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MATHEMATICS, , J{UV B¶ËVm {Vgar (B§J«Or ‘mܶ‘), , Maharashtra State Bureau of Textbook Production and Curriculum Research, Pune 411 004., , B§J«Or J[UV 3.ar, , 39.00

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The Constitution of India, Chapter IV A, , Fundamental Duties, ARTICLE 51A, Fundamental Duties- It shall be the duty of every citizen of India(a), , to abide by the Constitution and respect its ideals and institutions,, the National Flag and the National Anthem;, , (b), , to cherish and follow the noble ideals which inspired our national, struggle for freedom;, , (c), , to uphold and protect the sovereignty, unity and integrity of India;, , (d), , to defend the country and render national service when called upon, to do so;, , (e), , to promote harmony and the spirit of common brotherhood amongst, all the people of India transcending religious, linguistic and regional, or sectional diversities, to renounce practices derogatory to the, dignity of women;, , (f), , to value and preserve the rich heritage of our composite culture;, , (g), , to protect and improve the natural environment including forests,, lakes, rivers and wild life and to have compassion for living, creatures;, , (h), , to develop the scientific temper, humanism and the spirit of inquiry, and reform;, , (i), , to safeguard public property and to abjure violence;, , (j), , to strive towards excellence in all spheres of individual and, collective activity so that the nation constantly rises to higher levels, of endeavour and achievement;, , (k), , who is a parent or guardian to provide opportunities for education, to his child or, as the case may be, ward between the age of six, and fourteen years.

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First Edition : 2014, Seventh Reprint : 2021

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NATIONAL ANTHEM

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Preface, The ‘Primary Education Curriculum - 2012’ was prepared in the State of Maharashtra, following the ‘Right of Children to Free and Compulsory Education Act, 2009’ and, the ‘National Curriculum Framework 2005’. The Textbook Bureau has launched a, new series of Mathematics textbooks based on this syllabus approved by the State, Government for Stds I to VIII from the academic year 2013-2014. We are happy to place, the textbook of Standard Three in this series in your hands., Our approach while designing this textbook was that the entire teaching-learning, process should be child-centred, emphasis should be given on active learning and, constructivism and at the end of Primary Education the students should have attained, the desired competencies and that the process of education should become enjoyable and, interesting., Children have a natural liking for pictures and constantly try to ‘do’ things on, their own. Considering these factors, we have tried to make this book pictorial and, activity-oriented. As far as possible, expressive illustrations have been used which will, lead to a clearer understanding of mathematical concepts., Graded exercises and conversations have been included in order to ensure revision, and reinforcement of mathematical concepts and to facilitate self-learning. It is expected, that the children will solve the questions in the exercises on their own. We have tried to, provide a variety of exercises to make it interesting for the students., The language of presentation that the teacher is expected to use has been provided, in the textbook. Also, there are some instructions for the teachers themselves. The, instructions and the activities aim at making their teaching more activity-oriented., This book was scrutinized by teachers, educationists and experts in the field of, mathematics at all levels and from all parts of the State to make it as flawless and useful, as possible. Letters from teachers and parents as also reviews in newspapers have been, taken into account while preparing this textbook. The Bureau is grateful to all of them, for their co-operation. Their comments and suggestions have been duly considered by the, Mathematics Subject Committee while finalising the book., The Mathematics Subject Committee of the Bureau, the Panel, Shri. V. D. Godbole, (Invitee) and the artists have taken great pains to prepare this book. The Bureau is, thankful to all of them., We hope that this book will receive a warm welcome from students, teachers and, parents., , Pune , Date : December 4, 2013, Agrahayan 13, 1935, , (C. R. Borkar), Director, Maharashtra State Bureau of Textbook, Production and Curriculum Research, Pune.

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Part One, Introduction to Geometrical Figures, Revision, n Quadrilateral, Triangle, Circle, Quadrilaterals, , Triangles, , Circles, , F Look at the pictures below. Identify the geometrical figure., Draw it and write its name., Picture, , Figure, Name of the, Figure, , Rectangle, , F Identify the triangles, circles and quadrilaterals in the picture above. Colour the, triangles red, the quadrilaterals blue and the circles yellow., - For teachers : Cut cardboard into the shapes given above and various other shapes too, and place them on the, table. Have the children classify them into triangles, rectangles, squares and circles. Point out that some of, the shapes cannot be classified into any of the given categories., , 1

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Edges and Corners, Look at this piece of barfi., It is a quadrilateral., A quadrilateral has four edges and four corners., , Observe the surface of a table., F How many edges does the surface have ? , F How many corners does the surface have ?, F What is the shape of the surface of the table ?, n Rectangle, , Take a rectangular sheet of paper as shown below., F How many edges and how many corners does a rectangle, have ?, Now, let us fold the paper in the middle to bring the, opposite edges together., What do we see ?, The longer side falls exactly on the opposite side., The shorter side falls exactly on the side opposite, too., The opposite sides of a rectangle are of equal length., n Square, , Take a look at a handkerchief. It is a square., F How many edges and corners does a square have ?, Fold the handkerchief in the middle from top to bottom as, well as from side to side to see if the opposite sides are of, equal length., Now, we shall fold the handkerchief as shown alongside to, find out if each corner falls exactly on the one opposite., The corners match and so do the edges that make them up., Now fold the handkerchief over again., All the edges match in length., All the edges of a square are of equal length., , 2

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Note that we got a triangle when we folded the handkerchief., , n, , Triangle , , F How many edges does a triangle have ? How many corners ?, Find this shape in your surroundings., F Use sticks to make the following shapes., , Quadrilateral, rectangle, square, triangle, F Complete the table below., Figure, , Name of the, figure, , Number of edges, , Number of, corners, , - For teachers : Cut out shapes of rectangles, squares, triangles and circles from coloured paper. Tell the, children to examine them for their properties. Point out that the edge of a circle is curved and that the, circle has no corners., , 3

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n How to make a five-piece Tangram, Take a square piece of paper., Find the centre of the paper by folding it twice., Also, mark the centres of all the four edges., Draw lines to join the centres of the sides and the centre of the, square as shown in the picture., 1, , Now, make five pieces of the square by cutting along the lines, as shown in the picture., , 2, 3, , 5, , 4, , n Using the tangram here, answer the following questions., , F How many triangles are there in your tangram ?, F Are all the triangles alike ?, , 1, , 2, 3, , 5, , 4, , F Can we join two of the triangles to make a square ?, F Can we join two of the triangles to make a big triangle ?, F How many squares are there in this tangram ? How many quadrilaterals ?, F In the picture below, identify the figures drawn on the dotted paper., Colour the triangles red, squares blue and the rectangles green., , - For teachers : Tell the children to use string to make shapes of circles, rectangles, squares and triangles., Encourage the children to design many different tangrams and to obtain a variety of figures from them., , 4

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Number Work, , F In the table below, colour the boxes of the numbers from 1 to 10, red; the boxes of the, numbers 11 to 20, green; ..... . Thus colour all the boxes, using different colours., , 99, , 19, , 78, , 45, , 59, , 80, , 67, , 98, , 46, , 47, , 18, , 82, , 79, , 8, , 40, , 39, , 97, , 5, , 68, , 26, , 51, , 4, , 58, , 88, , 13, , 75, , 17, , 95, , 52, , 16, , 83, , 81, , 71, , 34, , 87, , 1, , 96, , 38, , 25, , 27, , 32, , 77, , 2, , 76, , 12, , 63, , 53, , 60, , 9, , 37, , 65, , 10, , 100, , 14, , 64, , 24, , 11, , 94, , 93, , 36, , 31, , 72, , 41, , 55, , 29, , 54, , 22, , 35, , 3, , 48, , 84, , 30, , 15, , 6, , 86, , 23, , 62, , 61, , 70, , 69, , 57, , 66, , 56, , 73, , 33, , 89, , 7, , 42, , 92, , 49, , 44, , 85, , 28, , 74, , 20, , 50, , 90, , 91, , 21, , 43, , n Writing the numbers from 26 to 99 in words., 26 twenty-six 27 twenty-seven 28 twenty-eight, , 29 twenty-nine, , 30 thirty, , 31 thirty-one, , 32 thirty-two, , 33 thirty-three, , 34 thirty-four, , 35 thirty-five, , 36 thirty-six, , 37 thirty-seven, , 38 thirty-eight, , 39 thirty-nine, , 40 forty, , 41 forty-one, , 42 forty-two, , 43 forty-three, , 44 forty-four, , 45 forty-five, , 46 forty-six, , 47 forty-seven, , 48 forty-eight, , 49 forty-nine, , 50 fifty, , 51 fifty-one, , 52 fifty-two, , 53 fifty-three, , 54 fifty-four, , 55 fifty-five, , 56 fifty-six, , 57 fifty-seven, , 58 fifty-eight, , 59 fifty-nine, , 60 sixty, , 61 sixty-one, , 62 sixty-two, , 63 sixty-three, , 64 sixty-four, , 65 sixty-five, , 66 sixty-six, , 67 sixty-seven, , 68 sixty-eight, , 69 sixty-nine, , 70 seventy, , 71 seventy-one 72 seventy-two, , 73 seventy-three 74 seventy-four 75 seventy-five, , 76 seventy-six 77 seventy-seven, , 78 seventy-eight 79 seventy-nine 80 eighty, , 81 eighty-one, , 82 eighty-two, , 83 eighty-three, , 84 eighty-four, , 85 eighty-five, , 86 eighty-six, , 87 eighty-seven, , 88 eighty-eight, , 89 eighty-nine, , 90 ninety, , 91 ninety-one, , 92 ninety-two, , 93 ninety-three, , 94 ninety-four, , 95 ninety-five, , 96 ninety-six, , 97 ninety-seven, , 98 ninety-eight, , 99 ninety-nine, , - For teachers : Write all the numbers on the floor or place number cards instead. Have the children stand, around them and play the game of looking for numbers in the proper sequence., , 5

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Introducing ‘Hundred’, Tony : Here are one hundred candies., , Nandu : I scored a century !, , Salma : I counted these bangles., They are 10 tens., , Sonu : I bought a hundred oranges., , Tai : All of you have the same number of things. But each of you said it in a, different way. A century has a hundred units. Or simply, it’s one hundred., Ten tens are also one hundred., , H, , Sonu put a hundred beads from, this string into a purse., , Here is a purse of ‘a hundred’., , ‘tens’ of sticks, makes one hundred sticks., , 5 notes of 20 rupees each makes, rupees., That is, 1 hundred, rupees., 6

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Whole hundreds / Hundreds, 9 beads and 1 bead together make 10 beads., A group of 10 things is called a ten., T U, 99 is the biggest two-digit number., 9 9, When we add 1 to it, we get the, + 1, three-digit number 100., 100, The new place on the left in the three-digit number 100 is the place of ‘Hundreds’., 100 means, H T U, , 100 is a three-digit number., 1 0 0, , , , , H, , H, , H, , H, , Two, hundred, H, , Four, hundred, , H, , H, , H, , H, , H, , H, , H, , H, , Three, hundred, , H, , H, , H, , H, , H, , Five hundred, , H, , H, , H, , H, , H, , Nine hundred, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , T, , 10 tens make a hundred., That is, one hundred (100)., 20 tens make 2 hundreds., That is, two hundred (200)., , 40 tens make 4 hundreds., That is, four hundred (400)., , 50 tens means 5 hundreds., That is, five hundred (500)., , 7

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Three-digit numbers : Introduction, F In the empty boxes, write the number in words., Number, Crayons, , H, , H, , H, , H, , H, , H, , H, , H, , H, , H, , Hundreds, , Tens, , Units, , In, figures, , In words, , 1, , 0, , 1, , 101, , A hundred, and one, , 1, , 0, , 2, , 102, , A hundred, and two, , 1, , 0, , 3, , 103, , 1, , 0, , 4, , 104, , 1, , 0, , 5, , 105, , 1, , 0, , 6, , 106, , 1, , 0, , 7, , 107, , 1, , 0, , 8, , 108, , 1, , 0, , 9, , 109, , 1, , 1, , 0, , 110, , - For teachers : Get the children to write the numbers using a box of a hundred crayons, a packet of ten, crayons and single crayons., , 8

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Three-digit numbers : Introduction, F As shown in the table, string the right number of beads on the wires., Write the number in figures and in words., , H, , H, , T, , T, , T, , T, , 254, U, , Two, hundred and, fifty-four, , 617, H T, , U, , Six hundred, and, seventeen, , H T, , U, , H T, , U, , H T, , U, , H T, , U, , H T, , U, , H T, , U, , T, , H T, , H, , H, , H, , H, , H, , H, , H, , H, , T, , H, , H, , T, H, , H, , H, , H, , H, , T, , T, , H, , T, , T, , H, , H, , H, , T, , T, , H, , H, , H, , T, , T, , T, , T, , H, , T, , T, , T, , T, , H, , T, , H, , T, , H, , H, , T, , T, , H, , H, , T, , T, , T, , T, , H, , T, , T, , H, , T, H, , T, , T, H, , T, , T, , T, , T, , H, , H, , T, , - For teachers : Give the children the task of making three-digit numbers using purses of hundred beads,, strings of ten beads and some single beads. Give them a lot of practice in writing the correct number, according to the value of the symbols used even when the purses, the strings and the single beads are, arranged in different ways., , 9

