by classklap MATHEMATICS TEXTBOOK - PART 2 Class 2 Name: ___________________________________ Section: ________________ Roll No.: _________ School: __________________________________ NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 1 12/19/2018 11:11:40 AM
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 presents the latest version of the Passport series – updated and revised after considering the perceptive feedback and comments shared by our experienced reviewers and users. Designed specifically for CBSE schools, the Passport series endeavours to be faithful to the spirit of the National Curriculum Framework (NCF) 2005. Therefore, 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 aim of the NCF 2005 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 Passport Mathematics textbooks and workbooks for CBSE schools offer the following features: Structured as per Bloom’s taxonomy to help organise the learning process according to the different levels involved S tudent 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 Word 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 Stepwise breakdown of solutions to provide an easier premise for learning of problem-solving skills Overall, the IMAX Passport 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 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 2 12/19/2018 11:11:40 AM
I Will Learn About I Recall Contains the list of learning objectives to be covered in the Discusses the prerequisite chapter knowledge for the concept from the previous academic I Think year/chapter/concept/term Introduces the concept and arouses curiosity among students I Remember and Understand Train My Brain Explains the elements in detail that Checks for learning to gauge the form the basis of the concept Ensures understanding level of students, that students are engaged in learning testing both skill and knowledge throughout Pin-up Note Contains key retention points concerning the concept I Apply I Explore (H.O.T.S.) Connects the concept to Encourages students to extend real-life situations by enabling the concept learnt to advanced students to apply what has been scenarios learnt through the practice questions Connect the Dots Maths Munchies A multidisciplinary section that Aims at improving speed of connects a particular topic to calculation and problem solving other subjects in order to enable with interesting facts, tips or tricks students to relate better to it Drill Time A Note to Parent Additional practice questions at Engages a parent in the the end of every chapter out-of-classroom learning of their child and conducting activities to reinforce the learnt concepts NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 3 12/19/2018 11:11:40 AM
Contents Class 2 6 Time 6.1 Days of a Week and Months of a Year........................................................ 1 6.2 Sequence the Events Over Longer Periods................................................. 7 7 Money 77.1 Add and Subtract Money without Conversion......................................... 16 08 Multiplication 1 +8.1 Concept of Repeated Addition................................................................. 23 3 -8.2 Skip Counting............................................................................................... 27 9456 x9 Measurements 8 29.1 Measure Lengths Using Standard Units...................................................... 40 9.2 Compare Objects Using a Simple Balance.............................................. 47 9.3 Compare Containers for Capacities......................................................... 52 10 Data Handling 10.1 Pictographs.................................................................................................. 60 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 4 12/19/2018 11:11:41 AM
Chapter Time 6 I Will Learn About • days of the week and months of the year. • the terms ‘decade’ and ‘century’. • features of a calendar. • seasons in a year. • sequence of events occurring over long periods. • reading and writing time. Concept 6.1: Days of a Week and Months of a Year I Think On 18th February, David’s mother planned to take the family on a picnic. They planned to go after the 2nd week of the next month. David wanted to know the exact date of the picnic. Do you know how David would know the exact date? 6.1 I Recall We do many activities throughout the day. Each activity takes some time to complete. Some events finish soon, while the others take more time. NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 5 1 12/19/2018 11:11:41 AM
