MATHEMATICS TEXTBOOK – PART 2 1 Name: ___________________________________ Section: ________________ Roll No.: _________ School: __________________________________
Preface IMAX partners with schools, supporting them with learning materials and processes that are all crafted to work together as an interconnected system to drive learning. IMAX Program presents the latest version of this series – updated and revised after considering the perceptive feedback and comments shared by our experienced reviewers and users. This series endeavours to be faithful to the spirit of the prescribed board curriculum. Our books strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. The books are split into two parts to manage the bag weight. The larger aim of the curriculum regarding Mathematics teaching is to develop the abilities of a student to think and reason mathematically, pursue assumptions to their logical conclusion and handle abstraction. The Mathematics textbooks and workbooks offer the following features: Structured as per Bloom’s taxonomy to help organise the learning process according to the different levels involved Student engagement through simple, age-appropriate language S upported learning through visually appealing images, especially for grades 1 and 2 Increasing rigour in sub-questions for every question in order to scaffold learning for students W ord problems based on real-life scenarios, which help students to relate Mathematics to their everyday experiences Mental Maths to inculcate level-appropriate mental calculation skills S tepwise breakdown of solutions to provide an easier premise for learning of problem-solving skills Overall, the IMAX Mathematics textbooks, workbooks and teacher companion books aim to enhance logical reasoning and critical thinking skills that are at the heart of Mathematics teaching and learning. – The Authors
Textbook Features Let Us Learn About Think Contains the list of learning objectives Introduces the concept and to be covered in the chapter arouses curiosity among students Recall Discusses the prerequisite knowledge for the concept from the previous academic year/chapter/ concept/term Remembering and Understanding Explains the elements in detail that form the Application basis of the concept Ensures that students are engaged in learning throughout Connects the concept to real-life situations by enabling students to apply what has been learnt through the practice questions Higher Order Thinking Skills (H.O.T.S.) Encourages students to extend the concept learnt to advanced scenarios Drill Time Additional practice questions at the end of every chapter
Contents 1Class 5 Subtraction 5.1 Subtract 1-digit and 2-digit Numbers ��������������������������������������������������������������1 6 Time 6.1 Earlier and Later �����������������������������������������������������������������������������������������������10 6.2 Long and Short �������������������������������������������������������������������������������������������������15 7 Money 7.1 Identify Common Currency Notes and Coins�����������������������������������������������23 7.2 Put Together Small Amounts of Money����������������������������������������������������������28 8 Measurements 8.1 Measure Short Lengths Using Non-Standard Units����������������������������������������33 8.2 C ompare Heavy and Light Objects���������������������������������������������������������������39 9 Data Handling 9.1 Collect, Represent and Interpret Data�����������������������������������������������������������49
Chapter Subtraction 5 Let Us Learn About • different methods of subtracting numbers. • subtracting numbers up to 99 without regrouping. Concept 5.1: Subtract 1-digit and 2-digit Numbers Think Bantei has 44 toffees. He gave 11 toffees to his sister. Bantei wants to know how many toffees remain with him. How do you think Bantei can find that? Recall Look at the vegetables given. A few of the vegetables are cut in each question. Find the remaining number of vegetables. Vegetables Number a) 1
Vegetables Number b) c) d) & Remembering and Understanding There are 5 animals in a farm. 3 of them went away. We now count the number of animals left in the farm. 2
This count gives the remaining number of animals in the farm. Counting the number of objects remaining or leftover is called subtraction. The answer we get on subtracting is called the difference. Subtract, left, remain and difference are some words used in subtraction. We use the symbol ‘−’ (read as minus) for subtraction. Example 1: Count and write the correct number of people/objects. One is done for you. a) 5 32 b) Subtraction 3
c) Methods of subtraction: 1) Subtraction using fingers 2) Subtraction using the number line 3) Vertical or column subtraction Let us understand these methods. Subtraction using fingers We have already learnt to show numbers using our fingers. Let us learn to subtract one number from the other using fingers. 4
