday life and for continuous learning in Mathematics and related disciplines. R ecognise and use connections among mathematical ideas and between Mathematics and other disciplines. R eason logically, communicate mathematically and learn cooperatively and independently. Each of these principles resonates with the spirit in which the ClassKlap textbooks, workbooks and teacher companion books have been designed. The ClassKlap team of pedagogy experts has carried out an intensive mapping exercise to create a framework based on the CISCE curriculum document. Key features of ClassKlap Compass series: Theme-based content that holistically addresses all the learning outcomes specified by the CISCE curriculum. The textbooks and workbooks are structured as per Bloom’s taxonomy to help organise the learning process according to the different levels involved. Student engagement through simple, age-appropriate content with detailed explanation of steps. L earning is supported through visually appealing images, especially for Grades 1 and 2. Increasing difficulty level in sub-questions for every question. Multiplication tables provided as per CISCE requirement. All in all, the Compass Mathematics books aim to develop problem-solving and reasoning skills in the learners’ everyday lives while becoming adept at mathematical skills as appropriate to the primary level. – The Authors
Workbook Features • Use of simple, age-appropriate language • Scaffolded approach for questions • Focus on subject-related vocabulary building I Recall I RUenmdeermsbtearndand Aimed at revising the Provides opportunities for prerequisite knowledge for practising the basic elements the concept from the previous involved in the learning of the year/chapter/concept/term concept I Apply I Explore(H.O.T.S.) Applying the understanding Extending the application of the of the concept to questions concept to more advanced based on the application of the and challenging questions that concept to real-life scenarios meet the criteria of higher order thinking skills
Contents 1 Shapes 1.1 Angles�������������������������������������������������������������������������������������������� 1 1.2 Nets and Views of Solids��������������������������������������������������������������� 8 2 Patterns 2.1 Rotational Patterns���������������������������������������������������������������������� 15 2.2 Patterns in Numbers�������������������������������������������������������������������� 22 3 Numbers 3.1 Large Roman Numerals�������������������������������������������������������������� 27 3.2 C ount Large Numbers Using Indian and International Systems���������������������������������������������������������������������������������������� 31 3.3 Round off Numbers���������������������������������������������������������������������� 36 4 Number Operations 4.1 Add and Subtract Large Numbers��������������������������������������������� 43 4.2 Multiply Large Numbers and Divide Numbers by 2-digit Numbers��������������������������������������������������������������������������� 48 4.3 BODMAS��������������������������������������������������������������������������������������� 54 5 Playing with Numbers 5.1 Prime and Composite Numbers������������������������������������������������� 62 5.2 H.C.F. and L.C.M������������������������������������������������������������������������� 68 6 Time 6.1 Convert Time������������������������������������������������������������������������������� 75 6.2 Add and Subtract Time��������������������������������������������������������������� 79
Shapes1Chapter 1.1 Angles I Recall Multiple Choice Questions 1) A line segment has ________ end points. [] (A) 4 (B) 3 (C) 2 (D) 1 2) AB is read as __________. [] (D) segment AB (A) ray AB (B) line AB (C) point AB 3) XY is read as ___________. [] (D) segment XY (A) line XY (B) ray XY (C) points XY I Remember and Understand Multiple Choice Questions [] 4) The angle in the given figure can be named as _______. AB C (A) ∠ACB (B) ∠CBA (C) ∠BAC (D) ∠B 5) The measure of an acute angle among these is __________________. [] (A) 100° (B) 60° (C) 0° (D) 180° 1