Tick the activity that takes more time in each of the following pairs. a) b) c) 6.1 I Remember and Understand 10 years make a decade. We see the days and months of a year in a calendar. 100 years make a Observe the given calendar. The days of the week in century. your class timetable can also be seen in this calendar. But it has another day which is not there in your class timetable. Do you know which day it is? 2 12/19/2018 11:11:41 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 6
Calendar of 2019 January Sat February Sat March Sat Sun Mon Tue Wed Thu Fri 5 Sun Mon Tue Wed Thu Fri 2 Sun Mon Tue Wed Thu Fri 2 12 9 31 1 9 1234 19 1 16 345678 16 6 7 8 9 10 11 26 345678 23 10 11 12 13 14 15 23 13 14 15 16 17 18 10 11 12 13 14 15 17 18 19 20 21 22 30 20 21 22 23 24 25 17 18 19 20 21 22 24 25 26 27 28 29 27 28 29 30 31 24 25 26 27 28 April Sat May Sat June Sat Sun Mon Tue Wed Thu Fri 6 Sun Mon Tue Wed Thu Fri 4 Sun Mon Tue Wed Thu Fri 1 13 11 30 8 12345 20 123 18 234567 15 7 8 9 10 11 12 27 5 6 7 8 9 10 25 9 10 11 12 13 14 22 14 15 16 17 18 19 12 13 14 15 16 17 16 17 18 19 20 21 29 21 22 23 24 25 26 19 20 21 22 23 24 23 24 25 26 27 28 28 29 30 26 27 28 29 30 31 july Sat august Sat september Sat Sun Mon Tue Wed Thu Fri 6 Sun Mon Tue Wed Thu Fri 3 Sun Mon Tue Wed Thu Fri 7 13 10 123456 14 12345 20 12 17 8 9 10 11 12 13 21 7 8 9 10 11 12 27 456789 24 15 16 17 18 19 20 28 14 15 16 17 18 19 11 12 13 14 15 16 31 22 23 24 25 26 27 21 22 23 24 25 26 18 19 20 21 22 23 29 30 28 29 30 31 25 26 27 28 29 30 October Sat November Sat December Sat Sun Mon Tue Wed Thu Fri 5 Sun Mon Tue Wed Thu Fri 2 Sun Mon Tue Wed Thu Fri 7 12 9 123456 14 1234 19 1 16 8 9 10 11 12 13 21 6 7 8 9 10 11 26 345678 23 15 16 17 18 19 20 28 13 14 15 16 17 18 10 11 12 13 14 15 30 22 23 24 25 26 27 20 21 22 23 24 25 17 18 19 20 21 22 29 30 31 27 28 29 30 31 24 25 26 27 28 29 The following are the features of a calendar: • Calendar is another way of reading time. • It shows time in days, weeks and months. • Days are given column-wise and dates are given row-wise. • Some calendars show days row-wise and dates column-wise. Time 3 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 7 12/19/2018 11:11:41 AM
• Some days are marked in red. These indicate holidays or special days. • In some calendars, special days are also written below the date. Week • There are seven days in a week. • The days of the week are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday. Month • A month has 30 or 31 days. • February is the 2nd month in a year. It has 28 or 29 days. • There are four full weeks in a month. Year A year has 12 months. They are January, February, March, April, May, June, July, August, September, October, November and December. Using a calendar, we can know the day and the date. Let us now learn to read a calendar. 4 12/19/2018 11:11:41 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 8
Example 1: Read the calendar of 2019 carefully. Answer the following questions. a) On which day does 15th August fall? b) How many Sundays are there in the month of June? c) How many weeks are there in February? Solution: a) 15th August is on a Thursday. b) The month of June has five Sundays. c) There are four weeks in February. Example 2: Read the calendar of 2019 and answer the following questions. a) 8th December is Sunday. When is the next Sunday? b) Name the 3rd month of the year. c) Name the 11th month of the year. Solution: a) There are seven days in a week. So, we add 7 to the given date to get the same day in the next week. 8 + 7 = 15. So, the next Sunday is 16th December. b) March is the 3rd month of the year. c) November is the 11th month of the year. Train My Brain Fill in the blanks. a) 7 days make a ________________. b) 12 months make a _____________. c) ________________ is the 2nd month of a year. 6.1 I Apply The Earth moves around the Sun. It takes around 365 days and 6 hours for one round. Time 5 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 9 12/19/2018 11:11:41 AM
