The Coordination Committee formed by GR No. Abhyas - 2116/(Pra.Kra.43/16) SD - 4 Dated 25.04.2016 has given approval to prescribe this textbook in its meeting held on 19.03.2019 and it has been decided to implement it from the educational year 2019-20. MATHEMATICS Standard Two Maharashtra State Bureau of Textbook Production and Curriculum Research, Pune - 411 004 Download DIKSHA APP on your smartphone. If you scan the Q.R.Code alongside, you will be able to access the full text. Q.R.Codes are given at the end of each chapter. Scanning these you will be able to access audio-visual study material as teaching and learning aid, related with some contents.

Preface My dear friends, Welcome to std II. You have read the books of std I and studied them well. And now you are in std II. You will enjoy the studies of std II as well, won’t you? Your friends Yash and Rama are also with you. You will have several occasions to play games as you study maths. You already know how to count objects. You will now learn to do small additions and then small subtractions. Make an effort to understand the method or procedure well. That will help you to experience the fun of maths. Just as you ask your teacher for help in school, you can get help from your parents, older brothers or sisters or anyone else, at home. While studying lines and various other shapes, you are to draw figures or pictures. Drawing pictures and colouring them is something you like and enjoy, isn’t it? You will get opportunities to do just that. You will also find some fun games useful for learning to add or subtract small numbers. Once you learn to add and subtract small numbers, you will find the maths problems of higher classes easier to solve. The different types of mathematics help to make many of our tasks easier to do. Adding the same number again and again is a boring task. See how multiplication will help to make it quick and easy. You could also play game of asking each other small multiplications from the tables. In order to understand how to subtract by borrowing, use ten-rupee notes and one-rupee coins. You can yourself make mock notes from paper and coins from card board. You don’t need to use real currency notes and coins. Q.R. Code is given at the end of each chapter. You will find interesting information in the Q.R Codes. Maths in Std II is really quite easy. Learn as you play and enjoy your studies. Pune (Dr. Sunil Magar) Date : 7 May 2019, Akshayya Trutiya Director Indian Solar Date : 17 Vaishakh, 1941 Maharashtra State Bureau of Text Book Production and Curriculum Research, Pune

Mathematics Standard II - Learning Outcomes Suggested Pedagogical Processes Learning Outcomes All learners may be provided The learner — opportunities in pairs/groups/ individually and encouraged to- • Telling the names of numbers and recognizing 02.71.01 Can carry out operations on two-digit their pattern of writing on paper. Reading and numbers. writing numbers up to 99. Can read numbers up to 99 and write numbers • Understanding the place value of a digit in a up to 50 in words. number and use it to recognize or form groups. Can make up tables of the numbers 2, 3, 4 and • Using addition facts up to 9 to carry out additions 5 with the help of easily available objects and of two-digit numbers up to 99. can use the tables. • Developing other methods of addition and Can use the place value of numbers while subtraction and using them. writing or comparing two-digit numbers. • Finding situations where addition or subtraction Can make the greatest and the smallest two- is involved, e.g. merging two groups, enlarging digit numbers using two given digits (with or a group by increasing the number of things in a without repetition of digit) group. Can solve simple everyday problems or • Framing questions/ problems based on addition questions involving addition of two-digit and subtraction, which the students themselves numbers. can relate to. Can solve simple everyday problems or • Creating a real or supposed situation in which questions involving subtraction of two-digit a particular number will have to be added numbers. repeatedly. Can put together an amount up to Rs 100 • Drawing diagrams of various faces of using various notes and coins of different three-dimensional objects and naming the denominations. corresponding two-dimensional shapes. 02.71.02 Can describe the visual characteristics of • Classifying various shapes by recognizing their two-dimensional and three-dimensional physical characteristics with the help of their objects. cut-outs or by folding a paper. Can recognize and name common three- • Describing the shape and physical characteristics dimensional shapes, e.g. cube, cylinder, cone of objects either by handling them or by and sphere. observation. Can draw two-dimensional diagrams of three- • Putting together an amount up to Rs 100 using dimensional objects mock money of different denominations. Can recognize two-dimensional shapes, e.g. • Observing various balances and scales used rectangle, square, triangle, circle. to weigh things and discussing the experiences gained. 02.71.03 Can distinguish between straight and curved lines. • Making a simple balance and weights and use them to compare weights of various objects. 02.71.04 Can draw straight lines in different ways – vertical, horizontal, inclined.