6) The angle between the directions North and East is a/an _______________. [] (A) right angle (B) obtuse angle (C) acute angle (D) zero angle Fill in the Blanks 7) The figure formed by two rays with the same initial point is called an _________________. 8) The unit used to represent the measure of an angle is ______________. 9) A _________________ is used to measure angles. Very Short Answer Questions 10) What is the measure of a complete angle? Solution: 11) Arrange the following angles in the increasing order of their measures. Reflex Acute Obtuse Zero Straight Right Solution: 12) The measures of some angles are given. Which of them are acute angles? 0º, 20º, 45º, 90º, 120º, 150º, 180º, 210º, 270º Solution: Short Answer Questions 13) Classify the following angles. 95º 133º 0º 82º 29º 90º Solution: 2
14) What is the measure of the angle at point O in each of the figures given? a) O A b) B O A What are these called and why? Solution: Long Answer Questions 15) Find the type and measures of the angles marked in the given figure using a protractor. CD A B E F Solution: Shapes 3
16) Fill in the following mind map. One has been done. Acute angle Right angle Obtuse angle Straight angle ANGLES Reflex angle Zero angle 180o 4
I Apply Short Answer Questions 17) C ount the number of acute, obtuse and reflex angles formed inside the given figure. Solution: 18) Identify and explain the different types of angles marked in the letter Z of the English alphabet. Solution: Shapes 5
Long Answer Questions 19) Write the types of angles made by the hands of the clocks (Consider only non-reflex angles.). a) b) c) d) Solution: 20) D raw the given angles: a) 30º b) 135º Solution: 6
I Explore (H.O.T.S.) Short Answer Question 21) M easure all the angles of the given figure. What is their sum? Solution: Long Answer Question 22) By what angle does the hour hand move between the time from 3 p.m. to 8 p.m.? Solution: Shapes 7
1.2 Nets and Views of Solids I Recall Multiple Choice Questions is _________. [] 1) The 2D shape of the base of (A) (B) (C) (D) 2) The face of a cuboid looks like a _________ when represented on paper. [ ] ] (A) cuboid (B) square (C) rectangle (D) cone 3) A figure with only two pairs of equal opposite sides is a _________. [ (A) cuboid (B) rectangle (C) triangle (D) circle I Remember and Understand Multiple Choice Questions 4) The net of a cube has __________ square faces. [] (A) 12 (B) 5 (C) 6 (D) 4 5) The solid shape which has six rectangular faces is a __________. [ ] (A) cone (B) cylinder (C) cube (D) cuboid 6) The respective numbers on the top, front and side views of the given die are __________. [] (A) 2, 4, 6 (B) 6, 4, 2 (C) 6, 2, 4 (D) 4, 6, 2 Fill in the Blanks 7) The 2D framework of a 3D solid is called its __________. 8
8) All the faces of a cube are _______________. 9) Perspective view is used in art and __________________. Very Short Answer Questions 10) How many circular ends does the net of a cylinder have? Solution: 11) H ow many circular ends does the net of a cuboid have? Solution: 12) How many circular ends does the net of a cone have? Solution: Short Answer Questions 13) Draw the net of a cone. Solution: 14) Draw the net of a cylinder. Solution: Shapes 9
Long Answer Questions 15) Draw five nets of a cube. Solution: 16) Draw the nets of the following: a) b) Solution: 10
I Apply Short Answer Questions 17) D raw the shape that can be folded into a cuboid? a) b) c) Solution: 18) Colour the correct net of the given 3D shape. Shape Nets Shapes 11
Long Answer Questions 19) Match the correct net with the given 3D shape. Shape Net a) A) b) B) c) C) 20) Circle the correct cube based on the given net. Net Cubes a) 12