Seasons are caused due to the Earth’s movement Summer around the Sun. The three main seasons in a year are: • Summer • Rainy • Winter Winter Rainy These three seasons are spread over the 12 months of a year. In India, the seasons and the months in which they fall are as follows: Summer Rainy Winter later days of February later days of June later days of October March July November April August December May September January earlier days of June earlier days of October earlier days of February Example 3: Answer these questions: a) Which season comes before winter? b) Which season falls between winter and rainy? c) Which season is it during August? Solution: a) Rainy season b) Summer season c) Rainy season Example 4: Answer the following questions: a) Which months fall under the rainy season? b) Which season is it in January? c) In which season does the Sun shine brightly? Solution: a) mid-June, July, August, September and mid-October b) Winter season c) Summer season 6 12/19/2018 11:11:41 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 10
6.1 I Explore (H.O.T.S.) Read the following examples. Example 5: If today is 9th May and it is summer now, what season was it four months ago? Solution: Winter season (because four months ago it was January). Example 6: If it is rainy now, what season will it be twelve months from now? Solution: Rainy season Concept 6.2: Sequence the Events Over Longer Periods I Think David now knows in which part of the day he does different activities. He wants to narrate the activities one after the other along with the time. Do you also want to narrate your daily activities in the same way? 6.2 I Recall When the Sun rises, we know that it is morning. The Sun is right above us at noon. After school, we play with our friends in the evening. We have dinner and go to sleep at night. Let us recall the events in a day. a) Stars twinkle ________ (at noon/at night). b) My father goes for a __________ (morning/noon) walk. c) The paper boy gets newspaper in the (morning/night). d) Boating is done during the _____________ (day-time/night-time). e) I went to the zoo during the ___________ (day-time/night-time). Time 7 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 11 12/19/2018 11:11:41 AM
6.2 I Remember and Understand We use a clock to find time. Numbers from 1 to 12 are written on the face of the clock. Minute Hand For every one complete Hour Hand round of the minute hand, the hour hand moves forward to the next number. This means that one hour is completed. The clock has two hands: 1) the short hand, known as the ‘hour hand’, and 2) the long hand, called the ‘minute hand’. Reading time When the minute hand points to 12 and the hour hand to any one of the numbers, we read it as the time at that hour. When the hour hand is on 3 and the minute hand on 12, we say it is 3 o’clock. Example 7: Read the time shown on these clocks. a) b) Solution: We can read the time as: 8 12/19/2018 11:11:41 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 12
The minute hand is on 12 and the hour hand is on 5. The time is 5 o’clock. a) The minute hand is on 12 and the hour hand is on 8. The time is 8 o’clock. b) Example 8: Read the time on these clocks and mention where the hour and the minute hands are. a) b) Solution: We can read the time as: The minute hand is on 12 and the hour hand is on 10. The time is 10 o’clock. a) The minute hand is on 12 and the hour hand is on 11. The time is 11 o’clock. b) Time 9 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 13 12/19/2018 11:11:41 AM
Train My Brain Read the time shown on these clocks. a) b) c) 6.2 I Apply We have learnt to read time from the clock. Let us now write activities in a sequence. Example 9: Arrange the following events according to the sequence in which they happen. a) Cutting woods at b) Packing bag at c) Hiking to reach the 5 o’clock in the 10 o’clock in the site at 12 o’clock evening morning in the noon d) c ooking food for dinner at e) building the camp at 7 o’clock in the night 2 o’clock in the afternoon Solution: Order in which the event happened is: b) c) e) a) d) 10 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 14 12/19/2018 11:11:41 AM
