Coral Gold Premium_G2_MATHS_TB_P2.pdf 1 8/10/2023 3:42:06 PM MATHEMATICS TEXTBOOK PART 2 Grade 2 Name: _________________________________________ Section: ________________ Roll No.: ______________ School: ________________________________________
TEXTBOOK FEATURES Art-Integrated Learning Collect 10 things from your home. Draw the outlines of their Lesson plans provided for art-integrated learning bases. Maths Lab Write the names of the objects. Also, write the names of the Activities that help students understand shapes of their bases. abstract concepts through concrete application Maths Munchies Student Reflection Aims at improving speed Captures student's perception of their of calculation and problem understanding of a lesson 9solving with interesting Write the numbers in the place value chart. facts, tips or tricks a) 51 b) 90 c) 16 Drill Time A number has 1 in the tens place and 4 in the ones place. What is the 8 Additional practice number? questions at the end of every concept Write the given digits in the place value chart as shown. T O I Explore 7 So, the number is 14. Encourages students to I Apply extend the concept to Connects the concept to real-life situations by enabling advanced scenarios using 6 students to apply what has higher order thinking skills been learned through practice questions Bantei has 44 toffees. He gave Anil has 8 stamps. He 11 toffees to his sister. Bantei gave 4 stamps to Rita and 2 stamps to Mahesh. wants to know how many How many stamps are left with Anil? patterns in shapes 2 toffees remain with him. How patterns in numbers do you think Bantei can find SKILL-BASED that? I Will Learn About I Think Indicates the learning Introduces the concept and 1outcomes to be covered in arouses curiosity among the chapter students Ascend_G2_Maths_TB2_V1.indb 2 04/08/2023 5:28:35 PM
EVS Fun Take your child to the shop when you go You have 28 milk teeth. If some of to buy groceries. Ask him or her to find them fall out, you can find the the amount you have to pay the remaining by subtraction. shopkeeper for the things you buy. Also, ask him or her to find the amount the Connect the Dots shopkeeper will return. This will improve his or her addition and subtraction skills. A multidisciplinary section to A Note to Parent 10 connect the lesson theme with other subjects Ideas to engage parents in out-of-classroom learning of 11their child to reinforce the concepts Write the number names of the following: Nina has these coins. How much money does she have in all? 1 ten and 4 ones =______________ To. find the total money, we add all the money Nina has. Train My Brain That is, `1 + `2 + `10 = `13 Checks for the acquisition of I Remember and Understand 5both skills and knowledge 4 Explains the fundamental through questions aspects of the concept in detail, and in an age-appropriate and engaging manner Let us recall the concept of INQUIRY-BASED position. Choose the correct word to fill the blanks. Concepts organised using a question-answer approach to foster a mindset of inquiry and b) The ball is ___________________ the box. reasoning (outside/inside) Reflection Time! I Recall Thought-provoking questions to encourage Activates the pre-requisite reflection on the concept and on how it is related to the student's life, experiences and 3knowledge needed for the the world around concept covered previously Ascend_G2_Maths_TB2_V1.indb 3 04/08/2023 5:28:36 PM
CONTENTS Theme 6) Time 01 06 Time 6.1) Days of the Week and Months in a Year Inquiry-Based 6.2) Sequence Events Over Longer Periods Inquiry-Based 7) Money 7.1) Add and Subtract Money without Conversion Art-Integrated Learning Skill-Based 12 Theme Money 8) Multiplication 19 8.1) Concept of Repeated Addition Skill-Based 25 Theme 8.2) Skip Counting Skill-Based Number Art-Integrated Learning Operations Ascend_G2_Maths_TB2_V1.indb 4 04/08/2023 5:28:42 PM
9) Division Readiness Skill-Based 35 Theme 9.1) Division as Number Equal Grouping Operations 10) Measurements 10.1) Measure Lengths Using Standard Units Art-Integrated Learning Inquiry-Based 43 47 Theme 10.2) Compare Weights Using 51 a Simple Balance Inquiry-Based Measurements 10.3) Compare Containers for Capacities Inquiry-Based 11) Data Handling Skill-Based 56 Theme 11.1) Pictographs 69 Data Handling Art-Integrated Learning Maths Lab Student Reflection 70 Ascend_G2_Maths_TB2_V1.indb 5 04/08/2023 5:28:47 PM
CLASSKLAP AND NCF 2023 Education plays a crucial role in shaping the future of our children and 251 empowering them to become well-rounded individuals. The National 4 3 Curriculum Framework (NCF) 2023, furthering the vision of the National Education Policy (NEP) 2020, focuses on fostering creativity, critical thinking, and problem-solving skills while also nurturing values of inclusivity, collaboration and democratic citizenship. The development of foundational literacy and numeracy is also a core goal of the NCF. ClassKlap by Eupheus partners with schools, supporting them through the steps of planning, teaching, learning, personal revision and assessment to equip students with the desired knowledge and skills relevant to the 21st century. The present series is a learning resource that not only meets the requirements of the NCF but also engages and captivates young minds. Here are some salient features of this series. NCF-aligned learning tool Description Skill-based lessons in textbook and workbook Lessons are structured as per Bloom’s Revised Taxonomy (Remember-Understand-Apply-Analyse-Evaluate-Create) and LSRW Inquiry-based lessons (Listening-Speaking-Reading-Writing) skills for English. in textbook and workbook Lessons are structured based on a Socratic approach using a question-answer format, aiming at discovery-based learning as per Highlight features NCF guidelines. Exploratory activities in the workbook facilitate holistic learning of the skills and concepts and foster a sense of curiosity and Practice Worksheets exploration among students. Features such as Poetry Appreciation, Maths Lab, Think Like a Scientist, Life Skills and others help learners engage in research, application-oriented learning and the development of scientific temper; Student Reflection sheets foster the skill of reflecting on one’s own learning progress. Practice Worksheets are aligned with the goals of sharpening critical thinking, evidence-based thinking and higher-order thinking skills, as per NCF guidelines. The books contain the following overarching features recommended in the NCF 2023: a logical and spiralling progression of frameworks adopted for Grammar, Maths and EVS inclusive representation of gender and diversity for the heterogeneous Indian classroom learner-centred content, vibrant illustrations, diagrams and photographs along with age-appropriate language a variety of question types with scaffolded and independent practice to meet the needs of different students We are confident that this series will serve as a valuable tool to accomplish the aims of the NCF 2023 and help transform teaching-learning in classrooms. We sincerely hope that our young learners develop genuine curiosity and love for learning. Ascend_G2_Maths_TB2_V1.indb 6 04/08/2023 5:28:51 PM