Net Cubes b) c) I Explore (H.O.T.S.) Short Answer Question 21) The top, side and front views of a solid are given. Draw the solid shape. Top Side Front Solution: Shapes 13
Long Answer Question 22) Draw the top view, side view and front view of these solids. a) b) c) Solution: 14
Patterns2Chapter [] [] 2.1 Rotational Patterns [] I Recall [] Multiple Choice Questions 1) The symmetrical letter among the following is _____. (A) F (B) D (C) R (D) Q 2) The symmetrical letter among the following is _____. (A) S (B) C (C) P (D) F 3) The letter ‘H’ has ______ lines of symmetry. (A) 2 (B) 3 (C) 1 (D) 0 I Remember and Understand Multiple Choice Questions 4) The anticlockwise 1 turn of the given shape is _______. 4 (A) (B) (C) (D) 15
5) The shape that looks the same for 1 turn and 1 turn is ________. [] 42 [] (A) (B) (C) (D) 6) The next shape in the given pattern is ________. (A) (B) (C) ______________ (D) Fill in the Blanks 7) The line that divides a shape into symmetrical halves is called the ______________________. 8) Turning a shape in the clockwise direction is called __________ of the shape. 9) Letters such as F, Q, R and S are ________________. Very Short Answer Questions 10) Identify the turn that the shape takes in the following pattern. Draw the next shape. Solution: 16
11) Draw how the given shape looks when it is turned through 1 turn. 2 Solution: 12) Draw how the given letter looks when it is turned through 1 of a turn in the 3 clockwise direction. Solution: F Short Answer Questions 13) Draw how the given shape looks when it is turned through 1 turn and 1 turn. 24 Solution: Patterns 17
14) Draw the two shapes for the given figure when it is turned by 1 turn in the clockwise and anti-clockwise directions. 4 Solution: Long Answer Questions 15) Take the required number of 1 turns for the given figure so that you get back its 4 original position. Draw the shapes for each turn. Solution: 16) Draw the 1 turn, 1 turn and 1 turn of the given figure in the clockwise and 4 2 anticlockwise directions. 18
Solution: I Apply Short Answer Questions 17) Draw a shape using a rectangle and triangle. Repeat twice by turning it 1 clockwise through turn each time. 4 Solution: 18) Draw the shapes after a 1 turn of the given shapes. 2 a) b) Solution: Patterns 19
Long Answer Questions and . 19) Draw two rotational patterns using Solution: 20) Complete the table to show how the shape will look after the given turns in the anticlockwise direction. Shape 1 turn 1 1 turn 4 2 turn 20
I Explore (H.O.T.S.) d) Short Answer Question 21) Which of the following figures completes the given pattern? a) b) c) ? Solution: Long Answer Question 22) Circle the shape that breaks the pattern. a) b) AS A S A SA A c) S S S A d) Patterns 21
2.2 Patterns in Numbers [] [] I Recall [] Multiple Choice Questions [] 1) The number that is next in the series 1, 3, 5, 7, 9... is _____. [] (A) 12 (B) 11 (C) 15 (D) 13 [] 2) The number that is next in the series 36, 34, 30, 28, 24... is ___. (A) 20 (B) 22 (C) 18 (D) 17 3) The number that is next in the series 5, 10, 7, 12, 9... is ____. (A) 15 (B) 14 (C) 16 (D) 13 I Remember and Understand Multiple Choice Questions 4) The missing term in the given pattern is __________. 95, 88, 81, 74, 67, ______, 53, 46 (A) 66 (B) 60 (C) 64 (D) 58 5) The next term in the pattern 4, 7, 10, 13 is ________. (A) 20 (B) 14 (C) 16 (D) 18 6) The missing term in the given pattern is ________. 3, 5, 8, 12, _______ (A)18 (B) 24 (C) 16 (D) 17 Fill in the Blanks 7) 1, 12, 123, 1234, _______ 8) 20, 19, 17, 14, 10, _______ 9) 13, 26, 39, ________ 22
Very Short Answer Questions 10) Write the pattern of perfect squares up to the number 50 in the increasing order. Solution: 11) W rite the pattern from 25 to 100 with each of its terms increasing by 25. Solution: 12) Complete the pattern by writing the next three terms of the series. 27, 25, 23... Solution: Short Answer Questions 13) Observe the pattern and write the next two terms. 2+1=3 3+2=5 5+3=8 Solution: 14) Observe the pattern and write the next two terms. 3+3=6 7 + 7 = 14 15 + 15 = 30 Solution: Long Answer Questions 15) Write down the triangular numbers from 1 to 10 and show them using a diagram. Solution: Patterns 23