Example 2: Subtract using fingers. Solution: a) 2 from 6 b) 3 from 5 c) 7 from 9 a) S ubtracting 2 from 6 O pen 6 fingers on the two hands. Close two fingers. Count the open fingers on the hands. They are 4 in number. So, the difference of the given numbers is 4. That is, 6 – 2 = 4. b) 5 – 3 Open 5 fingers. Close 3 fingers. Count the open fingers. They are 2 in number. So, 5 – 3 = 2. c) 9 – 7 Open 9 fingers on the two hands. Close 7 fingers. Count the open fingers. So, 9 – 7 = 2. Subtraction using the number line A line marked with numbers is called a number line. We can use the number line to subtract numbers. Let us see an example. Example 3: Solve using the number line: a) 5 – 3 b) 6 – 1 c) 7 – 4 Solution: a) To find 5 – 3 using the number line, we start from 5. Subtraction 5
D raw an arrow from 0 to 5 as shown. This shows the first number. 5 T hen, move 3 steps to the left. Draw arrows for each step as shown. 5 The number at which we end the steps is 2. So, 5 – 3 = 2. b) 6 6 So, 6 – 1 = 5. 7 c) 7 So, 7 – 4 = 3. 6
Vertical or column subtraction We can subtract by writing the smaller number below the bigger one. This is called vertical subtraction or column subtraction. Let us see a few examples. Subtraction of 1-digit numbers Example 4: Subtract 5 from 9 by writing the numbers in columns. Solution: Write the given numbers under the ones place, as shown. o 9 –5 4 Subtraction of 2-digit numbers Example 5: Subtract 32 from 75 by writing the numbers in columns. Solution: Follow the steps to subtract. Step 1: Subtract the ones Step 2: Subtract the tens T O TO 75 75 –3 2 –3 2 3 43 TO Solve these TO 84 47 –4 1 TO –2 3 87 –4 2 Subtraction 7
Application We now know how to subtract numbers. Let us see a few real-life examples of subtraction of numbers. Example 6: 1 8 parrots were sitting on a tree. 8 of them flew away. How many Solution: parrots were left on the tree? T O Example 7: 1 8 Solution: W rite the numbers one below the other. Subtract – 8 the numbers and write the difference as shown. 1 0 So, 10 parrots were left on the tree. K rish picked 12 sticks and Sanjay picked 22 sticks. How many more sticks did Sanjay have than Krish? Write the numbers one below the other. Subtract TO the numbers and write the difference as shown. 22 So, Sanjay had 10 sticks more than Krish. –1 2 1 0 Higher Order Thinking Skills (H.O.T.S.) Let us see another example. Example 8: A nil has 8 stamps. He gave 4 stamps to Rita and 2 stamps to Solution: Mahesh. How many stamps are left with Anil? O 8 Stamps with Anil – 4 Stamps given to Rita 4 Stamps remaining with Anil O 4 Stamps remaining with Anil – 2 Stamps given to Mahesh 2 Stamps remaining with Anil So, 2 stamps are left with Anil. 8
Drill Time Concept 5.1: Subtract 1-digit and 2-digit Numbers 1) Subtract the numbers using the number line. a) 3 from 6 b) 7 from 9 c) 1 from 7 d) 2 from 4 e) 3 from 4 2) Subtract the numbers by vertical or column method. a) 2 from 5 b) 4 from 8 c) 41 from 42 d) 23 from 46 e) 20 from 40 3) Word problems a) P ercy had 36 pencils. He lost 4 of them. How many pencils are left with him? b) S ahil has 4 marbles. Vivek has 15 marbles. Who has fewer marbles and how many less? Subtraction 9
Chapter Time 6 Let Us Learn About • the terms ‘earlier’ and ‘later’, ‘shorter’. • parts of the day. • sequencing the events happening in a day. Concept 6.1: Earlier and Later Think Bantei went to a wild safari with his parents. He told his classmates the names of the animals he saw from the beginning to the end of his visit. Can you also describe events in a sequence? Recall We wake up when the sun rises. We get ready and go to school. We study and have lunch. After returning home, we play with our friends. After studying and completing homework, we have dinner and go to bed. 10
These are the series of events we do every day. Let us recall identifying the time when a few events happen. Tick the correct word. a) The Sun rises in the (morning/evening). b) We go to school in the (morning/evening). c) We play in the (morning/evening). d) The day is the hottest (in the morning/at noon). e) We have our lunch in the (afternoon/evening). f) When it is dark, it is (afternoon/night). & Remembering and Understanding We do different activities in a day. We wake up in the morning. Then, we brush our teeth. So, waking up comes earlier and brushing teeth later. In the same way, we go to school and then study. Time 11
So, going to school is done earlier and studying later. ‘Earlier’ or ‘Later’ are words used for events happening at different times. Example 1: Tick the activity which is done earlier in the given pairs of activities. One is done for you. a) b) c) d) e) 12