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Three-digit numbers : Writing and Reading, F Write the correct number in the box and read it aloud., 101, , 211, , 102, , 212, , 103, , 213, , 104, , 214, , 105, , 321, , 431, , 541, , 432, , 761, , 871, , 981, , 652, , 762, , 872, , 982, , 764, , 874, , 543, , 323, 434, 325, , 651, , 544, 655, , 435, , 216, 107, , 217, , 109, , 219, , 110, , 220, , 875, , 985, , 766, 327, , 437, , 328, , 438, , 547, , 657, , 877, 768, , 988, , 659, 330, , 440, , 550, , 770, , 880, , 990, , F Make three-digit numbers using each of the given digits only once., 1, 123, 132, 213, 231, 312, 321, 2, 3, 3, 305,, , 350,, , 530,, , 503, , 5, 0, Note that 035, 053 are not three-digit numbers because these numbers are written, as 35 and 53 using only two digits., 4, 1, 3, 6, 5, 2, 7, 0, 7, 8, 6, 9, Take any three-digit number. Change the digit in its hundreds place and make a new, number. Likewise, change the digits in the tens and units places to make new numbers., - For teachers : Make many different numbers using a tap for hundreds, a clap for tens and a snap of your, fingers for units., , 10

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The number before; the number after, F Read the numbers in the number strips below., 99, , 100, , 101, , 102, , 103, , 104, , 105, , 106, , 107, , 108, , 109, , 110, , 215, , 216, , 217, , 218, , 219, , 220, , 221, , 222, , 223, , 224, , 225, , 226, , 399, , 400, , 401, , 402, , 403, , 404, , 405, , 406, , 407, , 408, , 409, , 410, , F With the help of the number strips above, write the next number D 105,, D 220,, D 409,, D 219,, F With the help of the number strips above, write the number just before D, , 400, D, , 107, D, , 218, D, , 110, F With the help of the number strips above, write the numbers just before and just, after D, , , 217 ,, , D, , D, , , 100 ,, , , 409 ,, , F By how much is the next number bigger than the given number ?, F By how much is the number just before a given number smaller than the given, number ?, F What is the number we get by adding 1 to 435 ?, F What is the number we get by taking away 1 from 435 ?, F Write the number just before and the number just after., D 118 , 119 , 120, , D, , , 200 ,, , D, , , 391 ,, , D, , D, , , 800 ,, , D, , , 707 ,, , , 599 ,, , F Write any three numbers that come after the given number., D 555,, , 600 , 650 , 977, , D 399,, , ,, , ,, , F Write any three numbers that come before the given number., D 99, , , 312 , 407 , 500, , D, , ,, , ,, , , 601, , - For teachers : Give practice in telling the numbers that come before and after numbers like 100, 199, 300,, 499, 201, 590., , 11

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Using symbols to show ‘smaller’ and ‘bigger’ ....... < , >, F Say which number is bigger and which, smaller., Number, , 8, 2, , 77, 59, , 39, 9, , 14, 35, , 67, 32, , Smaller Number, Bigger Number, n, , Using the symbols, , Y, Y, Y, Y, Y, , Y, Y, , 5 > 2 is read as : 5 is bigger than 2., , 27   , , Y, Y, , 2 < 5 is read as : 2 is smaller than 5., , 91, , 40, , 27 < 40 is read as : 27 is less than 40., , Y, Y, Y, Y, Y, ,   , , 049, , 91 > 49 is read as : 91 is greater than 49., , F Write the correct symbol in the box., 10, , > 9, , 9, , 10, , 5, , 3, , 3, , 5, , 50, , 49, , 49, , 50, , 23, , 25, , 73, , 75, , 500, , 499, , 499, , 500, , 500, , 300, , 600, , 400, , Tony : We can tell the smaller number and bigger number if the two given numbers, have two digits. But, what if one is a two-digit number and the other is a, three-digit number ?, Tai : First tell me the biggest two-digit number., Tony : That’s easy ! 99 is the biggest of all the two-digit numbers. The next number, after 99 is 100. And that’s a three-digit number., Tai : Then you know that a two-digit number may be 99 or a number smaller, than 99. Hence, any two-digit number is smaller than 100. A three-digit, number can be 100 or bigger than 100., Tony : This tells us that a three-digit number is always bigger than a two-digit, number., Salma : Just as we know that a two-digit number is always bigger than a one-digit, number, isn’t it ?, Tai : Absolutely right !, 12

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Smaller and bigger numbers (continued), Nandu : If we have two three-digit numbers, how do we tell which is bigger and, which is smaller ?, Tai, : Let’s take some easy examples. Take the numbers 500 and 300. Which of, these is the bigger number ?, Salma : 5 hundreds are bigger than 3 hundreds. So 500 > 300., Tai, : Now let’s look at 325 and 625. Here the units and the tens of the two, numbers are equal. But 6 hundreds are bigger than 3 hundreds., So 625 > 325., Tony : What to do if the units, tens and hundreds digits in two numbers are all, different ?, Nandu : Let’s take 495 and 812., Tai, : In 495, the number in the hundreds place is 4. It is smaller than the, hundreds in 812. This is important. What is the next whole hundred, number after 495 ?, Tony : That’s 500. And 495 < 500., Tai, : 812 has 8 hundreds. We know that 500 < 800 and 800 < 812. So,, 495 < 812. Got it ?, Tony : Yes. Not too difficult if we work it out like this., Nandu : It means that if two three-digit numbers are given, the one with the bigger, digit in the hundreds place is the bigger number., F Which is the bigger and which the smaller number ?, 721, 589, 423, 723, , 600, , 497, , Salma : But, what if the digits in the hundreds place of both the numbers are the, same ? Let’s take 718 and 720., Tai, : That’s easy, too. If the hundreds are the same, look at the numbers made by, the tens and units., Sonu : So we must compare 20 and 18 in 720 and 718, right ? 20 >18., So, 720 > 718., Tai, : Correct ! If the hundreds in two numbers are the same, then the number, with the bigger tens is the bigger number. And, if the hundreds as well, as the tens are equal, then look at the units to decide which is the bigger, number., F Put the right symbol <, > between the numbers in each pair., 427, , 267,, , 150, , 501,, , 813, , 79,, , 300, , 624, 13

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Ascending and descending order, These are the marks that Tony, Sonu, Salma and Nandu got in Maths :, Tony 70, Salma 87, Sonu 79, Nandu 85., Write their marks in ascending and descending order., Ascending Order : 70, 79, 85, 87, Descending Order : 87, 85, 79, 70, F Write the following numbers in ascending and descending order., Numbers, , Ascending Order, , Descending Order, , 55, 63, 40, 80, 69, 9, 59, 70, 14, 29, 47, 39, F Write the numbers 122, 360, 325 in F Write the numbers 801, 617, 847, 799, ascending and descending order., in ascending and in descending order., Smallest number : 122, Smallest number : 617, Biggest number : 360, Remaining numbers 801, 847, 799., Ascending Order : 122, 325, 360, The smallest of these numbers : 799., It can also be written as, Remaining numbers, now : 801, 847., , 122 < 325 < 360, The smaller of these two numbers : 801, Descending Order : 360, 325, 122, and the last one 847., It can also be written as, Ascending Order : 617, 799, 801, 847, , 360 > 325 > 122, Descending Order : 847, 801, 799, 617, F Ascending and descending order of numbers., Given Numbers, , Ascending Order, , Descending Order, , 217, 211, 215, , 211, 215, 217, , 217, 215, 211, , 500, 400, 100, 600, , 100, 400, 500, 600, , 600, 500, 400, 100, , 519, 419, 619, , 419, 519, 619, , 619, 519, 419, , 785, 757, 8, 81, , 8, 81, 757, 785, , 785, 757, 81, 8, , 15, 100, 81, 167, , 15, 81, 100, 167, , 167, 100, 81, 15, , F Write the following numbers in ascending and descending order., D 117, 69, 50, 8, D 217, 271, 270, D 365, 73, 12, 116, D 912, 27, 356, D 315, 215, 515, D 527, 8, 324, 63, D 88, 78, 75, D 500, 501, 499, D 285, 407, 589, 360, D 888, 788, 688, D 105, 107, 101, 102, D 909, 990, 999, 14

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Biggest and smallest numbers from given digits, Tai, : Let’s make three-digit numbers using the digits 2, 3 and 5., Sonu : Do we use one digit only once ?, Tony : Yes ! Otherwise, we’ll get too many numbers. 222, 232, 233, 323, 333,, 235, 253.... so many numbers like these., Salma : But if we use each digit only once, then, of course, we get only these, numbers : 235, 253, 325, 352, 532, 523., Tai, : Ok. Now compare these numbers and decide which ones are smaller and, which ones, bigger., Tony : 532 and 523 have the biggest hundreds digits. If we compare these two, 32, is bigger than 23, so 532 > 523. So 532 is the biggest of all the numbers we, can make from the digits 2, 3 and 5., Salma : Of the numbers we made here, take those with 2 in the hundreds place., That is, 235 and 253. Now, 35 < 53. So 235 < 253., Tai, : Very good !, Nandu : Instead of making all the numbers from the given digits, couldn’t we make, the biggest and the smallest numbers straightaway ?, Tony : Yes, of course ! The biggest number will have the biggest digit in the, hundreds place. Then, to make the bigger number from the remaining two, digits, we put the bigger digit in the tens place., Sonu : So, to make the biggest number, write the digits in the descending order. In, our example, the biggest number is 532., Salma : I’ll say how to make the smallest number from three given digits. Write the, smallest digit in the hundreds place and the biggest digit in the units place., The remaining digit goes in the tens place. It means that if we write the, given digits in the ascending order we get the smallest three-digit number., Here, it’s 235., Sonu : Suppose there’s a zero given. Do we still do the same ?, Tai, : No. If we do that we’ll get a two-digit number and not a three-digit, number. Let’s take 5, 0 and 2. If there’s zero in the hundreds place, we, get the numbers 025 or 052. But these can be written as 25 and 52 in two, digits. So they are really two-digit numbers., Nandu : So if a zero is given, let’s put the smaller non-zero number in the hundreds place., Salma : Then we’ll write zero in the tens place and the remaining digit in the units place., Tai, : Yes. So the smallest three-digit number from the digits 5, 0 and 2 is 205., F Make the biggest and the smallest three-digit numbers using the given digits., D 9, 4, 6, D 7, 0, 4, D 3, 9, 5, D 8, 5, 9, 15

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The expanded form of a number, Tai, : How many hundreds, how many tens and how many units are there in 824 ?, Sonu : 824 means 8 hundreds, 2 tens and 4 units., Tony : This means that 824 = 800 + 20 + 4., Nandu : By the same method, how to write 203 ?, Salma : 203 = 200 + 3., Tai, : That is right, of course. But it is better to write the expanded form as, 203 = 200 + 0 + 3 because it tells us clearly the digits in the hundreds, tens, and units places. In the same way, the expanded form of 80 will be 80 + 0., And if we take the single-digit number 9, its expanded form can only be 9 !, F Write the expanded form of the following numbers., D 998, D 34, D 287, D 534 D 76, D 301 D 90, Tai, :, , Salma :, Tai, :, , D 45, , D 13, , Now, can you write the number from its expanded form ?, Take 500 + 30 + 7. This is the expanded form of a number., I’ll try. 500 + 30 + 7 = 537, Very good !, , F Write the number from its expanded form., D 700 + 0 + 5, , D 400 + 60 + 7, , D 800 + 0 + 0, , D 30 + 9, , D 200 + 10 + 1, , D 100 + 50 + 0, , D 40 + 4, , D 300 + 0 + 6, , Place value, Tai, :, Nandu :, Salma :, Tai, :, , 16, , Tell me, of which number is this the expanded form : 400 + 40 + 7 ?, Easy ! 447., That’s funny. First we used the digit 4 for 400 and then we used it for 40., You must remember that the place of a digit determines its value. The, value of the 4 in the hundreds place is 400, but the value of 4 in the tens, place is 40. The 7 in the units place is equal to just 7. The value that a digit, has according to its place in a number is called its place value.