16) Represent the first six square numbers. Solution: I Apply Short Answer Questions 17) Complete the following patterns by writing the next three terms of the series. a) 5, 55, 555, 5555, 55555... b) 1, 11, 111, 1111... Solution: 18) T he given pattern is the amount saved by Riya every month. ` 56 ` 112 ` 224 ` 448 ` 896 May January February March April I f she continues to save in the same manner, what would her savings be in the month of August? Solution: 24
Long Answer Questions 19) a) Observe the pattern and write the next two terms. 1, (1 + 2), (1 + 2 + 3), (1 + 2 + 3 + 4), ... b) Observe the pattern and write the next three terms. (1 + 2) × 3, (2 + 3) × 4, (3 + 4) × 5, ... Solution: 20) Observe the pattern and write the next two terms: a) 9 × 9 + 7 = 88 98 × 9 + 6 = 888 987 × 9 + 5 = 8888 b) 2 + 4 + 6 + 8 = 20 12 + 14 + 16 + 18 = 60 22 + 24 + 26 + 28 = 100 Solution: Patterns 25
I Explore (H.O.T.S.) Short Answer Question 21) Find the product of 5 and 4 using a pattern. Solution: Long Answer Question 22) Find the products using patterns. a) 5 × 18 b) 5 × 22 c) 5 × 6 Solution: 26
Numbers3Chapter 3.1 Large Roman Numerals I Recall Multiple Choice Questions [] 1) T he Roman numeral for 11 is _____________ . [] [] (A) X (B) IX (C) XI (D) XII (D) 21 [] 2) The Hindu-Arabic numeral for XXII is ______________. (D) XXXIII [] [] (A) 20 (B) 22 (C) 23 3) The Roman numeral for 39 is ______________. (A) XXXIX (B) XXIX (C) XIX I Remember and Understand Multiple Choice Questions 4) The Hindu-Arabic numeral for D is __________. (A) 500 (B) 400 (C) 1000 (D) 100 (D) 100 5) The Hindu-Arabic numeral for M is _________. (D) LXIIII (A) 500 (B) 400 (C) 1000 6) The Roman numeral for 44 is __________. (A) XV (B) XLVI (C) XLIV Fill in the Blanks 7) The Roman numeral for 59 is ________. 8) The Hindu-Arabic numeral for DXXX is ________. 9) The Roman numeral for 95 is ________. 27
Very Short Answer Questions 10) Which Roman numerals are never repeated? Solution: 11) W hich Roman numerals can be repeated? Solution: 12) What is the Roman numeral for 90? Solution: Short Answer Questions 13) Write the Hindu-Arabic numeral for CLXVI. Solution: 14) W rite the Roman numeral for 172. Solution: Long Answer Questions 15) Write the Hindu-Arabic numerals for the following: a) DCL b) CLXI c) MDLXVI d) MDCC Solution: 16) Write the Roman numerals for the following: a) 181 b) 555 c) 1578 d) 99 Solution: 28
I Apply Short Answer Questions 17) In a competition, Seema scores LXXVI points and Raj scores XLV points. Who wins the competition? Solution: 18) Write the Roman numerals for the following year: a) when India got independence from the British rule. (Hint: 1947) b) when India won the Cricket World Cup for second time. (Hint: 2011) Solution: Long Answer Questions 19) Arrange the given Roman numerals in ascending order. CCCXX, MDV, MLXV, CCLXIX Solution: Numbers 29
20) R ahul scores MCL marks in the first semester and MDXX marks in the second semester. Express Rahul’s total marks in Hindu-Arabic numerals. Solution: I Explore (H.O.T.S.) Short Answer Question 21) Write the following Hindu-Arabic numbers in Roman numerals. a) 60000 b) 400500 Solution: Long Answer Question 22) Write the following Hindu-Arabic numbers in Roman numerals. a) 16000 b) 21001 c) 40002 d) 50032 Solution: 30