Suggested Pedagogical Processes Learning Outcomes • Measuring some lengths of small objects in the 02.71.05 According to their physical surroundings using non-standard unit such as a characteristics, can describe solid objects finger, hand-span, length of arm or foot, etc. in their own words. e.g. a ball rolls, a box slides, etc. • Being able to tell the criteria or characteristics used while classifying different solids/ shapes. 02.71.06 Can estimate and measure the length of objects using non-standard units such as • Discussing the household tasks done or time spent fingers, hand span, arm, foot, etc. with their family on some specific occasion. 02.71.07 Can compare two objects using a common • Visualizing both a feature that repeats itself in a balance and can express the comparison pattern as well as the final pattern obtained due in words such as ‘…..is heavier than….’, to that feature, and expressing in words what has ‘…is lighter than….’ been visualized. 02.71.08 Can tell the names of the days of a week • Extending the pattern formed from various and the months of a year. shapes, fingerprints, prints of leaves or numbers. 02.71.09 Can analyse the information collected • Collecting information from people in the and draw inferences from it. e.g. the surrounding, maintaining a record of the number of vehicles used in Sameer’s information collected and drawing conclusions house is more than those used in from it. Anjalee’s house. 02.71.10 Can tell the values of notes and coins up to hundred rupees and can carry out the operations of addition and subtraction on them. For teachers Please note that children are expected to learn to write in words, numbers from 1 to 50 only. The mathematical concepts to be taught are the same as before. Do give enough time and practice for learning addition by carrying over and subtraction by borrowing. It is important for children to learn how ten Units make a Ten, and how a Ten can be untied to obtain ten units. Besides using beads, strings and sticks of Ten, you will also find ten- rupee notes and one-rupee coins to be very useful. Get the children’s help in cutting out rectangular pieces of card paper of the same size to make ten-rupee notes and small discs of cardboard to make one-rupee coins. Encourage them to use these mock notes and coins to learn addition by carrying over and subtraction by borrowing. Also guide them in making the multiplication tables of the numbers 2, 3, 4 and 5. Give the children plenty of practice to solve examples through various activities.

Index Part One Part Two Let’s find the Shapes ! ................................. 1 Comparing numbers ................................... 36 Let’s handle geometric shapes ..................... 2 Neighbouring numbers on each side ......... 38 Fun with Line ............................................... 6 Ascending and Descending order of Let’s identify geometrical shapes ................ 8 numbers ................................................... 39 In the world of numbers ............................... 9 Come, let’s make numbers ......................... 41 Let’s read and write in words .................... 10 Cardinal numbers Ordinal numbers .......... 43 Counting in groups ..................................... 12 Reading Pictures ........................................ 46 Number given in a picture ......................... 13 A special way to add-by carrying over ..... 48 What is the meaning of ‘Place Value’ ? .... 15 Stories of Addition -2 ................................. 51 The expanded form of a number ............... 17 Let’s untie a ten in order to subtract .......... 53 Let’s count numbers in steps ...................... 19 Do you know Notes and Coins ? ............... 56 Fun with Addition ...................................... 20 Let’s measure Length ................................. 58 Addition-by counting forward ................... 21 Let’s weigh ................................................. 60 Addition – without carry over .................... 23 Let’s measure Capacity ............................. 62 Addition and subtraction of Zero .............. 25 Managing Information ............................... 64 Stories of Addition -1 ................................. 26 Patterns ....................................................... 66 Let’s reduce by subtraction ........................ 27 Multiplication Preparation ......................... 69 Addition and subtraction- a pair ................ 30 Let’s make Tables ...................................... 71 A subtraction story ..................................... 32 Maths in a story ......................................... 76 Twelve Months in a Year ........................... 33

Part I Let’s find the Shapes ! A picnic on Sunday, in farm fresh air All shaped veggies, we could find there When he dug the soil, Motya had found Cone like carrots, under the ground. Yash brought tomatoes red and round some long brinjals also he found. Rama got the cucumbers, green and fresh Some straight cylinders, some bent at the waist. Tarmarind from a tree and a little bit of garlic Was all that Gampu and Pussy could pick. Mamma roasted rotis, Pappa cooked veggies Such a nice picnic, could we come again, Please ? 1

Let’s handle geometric shapes Let’s collect : Match stick boxes, cartons of tooth paste, mithai etc. water bottles, balls of different sizes, a clowns cap and pipes made of card paper. Observe the objects on the table. Separate the objects of similar shapes. Cuboid or Parallelepiped : Pick up and handle a mithai box. A shape such as this is called a cuboid or a parallelepiped. Edge You must have seen bricks on construction sites. Any object shaped like a brick is called a Corner cuboid. How many edges does this shape have ? How many corners ? Let’s see. A cuboid has - edges and - corners. Now let us look at the surfaces of a cuboid .... They are all flat. A cuboid has six surfaces altogether. If we place a cuboid on a slide in a park, it will slip down the slope because of its flat surface. Find out The objects on the table of cuboid shape. 2

Cone : Now, let’s take a look at the clown’s cap you have made. It’s shape is called a cone. Cone - The shape like a clown’s cap or fool’s cap is called a cone. You are familiar with an ice-cream cone and a mehandi cone. A cone has one edge and one corner. The flat base of a cone is circular. See how the sloping surface of a cone turns continuously around. It is called the curved surface. Cylinder : Now look at the water bottle. The shape of the bottle is called a cylinder. Cylinder - A bottle like shape which has a circular base is called a cylinder or a circular prism. A cylinder has two edges but not a flat top surface single corner. The base and the top surfaces of a cylinder are alike, flat curved surface and circular. The turning surface between them is a curved surface. flat bottom surface Try this. Place a cylinder on a slide in a park. Does it slip downwards or roll down ? When we place an object with its flat surface on a slide it slips down, but if we place its curved surface on the slide the object rolls down. You can see this clearly with the help of a cylinder. 3