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Tai, , : In the number 576, the place value of 5 is 500, the place value of 7 is 70 and, that of 6 is 6. Now, let’s look at some other examples., , 9 3, 900, , Place value, , 4, , 30 4, , 7 0, , 5, , Place value, , 5, , 700 , , 0, , , , H, T, U , H, T, 4, , 4, , 4, , , , , , 4 , 40, , 6, , U, , 3, , 9, , 600, , Place value, , 400 , , 30, 9, , F Write the place values of the underlined digits., 919 , 135 , 20 , 305 , 480 , 32, n, , A number and its expanded form : Folding Fun, , Tai : Let’s make a folding card to show a three-digit number and its expanded form., , 4 00 + 3 0 + 5, , Take a strip of paper and fold it into, seven equal parts as shown alongside., Think of a three-digit number. Say, 435., , Write the expanded form of this number on the paper strip as shown above., Now fold the paper along the bold lines as shown in, the figure alongside. By folding the paper,, ‘00+’ and ‘0+’ are hidden and only the number, 435 can be seen., , Thus, we can show the number when the paper strip is, , folded and its expanded form when it is unfolded., , 4, , 4, , 3, , 5, , 3 5, , - For teachers : Give children the opportunity to grasp well the meaning of ‘the expanded form’ of a number and, the ‘place value’ of a digit by making paper strips for many different three-digit numbers., , 17

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Introducing the Number 1000, , T, , H, H, H, , H, H, H, , , , H, H, H, , TH, 1, , H, 1, , T, 1, , U, , 9, , 9, , + , , 1, , T, , T, , T, , T, , T, , T, , 9, , T, , T, , T, , , , T, , 10, 1, , 0, , 10, , 10, , 0, , 0, , H, , We get 100 when we add 99 and 1 (99   , +   , 1   , =   , 100). Now let us add, 1 to 999 in vertical arrangement. 9 units + 1 unit make 10 units. That makes 1 ten,, which is carried over. Now, 9 tens and 1 ten make 10 tens which is 1 hundred. 9, hundreds and 1 hundred make 10 hundreds. This again gives us a 1 which has, to be carried over. So, we make a new place for this carried over 1. This is the, ‘Thousands’ place. In the number 1000, there is 1 in the thousands place and there, are zeros in all other places. This number is read as ‘one thousand’., , 10 beads in 1 string, then, 1000 beads in 100 such strings., Hence, 100 tens also make 1000., 18

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Addition without, Carrying Over, , H, , H, , H, , H, , H, , H, , H, , H, , Tony has 3 purses each containing 100 beads., Sonu has 5 such purses. How many purses altogether ?, , 8, , purses., , How many beads altogether in the purses with Tony and Sonu ?, , 800, , beads., , F If Tony has 2 hundred rupee notes, 1 ten rupee note and 5 one rupee coins and, , Sonu has 1 hundred rupee note, 3 ten rupee notes and 2 one rupee coins, how, many hundred rupee notes do they have altogether ? How many ten rupee notes, and how many 1 rupee coins do they have altogether ?, F Observe the examples based on the pictures. Complete them by adding units to, , units, tens to tens and hundreds to hundreds., H, H, , H, , H, , H, , H, , T, , U, , 1H, , 2T, , 1U, , 1, , 2, , 1, , + 2H, , 1T, , 3U, , + 2, , 1, , 3, , H, , F Look at the pictures and write the numbers. Add the numbers., H, , H, , +, H, H, , , H, , T, , U, , H, , T, , U , , H, , T, , U, , T, , U, , +, , 19

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F Carry out and observe the following additions., 54    20 70 8 75 13, + 54, + 8, + 70, + 13, + 75, + 20, 74, , 74, , Even when the order of the numbers is changed, they add up to the same number., , F Add., , , , D 376 + 2, , D 403 + 64, , D 125 + 144, , D 513 + 365, , D 205 + 4, , D 540 + 35 , , H T U, , 3 7 6, +, 2, 3, , 7, , 8, , , D 142 + 6 , , D 20 + 436, , F Arrange vertically and add., D 664 + 220, , D 421 + 351, , D 713 + 205, , D 122 + 324, , D 207 + 102 , , D 270 + 312, , D 450 + 230, , D 541 + 320, , D 400 + 300, , D, , 22 + 342, , F Study the following addition carried out in the horizontal arrangement., H, , , , 4, , T, , U H, , 2, , 1, , +, , 3, , T, , U H, , 5, , F Add in horizontal arrangement. D 527 + 261, 20, , 1, , =, , T, , U, , , , 7, , D 623 + 215, , 7, , 2, , D 203 + 302

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Addition of three numbers, F Add., Maya bought an eraser for 2 rupees, a pencil, U, for 3 rupees and some coloured chalks for, 2, 4 rupees. How much should she pay the, 2 and 3 make 5., +, 3, shopkeeper altogether ?, +, 2+3=5, 4 5 and 4 make 9., `  , 2 for the eraser and `  , 3 for the pencil, 9, together make `  5. When we add the `  4 for the, chalks to these `  5, we will get `  9., Thus, `  2 + `  3 + `  4 = `  9. So, Maya should give the shopkeeper 9 rupees., F In the cupboard, there are 3 song books, 21 story-books and, , T, , U, , 14 picture books. How many books are there in the cupboard, altogether ?, , 2, , 1, , 1, , 4, , 21 + 14 + 3 = 38, There are 38 books in the cupboard., , +, , + , , F Add., , 3, , D T, , 2, +, 3, +, 3, , D, , U, , T, , 5 , , +, , 0 , , +, , 2 , , D 453 + 104 + 112, , 2, 1, 1, , D T, , U, , 1 5, +, 5 , +, 2 , , D 105 + 3 + 20, , H, , T, , U, , 4, , 5, , 3 , , + 1, + 1, , 0, 1, , 4, 2, , +, +, , U, , D, , T, , U, , 0 2, +, 2 , 1, +, 3 , , 5, , 3, 8, , 2, 1, , D 202 + 34 + 11, , +, +, , D 200 + 10 + 1, , D 143 + 2 + 2, , D 3 + 42 + 233, , D 352 + 313 + 21, , D 451 + 224 + 112, , D 104 + 2 + 3, , D 303 + 444 + 122, , D 5 + 12 + 372, , D 400 + 40 + 4, , 21

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Subtraction without Borrowing, , F Look at the picture., Study the example. , T, 2, - 1, 1, , F Look at the picture, arrange the, example and solve it., T, , U, 3, 2, 1, , U, , F, H, , H, , T, , U, , U, , U, , H, - 2, 1, 1, , T, 1, 1, 0, , U, 3 First subtract the units from the units., 1 Then subtract the tens from the tens., 2 Last, the hundreds from the hundreds., , F Ajit has 257 rupees. Use the picture below and work out how much money he, had left over after he gave 150 rupees to Manoj., , F In a cricket match, England scored 245 runs. India scored 123. How many more, runs must India make to equal England’s score ?, In order to equal England’s score, India must score, a total of 245 runs. So, we have to find out how many, runs they must score after 123 to make a total of 245., That is, 123 +, = 245. We must find out the missing, number in this. We shall get it by subtracting 123 from, 245., 22, , -, , H, , T, , U, , 2, , 4, , 5, , 1, , 2, , 3, , 1, , 2, , 2

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F Subtract., D, H, , T, , U, , D, , , H, , T, , U, , D , , H, T, U, , , 7, 4, 9, 5, 4, 5, 8, , , , - , , 2, , , , 5, , 3, , - 4, , 3, , 8, , , , - 2, , 0, , 2, , 5, , 4, , 3, , D, H, , T, , U, , D, H, , T, , U, , D, H, , T, , U, , 2, - 1, , , 3, , 7, , 6, , 5, , 4, , 3, , 4, - , , , 5, , 1, , 3, 6, - , , , 3, , 5, , H, D, , T, , U, , H, D, , T, , U, , H, D, , T, , U, , 4, - , , , 5, , 8, , 9, , 9, , 5, , 4, , 2, , 3, , 9, - 4, , , 5, , 4, , 8, - 5, , , 1, , 5, , F Arrange vertically and subtract., D 654 - 200 , D 674 - 242, H T U, , , , , 6, , 5, , 4, , -2, , 0, , 0, , F Subtract the smaller number from the bigger number., D 315, 517, D 470, 340, , D 772 - 341, , D 300, 700, , Subtraction in horizontal arrangement., Subtract the units from the units, the tens, H T U H T U , 3 4 5 - 2 4 3 = 102, from the tens and the hundreds from the, hundreds., F Subtract in horizontal arrangement., 417 - 305,, 504 - 201,, 779 - 250,, 420 - 220, 23

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Multiplication, , The children made a bunch of flowers to give to Tai on Teachers’ Day. Tony,, Sonu, Salma, John and Nandu each brought 2 flowers and Sonu tied them together., , Tai, , :, , Tony :, John :, Tai, , :, , Lovely ! What a big bunch of flowers ! And so pretty !, How many flowers are there in it altogether ?, Two flowers from each of the five of us makes a total of ten flowers., 2 flowers each from 5 of us means taking 2, 5 times and adding them, together. That is, 2 + 2 + 2 + 2 + 2 = 10., 2 + 2 + 2 + 2 + 2 is written as 2 Í 5., 10 is called the product of 2 and 5., Now, here are some pictures. Let us count the number of fruits in them., , Sonu : 4 lemons in each row and, two such rows., Twice 4 is 8 lemons., Twice 4 is taking 4, 2 times, and adding them., , Tony : 4 cucumbers in, a row and, four such rows., 4 times 4, so,, 16 cucumbers., , Salma : 4 guavas in a row, and three such rows, is 3 times 4 which, is 12., John : 4 mangoes in a row and, 10 such rows., 10 times 4, or, 40  mangoes., 24

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Multiplication, D, , Tony, , Sonu, , Nandu, , Salma, , If each of them has 3 balls, how many balls altogether ?, 3 + 3 + 3 + 3 = 12, An addition of 3 taken 4 times, is 4 times 3,, That is, 4 Í 3 = 12 (4 threes are 12)., D In the same way, fill in the boxes in the example below., , Six mangoes in each basket. How many mangoes in 3 baskets ?, 6 + 6 + 6 = means, , times 6. In other words, 6 Í, , =, , D Children are standing in 7 groups of 3 children each. How many children are, , there altogether ?, times three, three sevens =, , , 3Í, , =, , F Look at the picture and prepare an example like the one given above., , D One notebook costs ` 5. How much will 9 such notebooks cost ?, , An addition of 5 taken 9 times means 5 Í 9., 5 Í 9 = 45., Hence, the cost of 9 notebooks is ` 45., Tai : Tables are nothing but series of multiplications. Later on, we shall use tables, to carry out multiplications of large numbers., Let us recite the 2, 3, 4, 5 and 10 times tables., 25

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Multiplication, , In the form of objects, , As an, addition, , How many, times, , As a multiplication, , Total, number of, objects, , 2+ 2 + 2 + 2 + 2, , 2, five, times, , 52, , 10, , 5+5, , ... + ... + ... +, , twice, , ...  ..., , ...,, five times, , ...  ..., , ...................., , ten,, three times, , ...  ..., , ......., , ...................., , four,, six times, , ...  ..., , ......., , ...................., , ......., , ...  ..., , ......., , ... + ..., , 26, , ... ,

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6 times table, , 6, once, , 6Í1=6, 6 ones are 6, , 6, twice, , 6 Í 2 = 12, 6 twos are 12, , 6, thrice, , 6 Í 3 = 18, 6 threes are 18, , 6, four, times, , 6 Í 4 = 24, 6 fours are 24, , 6, five, times, , 6 Í 5 = 30, 6 fives are 30, , 6, six times, , 6 Í 6 = 36, 6 sixes are 36, , 6, seven, times, , 6 Í 7 = 42, 6 sevens are 42, , 6, eight, times, , 6 Í 8 = 48, 6 eights are 48, , 6, nine, times, , 6 Í 9 = 54, 6 nines are 54, , 6, ten times, , 6 Í 10 = 60, 6 tens are 60, , 27

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Multiplication tables of 7, 8 and 9, Let us make the 7, 8 and 9 times tables like the 6 times table., 71 =, , 7, , 81, , =, , 8, , 91 =, , 9, , 72 =, , 14, , 82, , =, , 16, , 92 =, , 18, , 73 =, , 21, , 83, , =, , 24, , 93 =, , 27, , 74 =, , 28, , 84, , =, , 32, , 94 =, , 36, , 75 =, , 35, , 85, , =, , 40, , 95 =, , 45, , 76 =, , 42, , 86, , =, , 48, , 96 =, , 54, , 77 =, , 49, , 87, , =, , 56, , 97 =, , 63, , 78 =, , 56, , 88, , =, , 64, , 98 =, , 72, , 79 =, , 63, , 89, , =, , 72, , 99 =, , 81, , 7  10 =, , 70, , 8  10 =, , 80, , 9  10 =, , 90, , Making a multiplication table, with the help of addition, Tai : To make the 6 times table,, we take 6 in two parts. As,, 6 = 4 + 2. Now we take the 4 and, 2 times tables and add them to, get the 6 times table., Tony : Just as we can make the, 6 times table using the tables of, 4 and 2, we can make it using the, tables of 5 and 1, too., Tai : That’s right. We can, make a new table using two, tables that we already know., Tony : So we can make the 7, times table with the help of the 4, and 3 times tables., , 4times 2 times, table, table, , Addition, , 6 times table, , 4, , 2, , 4+2=6, , 61=6, , 8, , 4, , 8 + 4 = 12, , 6  2 = 12, , 12, , 6, , 12 + 6 = 18, , 6  3 = 18, , 16, , 8, , 16 + 8 = 24, , 6  4 = 24, , 20, , 10, , 20 + 10 = 30, , 6  5 = 30, , 24, , 12, , 24 + 12 = 36, , 6  6 = 36, , 28, , 14, , 28 + 14 = 42, , 6  7 = 42, , 32, , 16, , 32 + 16 = 48, , 6  8 = 48, , 36, , 18, , 36 + 18 = 54, , 6  9 = 54, , 40, , 20, , 40 + 20 = 60, , 6  10 = 60, , - For teachers : Have the children make the 8 and 9 times tables with the help of two other tables. Point out, that tables can also be made by subtracting one table from the other., , 28