Example 2: Write ‘earlier’ and ‘later’ for the given pairs of activities. One is done for you. a) Earlier Later b) __________ __________ c) __________ __________ Parts of the day We know that the Sun rises only in the morning. It sets in the evening. It is right above our head at noon. Let us understand these parts with the help of a timeline. A timeline is a number line on which time is shown. 12 Mid 12 Mid Night Night 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 12 hours Mid-day 12 Hours Morning (Noon) Afternoon/Evening The time between 12 midnight and 12 noon is called morning. The time at 12 noon is called mid-day. The time between noon and 12 midnight is called afternoon/evening. Time 13
Application We have learnt the different parts of a day. The following table lists the activities done in a day. Activity Part of the day Waking up Early morning Brushing teeth Morning and at night Many activities with classmates Day (noon) Doing homework Evening Going to bed Night Complete this table of your activities: My activity Part of the day I take a bath and get dressed for school. I have my breakfast. I go to school. I have my lunch. I go to play with my friends. I have my dinner. We do our activities in a particular order or sequence. We wake up in the morning and brush our teeth. Then, take a shower, wear our clothes and then go to school. Example 3: Put the pictures in sequence by numbering them. One is done for you. a) 214 3 14
b) Higher Order Thinking Skills (H.O.T.S.) Read the question. Find the part of the day when the activities happened. Example 4: Answer these questions. a) R aju went to play after coming home from school. When did he go to play? b) How can we say whether it is morning or evening? c) Raju brushed his teeth and went to bed. When did he do this activity? d) When do we have our breakfast? Solution: a) in the evening b) by sunrise or sunset c) Raju brushed his teeth in the night before going to bed. d) in the morning Concept 6.2: Long and Short Think Bantei washed clothes in a washing machine daily. One day, there was no power. He spent more time washing clothes by hand. He wondered why it took more time for the same work. Time 15
Recall Recall that we do many activities during the day. We have learnt the concepts ‘earlier’ and ‘later’. Let us revise this concept. Tick the activity that is done earlier in each of the following. a) showering/brushing b) dinner/going to bed c) going to school/playing d) having breakfast/having lunch e) getting ready for school/waking up & Remembering and Understanding We observe that different activities take different amounts of time. For example, reading a page takes less time than writing a page. Example 5: T ick the activity which takes less time in the given pairs of activities. One is done for you. a) b) 16
c) d) Example 6: W hich one from the following pairs of activities takes more time? Circle the right one. a) eating/drinking water b) combing hair/showering c) drawing a house/colouring a house Solution: a) eating /drinking water b) combing hair/ showering c) drawing a house/ colouring a house Application Read some examples to find the time taken for different activities. Example 7: Observe the given pictures and fill in the blanks. One is done for you. a) W e do many activities during the day. (night/ day). Time 17
b) I spend more time ______________ (watching TV/ studying). c) I take more time while reading ___________(a page / a book). d) Travelling by _____________ (aeroplane / bus) takes less time. e) _ __________________ (Cooking /Eating) food takes more time. Example 8: Write ‘more/less’ in the blank according to the time taken by the activities. a) Watching a movie – ______________ time Watching a TV show – ____________ time b) Speaking – ____________ time Writing – ___________ time c) Wearing clothes – ___________ time Wearing shoes – ___________ time 18
Solution: a) Watching a movie – more time Watching a TV show – less time b) Speaking – less time Writing – more time c) Wearing clothes – more time Wearing shoes – less time Higher Order Thinking Skills (H.O.T.S.) Observe the class timetable given below. Does it look like the timetable of your class? English Hard Maths 1st Games EVS English Story English writing Lang Music EVS Library 1st Dance 1st EVS Music EVS Lang Lang A/V Dance English Library Hand Maths A/V Poetry Maths Writing PT Music Maths 1st A/V EVS Maths Karate 1st Lang Lang Maths Games Swim 1st Swim 1st EVS PT Draw Lang Lang Time 19
Now answer the following questions by looking at your class timetable. Example 9: Write answers in the space given. a) Which period is more in number on a Wednesday? b) How many days do you go to school in a week? Name them. c) Which day has more number of English periods? d) How many games periods are there in a week? Solution: a) ____________________ b) ____________________ c) ____________________ d) ____________________ Drill Time Concept 6.1: Earlier and Later 1) Tick the activity which comes later than the other in given pairs of activities. a) b) 20