Sphere : A ball is said to be spherical. Sphere - A shape like a ball is called a sphere. A sphere has no edges and no corners. No part of a sphere is flat. It turns continuously. Thus a sphere has only a curved surface. Try this. Does a sphere slip or roll down when it is placed on a slide ? * Match the pairs. Name of shape Shape 1) 1) Cylinder 2) 2) Cuboid 3) 3) Cone 4) 4) Sphere * Which of the following objects will slide, which ones will roll? 4

* Handle the objects shown below. Observe and write how many edges and corners each object has. Edges - Edges - Edges - Edges - Corners - Corners - Corners - Corners- * Say which of the objects in the pictures will slide, which ones will roll? Place many solid objects before the children. Ask them to identify known geometric shapes and to count the edges and corners of each. ICT Tools Using the ‘paint brush’ app draw various geometric shapes and colour them. 5

Fun with Line * If we hold a thread in our two hands and stretch it tight, we get a straight line. If we let it hang loose we get a curved line. (See how we get a straight line if we tie a stone to one end of a thread and let it hang.) In this book we shall be learning about the straight line. So when we say ‘line’ we mean ‘straight line’. Neha drew vertical or Anagha drew horizontal or Hamida drew inclined or standing line sleeping lines sloping lines * Activity : Fold a paper and show vertical, horizontal and inclined line. * Draw lines like the ones shown below. 6

* I draw a line with the help * I use a box to help me draw of a book. a line. * I used a ruler to draw a line. * I drew a line just by hand, without the help of any device. Identify the shapes and colour them Identify the shapes like , and , in the picture alongside. Colour red, yellow and the blue. See that the children carry out the above activities in their nootebooks. 7

Let’s identify geometrical shapes * As shown in the picture, trace the edges of the objects with your pencil and draw the shape of the object. Observe the sides of the object. This is a A circle has This is a This is a rectangle. square. A rectangle only one curved triangle. A square has 4 has 4 sides. edge and no A triangle has sides. 3 sides. straight side. Try the fun activities given below : * Activity 1 : Make a paper boat. Unfold it and count the numbers of triangles and four-sided figures; and colour any * Activity 2 : two triangles and four-sided two figures. * Activity 3 : * Activity 4 : Make triangles and four-sided figures using match sticks or small wooden strips. Find out the tools of games in which you see triangles, four-sided figues and circles. Make a picture using the shapes ∆, , etc. Give children practice in drawing various shapes using articles of daily use. Also give them practice in drawing these shapes free- hand. 8

In the world of numbers * Come, lets complete the numbers chart. 1 4 6 8 10 Let us try to read the numbers 12 13 15 17 19 on the butterflies’ wings. 21 24 26 28 30 1 26 82 36 32 35 37 39 75 69 77 51 41 43 44 48 50 52 54 56 59 63 65 68 70 19 64 99 43 72 76 79 56 83 30 12 81 84 87 90 92 95 98 100 Given along side is a number 18 chain. Read the numbers at the ends 33 of the chain. Recite all numbers between those numbers, in serial order. Observe the chains given below and recite the numbers in the middle, in serial order. 86 59 98 77 Take ‘number reading’, showing number cards of numbers from 1 to 100. 9

Let’s read and write in words Twenty-one to Hundred (Writing numbers from 21 to 100 in words) 21 Twenty and one - twenty one 31 Thirty and one - thirty one 41 Forty and one - forty one 22 Twenty and two - twenty two 32 Thirty and two - thirty two 42 Forty and two - forty two 23 Twenty and three - twenty three 33 Thirty and three - thirty three 43 Forty and three - forty three 24 Twenty and four - twenty four 34 Thirty and four - thirty four 44 Forty and four - forty four 25 Twenty and five - twenty five 35 Thirty and five - thirty five 45 Forty and five - forty five 26 Twenty and six - twenty six 36 Thirty and six - thirty six 46 Forty and six - forty six 27 Twenty and seven - twenty seven 37 Thirty and seven - thirty seven 47 Forty and seven - forty seven 28 Twenty and eight - twenty eight 38 Thirty and eight - thirty eight 48 Forty and eight - forty eight 29 Twenty and nine - twenty nine 39 Thirty nine - thirty nine 49 Forty and nine - forty nine 30 Thirty 40 Forty 50 Fifty N. B. It is expected that children should be able to recite numbers upto 100 and write upto 50. 51 Fifty and one - fifty one 61 Sixty and one - sixty one 71 Seventy and one - seventy one 52 Fifty and two - fifty two 62 Sixty and two - sixty two 72 Seventy and two - seventy two 53 Fifty and three - fifty three 63 Sixty and three - sixty three 73 Seventy and three - seventy three 54 Fifty and four - fifty four 64 Sixty and four - sixty four 74 Seventy and four - seventy four 55 Fifty and five - fifty five 65 Sixty and five - sixty five 75 Seventy and five - seventy five 56 Fifty and six - fifty six 66 Sixty and six - sixty six 76 Seventy and six - seventy six 57 Fifty and seven - fifty seven 67 Sixty and seven - sixty seven 77 Seventy and seven - seventy seven 58 Fifty and eight - fifty eight 68 Sixty and eight - sixty eight 78 Seventy and eight - seventy eight 59 Fifty and nine - fifty nine 69 Sixty and nine - sixty nine 79 Seventy and nine - seventy nine 60 Sixty 70 Seventy 80 Eighty 81 Eighty and one - eighty one 88 Eighty and eight - eighty eight 95 Ninety and five - ninety five 82 Eighty and two - eighty two 89 Eighty and nine - eighty nine 96 Ninety and six - ninety six 83 Eighty and three - eighty three 90 Ninety 97 Ninety and seven - ninety seven 84 Eighty and four - eighty four 91 Ninety and one - ninety one 98 Ninety and eight - ninety eight 85 Eighty and five - eighty five 92 Ninety and two - ninety two 99 Ninety and nine - ninety nine 86 Eighty and six - eighty six 93 Ninety and three - ninety three 100 Hundred 87 Eighty and seven - eighty seven 94 Ninety and four - ninety four 10