Example 10: Look at the clocks and write the time. Also arrange the events. One is done for you. a) I drink milk and have b) I eat my snacks and c) I watch TV at my breakfast at do homework at 8 _____ o’clock in the _____ o’clock at night. evening. f) I have my dinner at _____ o’clock in the morning. e) I reach school at d) I go to bed at _____ o’clock at night. _____ o’clock in the _____ o’clock at night. g) I go to play at morning. i) I come home from h) I have my lunch at school at _____ o’clock in the _____ o’clock in the _____ o’clock in the evening. afternoon. afternoon. Solution: a) e) h) i) b) g) c) f) d) 6.2 I Explore (H.O.T.S.) Let us learn to draw hands on the clock when time is given. Time 11 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 15 12/19/2018 11:11:41 AM
Example 11: Draw the hands of the clock to show the given time. One is done for you. Solution: We can draw the hands of the clock as: a) b) c) 2 o’clock 12 o’clock 10 o’clock d) e) f) 11 o’clock 4 o’clock 3 o’clock g) h) i) 5 o’clock 8 o’clock 9 o’clock Maths Munchies 213 Skip counting to tell the time To tell the minutes, we need to skip count by 5. Number on the 1 2 3 4 5 6 7 8 9 10 11 12 clock Number of 5 10 15 20 25 30 35 40 45 50 55 60 minutes 12 12/19/2018 11:11:41 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 16
Connect the Dots English Fun Let us read a funny poem on calendar. 30 days have September, April, June and November. All the rest have 31, Except for February alone, Which has 28 days clear, And 29 in a leap year. EVS Fun Go out and observe your shadow in the morning, noon and evening. Is there any change in the length of the shadow? Drill Time Concept 6.1: Days of a Week and Months of a Year 1) Name the seasons that fall in the following months. a) later days of October b) January c) April d) earlier days of June e) December Time 13 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 17 12/19/2018 11:11:41 AM
Drill Time 2) Read the calendar of February 2019 and answer the following. February Sun Mon Tue Wed Thu Fri Sat 12 3456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 a) How many days are there in the month of February? b) How many weeks does February 2019 have? c) If 20th February falls on a Monday, when is the next Monday? d) What is the date on the last day of the month? e) How many Saturdays are there in this month? Concept 6.2: Sequence the Events Over Longer Periods 3) Read the time shown by the clocks given below. a) b) c) d) e) f) 14 12/19/2018 11:11:41 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 18
Drill Time 4) Number the pictures in sequence in each of the following. Begin with 1 for the first activity. A Note to Parent Help your child make his or her own clock using a paper plate and straws of paper for arms. Explain how the arms of the clock move from 4 o’clock to 5 o’clock. Time 15 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 19 12/19/2018 11:11:41 AM
Chapter Money 7 I Will Learn About • a dding and subtracting amounts without conversion. • estimation of amounts. Concept 7.1: Add and Subtract Money without Conversion I Think David and his mother bought a few items from a shop. When David’s mother paid the bill, the shopkeeper gave her some change. David wondered why the shopkeeper gave his mother some money. Do you know why? 7.1 I Recall We add or subtract numbers by writing them one below the other. This method is called the column method. 16 12/19/2018 11:11:42 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 20
Solve the following to recall the addition and subtraction of numbers. T O T O T O T O 2 6 3 4 3 4 8 0 +1 1 +2 2 –1 3 –1 0 Let us revise the concept of addition of notes and coins. Complete the table with the number of notes and coins that will add up to the given value. One is done for you. ` 20 note ` 10 note ` 5 coin ` 2 coin ` 1 coin ` 47 2 11 ` 23 ` 35 ` 78 ` 99 7.1 I Remember and Understand In the column method, we write rupees under rupees. Then we write paise under paise, exactly one below the other. When paise Money is written in is not given, we put 00 in the paise column. Then we rupees and paise, add or subtract as usual. separated by a dot. Addition of money Let us understand adding amounts through an example. Example 1: Add: ` 45.50 and ` 32.20 Solution: Arrange rupees and paise in two columns. Steps Solved Solve these Step 1: Add the paise. `p `p Write the sum in the paise 45 . 50 11 . 11 column. +32 . 20 +22 . 22 70 Money 17 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 21 12/19/2018 11:11:42 AM