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It’s special - the 9 times table !, Tai, , 09, , : Come, I’ll tell you something about the 9 times table., Write the numbers in reverse order - 9, 8, 7 ... up to 0 in the units, place. Now, in the tens place before them, write 0, 1, 2, .... 9 in serial, order. And look, we have the 9 times table all ready !, Isn’t that wonderful ?, , 18, 27, 36, 45, , Sonu : Wow ! I can see something else. If we add the digits in the units 54, and tens places in each number, we always get nine ! Now, that’s 63, interesting, too., 72, 81, , F The multiplication 5  3 = 15 has been shown in the table below., Fill in the right numbers in the empty boxes., , 90, , , , 1, , 2, , 33, , 4, , 5, , 6, , 7, , 8, , 9, , 10, , 1, , 1, , 2, , 3, , 4, , 5, , 6, , 7, , 8, , 9, , 10, , 2, , 2, , 4, , 6, , 8, , 10, , 3, , 3, , 6, , 9, , 4, , 4, , 8, , 5, , 5, , 10, , 6, , 15, , 20, , 25, 36, , 7, , 49, , 8, , 64, , 9, 10, , 16, , 81, 10, , 100, , - For teachers : Get each child to prepare his/her own table of the numbers 1 to 100. Ask each child to, choose one multiplication table between 2 and 10, then colour the numbers which appear in that table,, and observe the pattern that is formed., , 29

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F Carry out the following multiplications., 3 5 , Í6, Í3, , 7 , Í 5, , 8 , Í 3, , 6 7, Í 4, Í8, , F From the pictures given below, make examples of multiplication and solve them., D The example made from the following picture :, There are 6 flowers in each row., How many flowers in 4 such rows ?, Flowers in one row, , , , Number of rows, Total number of flowers, , D, , balls in one box. Then in, , `8, , D, , `8, , boxes,, , `8, , balls in all., , `8, , `8, , D, , - For teachers : Get the children to prepare new examples using 2 one-digit numbers and to solve them., , 30

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Using tables for multiplication, D On his birthday, Chintu bought 6 pens at `  5 per pen. How much must he pay the, , shopkeeper for them ?, To find out the total cost, we must say, the 5 times table up to 5 sixes., , 6, , Pens, Cost of one pen, ,  5, 30, , 5 sixes are thirty, that is 5  6 = 30, , Total cost, , So Chintu must pay `  30 altogether., D How many trees in 5 rows if there are 8 trees in one row ?, , Rows 5, trees in each row 8, Operation : Multiplication, We shall use the 8 times table., Eight fives are forty ., Total trees = 40., , 5, , Rows, ,  8, , Trees in each row, , 40, , Total number of trees, , D If 9 laddoos can be put in one box, how many can be put in 7 such boxes ?, , Operation : Multiplication, We shall say the 9 times table., Nine sevens are, , 7, , Boxes, ,  9, , Laddoos in one box, Total number of laddoos, 4, , D 7 days in one week, so how many days in 4 weeks ?, ,  7, , Say the 7 times table., Seven fours, , Weeks, Days in one week, Total days, , D 8 tiles in one row, how many in 3 rows ?, , 8, ,  3, , Tiles in a row, Rows, Total number of tiles, , D One guava costs `  6., , How much money will be needed to buy, one guava for each of the four friends, Tony, Sonu, Nandu and Salma ?, , 3, , Rows, ,  8, , Tiles in a row, Total number of tiles, 6, ,  4, , Cost of one guava, Number of children, Rupees in all, 31

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Properties of Multiplication, , , 3, 5, , , , , , , 35, , =, , 5, , 3, , 53, , F Carry out the following multiplications and observe., 65=, , 83=, , 76=, , 92=, , 56=, , 38=, , 67=, , 29=, , The product of two numbers remains the same even if their order is changed., For example : 6  5 = 5  6 ; 8  3 = 3  8 ; 7  6 = 6  7 ; 9  2 = 2  9, F The multiplicative property of zero, , , , , , 2 + 2 + 2 + 2 is the same as 2  4 = 8, 1 + 1 + 1 + 1 is the same as 1  4 = 4, 0 + 0 + 0 + 0 is the same as 0  4 = 0, , When we multiply ‘zero’ by any number or when we multiply any number by, ‘zero’, the product is always ‘zero’. 0  4 = 4  0 = 0, F Carry out the following multiplications., , n, , 24=, , =42, , 70=, , =07, , 98=, , =89, , 73=, , =37, , 80=, , =08, , 63=, , =36, , Multiplicand, multiplier, product, Tai : In the multiplication 6  5 we multiply, , 6 Multiplicand, 5 Multiplicand, the first number 6. It is the multiplicand. We,  5 Multiplier  6 Multiplier multiply by the second number, 5. It is the, 30 Product, , 30 Product, , multiplier. The answer is 30. It is known as, the product., , Similarly, in the multiplication 5  6, 5 is the multiplicand, 6 is the multiplier and 30, is the product., 32

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Coins and Currency Notes, , F Look at the pictures of the currency notes given below. Write their values in, the boxes., , The value of this note is, , The value of this coin is `, , rupees., , ., , The value of this note is, , rupees., , This coin has a value of `, , ., , F Write the total amount (value) in the empty boxes., D, , 650, rupees, D, , rupees, , D, , rupees, 33

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Tony : I have 3 notes. Their total value is 75 rupees., Salma : I, too, have 75 rupees. But I have 5 notes., Tony : How can that be ?, Tony has these notes. , Total, , , , , rupees, , And Salma has these notes., , , , Total, rupees, , , , It means that both Tony and Salma are right., , Sanju : I have a hundred rupee note, 4 notes of 20 rupees, 6 coins of 1 rupee each., How much money do I have ?, , Raju : You have 186 rupees altogether., Anita : I have 4 notes. They are worth 170 rupees altogether. Can you guess which, notes I have ?, `, , 100, , `, , 50, , `, , 10, , `, , 10, , F Can we give `  170 using 4 notes in any other way ?, , - For teachers : Get the children to make mock currency notes by writing numbers on cards and use them, to conduct games., , 34

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Measurement, Length, Tai told Nandu and Sonu to measure the length of the table., , Nandu : The length of this table is 11 spans of my hand., Sonu : The length of the table measures 12 spans of my hand., Salma : Both of you used your hand spans. Then why is there a difference in your, measurement ?, Tony : Are their hand spans equal ?, Nandu : Mine is bigger than Sonu’s. That’s what caused the problem., : All right. I’ll give paper strips of equal length to both of you. Use them to, Tai, measure this length., , Nandu : The length of the table is 9 of these strips., Sonu : When I measured it, it was 9 strips, too., Nandu : The strips you gave us were of equal length. That’s why the length of the, table measured the same., Salma : So, if we measure the length of something using similar means, it, measures the same., Sonu : If I have to measure a chalkstick, can I use this strip ? This strip is longer, than the chalkstick., 35

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Tai, Tony, , : We will fold this paper strip to make equal parts. These small parts will be, useful for measuring the piece of chalk., : Let’s fold the strip three times and get 8 equal parts., , Salma : I’ll place the chalk along the paper strip., This chalk is equal in length to five of these small parts., Nandu : Now, shall we use this strip to measure the distance between the two posts, of the main gate ?, Salma : No, this strip is too short., Tai, : I have a long string. Let’s use that., , Nandu : Yes, let’s use the string to measure the distance between the gate posts., Tony : The distance between the gate posts is equal to three strings., Tai, : It’s easier to measure a great distance using something of greater length., And, to measure shorter lengths, it is easier to use a shorter thing. You, have seen that for yourselves, haven’t you ?, , 36

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Tai, , : A sheet of cloth must measure the same, no matter who measures it. That, is why a long metal scale is used to measure cloth in a cloth shop., , This scale is one metre long. The metre is a standard unit which is used for, measuring length. If we divide a metre into 100 equal parts, each part is, called a centimetre., 1 metre = 100 centimetres, Salma : We measured the distance between the gate posts with a string. Now let’s, use this metre scale and measure it again in metres and centimetres., Nandu : The distance between the posts is 3 metres and 80 centimetres., Tony : My big brother uses a small ruler from his compass box to measure short, distances., Tai, , : The numbers 1, 2, 3, 4, .... written beside the bigger markings on this ruler, show centimetres. Between two big markings there are smaller markings., They show units of length smaller than centimetres., , Nandu : Let’s use this standard scale to measure the chalkstick again., Salma : The chalk is 8 centimetres long., , 37

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Metre-Centimetre, A metre is hundred times as long as a centimetre. We use the standard unit metre, to measure bigger distances., , A metre scale, F In the table, write whether you will measure the following lengths/distances in, centimetres or metres., Length of a pencil, Distance between, two buildings, Width of a road, , Length of your notebook, Length of a mobile phone, Distance between two poles, , F Measure the following distances in standard units. Get your friends to do so too., Compare your observations. And measure again if there is a difference., D Length of the school compound wall D Length of a book, D Length of a newspaper, D Length of a table, D Length of the verandah, D Height of a table above the floor, F Find out the lengths of the following., D A sari, D Cloth required to make Father’s shirt, D A dupatta, D A towel, D A handkerchief, F Make an estimate of the measures of the following things. Then check your, estimate against an actual measurement., Name, Estimate, Actual measurement, using tape/scale, Length of a ladyfinger, Length of a cluster bean (guar) pod, Height of a jowar plant, The girth of a banyan tree trunk, Distance between two trees in your, school, - For teachers : Fix a strip showing metres and centimetres on a wall of the classroom. Let the children, measure each other’s height against it., , 38

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Measurement : Weight (Mass), , , Sonu : The weight of this ball is 17 marbles., , Nandu : The same ball weighs 10 of my marbles., Salma : How is that possible ? How can the same ball have different weights ?, Tony : The marbles that Sonu brought were smaller than the marbles that Nandu, brought. That’s the reason for this confusion., : That’s the reason why shops keep weights which are the standard units for, Tai, measuring weight., , If something is weighed using standard weights, it measures the same, no matter who does the weighing., The kilogram is a standard unit for measuring weight., , I want, 1 kilogram of, sugar., , I want, 5 kilograms, wheat., , Please, give me, 2 kilograms, of jowar., , 39

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Make a guess about the weight of the given things : Is it greater than or less than, 1 kilogram ? Then go to a shop and check if you guessed right., Things, , Estimated weight : 1 kg/, more than 1 kg/less than 1 kg, , Actual weight, , A packet of salt, One big lump of jaggery, 50 biscuits, 5 cups of sugar, Tony : My mother wanted half a kilogram of sugar to make some halwa. And we, had a bag of one kilogram of sugar., Salma : Then what did you do ?, Tony : Little by little, I put all the 1 kg sugar in the two pans of the balance and, brought them at the same level. In this way, I separated the sugar into two, equal parts. Thus, each pan held half a kilogram of sugar. This is how I, gave my mother half a kilogram of sugar., Salma : My mother also often needs half a kilogram of something or the other., Tony : I’ll make a half-kilogram measure for your mother. I’ll put the left over, half a kilogram of sugar in one pan and some small stones in the other to, balance the sugar. I’ll tie those stones in a handkerchief and that’ll be a, half-kilogram measure., Salma : We could even make a quarter kilogram measure in the same way !, F Use a 1 kilogram weight and a balance to measure out the following weights, of rice / wheat / jowar., D 2 kilograms D 5 kilograms D 3 kilograms D Half a kilogram, F Find out your own weight. Also find out by how much it is more or less than, the weight of one of your classmates., F Find out about various kinds of balances and use them yourself., For example :, D The spring balance D Electronic balance/scales D The common balance, D Scales for body weight., , 40

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Measurement - Volume and Capacity, These are some vessels full of water., Observe them and tell which ones can hold, more water and which ones, less., The bucket will hold the most water and the bowl the least., , This bucket became full when, 40 glasses of water were poured into it., , This bucket became full with, 10 pitchers of water., , The same amount of water measures different because different means were, used to measure it., ., F, 1l, , No matter who fills water in the bucket, it should measure the same., For that, we must use a standard measure., This is a measure of 1 litre. The milkman keeps this., It is used to measure out liquids such as milk and oil., We can easily get a one-litre water bottle., , 1l, , The picture alongside shows a measure, used especially for kerosene., The litre is a standard unit for measuring liquids., , D Take various vessels such as a pitcher, a box, a pan, etc. and make an estimate, of how much water they can hold 1 litre / less than 1 litre / more than 1 litre., Verify your guess by actually using a one-litre bottle., , 41, 41C M Y K

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Pour 3 litres of water into each of the above containers. The water will take a, different shape in each container because each container is of a different shape. But, the volume of water in each container is 3 litres., Five 1- litre bottles of water were poured into this bucket. The volume of the water, in the bucket is 5 litres., Find out how much more water can be added to fill this bucket, completely., This bucket can hold 12 litres of water. It means that the capacity of, this bucket is 12 litres., The amount of water that is needed to fill any container such as a pot,, a bucket, a drum, or a pan is called the capacity of the container., F Take a bottle with a quarter-litre capacity. Using this as a measure, mark the, following measures on a container., D 2 litres, D Half a litre, D One and a half litre, D A quarter litre, F Note how many litres of water you use for the following purposes in your house., D Bathing, D Washing kitchen utensils D Brushing teeth, D Mopping the floors, D Drinking, D Watering the garden, D Cooking, D Making 10 cups of tea, D Washing vehicles, F Make a list of all those places where water is wasted. Make an estimate of how, much water is wasted and suggest ways of reducing the wastage., No., , 42, , Place, , Approximate, amount of, wastage, , Remedy

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Patterns, F Note the pattern in the sequence of letters below., A, , B, , A, , B, , A, , B, , A, , B, , A, , A, , A, , B, , A, , A, , B, , A, , A, , B, , B, , F Look at the patterns below. Which one is like ABAB, which one like AAB AAB and which, one like ABC ABC ?, D , , , D, , D, , D, , , D, , , D, F In the boxes below, make a pattern of your own like AAB AAB., , F In the patterns given below, draw the pictures which follow., D, D, , .............................., ................, , - For teachers : Collect and exhibit the patterns made by the children., , 43, 43C M Y K