* Complete the activity given below : 21 Fifty and three Sixty Fifty-three 48 18 Thirty and three Thirty-three Forty and six Forty-six Twenty and six 37 Twenty-six 40 Sixty and 29 Seventy and six two Sixty-six Seventy-two 44 Eighty and six 32 Eighty-six When writing numbers in words, children are expected to write in one way only. For example, 47 as either ‘forty and seven’ or ‘forty-seven’. 11

Counting in groups Count and write. Yash and Rama counted these sticks by two different methods. Like this : 1, 2, 3, 4, ........ 35. And like this : 3 tens and 5 units or singles. It is easier to count if we make groups of ten. Ahmed’s friends have some sticks. They have been counted by making groups of ten. Salma had 24 sticks Sharad had 45 sticks 2 T + 4 U = 24 T+ U= Let us also count the things shown below, in the same way. Tens + Units = Tens + Units = Tens + Units = 12

Number given in a picture See how the numbers given in the pictures have been written. Tens Units Tens Units Tens Units 12 28 47 Twelve Twenty Eight Forty Seven Look at the pictures and write the numbers in words as well as in numerals. Tens Units Tens Units Tens Units Write the proper number in the blank space. Tens Units Tens Units Tens Units Twenty Six 13

Think : * Look at the objects, count them and write their number in the circle below. Tens Units Tens Units Tens Units 34 * Read the numbers and show the same number of things. (strings of beads - singles, bundles of sticks - singles) 39 41 22 Tens Units Tens Units Tens Units Place value of the digits in a number. Thirty Seven To understand a two-digit number we look at how many bundles of ten there are in the tens place and how many units or singles there are. 37 For example, in 37 there are three bundles in the tens place 37 and 7 single sticks in the units place. 14

What is the meaning of ‘Place Value’? 35 50 3 Tens 5 Units 5 Tens 0 Units Thirty and Five / Thirty-five Fifty and zero / Fifty In the number 35, we have 3 in In the number 50, 5 is in the the tens place. If we open three tens place. When we open 5 tens bundles we get 30 units. tens bundles we get 50 units. That is why, the place value of Therefore, in the number 50, 3 in the number 35 is 30. As 5 the place value of 5 is 50. In is in the units place; its place the units place we have 0 value is 5. whose place value is also 0. Can you tell the value of each digit in the numbers shown below ? Units Tens Units Tens Units Tens Units 6 26 6 20 6 15

Tell the place value of each underlined digit. 18 The place value of 1 is 10 as 1 is in the tens place. 23 The place value of 3 is 3. as 3 is in the units place. 65 The place value of 5 is 5 as 5 is in the units place. 72 The place value of 7 is 70 as 7 is in the tens place. 50 The place value of 0 is ................. 40 The place value of 4 is ................. 88 The place value of 8 is ................. 88 The place value of 8 is ................. 61 The place value of 6 is ................. Now write the place value of each digit in the numbers given below. 22 38 41 60 95 20 2 16

The expanded form of a number The place value of 3 in the number 35 is 30. The place value of 5 is 5. Therefore the number 35 means 30 + 5. 30 + 5 is called the expanded form of 35. The expanded form of 94 is 90 + 4. The expanded form of 60 is 60 + 0. 35 24 73 49 40 9 30 5 20 4 70 3 Forty and nine Thirty and five Twenty and four Seventy and three 30 + 5 20 + 4 70 + 3 40 + 9 From the above, can you see that the expanded form of 35 is → 30 + 5 24 is → 20 + 4 73 is → 70 + 3 49 is → 40 + 9 Write the expanded forms of the following numbers. Number Number in words Expanded form 32 Thirty and two 30 + 2 10 ........ and ........ 64 ........ and ........ 17 ........ and ........ 17