Steps Solved Solve these Step 2: Add the rupees. `p `p Write the sum in the 45 . 50 20 . 19 rupees column. +32 . 20 +32 . 20 77 . 70 Subtraction of money Let us understand subtracting amounts through an example. Example 2: Subtract: ` 25.40 from ` 75.60 Solution: Arrange rupees and paise in two columns as shown. Write the larger amount above the smaller amount. Steps Solved Solve these `p Step 1: Subtract the paise. `p Write the difference in the 75 . 60 45 . 45 paise column. –25 . 40 –12 . 12 Step 2: Subtract the rupees. 20 `p Write the difference in the 98 . 43 rupees column. `p –46 . 22 75 . 60 –25 . 40 50 . 20 Train My Brain Solve the following: b) ` 21.25 + ` 42.23 c) ` 76.24 – ` 12.10 a) ` 34.33 – ` 24.22 7.1 I Apply Let us see some real-life examples of addition and subtraction of money. 18 12/19/2018 11:11:42 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 22
Example 3: Five bananas cost ` 20 and two pencils cost ` 12. What is their Solution: total cost? ` Cost of five bananas = ` 20 20 Cost of two pencils = ` 12 +12 Their sum = ` 20 + ` 12 = ` 32 32 So, the total cost of bananas and pencils is ` 32. Example 4: Veer bought a ball for ` 10 and gave the shopkeeper ` 20. How much change did the shopkeeper give Veer? Solution: The amount Veer paid the shopkeeper = ` 20 ` Cost of a ball = ` 10 20 Difference in the amounts = ` 20 – ` 10 = ` 10 –10 So, the shopkeeper gave back ` 10. 10 7.1 I Explore (H.O.T.S.) Read a few examples of addition and subtraction of money. Example 5: Vani has ` 500. How many of the given items can she buy? Write any four combinations. Bucket Bag of rice Fruit basket Toy robot Clock ` 100 ` 250 ` 150 ` 350 ` 200 Solution: The total cost of the items that Vani can buy must be less than or equal to ` 500. A few of the possible combinations are: Money 19 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 23 12/19/2018 11:11:42 AM
a) Combination 1 b) Combination 2 ` 100 ` 250 ` 150 ` 100 ` 350 c) Combination 3 d) Combination 4 ` 150 ` 350 ` 250 ` 200 Maths Munchies 213 Presently we have 2000, 500, 100, 50, 10 and 5 rupee notes. The new ` 2000 and ` 500 notes were introduced in November 2016. They look like the images given here. The old ` 500 notes and ` 1000 notes looked like the images given here. These notes are no longer used. 20 12/19/2018 11:11:42 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 24
Connect the Dots EVS Fun Have you seen ATMs in your city or town? ATM stands for ‘Automated Teller Machine’. Every bank has its own ATM. Most ATMs work for 24 hours. We can go there at any time and get money! English Fun Think of at least three rhyming words for ‘money’. Drill Time Concept 7.1: Add and Subtract Money without Conversion 1) Add: b) ` 35.88 + ` 12.11 c) ` 46.37 + ` 10.10 a) ` 27.17 + ` 12.12 e) ` 11.11 + ` 22.22 d) ` 87.22 + ` 12.77 2) Subtract: b) ` 45.23 – ` 11.13 c) ` 76.43 – ` 15.20 a) ` 99.99 – ` 11.11 e) ` 65.65 – ` 35.35 d) ` 39.28 – ` 27.10 3) Word problems a) Abdul has ` 52 and Shama has ` 15.00. How much money do they have in all? b) Sam bought chocolates for ` 41.00. Rehan bought some chocolates for ` 24. How much amount did they spend in all? Money 21 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 25 12/19/2018 11:11:42 AM
A Note to Parent Take your child for grocery shopping on weekends. Ask them to count the coins and notes before paying the shopkeeper. Such practical experiences will strengthen your child’s concepts in understanding money. 22 12/19/2018 11:11:42 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 26
Chapter Multiplication 8 I Will Learn About • repeated addition. • skip counting. • multiplication tables from 2 to 6. Concept 8.1: Concept of Repeated Addition I Think David has five pet cats. He wants to know the number of legs they have altogether. How can David find that? 8.1 I Recall We already know how to add some objects by counting. Let us recall the same through the following exercise. NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 27 23 12/19/2018 11:11:42 AM
Count, add and write the number of objects. 12/19/2018 11:11:42 AM a) Number of honey bees = _____________ b) Number of trees = ___________ c) Number of birds = ___________ d) Number of windows = ___________ 24 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 28