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F Spot the pattern and fill in the empty boxes., , 1  1 = 1 2  2 = 4 3 3 = 9 ......., , 5, , 10, , 15, , 2, , 9, , 16, , F Make a pattern of your own., , 44, , 66 =36, , ......., , 30, , 30, , 44

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F In the pattern given below, each figure has been given a number., , ...., 1, , 2, , 3, , 4, , 5, , 6, , 7, , 8, , 9, , In the pattern above, at which serial numbers are the triangles ?, At which serial numbers are the circles ?, , The third figure is a triangle. The sixth figure is a ........... . The eighth will be, a ........ . The eleventh will be a ..............., the fifteenth will be a ............., the, twentieth will be a ............ and the twenty-fifth will be a ................ ., F In the sequence of figures in the table below, draw the next figure and write the number, of marbles., , The serial number, of the figure, , 1, , 2, , 1, , 3, , 3, , 4, , 5, , 6, , Arrangement of, marbles, Number of marbles, , There are ..... marbles in the third figure. There are ..... marbles in the fourth figure., F Can you tell how many marbles there will be in the seventh figure without drawing it ?, Write down your answer. Now draw the figure and check your answer., How many marbles will there be in the tenth figure ?, , Tony : Hey, look what I found in this calendar! Another pattern. If we add these, three numbers in a row, we get 27. And the sum of these three numbers in, the middle column is 27 too., Sonu : These three numbers, crosswise, also add up to 27 !, Salma : Look at the 3 numbers in SUN MON TUE WED THU FRI SAT, the three rows in the box, 1, 2, 3, 4, on the left. In it, the three, 5, 6, 7, 8, 9, 10, 11, numbers in the middle, column, those in the 12, 13, 14, 15, 16, 17, 18, middle row and the, 19, 20, 21, 22, 23, 24, 25, crosswise ones all add up, 26, 27, 28, 29, 30, 31, to the same number., - For teachers : Encourage the children to find more patterns in the numbers on one page of the calendar., , 45

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F Observe the patterns in the arrangements of tiles shown below. The tiles have been, arranged in a particular manner. Note that there is no empty space between any two tiles., In other words, no part of the ground is left uncovered., , F Observe the patterns below, which have been made using tiles of only one kind., Try to make another pattern using the same tiles., , F Observe the patterns carefully. Match the tiles and the patterns they make., , - For teachers : Tell the children to observe the patterns made from tiles in their surroundings. Discuss their, special features. Visit an agricultural field and try to spot a pattern in which the crops have been planted., , 46

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Symmetry, Observe the leaf shown alongside., Take another leaf like this one, which has many veins., In the middle, there is a vein that runs the full length of the leaf., Fold the leaf along that vein., What do you see?, One part of the leaf falls exactly on the other., Fold the leaf in different ways along other veins. What do you see?, One part of the leaf does not fall exactly on the other., Take a triangular piece of paper as shown alongside., Fold it along the dotted line., Does one part of the triangular piece of paper fall exactly on, the other ?, Take another triangle, as shown in the second figure, and, fold it along the dotted line. Does one part of the triangle, fall exactly on the other ?, If the two parts of a figure made by a line fall exactly on one another, then the figure, is said to be symmetrical about that line. And, if the two parts do not fall exactly on, one another, then the figure is not symmetrical about that line., F Some of the following figures are symmetrical about the given dotted line, and some are, not. Observe them carefully., , Symmetrical, , Not symmetrical, , Symmetrical, , Not symmetrical, , Not symmetrical, , Not symmetrical, , Symmetrical, , Not symmetrical, 47

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Symmetrical, , Symmetrical, , Not symmetrical Symmetrical, , Not symmetrical, , F Determine whether the figures given below are symmetrical about any line or not. Put a, tick below the picture if it is symmetrical and a cross if it is not., , F For each of the figures below, draw a line along which you would fold the figure to show, that it is symmetrical., , F In each of the symmetrical figures given below, colour the two symmetrical parts in, different colours., , F Take a square piece of paper. Examine its symmetry by folding it in different ways., , - For teachers : Conduct an activity to let the children check the symmetry of different shapes such as an, equilateral triangle, an isosceles triangle, a parallelogram, a circle., Get them also to make a collection of symmetrical pictures of animals, birds, leaves, flowers, etc., , 48

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Closed figures and open figures, , C, , Closed, , Open, , Some closed figures, , Some open figures, , A, , B, , Think !, , F, P, M, , Can we join points ‘A’ and ‘B’ with, a line that does not touch the given, figure ?, Can we join points ‘B’ and ‘C’ in the, same way ?, , Can we join points ‘P’ and ‘F’ with, a line that does not touch the given, figure ?, Can we join points ‘P’ and ‘M’ in the, same way ?, , F Find the open and closed figures from those given below., , DM, F Observe the closed and, open figures in the rangolis, shown here., Colour the rangolis., , 49

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Part Two, Addition by Carrying Over, Salma has 7 strings of ten and 7 single beads which make 77 beads., Sonu has 8 strings of ten and 5 single beads. That makes 85 beads., Salma, , Sonu, When they put together the strings and beads that the two of them have, they got, 15 strings of ten and 12 single beads., Now, 10 units is one ten. So, they made one string of ten using 10 of the 12, single beads. So, they had two single beads left. Now, they had 16 strings of ten, altogether., 10 tens make a hundred. So, they strung together 10 strings of ten and got 1, string of hundred. Then they had 6 strings of 10 left over., , Thus, on bringing together all their beads, they got 1 string of hundred, 6 strings, of ten and 2 single beads. That is, they have 162 beads., F Write the proper numbers in the empty boxes., , 12 T means, , 1, , H, , 2, , T, , 1H 2T =, , 12, , T, , 15 T means, , H, , T, , 1H 4T =, , T, , 17 T means, , H, , T, , 3H 2T =, , T, , 18 T means, , H, , T, , 4H 3T =, , T, , 21 T means, , H, , T, , 5H 9T =, , T, , 50, , 50C M Y K

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n Addition, , by carrying over, , H, , T, , H, , H, , T, T, , U U, , U U, , U U, , U U, , , 1H, 2T, +, , U U, , 2H, , U U U U, , 8U, 6U, , 1T, , , 3H, 3 T 14 U, 1 T 4 U, , On adding the units, we get 14 units. 14 units make 1 ten and 4 units., Let’s take this ten to the tens place. Look at the addition now., 4 units left in the units place., H, T, U, In the tens place, we add this new ten to the 2 tens and, 1 ten already there. Thus, we get 4 tens. We write these, Carried, 1, over, under the line in the tens place. The digits in the hundreds, 1, 2, 8, place add up to 3. We write that in the hundreds place, + 2, 1, 6, under the line., Thus, the addition of the two numbers gives 3H 4T 4U, 3, 4, 14, that is, 344., F, , H, H, , T, , 1 H , , T T T T U U, , 1H, , +, , T T T T U U, U, T, T, T, , 5T, , 1H 7T, 3 H 12 T, , H, Carried, 2 U over, , 3U, 5U, , T, , U, , 5, , 2, , 1, 1, , + , 1, 7, 3, , 3, , 12, , 5, , 12 tens make 1 hundred and 2 tens. We write this new 1 hundred in the hundreds, place. So we have 2 left in the tens place. We add the hundreds. The earlier 2, hundreds and 1 new hundred together make 3 hundreds. So the total is 325., F Study the example of addition given below., , , H T U , , 2 6 7 , + 5 3 9, , H, , T , , 1, , 1, , 2, , 6 , , 7, , 3, 10, , + 5, , T, , 9, , H, Carried 1, over, 2, +5, , 16, , 8, , U, , U, , 1, 6, , 7, , 3, , 9, , 0, , 6, , 1H0T 1T6U, 51

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Addition, F Carry out the additions below., , n, , H, , T, , U, , H, , T, , U, , 1, +, 4, , 3, 7, , 5 2, +, 6, 5, , 4, 1, , H, , T, , U, , H, , , 3, +, , 5, 6, , 6 , 5, +, 5, , H, , T, , U, , H, , T, , U, , 7 3, +, 7, 2, , 4, 1, , 9 4, +, 9, 3, , 6, 3, , 5, 5, , T, , U, , T, , U, , H, , T, , U, , 4, 1, , 9 7, +, 9, , 4, 2, , 2 8, +, 8, , 5, 6, , 0, 0, , H, , Look at the following examples., Now, let us add three numbers. The method is the same., , H, T U, Start with the units. The units add up to 16., 1 1, 16 units is 1 ten and 6 units. Write 1 at the top of the tens place, and 6 under the line in the units place. Now add the digits in, 2 1 7, the tens place. We get 17 tens. 10 tens make 1 hundred. Write, + 1 6 5, the hundred at the top of the hundreds place and the 7 under the, line in the tens place. Finally, add the digits in the hundreds, + , 9 4, place. The hundreds add up to 4. Write this under the line in the, 4 7 6, hundreds place. The total is 476., , F Carry out the additions given below. , , H, , T, , U, , H, , T, , U, , H, , T, , U, , H, , T, , U, , 4 , + , + , , 3, 9, , 2, 4, 5, , 3 , + , + , , 9, 6, 8, , 5, 2, 4, , 4 , +2, +1, , 7, 0, 4, , 2, 9, 2, , 2 , +3, + , , 5, 4, 2, , 0, 5, 4, , F Add., 1, D, , 7, + 3 9, + 2 3, , 52, , 2, 4 , 8 , , D, , 5 0 0, D, 6 4 3, + 2 8 0 , +, 5 7 , + 1 2 0 , +, 6 , , D, , 4 3 7, + 1 2 3, + 2 4 5

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F, , Arrange vertically and add., , D 235 + 146, , D 346 + 129, , D 536 + 236 + 19, , D 749 + 128, , D 275 + 246, , D 382 + 199, , D 455 + 267, , D 545 + 165, , D 270 + 196 + 58, , D 370 + 195, , D 307 + 245, , H, , T, , U, , D 162 + 375, , F Add in horizontal arrangement. (If you have to carry over a number, keep it in your mind.), D 396 + 45, D 575 + 31, D 644 + 308, D 742 + 9, D 547 + 8, D 609 + 8, D 199 + 1, D 299 + 1, D 399 + 1, D 599 + 1, D 699 + 1, D 799 + 1, F Write such pairs of numbers which will add up to 100., F Write such pairs of numbers which will add up to 120., , D, D, D, D, , 647 + 56, 701 + 9, 499 + 1, 899 + 1, , D 999 + 1, , - For teachers : Give the children plenty of practice in doing additions., , 53

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Word Problems, F Solve the following problems., D If 365 women and 276 men took part, , H, , T, , U, , 3, , 6, , 5, , Women, , 2, , 7, , 6, , Men, , in the Clean Village Campaign,, how many people took part altogether?, Altogether,, , +, , people took part., , D Malatibai gifted 350 books to the school, , library. Vasantrao gave 400 and Jayantrao,, 165. What was the total number of books, gifted to the school library?, , D If 230 gulmohur trees, 375 neem trees and, , 160 teak trees were planted on the hillside,, how many trees were planted altogether?, , D At the pollution testing centre,, , 193 two-wheeler and 297 four-wheeler, vehicles were tested. What was the total, number of vehicles tested for pollution?, F Use the given information to prepare a word problem of, addition. Solve it., , H, , T, , U, , Information : A tree planting drive, 345 boys, 275 girls. 3, +, Problem : If 345 boys and 275 girls participated in a, , 2, tree planting drive, how many children took part in it, altogether ?, , 4, , 5, , Boys, , 7, , 5, , Girls, , Altogether,, , Children, , children took part in the tree planting drive., , D Story-books 50, books of poems 75. D In the basket, 35 mangoes, 45 guavas., D Cost of a dress, 275 rupees; cost of a shirt, 399 rupees., , 54, , 54C M Y K

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Subtraction by Borrowing, Subtraction by borrowing (Preparation), F, , 10 rupees means 10 coins of 1 rupee each., , 100 rupees means 10 notes of 10 rupees each. It also means 100 coins of 1 rupee., , If there are 10 sugarcanes in a bundle, then 10 such bundles means 100 sugarcanes., Sonu : I have 2 notes of hundred rupees. I have to give Nandu 70 rupees., Salma : How will you do that?, Sonu : I will exchange one hundred-rupee note for 10 ten-rupee notes., Nandu : You could give me 7 ten-rupee notes from those., Salma : Then Sonu will be left with 1 hundred-rupee note and 3 ten-rupee notes., Sonu : Right. I will have 130 rupees left., 1 Hundred = 10 Tens, 2 Hundreds = 1 Hundred 10 Tens., , 4 Hundreds = 3 Hundreds 10 Tens., , 3 Hundreds = 2 Hundreds 10 Tens., , 7 Hundreds = 6 Hundreds 10 Tens., , 5 Hundreds = 4 Hundreds +, , Tens. 6 Hundreds =, , Hundreds  + 10   Tens., 55