A little bit of fun : Look at the chart you completed on page 9 and tell. • In the numbers from 10 to 100... → How many times do we see the digit 5 in the tens place? → Write those numbers in your notebook. • In the numbers from 10 to 99... → How many times do we see the digit 0 in the units place ? → Write those numbers in your notebook. Practice : • Write the place value of the underlined digit. 16 = ........ 77 = ........ 48 = ........ 82 = ........ 54 = ........ 91 = ........ • Write the number from its expanded form. 70 + 8 = 90 + 7 = 60 + 1 = 80 + 0 = • Fill in the blank spaces. 10 1 52 98 50 8 76 4 Tens 0 Units 87 7 Tens 7 Units 18

Let’s count numbers in steps • Look at the rabbit’s jumps. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Look at the numbers in boxes from which the rabbit jumped. 3 6 9 12 15 If we count 3 numbers after the number 3 we get the number 6. On counting 3 numbers after 6 we get 9. Here, by counting 3 forward every time, we get each next number. Starting from 3 and counting in steps of 3 the numbers we get are 6, 9, 12, 15. • Now look at the deer’s jumps. 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 Write the numbers from which the deer takes a jump. From 4 onwards, the numbers we get by counting in steps of 5 are 9, 14, 19, 24. Look at the numbers in the coloured boxes, given below. We get these numbers when we count in steps of a certain number. Which is that number? 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 Draw as large a grid as possible on the floor or ground and write numbers in it in serial order. Now conduct an activity in which you give any number and the children jump from one box to the next in steps of that number. 19

Fun with Addition 5 + 2 = 7 2 + 5 = 7 5 and 2 make 7 It means that together and so do 2 changing the and 5 together. What order does not a fun ! That’s nice ! change the sum. That’s right ! Now, to check this out, do the following additions. 4+1= 1 + 4 = 5+9= 9 + 5 = 3+7= 7 + 3 = 8+3= 3 + 8 = 8+4= 4 + 8 = 5+6= 6 + 5 = 0+3= 3 + 0 = 20

Addition-by counting forward Teacher : Salma, take these two seedlings and plant them in your garden. Salma : Sure, Ma’m, I already have 5 in my garden. Teacher : Now, children, how many plants will there be in Salma’s garden altogether ? How Rama counted How Yash counted 2 f inger s + 5 finge rs 5 fingers + 2 fingers Seven Seven (Rama counted 1, 2, 3... on her fingers from 1 to 7 while Yash counted only two fingers, forward from 5, that is 6, 7.) Teacher : Both got the same sum and both are right. But, whose addition was quicker? Yash : Mine ! Teacher : Suppose we put together 9 sticks and 3 sticks in order to add them. What answer would we get? Rama : The answer is 12. I counted from 1 to 12. + Teacher : But you get 12 even if you count 10, 11, 12 forward from 9. Here, knowing that we have 9 sticks, we counted serially only the extra sticks we got. Yash : Even if we have 3 sticks and get 9 new sticks and we count forward from 3, we get the same answer 12. However, it is easier to count 3 forward from 9 than to counting 9 forward from 3 ! Add by counting forward. 25 + 3, 5 + 38, 5 + 19, 4 + 23. 21

In the boxes given alongside, write the numbers from 1 to 50 in serial order. This is now your counting tape. Use it to carry out additions. In order to add 8 and 9, place your finger on the digit 8 and count 9 boxes forward from there. Did you reach the number 17 ? Thus, the sum of 8 and 9 is 17. • Add by counting forward. • Rama has 8 peanuts and Yash has 7. How many do they have together ? What is given ? Rama’s and Yash’s peanuts Rama’s peanuts What is asked ? Total peanuts + Yash’s peanuts What to do ? Addition Total peanuts • Anand has 27 stickers. He bought 5 more. How many stickers does Anand have now ? What is given ? What is asked ? + What to do ? • Add by counting forward. 2 54 41 12 15 6 + 5+ 4+ 3+ 8+ 9 27 + 8 = 8 + = 14 67 + 3 = + 9 = 16 54 + 9 = 49 + 2 = 22

Addition - Without carry over Revision : Addition of single-digit numbers. Units Units There are 4 units. We write them in the units place. 2 are also units. We 4 write them too in the units place. ++ On adding them we get 6 units. So 2 we write 6 in the units place. 6 5+3 6+2 5+4 4+4 3+6 Units Units Units Units Units Addition of two-digit numbers : 23 + 12 = ? Tens Units Tens Units 2 Tens 3 Units 2 3 + 1 Ten 2 Units + + 3 Tens 5 Units 12 35 + + Tens Units Tens Units Tens Units Tens Units Tens Units Tens Units Tens Units 23 24 12 47 +3 2 +3 +3 6 +4 1 55 27 48 88 23