8.1 I Remember and Understand In repeated addition, we put the objects Repeated addition is adding the same number into equal groups to repeatedly (again and again). find their total. Let us see a few examples. Example 1: Use repeated addition to find the total number of houses. Solution: Number of groups = 4 The number of objects in each group = 2 Total number of objects = 2 + 2 + 2 + 2 = 8 So, there are 8 houses in all. We read it as 4 groups of 2 is 8. Example 2: Count and add: Solution: Number of groups = 3 Number of equal number of objects in each group = 4 Total number of objects = 4 + 4 + 4 = 12 We read it as 3 groups of 4 is 12. Multiplication 25 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 29 12/19/2018 11:11:43 AM
Train My Brain Identify the number of groups. Write the number of items present in each group. a) b) c) 8.1 I Apply Let us now apply the concept of repeated addition. Example 3: Suresh has three pet dogs. How many legs do these dogs have altogether? Solution: Suresh has three pet dogs. So, the number of groups is 3. Each dog has 4 legs. So, the number of equal objects in each group is 4. 4 + 4 + 4 = 12 So, 3 groups of 4 is12. Therefore, the three dogs have 12 legs altogether. 26 12/19/2018 11:11:43 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 30
Example 4: A star has 5 corners. How many corners will such 4 stars have? Number of stars (groups) = 4 Solution: Number of corners (objects) in each star = 5 That is, 5 + 5 + 5 + 5 = 20. So, 4 groups of 5 is 20. So, 4 stars have 20 corners. 8.1 I Explore (H.O.T.S.) Let us see an example based on repeated addition. Example 5: Sudha wanted to buy beads to make necklaces for her daughter and for herself. To make a necklace, she needs at least 25 beads. How many beads are needed to make necklaces for both of them? Solution: Number of necklaces (groups) = 2 Number of beads (objects) = 25 That is, 25 + 25 = 50. So, 2 groups of 25 = 50. So, the total number of beads required to make two necklaces is 50. Concept 8.2: Skip Counting I Think While playing hopscotch, David knows to jump by skipping some of the boxes. Similarly, he can count numbers by skipping some of them. How could he do that? Multiplication 27 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 31 12/19/2018 11:11:43 AM
8.2 I Recall [] Recall the concept of repeated addition through these examples. Write the values of the following. a) 5 groups of 2 b) 3 groups of 9 [ ] c) 2 groups of 8 [] d) 6 groups of 1 [] Skip Counting is counting by a 8.2 I Remember and Understand number that is not 1. Skip Counting helps you • to count many things quickly. • to learn multiplication tables. 28 12/19/2018 11:11:43 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 32
Count by 2s In counting by 2s, we begin with the given number and count every alternate number. Example 6: Help the frog to find its way to the snail. You can do so using skip counting by 2. Write the numbers on which it jumps. One is done for you. a) b) c) Count by 3s In counting by 3s, we count every third number from the given number. Example 7: Begin with the given number and count by 3s. Write the numbers in the boxes given. One is done for you. a) Multiplication 29 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 33 12/19/2018 11:11:43 AM
b) c) We now know the concepts of repeated addition and skip counting. Let us now learn to construct the multiplication tables of numbers from 2 to 6. Observe the following figure. It is a group of 2 stars. So, we see that 1 group of 2 is 2. We write it as ‘2 × 1 = 2’ which means ‘2 times 1 is 2’. The symbol ‘×’ is used for multiplication. It is read as ‘times’. We read it as ‘2 ones are 2’. There are 2 groups with 2 stars in each. We write it as 2 + 2 = 4 and read it as 2 groups of 2 is 4. We can also write it as ‘2 × 2 = 4’ which means ‘2 times 2 is 4’. We read it as ‘2 twos are 4’. These are 3 groups with 2 stars in each. We write it as 2 + 2 + 2 = 6 and read it as 3 groups of 2 is 6. 30 12/19/2018 11:11:43 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 34
This can be written as ‘2 × 3 = 6’ which means ‘2 times 3 is 6’. We read it as ‘2 threes are 6’. In this way, we can form the multiplication table of 2. Forming the multiplication table of 2 2×1=2 1 + 1 2 times 1 is 2. 2×2=4 2 + 2 2 times 2 is 4. 2×3=6 3 + 3 2 times 3 is 6. 2×4=8 4 + 4 2 times 4 is 8. 2 × 5 = 10 5 + 5 2 times 5 is 10. 2 × 6 = 12 6 + 6 2 times 6 is 12. Multiplication 31 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 35 12/19/2018 11:11:43 AM