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F When we subtract, sometimes we have to untie 1 hundred or 1 ten. We need to untie only, one ten or one hundred, even when there are many hundreds or tens., 3 hundred, Let us untie 1 hundred and make10 tens., , 100 100, , 10, , 100, , 10, , 10, , 10, , 10, , 10 10, , 10, , 10, , 10, , 3 hundred means 2 hundreds and 10 tens, , 2 hundred, Let us convert 1 hundred into tens, and 1 tens into units., , 100, , 100, 10, , 10 10, , 10, , 10 10 10, , , 10 10, , 10, , 1, , 1, , 1, , 1, , 1, , 1, , 1, , 1, , 1, , 1, , 2 hundred means 1 hundred and 10 tens., , Subtraction : By untying a ten, , It also means 1 hundred 9 tens and 10 units., , F Study the example given below., , T U, -, , 5 1, 4, , I cannot give 4 units from 1 unit. So, I’ll exchange one 10-rupee note, for 10 single rupees., , T U, , Now I have 4 ten-rupee notes. And, these 10 single rupees along with, the 1 single rupee I already had makes 11 single rupees., , 2 , , 4 11, -, , I have 51 rupees. Five 10-rupee notes and a one-rupee coin. I have to, pay a shopkeeper 24 rupees., , 5 1, 2 , , 4, , 2, ,    7, , I shall give 4 single rupees from the 11 single rupees. So, taking away, 4 from 11, I will have 7 single rupees. Write these 7 under the units., Now I’ll subtract the tens. Subtracting 2 tens from 4, 2 tens remain., The answer is 27. Thus, I have 27 rupees left., , F Subtract., , T U, , T U, , T U, , T U, , 5 12, -, , 56, , 6 2, 2 , , 7, , 3, ,    5, , -, , 7 3, 4 , , 5, , -, , 8 1, 5 , , 8, , -, , 9 0, 6 , , 9

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Subtraction : By untying a hundred, F Nandu has 5 notes of 100 rupees, 2 notes of 10 rupees and 7 coins of 1 rupee. He gave, Sonu 318 rupees. How many rupees does he have now ?, , H, , -, , T, , U, , 1, , 17, , 5, , 2, , 7, , 3, 2, , 1, 0, , 8, 9, , 8 coins cannot be given out of 7 coins. So, we have to, change one of the two 10-rupee notes for one rupee coins., 10 rupees from the 10-rupee note and the earlier 7 rupees., So now, we will have 17 single rupees. From these 17, we, give 8. There is one 10-rupee note left. We shall give that,, too. So there will not be any ten-rupee note left. We can, give 3 of the 5 hundred-rupee notes., Thus, Nandu will be left with 209 rupees., , F Subtract. 545 - 265, , H, 4, , T, 14, , U, , 5, 2, , 4, , 5, , 6, , 5, , 2, , 8, , 0, , 545 means 5 hundreds, 4 tens and 5 units. We have to, subtract 265 from that. We can subtract 5 units from 5, units, zero units remain. Now, we cannot subtract 6 tens, from 4 tens, but we do have 5 hundreds. We shall untie, one of them. So, 4 left in the hundreds place. One hundred, gives us 10 tens. These 10 and the previous 4 make 14 tens., Take away 6 tens, 8 remain. Now we subtract 2 hundreds, from 4, two hundreds remain. The answer is 280., , F Subtract., , H, , T, , U, H, , T, , U, , 2, 1, , 7, 3, , 1 , 6, 8, , 5, 5, , 4, 6, , H, , T, , U, , H, , T, , U, , 5, 2, , 6, 4, , 7, 9, , 6, 6, , 5, 4, , 0, 5, , -, , -, , -, , -, , H, , T, , U, , 7, 2, , 3, 4, , 1, 8, , H, , T, , U, , 7, 3, , 7, 9, , 5, 7, , -, , -, , H, , T, , U, , 8, 2, , 3, 5, , 5, 8, , H, , T, , U, , 6, 1, , 8, 5, , 0, 4, , 57

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F Subtract : 507 - 288, , H, 4, 5, 2, , T, U, 9, 10 17, 0, 7, 8, 8, , 2, , 1, , 9, , 8 units cannot be subtracted from 7 units. So we must untie, one ten. But there is nothing in the tens place. So we shall, untie one hundred and get 10 tens. When we untie one of, these tens, we get 10 units. These and the first 7 units make, 17 units. Subtract 8 units from them and we have 9 units, left. Write them in the answer. Now, there are 9 tens in the, tens place. We subtract 8 tens from them, 1 remains. Finally,, 4 hundreds are left. Subtracting 2 from them, 2 hundreds, remain. Write these in the answer, which is 219., , F Subtract : 900 - 365, , H, 8, 9, 3, 5, , T, 9, 10, 0, , U, 10, 0, , 6, 3, , 5, 5, , Here, 5 units cannot be subtracted from 0 units. So we need, to untie a ten. But there is nothing in the tens place either. So, we untie a hundred and obtain 10 tens. Then we untie one, of these tens and obtain 10 units. From these, we subtract 5, units. 5 units remain. We write these in the answer., Now, we have 9 in the tens place. Subtracting 6 tens from, them, we write the remaining 3 in the answer. Then we have, 8 hundreds left. Subtract 3 hundreds from them and write the, remaining 5 in the answer. It is 535., , F Subtract., , -, , H, , T, , U, , 2, , 0, , 5, 6, , -, , H, , T, , U, , 3, , 0, 9, , 0, 5, , -, , H, , T, , U, , 8, 2, , 0, 0, , 0, 7, , -, , H, , T, , U, , 7, 3, , 0, 4, , 0, 8, , F Arrange vertically and subtract., D 245 - 6, , D 348 - 59, , D 556 - 368, , D 407 - 240, , D 845 - 657, , D 932 - 754, , F Write the biggest possible three-digit number and the smallest possible three-digit, number using the given digits. Subtract one from the other., D 3, 5, 4, , 58, , D 6, 5, 1, , D 7, 2, 5, , D 3, 4, 8

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Word Problems, D There are 175 trees in Maharaj Park and, , H, 268 in Sayaji Park. How many more, trees are there in Sayaji Park than there , are in Maharaj Park ?, 2, There are more trees in Sayaji Park., 1, From their number, we shall subtract, the number of trees in Maharaj Park., more trees., Sayaji Park has, , T, , U, , 6, , 8 Trees in Sayaji Park, , 7, , 5 Trees in Maharaj Park, More trees, , D There were some books in a book shop., , The shopkeeper brought 125 more. Now there are, 234 books in the shop., How many were there in the beginning ?, , D There are 350 girls and 215 boys in a school., , How many more girls are there than boys ?, , D Mary had 500 rupees. She bought books, , worth 275 rupees. How much money will be left with her ?, , F Using the given information, make word problems of your own and solve them., , Information : Beads with Aman : 325;, beads with Sulabha : 150., Problem : Aman has 325 beads and Sulabha has 150., How many more beads should Sulabha take so that, they will both have an equal number of beads ?, Sulabha should take, beads., , H, , T, , U, , 3, -1, , 2, 5, , 5, 0, , Beads, Beads, , F Using the given information, make word problems of your own and solve them., D 257 beads, 300 beads, D 188 mango trees, 275 guava trees, D 195 black bicycles, 100 red bicycles, , D 324 hapoos mangoes, 268 paayari, D 932 sacks of wheat, 750 of jowar, D 168 rupees, 622 rupees, , 59

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Addition and Subtraction, F Solve the following problems orally., D, , If Malti has 15 blue and 7 red balloons, how many balloons does she have, altogether ?, D Ajit had some seeds. Sagar gave him 25 more. Now Ajit has 65 seeds. How, many seeds did Ajit have before ?, D There are altogether 80 rose and jasmine flowers in a basket. Thirty of them, are roses. How many jasmine flowers are there in the basket ?, D, , A hundred children took part in a tree planting drive. If 60 of them were, girls, how many boys participated ?, , D, , Akbar peeled 42 potatoes. Salma peeled 35. How many more potatoes, should Salma peel to equal the number peeled by Akbar ?, , F Using the given information, make word problems of your own and solve them., D, D, D, D, , Tony has 75 books. Sonu has 40 books. Nandu has 80 books., How many books do Tony and Sonu have together ?, How many more books does Tony have than Sonu ?, How many more books does Nandu have than Tony ?, How many books should Sonu buy so that Tony and Sonu can have an equal, number of books ?, , F Make problems of your own and solve them., D 150 red marbles, 220 blue marbles, 75 green marbles, D Salma’s marks - 272,, Nandu’s marks - 245, Sonu’s marks - 331., The scoreboard : D Ashok - 110, , 60, , D Salim - 92, , D David - 48

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Multiplication, Multiplication of tens, Tony : Multiplying a number by ten means taking ten times that number., Thus, 3  10 is ten times 3 or three tens, or 3  10 = 30., Also, 4  10 = 40,, , 5  10 = 50,, , 6  10 = 60,, , 10  10 = 100., , Sonu : Then 13  10 will be 130, 24  10 = 240 and 40  10 = 400., Tai : Yes. To multiply a number by ten, we just need to put a zero after it., Salma : 20  3 means 20 + 20 + 20. And that is 60., Tony : 20  3 means three times 2 tens = 6 tens = 60., Tai, , : To find 20  3, we can multiply 2 and 3 and place a zero after it. So the, product is 60. In this way,, 20  6 = 2T  6 = 12T = 120, , 50  7 = 35 T = 350, , 80  3 = 24 T = 240, 40  5 = 4T  5 = 20T = 200, Sonu : If there’s a zero in the units place of both numbers, what do we do ?, : When multiplying 30  20, write one of the numbers in the tens form., 30  20 means 30  2T, Salma : But this gives us 60T. That means 600., Tai, , Sonu : So 30  20 is 600, right ?, Tony : 3T  2T is 6H !, Tai, , : Right ! It means that in 30  20, first carry out 3  2 and then write two, zeros after their product., Try it. 40  20 = 800., , 30  30 = 900., , If there is a zero in the units place of both numbers, then,, multiply the digits in their tens places and, write two zeros after the product., F Multiply., D 4  50 =, , D 3T3T=, , D 70  10 =, , D 6  20 =, , D 4T2T=, , D 20  20 =, , 61

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Multiplication of a two-digit number by a one- digit number : the lattice method, Sonu : Yesterday I bought two books for 34 rupees each., Guess how much I must have paid for them., Salma : To find it out, we must multiply 34 by 2., Tai, , : I will tell you a trick for doing this multiplication. For making the 6 times, table, we had divided 6 into two convenient parts, 4 and 2. Let’s do the, same here. We shall split 34 into two convenient parts, 30 and 4. As 30 is a, tens number, it is easy to multiply., 30, (3 T), , , 2, , 4, (4 U), , (30  2 ), , (4  2), , 60, , 8, , Sonu : First, we multiply 30, that is 3 tens, by 2. We get 6 tens, which is 60., Then, 4 units  2 = 8, Lastly, we add 60 and 8., 60 + 8 = 68. So, 34  2 = 68., , F Multiply., D 37  4 , , , , 30, , 7, , 4, , 120, , 28, , D 56  3, , 120, + 28, , , , 50, , 6, , 3, , 150, , 18, , 148, , 168, , 37  4 = 148, , 56  3 = 168, , F Use the above method to carry out the following multiplications., D 42  3, , , , 40, , D 51  6, , 2, , 3, , , , 5, 62, , 50, , 1, , 6, , D 73  5 , , , , 70, , D 39  8, , 3, , 150, + 18, , , 8, , 30, , 9

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Multiplying two two-digit numbers : the lattice method, D Twelve rupees are to be collected from each child for a visit to the zoo. If 25, , children are going, how much money will be collected ?, Nandu : To find it out, we have to multiply 25 by 12., : We shall again split the numbers into convenient parts and multiply using, Tai, the lattice method., Let’s split the numbers like this : 25 = 20 + 5 and 12 = 10 + 2., 200,  20 5, + 50, 10 200 50, + 40, 25  12 = 300 rupees will be collected., + 10, 2, 40 10, 300, F Multiply., D 43  23, , , , 40, , D 62  13, , , , 3, , 60, , 20, , 10, , 3, , 3, , 43  23 =, , 62  13 =, , D 32  14, , , , 30, , 2, , D 13  27, , 2, , 10, , , , 10, , 20, , 4, , 7, , 32  14 =, , 3, , 13  27 =, , F Multiply., D 56  16, , D 71  12, , D 29  29, , 63

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Multiplication : Vertical Arrangement, Tai : We have learnt to multiply using the lattice method. Let us learn another way, to do the same. We have understood the operation. We shall only write it in a, different way., F Multiply : 34  2 , , T, , H, , 3, , , , 4, , 6, , 8, , 2, , First multiply the 4 in the units place by 2. 2 fours, are 8. Hence, write 8 under the line in the units, place. Now, multiply the 3 in the tens place by 2., 2 threes are 6. Write this 6 under the line in the tens, place. The product is 68., , Tony : Good ! This is a quick method., F Multiply., , T, , U T, , U T, , U T, , U, , 4, , , , 2, , 2, , 4, , 2, , 2, , 3, , 1, , 2, ,  , , 2, ,  , , 4, ,  , , 3, , 8, , 4, T, , U, , , 2,  , , 6, 3, , : From these eighteen units, we take 10 units T, to, make 1 ten or 1T. We write this ten at the top in the, 1, tens place. We write the remaining 8 in the units, place under the line. Multiply the 2 in the , tens, 2,  , place by 3. Three twos are 6, and with the new, 1 ten, we get 7 tens. This, we write in the tens, 7, place in the answer., The product is 78., , U, , Multiplication by carrying over, Tony : How to multiply 26 by 3 ?, Salma : Let’s arrange the multiplication vertically., First multiply the 6 in the units place by 3., 3 sixes are 18., , Tai, , 64, , 6, 3, 18, , carrying, over