• Carry out the following additions. TU TU TU TU TU 16 37 12 15 24 +2 3 +2 +1 3 +1 2 + 5 • Write ‘T’ for tens and ‘U’ for units and carry out the additions. TU 1 5 12 17 33 1 7 + 2 1 + 3 5 + 2 2 + 1 6 + 3 2 2 3 52 18 44 61 + + + + + 3 6 20 30 14 24 • Make your own examples of addition and solve them. + + + + + 24

Addition and subtraction of Zero Adding zero and subtracting zero. Three apples in one dish. None in the other. Only three apples in all. 3 + 0 = 3 Rama has 2 apples. Her little sister loves apples. So, she kept both for her. She did not eat any. 2 − 0 = 2 If zero is added to any number, we get the same number again. We get the same result when we subtract zero. Write the proper number in each empty box : 2 + 0 = 4 + 0 = 7 + 0 = 19 + 0 = 27 + 0 = 65 + 0 = 78 + 0 = 0 + 0 = 6 + = 6 3 − 0 = 5 − 0 = 8 − 0 = 11 − 0 = 55 − 0 = 19 − 0 = 23 − 0 = 82 − = 82 − 0 = 17 25

Stories of Addition - 1 • Manjyot planted 14 almond trees and 21 guava trees. How many trees did he plant altogether? What is given ? Almond and TU guava trees 1 4 Almond trees Guava trees What is asked ? Total trees + 2 1 What shall we do ? Add 3 5 Total trees • Ravi has 15 balloons and Neeta has 21. How many do they have together ? What is given ? + What is asked ? What shall we do ? Solve : • Dada had 15 rupees. His aunt gave him 20 more. How many rupees does he have now ? • There were 24 books in a cupboard and 12 more were placed in it. How many books are there in the cupboard now ? • There were 18 boxes in the house, mother bought 11 more boxes from the market. How many boxes are there altogether in the house now ? • Sajid has 24 eggs and Shabana has 32. How many eggs in all do they have ? • Maria collected 30 coins. Mihir has 24 coins. How many coins do they have altogether ? 26

Let’s reduce by subtraction 5 − 3 = Kshitij had 5 cups. He gave 3 cups to Aanchal. How many cups are left with Kshitij ? Units 5 Cups with Kshitij − 3 Cups given to Aanchal Cups left with Kshitij Subtraction by pairing off. • There are 8 paper lanterns and 4 lamps. How many more lanterns are there than the lamps ? 8 − 4 4 There are 4 more lanterns than there are lamps. • There are six slates and 11 books. By how many is the number of slates less than the number of books ? − There are fewer slates than there are books. • There are 8 strawberries and 6 pomegranates. How many more strawberries are there ? Let us subtract to find the answer. − 8 Hence, there are two more strawberries than pomegranates. 6 Or, there are 2 fewer pomegranates than strawberries. 2 27

Subtraction by counting backward Try playing the game given below. I have this chart. Let us place The one who has to 49 blocks on it. Pick off 5 or less pick up the last block, than 5 blocks at a time. You will loses the game. get one chance at a time, but you cannot pick off zero blocks. Rama started the game. Counting backward from 49 she picked up 4 blocks. 45 blocks are left. Now it is Yash’s turn to pick up blocks. Playing on like this, Yash picked up the last block. So, Rama won. At first Picked Remaining At first Picked Remaining there were off there were off 49 − 4 = 45 23 − 5 = 18 Rama Rama 45 − 5 = 40 18 − 5 = 13 Yash Yash 40 − 5 = 35 13 − 5 = 8 Rama Rama 35 − 4 = 31 8 − 4 =4 Yash Yash 31 − 3 = 28 4 − 3 =1 Rama Rama 28 − 5 = 23 1 − 1 =0 Yash Yash 28

Suresh and Ramesh decided to make Diwali greeting cards. They had to bring the required materials. Suresh had 9 rupees. Ramesh also brought some. Altogether they had 14 rupees. How many rupees did Ramesh bring ? Rama : So we must subtract 9 from 14. Yash : I drew 14 circles and crossed out 9. Circles left are 5. It means that Ramesh brought 5 rupees. Rama : I counted numbers forward from 9 up to 14. There were 5 numbers. My answer is 5 too. Discuss whose method is the easier one. We can use the number line to carry out a subtraction by counting either backward or forward. Let us see the subtraction 14 - 9. 9 + 5 = 14. Therefore, 14 - 9 = 5 0 1 2 3 4 5 6 7 8 9 10 111213 14 14 - 9 = 5 . 0 1 2 3 4 5 6 7 8 9 10 111213 14 In the first diagram above, there were 5 jumps towards the right from 9 to 14. In the second, 9 jumps were taken towards the left from 14, which stopped at 5. Both the methods give us the answer 5. Thus, subtraction can be done by both methods using the number line. Practise this by carrying out the following subtractions. (1) 12 - 8 = (2) 32 - 1 = (3) 15 - 10 = (4) 43 - 2 = (5) 13 - 11 = (6) 39 - 3 = (7) 20 - 18 = (8) 44 - 40 = (9) 11 - 2 = While carrying out the subtraction 43 - 2, which is easier ? Counting the jumps towards the right from 2 to 43, or counting two jumps towards the left from 43 ? While carrying out the subtraction 44 - 40, what is easier ? Counting 40 jumps towards the left of 44 or count jumps from 40 to 44 to the right ? 29