2 × 7 = 14 7 + 7 2 times 7 is 14. 2 × 8 = 16 8 + 8 2 times 8 is 16. 2 × 9 = 18 9 + 9 2 times 9 is 18. 2 × 10 = 20 10 + 10 2 times 10 is 20. The following are the multiplication tables of 3, 4, 5 and 6. Read them aloud. 3 4 5 6 3×1=3 4×1=4 5×1=5 6×1=6 3×2=6 4×2=8 5 × 2 = 10 6 × 2 = 12 3×3=9 4 × 3 = 12 5 × 3 = 15 6 × 3 = 18 3 × 4 = 12 4 × 4 = 16 5 × 4 = 20 6 × 4 = 24 3 × 5 = 15 4 × 5 = 20 5 × 5 = 25 6 × 5 = 30 3 × 6 = 18 4 × 6 = 24 5 × 6 = 30 6 × 6 = 36 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35 6 × 7 = 42 3 × 8 = 24 4 × 8 = 32 5 × 8 = 40 6 × 8 = 48 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 3 × 10 = 30 4 × 10 = 40 5 × 10 = 50 6 × 10 = 60 32 12/19/2018 11:11:43 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 36
Train My Brain Count and write the numbers in each of the following: a) Start from 20 and count by 4’s. b) Start from 35 and count by 5’s. 8.2 I Apply Let us solve some examples using the concept of skip counting. Example 8: Show the path the rabbit takes to reach the carrot by crossing the boxes using skip counting by 3. START 1 20 21 40 41 2 19 22 39 42 3 18 23 38 43 4 17 24 37 44 5 16 25 36 45 6 15 26 35 46 7 14 27 34 47 8 13 28 33 48 9 12 29 32 49 10 11 30 31 50 END Multiplication 33 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 37 12/19/2018 11:11:43 AM
Solution: START 1 20 21 40 41 2 19 22 39 42 3 18 23 38 43 END 4 17 24 37 44 5 16 25 36 45 6 15 26 35 46 7 14 27 34 47 8 13 28 33 48 9 12 29 32 49 10 11 30 31 50 Example 9: Radha counts the balloons using skip counting by 8. Write the numbers in the boxes. How many balloons are there altogether? Solution: 8 16 24 32 40 48 56 There are 56 balloons altogether. 34 12/19/2018 11:11:43 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 38
8.2 I Explore (H.O.T.S.) Let us see another example of skip counting. Example 10: Complete the wheel of skip counting by 3 and 5. Solution: We can skip count by 3 and 5. Maths Munchies 213 a) The product when any number is multiplied by zero is always zero. b) The product when any number is multiplied by one is always the number itself. Connect the Dots English Fun Read and make interesting poems as given here. One and two climb a tree. They find the number three. Three and eight got on the floor. Three times eight is twenty-four. Multiplication 35 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 39 12/19/2018 11:11:43 AM
EVS Fun 12/19/2018 11:11:43 AM Each tree has one big trunk that leads to different branches. These branches multiply to form many other branches. Thus, you can see a big tree growing with many branches. Drill Time Concept 8.1: Concept of Repeated Addition 1) Count and add: a) b) c) 36 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 40
Drill Time d) 2) Word problems a) Seeta observed that there were 4 cars parked in a row. How many wheels could she count on the cars? b) A farm had 6 hens. How many legs do they have in all? Concept 8.2: Skip Counting 3) Skip count and fill in the blanks. a) Skip count by 2 2 8 b) Skip count by 3 15 3 Multiplication 37 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 41 12/19/2018 11:11:43 AM
Drill Time c) Skip count by 4 4 24 d) Skip count by 5 5 45 4) Word problems a) Harry counts some flowers using skip counting by 5. How many flowers does he count altogether? b) Saket counts sheep using skip counting by 4. How many sheep does he count altogether? 38 12/19/2018 11:11:43 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 42
A Note to Parent Make your child practice multiplication tables regularly. Knowing tables by heart is important, as it allows children to do mental calculations faster. Multiplication 39 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 43 12/19/2018 11:11:43 AM
Chapter Measurements 9 I Will Learn About • m easuring lengths and distances using standard units. • c omparing weights of two or more objects. • using simple balance to compare weights. • o rdering containers based on their capacities. Concept 9.1: Measure Lengths Using Standard Units I Think David’s mother bought 3 cubits of garland. David observed that the same garland measured 5 cubits with his cubit. He wondered how he got more cubits than his mother. Do you know the reason for the difference? 9.1 I Recall Remember that the length of an object is the distance between its two ends. We can measure the lengths of long objects using some shorter objects. Also, we can measure objects using our hands, palm, foot and so on. 40 12/19/2018 11:11:43 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 44