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F Multiply : 18  4, , T, , U, , 3, , 1,  , , 8, 4, , , 7, 32, , First multiply 8 units by 4. Four eights are 32., 30 of these 32 units make 3 tens. Write these 3 tens in, the tens place at the top and the 2 units under the line in, the units place. Now multiply the 1 in the tens place by 4., 4 ones are 4, and, alongwith the 3 written at the top, we, have 7 tens. Write these in the tens place under the line., The product is 72., , F Multiply., , T, , U, , T, , U, , T, , U, , T, , U, , 1, , 5, , 2, , 4, , 2, , 7, , 1, , 5, ,  , , T, , U, , 2, 2, , 3, 7, ,  , 1 , , H , , 1 6, , 2 1, , H, , T, , U, , 1, , 6, , 1, , T, , U, , 3, , 6, ,  , ,  , , 5, , 4, , 3, ,  , , 3, ,  , , 6, , Now, look at this carefully. We have to multiply, 23 by 7. First we multiply 3 units by 7. Seven, threes are 21. Of these 21 units, we make 2 tens, and write them at the top in the tens place. 1 is, left in the units place. Now, 7 twos are 14, and, together with the carried over 2, we get 16 tens., Salma : 16 tens means 1 hundred, 6 tens., So the product is 161., , Tai, , H , , :, , T, , U, , 4, ,  , , H , , T, , U, , 0, , 5, , 4, , 8, ,  , , 7, , H , , T, , U, , 9, , 2, 8, ,  , , 65

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Word Problems, D If one book costs 85 rupees, what is, , D How many chocolates in 9 jars, , if there are 34 chocolates in 1 jar ?, , the total cost of 5 such books ?, , 3, , 3 4, , , Chocolates in 1 jar, ,  9 Number of jars, , 3 0 6 Number of chocolates, Total number of chocolates 306, , 85, , Cost of 1 book, , , , Number of books, , 5, , Rupees, Total cost, , rupees, , D One metre of cloth costs `  95., , D One litre of milk costs 40 rupees., , How much will 6 metres of cloth, cost ?, , How much will 3 litres of milk, cost ?, , Cost of cloth, , Cost of milk, , rupees, , rupees, , F Solve the following problems., D 25 children in a row. How many in 7 rows ?, D How much will 6 towels cost at 53 rupees a towel ?, D 72 apples in 1 box. How many in 5 boxes ?, D One box holds 40 laddoos. How many laddoos do 9 boxes hold ?, F Make your own problems of multiplication and solve them., , Information : 8 rupees for 1 book,, 45 books, Problem : If one book costs 8 rupees,, how much do 45 books cost in all ?, 45, , Information : 48 pomegranates in 1 box, 7 boxes, Problem : If there are 48 pomegranates, in 1 box, how many are there in 7 boxes?, , books, ,  8 cost of 1 book, 360 rupees, Total cost of 45 books : 360 rupees., , Total number of pomegranates, in the 7 boxes is, , D 15 trees in one row, 9 rows, , D 20 laddoos in one box, 8 boxes, , D 16 toys, cost of each toy `  10., , D Cost of one book `  36, 7 books., , 66

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Division, , Making equal shares, Raju : My mother has given me 6 sweets., Let’s share them equally., Sanju : Ok, you take one, I’ll take one, turn, by turn., Raju : I got 3 sweets., , Total sweets, , Sweets for each, , 6, , 3, , Sanju : I also got three. So, we got three, sweets each., , D These are pictures of some boys and girls. Count to see how many children, , there are. There are some guavas too. They have to be shared equally among the, children. How will you do that ?, , Total, Suma Raju Meena Anju, guavas, , How many guavas did each child get ?, D There are 12 biscuits in a packet. Equal shares must be given to three children, , - Raju, Sanju and Anita., , Total, biscuits, , Each one’s share, Raju Sanju Anita, , On sharing the biscuits equally, each one got, , biscuits., 67

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D 18 fruits are shown in the picture, , alongside. If they are shared equally, between two people, how many will, each one get ?, D If 18 fruits are shared by 3 people, , equally, how many will each get ?, D If 18 fruits are shared equally by 6, , people, how many does each one get ?, Forming groups or making shares or lots, Mother : I have brought 6 mangoes., Sucheta, make lots of 2 mangoes to a lot., How many lots do you get ?, Sucheta : 3 lots. Now, shall I make lots of, 3 mangoes each ?, Mother : Sure. Do it and see how many lots, there are., Sucheta : There are only 2 lots this time., The table below shows how Sucheta distributed the mangoes., Total number of mangoes, , Mangoes in each lot, , Total number of lots, , 6, , 2, , 3, , 6, , 3, , 2, , D Mark the lots in the picture and complete the table., , 68, , Total, number of, mangoes, , Mangoes in, one lot, , 8, , 2, , 8, , 4, , Total number, of lots

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D Mark the lots in the picture and complete the table., , Number of, Total number, cucumbers in, of cucumbers, one lot, 10, 1, 10, , 2, , 10, , 5, , 10, , 10, , Total, number, of lots, , D There were 12 children with Tai. She said to them, ‘Let’s play the game of, , making groups. You must make groups of as many children as the number of, fingers I show’. , Tai showed 4 fingers., How many groups were formed ?, Tai made a hand-sign of 3 fingers. , How many groups were formed ?, Tai showed 2 fingers. , How many groups were formed ?, Tai made a hand-sign of 6 fingers., How many groups were formed ?, D One carton can hold 6 laddoos. How many cartons will be needed to pack 48, , laddoos ? Let’s see if you can work that out., Total, laddoos, 48, , Number of laddoos, in one carton, 6, , Number of, cartons, , >, , D One carton can hold 10 tiles. A certain room needs 60 tiles for the floor. How, , many cartons of tiles will be needed ?, Total number Number of tiles in, of tiles, one carton, 60, , 10, , Number of, cartons, , >, 69

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D One carton contains 8 candles., , How many cartons do we need for, packing 24 candles ?, , Making equal lots from a collection of objects is called division., , D Subtracting the same number again and again, , From these 8 flowers, we shall take away 2 every time., , The first time, we take away 2 flowers from 8., 6 flowers left., 8-2=6, , The second time, we take away 2 flowers from 6., 6 - 2 = 4., 4 flowers left., , The third time, we take away 2 flowers from 4., 4 - 2 = 2., 2 flowers left., The fourth time, we take away 2 flowers from 2., No flowers left., 2 - 2 = 0., In other words, zero (0) flowers are left., Four is the maximum number of times that we could take away 2 flowers at a, time from 8 flowers., D The doctor gave Nandu 15 pills and told him to take 3 pills every day. How many, , days does Nandu have to take the pills ? Draw pictures as shown above to show it., , 70

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Tai, , : I have brought some jamuns. Who is present today ?, , Sonu : Three of us - Salma, Tony and me., Tai, , : Count these jamuns. And share them equally among, the three of you., , Sonu : These are 12 jamuns. I’ll distribute them giving each, one jamun at a time., , Tai, : How many did each of you get ?, Sonu : Each of us got four., Salma : May I distribute them in a different way ?, Tai, , : Certainly. How do you want to do it ?, , Salma : Three of us have to share them, so I’ll, make groups of three jamuns. Then each, of us will take one from each group., Tony : Oh, yes ! One from each group means, 4 jamuns for each of us., Tai, , : And, did you notice this ? When Salma was, making the groups, she was taking away three, jamuns every time. In other words, from 12, she, was subtracting 3 again and again., , Salma : Yes, Tai ! And when she did this four times,, no jamuns were left., Tai, , : So, now you must have understood that sharing, twelve jamuns equally among three or making, groups of three jamuns from them is the same as, taking away 3 jamuns from 12 again and again., The outcome of all these actions is the same., , 71

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Tony : Yes, Tai., Tai, , : That is why all these actions are given the same name in mathematics,, which is division., D Division means distributing things equally., D Division means making equal groups of things., D Division also means taking away the same number of things again, , and again from a certain number of things., Tony : Tai, we know the method of writing a multiplication using a sign. There, must be a sign for division too !, Tai, , : This is the sign for division ‘’. This is how we use it, 12  3 = 4. It is read, as ‘12 divided by 3 is equal to 4’., , Salma : I understood ! 4 threes are 12. It means that when we put together 4 groups of, 3 things each, we get 12 things. And if we make groups of 3 things using 12, things, the number of groups we get is 4., Tai, , : Excellent. When making groups of three, we say the 3 times table up to, 12. We come to know how many groups of three we can get from twelve., When making 3 equal shares out of 12 also, we say the 3 times table. When, we come to ‘3 fours are 12’ we know that each one will get 4 things., , There are 9 laddoos in one box. They have to be shared equally by four people., After giving 2 laddoos each to 4 people, 1 laddoo remains. It means that if we have, to give whole laddoos, we cannot make equal shares. Had there been only eight, laddoos in the box, there would be no laddoos left over after the equal shares had, been made. Sometimes, things get left over after making equal shares containing, whole things only. This number of remaining things is called the ‘remainder’. Look, at the vertical arrangement which shows numbers instead of things., , Shared among, 4 persons., , 72, , 2, 4 )     9, -8, , 1, , Number of laddoos in each share, Number of laddoos to be shared, Number of laddoos shared, Remaining laddoo

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D 12 flowers shared equally among 4 children., , , (Quotient), each one got, 3 Flowers, , (Divisor), 4) 12 (Dividend) Total flowers, 12 Flowers, , shared, 0 (Remainder) Flowers left., , Each one gets 3 flowers,, because 4 threes are 12., This division is written vertically, as shown alongside., 12 divided by 4, remainder 0., , D 15 laddoos were shared among 5 children., , Each one gets three laddoos., Because 5 threes are 15., The number of laddoos that, each one gets is called the, ‘quotient’., All the laddoos are finished., Nothing remains., That is, remainder 0., , , 3 (Quotient), , (Divisor), 5) 15 (Dividend), 15, , 0 Remainder, , D 22 rupees to be distributed equally among 5 people., , Tony : Here, 22 is the dividend and 5, the divisor., 5) 22, , 4 Quotient, Divisor 5) 22 Dividend, 20, 2 Remainder, , F Divide., , 4, 9) 36, 36, 0, 7, 8) 58, 56, 2, , Salma : Here, 5 is the divisor, so we shall use the, 5 times table. 5 fours are 20 and 5 fives, are 25., Tony : We can’t give away 25 rupees from 22., But we can give 20 from 22., Sonu : So, we use 5 fours are 20 and we write 4, in the units place above the line., Nandu : We mustn’t write this 4 in the tens place, because each one gets 4 rupees and not 4, tens. That would be 40 rupees !, , 7) 42, , 8) 64, , 6) 54, , 6) 49, , 5) 47, , 7) 29, , 73

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Measurement of Time, n, , Tai, , Reading the clock, , : You had asked me how to tell the time using a clock., Today, I have brought a big clock to help you to learn that., Look at the long hand and the short hand of the clock., When both are at 12, it is twelve o’clock., , Salma : When the short hand is at 4 and the long one at 12, it is, 4 o’clock., Nandu : We can also show 5 o’clock and 9 o’clock like this., Sonu : The short hand goes slowly, but the long one moves faster !, : Yes. The short hand shows hours and the long one shows, Tai, minutes. That is why they are also called the hour hand, and the minute hand. The long hand has reached 1. So it, is 5 minutes past 12 o’clock., Nandu : When the minute hand reaches 2, it will be 10 minutes, past 12, and, when it reaches 3, it will be 15 minutes past, 12. Then we will see that the hour hand has also moved, forward a little., : That’s right. Between two adjacent numbers, there is a, Tai, difference of five minutes., Sonu : That means, we can use the 5 times table for counting, minutes. So when the hour hand is between 12 and 1 and, the minute hand is on 9 we can tell that it is 45 minutes, past 12. Because 9 fives are 45., : Great ! When the minute hand moves forward starting, Tai, from 12 and reaches 12 again, it has completed one round., The time it takes to do this is 60 minutes or 1 hour. In, that time, the hour hand moves from 12 to 1. And at that, moment, the time is 1 o’clock., Tony : I got it. If the hour hand is between 4 and 5 and the minute, hand is on 8, then, because 8 fives are 40, it is 40 minutes, past 4., , Hour and minute are the units for measuring time., 74

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F Write in hours and minutes the time that each clock is showing., , F Read the given time and draw the hands of the clock below to show that time., , 10 minutes past 5, , 5 minutes past 9, , 20 minutes past 6, , 35 minutes past 11, , F Write in the table below, approximately how many minutes or hours or days it takes for, each of the following to happen., , Rice gets, A cow is, cooked in the, milked, pressure cooker, , Mother, cooks a, meal, , The water A sweater is A rose bud, tank gets, knitted, blooms into, filled, a flower, , F In the table below, fill in the main things you do in a day, the times at which you do them, and the positions of the hands of the clock at each of those times., , S.No., , What I do, , Time in the clock, , Positions of the hands of the clock, , 1., , Get up in the, morning., , 15 min past 6, , Short hand just after 6,, long hand at 3., , F Find out what you can about the following kinds of clocks/watches., , D The clock in the mobile phone, D The clockwork clock, D The pendulum clock, D The automatic clock or watch, D The stop-watch, D The hourglass, D The sundial, - For teachers : Tell the children to make clocks using thick cardboard and some pins. Give them practice in, telling the time using these clocks., , 75