3.2 Count Large Numbers Using Indian and International Systems I Recall Multiple Choice Questions 1) T he number name of 1,55,582 in the Indian system is ________. [] (A) One lakh fifty-five thousand five hundred eighty-two [] [] (B) One lakh fifty-four thousand five hundred eighty-two (C) One lakh fifty-five thousand five hundred fifty-two (D) One lakh fifty-five thousand five hundred eighty-three 2) The successor of 190000 is ____________. (A) 190001 (B) 190002 (C) 189999 (D) 189998 3) The digit in the hundreds place of 214568 is ___________. (A) 8 (B) 5 (C) 1 (D) 6 I Remember and Understand Multiple Choice Questions [ ] 4) 10 lakhs = _____________ (D) 10 hundreds (A) 10 hundreds (B) 100 thousands (C) 1 million 5) The greatest 8-digit number is _________. [] (A) 99999 (B) 100000 (C) 9999999 (D) 99999999 6) The predecessor of 7000000 is ___________. [] (A) 7000002 (B) 6999998 (C) 6999999 (D) 7000001 Fill in the Blanks 7) T he numeral for twenty-one lakh twenty-five thousand one hundred twenty-three is ___________________. 8) T he number name of 12530223 in the international system is __________________ _____________________________________________________________________________. 9) In the international system of numeration, all the periods have _________ places each. Numbers 31
Very Short Answer Questions 10) How many crores are there in 10 million? Solution: 11) Write the numeral for one crore six lakh forty thousand six hundred fifty-one. Solution: 12) Write predecessor and successor of 111720001. Solution: Short Answer Questions 13) In 243908623, separate the periods using commas. Write the number names in the Indian and the international systems of numeration. Solution: 14) Write the expanded forms of the following numbers. a) 4105625 b) 49104810 Solution: 32
Long Answer Questions 15) Write the following numbers in the place value chart according to the Indian system of numeration. a) Two crore thirteen lakh sixty-nine thousand one b) Thirteen lakh sixty-seven thousand two hundred fifteen c) Three crore forty-seven lakh eighteen thousand two hundred three d) Five crore sixty-one lakh thirty-three thousand three hundred fifty-seven Solution: 16) Write the following numbers in the place value chart according to the international system of numeration. a) Forty million three hundred sixty-nine thousand two hundred forty-one b) Nine hundred forty-seven thousand two hundred seventeen c) Six million seven hundred eighteen thousand three hundred one d) Eight hundred twenty-one thousand three hundred fifty-nine Solution: Numbers 33
I Apply Short Answer Questions 17) Compare 12395678 and 5487324. Solution: 18) Form the greatest 7-digit number with the digits 3, 1, 8, 6, 4, 5 and 7 without repeating any digit. Solution: 34
Long Answer Questions 19) Arrange the given numbers in the ascending and descending orders: 98348597, 24327817, 97124127, 13187524. Solution: 20) The names of a few countries and their populations are given below. Use this information to answer the questions that follow. France: 65447374 Iceland: 317900 Iran: 75078000 Italy: 60340328 a) What is the population of France? Write the number in words. b) What is the population of Italy? Write the number in words. c) Which of the countries, Iceland or Iran, has more population? Solution: Numbers 35
I Explore (H.O.T.S.) Short Answer Question 21) Find the face values and place values of the underlined digits in the given numbers. a) 9800234 b) 4123059 Solution: Long Answer Question 22) What is the difference between the place value and the face value of the digit 6 in the number 16700925? Solution: 3.3 Round off Numbers [ ] (D) Both (A) and (B) ] I Recall ] [ Multiple Choice Questions (D) Both (B) and (C) Compare the given numbers using <, > or = sign. 1) 5 ___ 7 [ (A) < (B) > (C) = (D) Both (A) and (B) 2) 240 _____ 200 (A) > (B) < (C) = 3) 25 ___ 25 (A) < (B) > (C) = 36
I Remember and Understand Multiple Choice Questions 4) 1563 rounded off to the nearest ten is __________. [] (A) 1562 (B) 1560 (C) 1571 (D) 1570 5) 190 rounded off to the nearest hundred is ___________. [] (A) 200 (B) 191 (C) 250 (D) 150 6) In rounding off a number, if the digit in the ones place is less than 5, it is replaced with _____________. [] (A) 2 (B)1 (C) 0 (D) 5 Fill in the Blanks 7) 16769 rounded off to the nearest ten is _________. 8) 21741 rounded off to the nearest hundred is __________. 9) 92478 rounded off to the nearest thousand is ___________. Very Short Answer Questions 10) What is 1234 rounded off to the nearest ten? Solution: 11) Round off 21762 to the nearest hundred. Solution: 12) Round off 24190 to the nearest thousand. Solution: Numbers 37