c) d) 2) Arrange the activities from morning to evening by giving numbers in the boxes. Use 1 for the first activity done in the morning. Concept 6. 2: Long and Short 3) Tick ‘’ the activity that takes more time and cross ‘’ the activity that takes less time. a) Time 21
b) c) d) 22
Chapter Money 7 Let Us Learn About • different coins and notes of Indian currency. • adding small amounts of money. • guessing price of items. • adding rupee and paise. Concept 7.1: Identify Common Currency Notes and Coins Think Bantei saw different coins and notes in his mother’s purse. Have you also seen such coins and notes? Recall We use notes and coins to buy things. In olden days, people did not use money. They bought things they needed by giving things that were more with them. 23
But, the value of things exchanged was not the same. So, coins and notes were made. The early coins were made of metals such as bronze and silver. & Remembering and Understanding The money used in a country is called its currency. Different types of coins were used in the olden days as shown. The number on the coin or note is its value. The Indian currency is Rupee (`). We write 1 rupee as ` 1. The following are the different coins and notes we use. Coins ` 1 ` 2 ` 5 ` 10 Notes ` 10 ` 20 ` 50 ` 100 24
` 200 ` 500 ` 2000 Let us see a few examples of writing the value of a coin or a note. Example 1: Write the value of the given coin in figures and words. Solution: ` 5; Rupees five Example 2: Write the value of the given note in figures. Solution: ` 500 Application We use money to buy the things we need. The value of the goods is called their ‘Rate’ or ‘Price’. Let us see some examples where we use money. Example 3: Guess the price of these items and tick it. One is done for you. `5 ` 50 ` 3 ` 30 a) a pot b) a sharpener `1 ` 10 ` 2 ` 20 c) a chocolate bar d) a ball Money 25
Example 4: Observe the rate of each kind of fruit given beside it. Grapes Bananas Watermelon ` 60 ` 40 ` 60 Pear Apple ` 25 ` 40 Orange Blueberries Strawberry ` 40 ` 90 ` 10 Fill in the blanks with the rates of the fruits given. One is done for you. ` 40 26
Higher Order Thinking Skills (H.O.T.S.) Sometimes, we guess the money needed to buy the things we need. Let us see a few examples. Example 5: Mona has a note of ` 100 and a note of ` 50. She also has a note of ` 20. The box shows some objects with their rates. Write the names of the objects that Mona can buy for: a) ` 50 b) ` 20 c) ` 100 Item Price Item Price A pair of ` 20 A pair of ` 50 socks slippers A frock ` 80 A big colouring book ` 100 Money 27
Solution: Things that Mona could buy for a) ` 50: A pair of slippers b) ` 20: A pair of socks c) ` 100: A big colouring book Concept 7.2: Put Together Small Amounts of Money Think Bantei likes a sticker of Batman. He wants to buy it. It costs ` 7. How can Bantei pay for the sticker using different coins? Recall We have learnt about coins and currency notes. Identify the coins and notes. Write them in figures. a) b) _____________ _____________ c) d) _____________ _____________ e) __________________ 28
& Remembering and Understanding Money is written in rupees and paise, separated by a dot. We can take smaller amounts of money together to make a larger amount. Just as we add two numbers, we can add money too. Let us see some examples. Example 6: Nina has these coins. How much money does she have in all? Solution: To find the total money, we add all the money Nina has. Example 7: That is, ` 1 + ` 2 + ` 10 = ` 13 Ashok has three notes of ` 10 and 2 coins of ` 10. How much Solution: money does he have in all? Ashok has the following amount: ` 10 + ` 10 + ` 10 + ` 10 + ` 10 = ` 50 So, Ashok has ` 50. Application Let us see a few examples involving addition of money. Example 8: C ircle the coins used to buy the given things. One is done for you. Money 29
Item Rate a) ` 15 b) ` 10 c) ` 25 d) ` 30 e) ` 50 30
Example 9: Arun and Beena have money as shown below. How much money does each of them have? Solution : Money Arun has = ` 1 + ` 2 + ` 5 + ` 10 = (` 1 + ` 2 + ` 5) + ` 10 = ` 8 + ` 10 = ` 18 Money Beena has = ` 5 + ` 1 + ` 2 + ` 50 = (` 5 + ` 1 + ` 2 + ` 50) = ` 58 Higher Order Thinking Skills (H.O.T.S.) We sometimes guess the money needed to buy things. It helps us to know whether we have enough money. Let us see an example. Example 10: Rita wants to buy a pencil for ` 3 and an eraser for ` 4. How much money should she have? Solution: Cost of a pencil = ` 3 Cost of an eraser = ` 4 Total money Rita should have to spend is less than ` 3 + ` 4 = ` 7 Therefore, Rita should have at least ` 7. Money 31
Drill Time Concept 7.1: Identify Common Currency Notes and Coins 1) How are the following currencies written in figures? a) 500 rupees b) 10 rupees c) 2000 rupees d) e) Concept 7.2: Put Together Small Amounts of Money 2) What is the total amount in each of the following? a) ` 1 + ` 2 + ` 5 + ` 10 b) ` 2 + ` 10 + ` 20 + ` 50 c) + + + + d) e) ` 10 + ` 50 + ` 1 3) Word problem a) P ayal wants to buy a notebook for ` 5 and a pencil for ` 4. How much money should she have? 32