Addition and subtraction - a pair 10 + 12 = 22 22 - 10 = 12 22 – 12 = 10 From every example of 71 + 22 = 93 addition we can get two examples of subtraction. Check this for yourself. 93 - 71 = 22 93 - 22 = 71 But from 5 + 5 = 10, we get only one subtraction 10 - 5 = 5. Fill in the boxes. 12 87 + 12 = 99 99 − 12 = 87 99 − 87 = 12 99 87 50 34 + = = − = − 84 34 += − = − = 75 Make one example of your own, like the above, and solve it. += − = − = 30

• Vedashree read 9 pages of a book. How many more pages should she read to finish reading 15 pages? What is given ? Number of pages to be What should we do ? read, number of pages already read. Add or subtract ? I will subtract. I’ll I will count take away 9 from 15 from 9 forword and see how many upto 15 to get are left. the subtraction. 15 − 9 = 9 + = 15 Therefore, 15 - 9 = 6 • Hasan collected 30 seeds. Some of them are chikoo seeds and the remaining 22 are of custord apples. How many chikoo seeds are there? What is given ? What is asked ? − 22 = 22 + = 30 Therefore, - = Solve. = 17 therefore, − 9 = 8 and 17 − 8 = 8+ = 32 therefore, − 3 = 29 and 32 − 29 = = 49 therefore, − 7 = 42 and 49 − 42 = 29 + 42 + 31

A subtraction story • Vaishali had brought 54 beads. She had 21 beads left after making a string of beads. How many beads did she thread into the string? What is given ? Vaishali brought 54 beads and had 21 beads left. What is asked ? How many beads were threaded in the string ? What must be done ? Subtraction . Tens Units 5 4 beads brought − 2 1 beads left 3 3 beads threaded • Carry out subtraction by the above method. Tens Units Tens Units Tens Units Tens Units 27 37 68 98 −1 3 −2 5 −3 4 −4 0 • Anand read 28 story books. Sagar read 14. How many more books did Anand read than Sagar ? • Sudhir had 46 marbles. He lost 12 of them. How many does he still have ? • In a basket, there are 58 periwinkle (sadaphuli) flowers and 32 of hibiscus. (jasvanda) By how many are the hibiscus flowers less than the periwinkle flowers ? • There were 16 bananas in a basket. Manpreet added some bananas to the basket and then there were 29 bananas in it. How many bananas did Manpreet add ? 32

Twelve Months in a Year Months of the English Calendar Winter December January 31 days 31 days February November 30 days 28 Or 29 October 12 1 days 11 2 March 31 days 10 English Months 3 31 days September 9 (Gregorian Year) 4 April 30 days 8 5 30 days Summer 6 May August 7 31 days July 31 days 31 days June Rainy Season 30 days The year begins with the month of January and ends with December. • Name the months that have 30 days. • How many months of 31 days are there in the whole year ? • How many days does February have ? • Which month comes before June ? • Which is the month before January? Thirty days has September, April, June and November, All the rest have thirty-one, Except February alone. 33

Months of the Indian Calendar Vasant Shishir Phalgun Chaitra Magh Vaishakh 12 1 11 2 10 3 GrishmaPaushJyeshtha Hemant Agrahayan Indian Months Ashadh 94 85 76 Kartik Shravan Ashwin Bhadra Varsha Sharad The year begins with the month of Chaitra and ends with Phalgun. Observe the picture above and fill in the empty boxes. Season Vasant Grishma What are the names of the months on the coaches under the bridge ? Chaitra Vaishakh Bhadra Ashwin 34

A school calendar Rama : Yash, do you know Month - December which events will take place Sun 1 8 15 22 29 in our school in December? Yash : Yes, of course! Its given in our school calendar ! Mon 2 9 16 23 30 Rama : Ok, now tell me, on which day is the drawing competition? Tue 3 10 17 24 31 Yash : Rama : And the sports Wed 4 11 18 25 competition ? Christmas Yash : 5 12 19 26 It’s your turn now. Which Thu Sports festival do we celebrate on 25 competition December? Fri 6 13 20 27Sports Rama : Easy! It’s . Drawing Yash : Ok then, I’ll leave competition competition Sat 7 14 21 28 now. I have to get ready for Picnic the picnic tomorrow. Think : Can you give the date on which Rama andYash had this conversation? Activity : Take any calendar and tell : • What is special about the dates of any month, that fall on a Tues- day? • What is special about the dates of any month, that fall on a Friday? Think : • The date on a Wednesday of a month is 4. What is the date on the following Wednesday? 35