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The Calendar, Using a Calendar, F Look up this year’s calendar. Write the information in the table below., n, , The festivals, in the month of, October, , The holidays How many days after, in the month of the 5th of December, August, is Christmas ?, , The dates of, the Sundays, in June., , January 2015, S, , M, , T, , W, , T, , F, , S, , 1, , 2, , 3, , 4, , 5, , 6, , 7, , 8, , 9, , 10, , 11, , 12, , 13, , 14, , 15, , 16, , 17, , 18, , 19, , 20, , 21, , 22, , 23, , 24, , 25, , 26, , 27, , 28, , 29, , 30, , 31, , Today is the 15th of January., Remember, we have to go for, Sonu’s birthday ?, , Salma : In which year were you born ?, Sonu : I was born on the fifteenth of January two thousand and five., Tony : Today’s date is 15th January 2015. It means that Sonu is 10 years old, today., Salma : My date of birth is 12th March 2006. In whole years, I am 8 years old, today., Tony : So, your birthday will be on 12th March 2015 and that day you will be 9, years old., To tell someone’s age, count forward from the year of, birth till the current year., 76

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F Some people’s dates of birth are given in the table below. Write how many years of age, they complete this year, on their birthdays., , Name, , Sarika, , Mohan, , Ahmed, , Makhan Singh, , Date of Birth, , 18.7.2002, , 14.5.2000, , 01.2.2003, , 13.7.1977, , Age, F Write the dates of birth of the people in your family and complete the table below., , Person, , Date of, Birth, , Date on 25th, birthday, , Age today in, whole years, , Date of 40th, birthday, , Mother, , Father, , Sister, , Brother, F Find out -, , D Whose birthday comes every four years ? Why ?, D Which is your favourite festival ? On which date did it fall last year ? What is, its date this year ?, D About different types of calendars., D How to work out age in whole years, in months, in days., D Our country became independent on 15th August 1947. How many years have, we completed after that ?, D India launched the satellite ‘Aryabhatta’ into space. The year 2005 was the, 30th year after this event. In which year was this satellite launched ?, D ‘The year 1987 was the centenary of the birth of the great Indian mathematician, Ramanujan.’ What does this tell us ?, 77

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Fractions, , Half, Tony and Nandu were hungry. Salma had one bhakari., She quickly made two pieces of the bhakari and, gave it to them., Tony : I got less of the bhakari., Nandu : That’s true. I really got the bigger piece., Salma : Oh, I’m sorry ! It’s because I broke it in, a hurry. I have a puri, too. I’ll divide it, equally into two parts for you., Tony : Yes, this time we have equal pieces., Sonu : Both of you got exactly half the puri., Sonu has a large sheet of paper. Both Sonu and Salma want to draw a picture., Sonu : Let’s divide this sheet into two equal parts., Tony : Come, I’ll do it., Full sheet of paper, , Half Half, , Sonu and Salma both got half a sheet of paper., When something is divided into two equal parts,, each of the parts is a half of that thing., F Observe the pictures given below., , 78, , A whole, guava, , Half a, guava, , A whole, apple, , A whole, cake, , Half a, cake, , A whole, watermelon, , Half an apple, , Half a, watermelon

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F Colour a half of each of the pictures given below., , F A line has been drawn in each of the figures given below. Put a tick mark (ü) under the, figures which get divided into two equal parts by that line., , A quarter, : Salma, Nandu, Sonu, Tony, come here all of you. I have a large sheet of, kite paper. Each of you, use it to make a kite for yourself., Tony : It means that we will have to make 4 equal parts of that paper., Nandu : I’ll make the four equal pieces., : Excellent. Each of these parts is a quarter of the big sheet of paper., Tai, Tai, , A quarter part, , When something is divided into four equal parts,, each of the parts is a quarter of that thing., F Observe the pictures below to understand the meaning of ‘quarter’., , A whole, cucumber, , A quarter of a, cucumber, , A whole cake, , A whole, watermelon, , A quarter, watermelon, , A quarter of a cake, 79

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n, , A whole, a half and a quarter, A Half, A Whole, , A Quarter, , If we divide a half into halves again, we get two quarters., We have seen already that when a whole is divided into four equal parts,, we get a quarter., If we put two quarters together, we get a half., Similarly, if we put four quarters together, we will, get a whole., F Colour a quarter part of each picture below., , F In each of the pictures below, lines have been drawn to divide the figure into four parts. If, a figure is divided into equal parts, put a tick (P) mark under it., If not, put a (Î) cross., , 80

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Three quarters, Nandu : I have drawn lines in this picture so that it gets divided, into four equal parts. Three of these parts have been coloured. In, other words, three quarters of the paper has been coloured., If a whole is divided into four equal parts and we take three of them,, the part that we have taken is called ‘three quarters’., Half a guava, , A quarter of a guava, , A half and a quarter make three quarters., , Three quarters may also be called, a three quarter part of the whole., When we take away a quarter from a whole, what, we have left is also three quarters., F Colour three quarters of the pictures below., , F Say whether the coloured and the white parts of the figures below are a quarter, a half or, three quarters., , Figure, , Coloured, part, , Half, , White, part, 81

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A quarter, a half, and three quarters of a collection, The picture shows a collection of eight balls., We divide the collection of eight balls into two equal parts., Each part is a half of the collection of eight balls. There are, four balls in each part., In this picture, a collection of eight balls has been, divided into four equal parts. Each part is a quarter of the, collection. Each quarter contains two balls. When a half of, a collection is halved again, what do we get ?, A half and a quarter together make three quarters. Hence,, a quarter and a half of a collection together make three, quarters of that collection., The picture shows a three quarter part of a collection of, eight balls. When a quarter is taken away from a whole, we, get a three quarter part., When three quarters of a collection are brought together,, what is the name of the part we get ?, F Show a half of this collection., , F Colour three quarters of the collection, shown below., , F Show a half of the collection given below., , F Show a quarter of the collection given, below. Colour the remaining part and, say what part of the whole collection it is., , 82

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Using Half, Quarter, Three quarters, F Study the following examples., D The length of the school ground is 20 metres. Half the length of the ground is half, , D, D, D, D, , of 20 metres, which means 10 metres. A quarter of the length of the ground is, 5 metres and three quarters is 15 m., One hour has 60 minutes. A half hour/ Half an hour has 30 minutes., A quarter of 4 litres is 1 litre., Jivraj has 200 rupees. He gave three quarters of that amount to Meena. It means, that Jivraj gave Meena 150 rupees., One dozen bananas means 12 bananas. Half a dozen bananas means 6 bananas., Three quarters of a dozen bananas means 9 bananas., , F Solve the following problems., D Anand is 8 years old today. Shruti is half as old as Anand. Then how old is Shruti ?, D Sonali has a length of 10 metres of cloth. She gave half of it to Ramu. What, , length of the cloth does she have left? How much did she give Ramu?, D Anagha has a hundred rupees. If she gives a quarter of that amount to her brother,, what is the amount of money she gives him ?, D A rope has a length of 16 metres. If a three-quarter length is to be cut off, what, length should be marked off from one end ?, D It takes 6 hours to travel from Solapur to Nanded. It takes half that time to reach, Latur from Solapur. How long does it take to travel from Solapur to Latur ?, F How much is each of the following ?, D Half of a 24 metre length of cloth., D A quarter part of 80 rupees., D Three quarters of 40 kilograms of sugar., D A quarter of 12 litres of kerosene., D Half of 4 hours 40 minutes., D Three quarters of 60 rupees., , 83

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Handling Data, , It was Sonu’s birthday. Her friends had come for her birthday party. Everyone, wished her a Happy Birthday and also gave her gifts. Nandu had not gone for the, party. He asked Sonu :, D Who had come for the party ? How many boys ? How many girls ?, D What gifts did you get ? How many of them ?, Sonu told Nandu the names of all those who had come., Tony : Let us see the gifts first. We can answer Nandu’s questions later., Tony put the gifts into groups. , Salma counted the books., Gifts, Number, Pencils, 17, Sonu counted the pens. Tony counted the pencils., Nandu wrote down this information on a slate., Pens, 4, Sonu : So, I got 30 gifts in all !, Books, 9, Tony : Hey, this has become a table !, Total gifts, 30, F Next day when Nandu came to the class, he asked each boy and girl, ‘How do you come to, school ?’ He took down their answers as shown below :, , Rohit - Bus, Vijay - Rickshaw, Maya - Bus, Gopal -Walking, Rekha Rickshaw, Krishna - Bicycle, Abha - Car, Mahadev - Walking, Roger Walking, Faroukh - Rickshaw, Ahmed - Bus, Sanika - Bicycle, Smita - Bus,, Nandu - Rickshaw, Sonu - Rickshaw, John - Bus, Sarabjit - Bus, Swara - Car,, Ramnath - Walking, Alan - Walking, Vikas - Rickshaw, Anthony - Rickshaw,, Sarah - Bus, Satish - Bicycle, Albert - Bus, Ramswami - Walking, Neeta - Bus,, Alaka - Bus, Nagesh - Bicycle, Kailas - Bicycle., Nandu made a table and presented the same information in it as shown below., Come by bus, , Rohit, Smita, Maya, Sarah, Ahmed, John, Sarabjit,, Albert, Neeta, Alaka, , 10, , Come by rickshaw, , Vijay, Rekha, Sonu, Nandu, Faroukh, Vikas, Anthony, , 7, , Come walking, , Gopal, Ramswami, Mahadev, Roger, Ramnath, Alan, , 6, , Come on a bicycle, , Krishna, Sanika, Satish, Nagesh, Kailas, , 5, , Come by car, , Abha, Swara, , 2, , 84

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F It was not required to wear the uniform on Thursday. Children had come to school, wearing clothes of different colours. Alan made a table showing this. Salma suggested, that instead of writing names, they could put one mark for each child., , , The table that Alan made , , The table that Salma made, , Colour of, clothes, , Names of, children, , Number of, children, , Colour of, clothes, , Red, , ........, , 4, , Red, , 4, , Green, , ........, , 2, , Green, , 2, , Yellow, , ........, , 7, , Yellow, , 7, , Blue, , ........, , 10, , Blue, , 10, , Tony, , Tally, Marks, , Number of, children, , : My clothes are red. So I am in the first group., , Salma : But, is the number of marks the same as the number of children ?, How can we tell ?, Sonu : The number of children wearing red is 4, and so is the number of marks,, that’s how ! That’s why they’re called tally marks, you see., , F Mary made a table giving information about the flowering plants in her garden., , Rose, , Hibiscus, , Mogara, , Champa, , 85

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Sonu : You are good at drawing pictures. So the table looks pretty., Tony : But I can’t draw such nice pictures like you. And it takes so long to draw, them well. So we’ll make tally marks instead of drawing pictures of things., That will be quicker., Name of plant, , Tally marks, , Total number of plants, , Rose, Hibiscus, Mogara, Champa, F Rita asked her friends to name their favourite sweet dish. She showed their answers in, a table using tally marks. Count the tally marks to write the answers to the following, questions., , Name of sweet dish, , Tally marks, , Number of children, , Jalebi, Laddoo, Gulabjamun, Other sweet dishes, D Which is the most popular dish among the children?, D By how much is the number of children who like laddoos more than the, number who like jalebis ?, F Collect the following information. Use pictures or tally marks to make tables., , D In which months are the birthdays of the children in the class?, D Things in the kitchen and their number, (e.g. bowls, glasses, plates, pots, cups, saucers, spoons, etc.), D Which pet animal do the children in the class like the most ?, , 86

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F Look at the table below and answer the questions., , Name of the crop in the field, , Number of farmers growing it, , Wheat, Jowar, Rice, Peas, Peanut, Sugarcane, D, D, D, D, , About how many crops does the table give us some information ?, How many farmers grow peanuts ?, Which crop is grown by the smallest number of farmers ?, Which crop is grown by the largest number of farmers ?, , F What did you do to entertain yourself on Sunday evening ? The answers that the children, gave to this question have been tabulated as shown below., , Form of entertainment, , Tally marks, , Number of children, , Played games, Watched TV, Took a walk in a garden, Read a story-book, D About how many children does the table inform us ?, D How many children took a walk in the garden ?, D What did the least number of children do ?, F Collect information about children’s favourite fruit and present it in a table., , Favourite fruit, , Tally marks, , Number of children, , Mango, Guava, Apple, Pomegranate, , 87

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F Write down all the information that you get from this table., , D Which fruit do the greatest number of children like?, D The number of children that like mangoes is greater than the number of, children that like ………………. ., , F Find out the answers to the following questions and prepare tables showing the, information collected., , D When school gets over, how many two-wheelers, three-wheelers and, four-wheelers come to the school gate to pick up the students ?, D How many plastic, iron and wooden chairs are there in your school ?, D What are the colours of the school bags of the children in your class ?, D What fuel is used for cooking in the homes of the children in your class gas, kerosene or wood ?, D Visit the homes of 10 farmers in your village or town and collect information, about how many domestic animals they keep., , ***, , - For teachers : Tell children to collect information about various events and tabulate it. They may use either, pictures or tally marks. Ask qualitative and quantitative questions based on these tables., , 88

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MATHEMATICS, , J{UV B¶ËVm {Vgar (B§J«Or ‘mܶ‘), , Maharashtra State Bureau of Textbook Production and Curriculum Research, Pune 411 004., , B§J«Or J[UV 3.ar, , 39.00