Chapter Measurements 8 Let Us Learn About • measuring short lengths using hand span, cubit, foot and pace. • identifying heavier and lighter objects. • comparing weights using scale. Concept 8.1: Measure Short Lengths Using Non-Standard Units Think Bantei collected paper ribbons from his school. He placed them one above the other. But he did not know which ribbon was the smallest. Do you know to arrange ribbons in the order of their lengths? Recall We have learnt to compare the: • short distances between objects. • lengths of objects. • heavy and light objects. • heights of objects. 33
L et us recall them. Short Tick as directed. One is done for you. Low Tall High Near Far 34
Thin Thick Marker Heavy Light & Remembering and Understanding In olden days, people measured lengths and distances using: Hand span Cubit Foot Pace Hand span, cubit, foot and pace are called non-standard units of measurement. To measure length, we use one of these methods Read a few examples of measurement of length. Example 1: Measure the following objects with the given hand span. Note down your answer. One is done for you. Measurements 35
Object Measuring the length of the Number of object hand spans 3 Example 2: Measure these objects with the given cubit. Write down your answer. One is done for you. Object Measuring the length Number of cubits 3 36
Object Measuring the length Number of cubits Application Read a few real-life examples which involve measuring the lengths of some objects. Example 3: Measure the lengths of the objects as directed. Write the values in the table after measuring. Object Measure a) Length of a textbook Measured using Length of a TV stand hand span Length of a window Measurements 37
Object Measure b) Length of a table Height of a table Measured using Edge of a chair cubit Length of a rack c) Length of a mat Measured using Width of a mat a foot Length of a blanket Width of a blanket Measured using d) Length of your pace classroom Width of your classroom Higher Order Thinking Skills (H.O.T.S.) Estimation of lengths and distances Sometimes, we need not know the exact length of an object. A value closer to the actual value will be enough. In such cases, we guess the lengths and distances. To guess the values is called estimation. Let us now understand estimation of lengths. Example 4: Estimate the lengths using your hands and feet. Write the values in a table. Check if your guess is close to the actual measure. Object Estimate Actual length Maths textbook Lunch box 38
Object Estimate Actual length Water bottle Desk Duster Friend’s height Distance between the door of my classroom to the door of the next classroom Length of the school corridor Concept 8.2: Compare Heavy and Light Objects Think Bantei went to the supermarket with his father. His father bought some fruits and vegetables. He gave Bantei two small packets to hold. Bantei felt that holding one of the packets was easier than the other. Why was it so? Recall We can compare heavy objects with the light ones. Let us recall the same through some examples. Tick as directed. a) Lightest: Measurements 39
b) Heavier: c) Heaviest: d) Lighter: & Remembering and Understanding We can guess the weight of objects and compare them. Let us understand through some examples. Objects that weigh more are heavier and those which weigh less are lighter. Example 5: Look at these objects. Write 5 for the lightest and 1 for the heaviest. 40
Solution: 23145 Example 6: Compare the following objects. Write numbers 1, 2, 3, 4 and 5 in the boxes below them. Write 1 for the lightest and 5 for the heaviest. One is been done for you. a) 1325 4 b) c) d) Measurements 41
e) Application We compare the weights of objects using a simple balance. The pan of the simple balance with the heavier object goes down. The pans are balanced if the objects on them are of the same weight. An orange is heavier A watermelon is lighter Both the bottles are of than a banana. than 4 footballs. the same weight. Example 7: Look at the objects on the simple balance. Tick the heavier object and cross the lighter one. One is done for you. Simple balance Objects 42
Simple balance Objects Measurements 43
Example 8: C ompare the weights of these objects. One is done for you. a) __1___ = __3___ b) _____ = _____ c) _____ = _____ d) _____ = _____ 44
e) _____ = _____ Higher Order Thinking Skills (H.O.T.S.) Look at these containers of different sizes. They have different heights and weights. They hold different amounts of water, milk or oil. A bigger container can hold more water than a smaller one. Example 9: Tick the object that can hold more water. One is done for you. a) Measurements 45
b) c) Drill Time Concept 8.1: Measure Short Lengths Using Non-Standard Units 1) Long and short Look at the picture given and answer the following questions. (A) (B) (C) a) Which pencil is the longest? b) Which pencil is the shortest? c) Which pencil is of medium length? 46
Search