hand span cubit foot pace For example, consider the following: a) 9 paper clips long b) 5 erasers long c) 12 hand spans long d) 4 crayons long 9.1 I Remember and Understand When different people measure an object using their body parts, they all get different lengths. The measures are different because the length of the body part is different for different people. Measurements 41 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 45 12/19/2018 11:11:43 AM
So, measures such as hand span, cubit, foot, leg span are called non-standard units. The standard unit of measurement of length is called metre. It is used to measure the length of a room, width of a room, height of a building and so on. We also use metre to measure the amount of cloth needed to make a dress. The unit ‘metre’ is written in short as ‘m’. To measure lengths smaller than a metre, we use another unit called the centimetre. Centimetre is used to measure a line, length of a ribbon and so on. We write ‘centimetre’ in short as ‘cm’. To measure lengths larger than a metre we Comparison use a larger unit called the ‘kilometre’. It is written in between units of short as ‘km’. It is used to measure the length of a length. road, the distance between two places, lengths of bridges, tunnels and so on. 1 km > 1 m > 1 cm Using these standard units, we can measure the lengths of objects accurately. Standard units give the same measure of the object anywhere in the world. The standard instruments used to measure length are a ruler (or a scale), a measuring tape and so on. A ruler is used to measure the length in centimetres and inches. A measuring tape is used to measure longer lengths in metres and kilometres. Measuring objects using a ruler A ruler is made of plastic or metal. It has two scales on both sides as shown below. On one side, there is a centimetre scale and on the other side is the inch scale. We measure lengths of small objects such as a chalk, duster, sketch pen, pencil, pencil box and so on using any of these scales. 42 12/19/2018 11:11:43 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 46
The distance between 0 and the number at the other end of the object on a ruler is the length of the object. To measure the length of an object using a ruler, follow these steps: Step 1: Keep one end of the object at the zero of the ruler. Step 2: Note the number on the ruler which is at the other end of the object. Step 3: Write the units beside the number noted in step 2. The number along with the unit denotes the length of the object. Observe the following: a) The distance between the two ends of the pencil is 6 cm. So, the pencil is 6 cm long. Similarly, b) The water bottle is 12 cm long. c) The cell phone is 9 cm long. Measurements 43 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 47 12/19/2018 11:11:43 AM
Let us consider a few examples. Example 1: Measure these objects and write their lengths with the correct unit. One is done for you. Example 2: Measure the length of these pictures using your own ruler. Note down their lengths. S. No. Picture Length a) b) c) d) e) 44 12/19/2018 11:11:43 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 48
Train My Brain Tick the unit we use to measure the following distances. Distance to be measured Units km mm cm m a) Distance between your house and school b) Distance between your desk and the blackboard c) Distance between your wrist and the tip of your middle finger 9.1 I Apply We measure longer objects in metres and distances in kilometres. Let us now learn how these units are related. On the centimetre ruler, we see that the distance between any two consecutive numbers is 1 cm. We see 10 equal divisions in a centimetre. Each of these divisions is called a ‘millimetre’, written in short as ‘mm’. Example 3: Tick the unit used to measure the lengths of the following. One is done for you. Object cm Units km Blue whale m Book Measurements 45 NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 49 12/19/2018 11:11:44 AM
Object cm Units km Toothbrush m Table Road Example 4: Tick the unit used to measure the following. One is done for you. Object Units mm cm m km Window Ribbon Rope Cloth 46 12/19/2018 11:11:44 AM NR_BGM_9789388700979 PASSPORT G02 MATHS TEXTBOOK PART 2_Text.pdf 50
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