Part II Comparing numbers Comparing two numbers • Circle the smaller number in each box. 3, 8 1, 9 2, 20 • Circle the bigger number in each box. 4, 7 2, 7 8, 9 The symbols for ‘smaller than’ and ‘greater than.’ * The symbols ‘<’ stands for ‘smaller than’ and ‘>’ stands for ‘greater than.’ From the examples below, we shall see how they are used. 3 < 7 1 < 9 20 > 2 3 is less than 7. 1 is less than 9. 20 is greater than 2. 7 > 3 9 > 1 2 < 20 7 is greater than 3. 9 is greater than 1. 2 is less than 20 72 The crocodile is greedy. It eats the bigger number. * If we take any two 2-digit numbers how would we decide which one is the greater number? The number with the greater tens digit is the greater number. Yash : Let’s take 37 and 52. There are 3 tens in 37 and 5 tens in 52. Therefore, 52 > 37 as also 37 < 52. 36

Rama : Quite right ! When we count numbers on a measuring tape, 37 comes first and 52 comes later. The number that comes later is bigger. If both the numbers have the same digit in tens place, how do we decide? If the tens are equal, the digits in units' place will help. Yash : Let’s take 72 and 78. 2 < 8. So, 72 < 78. Let us expand numbers and verify the rules for comparing numbers. 43 and 28 In the number 43, the tens place 43 = 40 + 3 digit is 4 while 2 is the tens place digit in the number 28. 28 = 20 + 8 So, 43 > 28 31 and 33 In both numbers, the tens place digit 31 = 30 + 1 is 3, i.e. the tens digits are equal. However, 33 has 3 in the units place 33 = 30 + 3 and 31 has 1 in the units place. So, 31 < 33 Now, compare the numbers in each pair given below and insert the sign ‘<’ or ‘>’ between the two numbers. 43, 46 84, 86 67, 57 43 < 46 30, 50 13, 9 23, 32 Try this : Take 10 pairs of any numbers and compare the two numbers in each pair. 37

Neighbouring numbers on each side Here is how we get a number line. A mark is made for the number zero at the left side of a line. From there counting forward towards the right, the numbers 1, 2, 3, 4, ...... are marked, at equal distances. 0 1 2 3 4 5 6 7 Look at any part of this line. Let us take any number on this line, say 23. 22 23 24 25 26 27 The number before is 22 23 24 is the number after. What do we see ? For any number, the neighbour on the left is one less and the neighbour on the right is one more! In the empty boxes, write the number that comes immediately before and the one that comes immediately after. 54 79 40 37 62 99 50 78 32 39 30 68 38

Ascending and Descending order of numbers Let us see how to put the numbers 36, 23, 17 in ascending (increasing) order. First, let us compare the pairs (36, 23) (23,17) (36, 17) 36, 23, 17 • 23 < 36, 17 < 23 and 17 < 36. So 17 is the 17 smallest number. Cross 36, 23, 17 out 17 and write it on your slate. 17, 23 36, 23, 17 • Oftheremainingnumbers, 17, 23, 36 36, 23, 17 23 is the smaller number. So, we cross out 23 and write it after 17. • Now cross out the last number 36 and write it after 23. That is the ascending order of the numbers! Let’s write it like this 17 < 23 < 36 In the same way, put the three numbers in each set given below in ascending (increasing) order. (1) 25, 12, 54 (2) 67, 9, 32 (3) 44, 92, 30 39

Let us see how to put the numbers 36, 23, 48 in descending (decreasing) order. • Observe the numbers 36, 48 23 and 48 and find out the 36, 23, 48 greatest number. It is 48. Cross it out and write it on your slate. 48, 36 36, 23, 48 • Now, choose the bigger number from the two remaining numbers. Cross it out and write it after 48. 48, 36, 23 36, 23, 48 • Now cross out the last number left and write it at the end. That’s the descending order of the numbers! We can write it like this. 48 > 36 > 23 Put the given numbers in ascending and descending order. Number Ascending order Descending order 26, 19, 47 62, 85, 50 19 < 26 < 47 47 > 26 > 19 32, 9, 13 43, 76, 89, 60 43 < 60 < 76 < 89 89 > 76 > 60 > 43 15, 9, 75, 52 Teachers can make number cards of different numbers, give each child any 3 or 4 of them and tell them to put their set of numbers in ascending or descending order. 40

Come, let’s make numbers. Rama and Yash are playing the game of making numbers. Let’s join them. Some numbers are given in circles. Each child should choose two digits and make two numbers. Digits 7 , 8 Digits 1 , 3 Numbers , Digits 7 , 5 Numbers 75 , 57 Numbers 13 , 31 Digits , 1 7 5 Digits , Numbers , 6 3 8 Numbers , 4 9 2 Digits , Digits , Numbers , Numbers , Digits , Numbers , Activity : Cut out 5 or 6 discs from a thick paper. On each disc, write a non-zero number and place the discs with the number side down. Each child is to pick up any two discs and make two numbers from the digits seen on them. 41

# 2nd math english medium

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**Description: ** 2nd math english medium

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