Short Answer Questions b) 145 13) Round off to the nearest ten: a) 999 Solution: 14) Round off to the nearest hundred: a) 459 b) 263 Solution: Long Answer Questions 15) Round off the following numbers to the nearest ten, explaining the reason. a) 612 b) 567 Solution: 38
16) Round off the following numbers to the nearest hundred, and state the reason for your answer. a) 1183 b) 14749 Solution: I Apply Short Answer Questions 17) There are 25 girls in Class 4 of a school. How many chairs, rounded to the nearest ten should be arranged in the classroom so that all the girls can be seated? Solution: 18) There are 851 pages in a book. How many stamps, rounded to the nearest hundred must be bought if a stamp is to be placed on each page? Solution: Numbers 39
Long Answer Questions 19) 5836 students of a school are to be given an apple each. How many apples, rounded to the nearest thousand, should be bought? Solution: 20) Round off 765 and 845 to the nearest hundred. Find the sum of the numbers obtained. Solution: 40
I Explore (H.O.T.S.) Short Answer Question 21) Round off 23745 to the nearest tens, hundreds, thousands and ten thousands. Solution: Long Answer Question 22) Form the greatest 7-digit number with the digits 6, 5, 3 and 8 by repeating the digits. Use all the digits at least once. Solution: Numbers 41
42
4Chapter Number Operations 4.1 Add and Subtract Large Numbers I Recall Multiple Choice Questions 1) The sum of two numbers is 50000. The numbers are________. [] (A) 20000 and 29000 (B) 40000 and 20000 [] [] (C) 45000 and 5000 (D) 4000 and 47000 2) The difference between 9003 and 9000 is ____________. (A) 3 (B) 300 (C) 8997 (D) 1997 3) T he sum of 380000 and 210000 is ____________. (A) 480000 (B) 590000 (C) 580000 (D) 59000 I Remember and Understand Multiple Choice Questions 4) The sum of the digits in the ten lakh places of the numbers 11222022 and 36578194 is __________. [ ] [ ] (A) 1 (B) 2 (C) 3 (D) 7 [ ] 5) The difference between the digits in the crore places of 234789232 and 234789232 is ____________. (A) 0 (B) 8 (C) 1 (D) 2 6) T he sum of the digits in the billions and the millions places of the number 4592317834 is ___________. (A) 10 (B) 1 (C) 0 (D) 6 43
Fill in the Blanks 7) The sum of the largest 8-digit number and its successor is __________________. 8) The difference between the smallest 7-digit number and its predecessor is ________. 9) The sum of 1000000 and 1 is ________________. Very Short Answer Questions 10) Find the difference when we subtract 5000000 from 8000000. Solution: 11) Add: 22222222 and 33333333 Solution: 12) Solve: 47777342 − 47777341 Solution: Short Answer Questions 13) Add 1050000 to 4000000 and subtract 2000000 from the sum. Solution: 14) Solve: 555555 + 444444 Solution: Long Answer Questions 15) Solve the following: a) What should be added to 10012842 to get a sum of 23712900? b) By how much is 14607862 less than 23700975? 44
Solution: 16) Solve: 4321181 + 3848132 + 1132008 Solution: I Apply Short Answer Questions 17) A mit has two apartments in Pune. The price of the first apartment is ` 21218116 and the price of the second apartment is ` 30817108. What is the total price of both the apartments? Solution: Number Operations 45
18) A factory manufactures 11213118 nuts and 1208108 bolts in a year. How many more nuts than bolts does it manufacture? Solution: Long Answer Questions 19) The population of a country A is 124755990 and the population of country B is 105678880. By what number is the population of B less than that of A? Write the number in words. Solution: 46
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