6 Time I Will Learn days of the week and months in a year About the terms ‘decade’ and ‘century’ features of a calendar seasons in a year sequence of events in a day 6.1: Days of the Week and Months in a Year We see the days and months of a year on a calendar. 10 years make a decade. Observe the calendar given on the next page. The days 100 years make of the week in your class timetable can also be seen on a century. this calendar. But it has another day which is not there on your timetable. Do you know which day it is? What are the features of a calendar? 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. 1 Ascend_G2_Maths_TB2_V1.indb 1 04/08/2023 5:28:53 PM
• Some calendars show days row-wise and dates column-wise. • Some days are marked in red. These indicate holidays or special days. • In some calendars, special days are also written below the date. For example, 26th January or 15th August would be circled in some calendars to show that these are national holidays. 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 What is a week? • There are seven days in a week. 2 Time Ascend_G2_Maths_TB2_V1.indb 2 04/08/2023 5:28:53 PM
• The days of the week are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday. What is a month? • A month has 30 or 31 days. • February is the 2nd month of a year. It is the only month in a year that has 28 or 29 days. • There are usually four full weeks in a month. What is a year? A year has 12 months. They are January, February, March, April, May, June, July, August, September, October, November and December. A year has 365 days. How do we read a calendar? Using a calendar, we can know the day of the week and the date. Let us now learn to read a calendar using an example. Let us take a look at the given calendar carefully. Can you find the day on which the 15th of August falls? It is a Monday. You can also see that January, May, July and October have five Sundays. Whereas, other months have four Sundays. Time 3 Ascend_G2_Maths_TB2_V1.indb 3 04/08/2023 5:29:01 PM
Now, read the calendar of this year and answer the following questions. a) When is the first Sunday of December? b) Name the 3rd month of the year. c) Name the 11th month of the year. The Earth moves around the Sun. It takes about 365 days and 6 hours for one round. During this period, the Earth goes through different seasons. What are seasons? Summer Seasons are caused due to the Earth’s movement around the Sun. The three main seasons in a year are: • Summer • Rainy • Winter These three seasons are spread over the 12 months Winter Rainy of a year. In India, the seasons and the months in which they fall are as follows: Summer Rainy Winter Late February Late June Late October March July November April August December May September January Early June Early October Early February Let us better understand seasons using some examples. Using the table above, we can tell which season comes before winter; it’s the rainy season. Can you tell which season occurs in the month of May? It’s the summer season. 4 Time Ascend_G2_Maths_TB2_V1.indb 4 04/08/2023 5:29:08 PM
Answer the following questions. a) Which months fall in the rainy season? b) What season do we experience in January? c) In which season does the Sun shine brightly? Reflection Time! 1) Every day, the teacher writes the date on the board. They also ask you to write it in your book and notebook, don’t they? Why do we write the date in our books and notebooks at school every day? 2) Have you ever used a calendar before? Can you think of any three reasons why we use a calendar in our daily lives? 3) When do you have your vacations at school? Mention the months and the season. Drill Time 6.1: Days of the Week and Months in a Year 1) Name the seasons that fall during the following months. a) late October b) January c) April d) early June e) December f) August 2) Read the given calendar of February and answer the following questions. 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 Time 5 Ascend_G2_Maths_TB2_V1.indb 5 04/08/2023 5:29:09 PM
Drill Time a) How many days are there in the month of February? b) How many weeks does February have in this calendar? c) If 18th 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? 6.2: Sequence Events Over Longer Periods We do many different things in a day such as waking up, getting ready, going to school and so on. Do you know that you can use a clock to know when to do what? How can we read time? We use a clock to tell time. Numbers from 1 to 12 are written on the face of the clock. Minute Hand With 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: ● the short hand is known as the hour hand ● the long hand is called the minute hand 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. For example, when the hour hand is at 3 and the minute hand is at 12, we say it is 3 o’clock. How do we tell the time by looking at the clock? Let us look at two examples. The clocks in the table show two different times of the day. Here is how we can read them and tell the time accurately. 6 Time Ascend_G2_Maths_TB2_V1.indb 6 04/08/2023 5:29:10 PM
a) The minute hand is at 12 and the hour hand is at 5. The time is 5 o’clock. b) The minute hand is at 12 and the hour hand is at 8. The time is 8 o’clock. Can you read the time on these clocks? Mention where the hour and the minute hands are. a) b) We have learnt to read the time from a clock. Now, can you arrange the following events in a sequence? a) Cutting wood at b) P acking bag at c) Hiking to reach the 5 o’clock in the 10 o’clock in the site at 12 o’clock in evening morning the noon Time 7 Ascend_G2_Maths_TB2_V1.indb 7 04/08/2023 5:29:17 PM
d) Cooking food for dinner at e) Building the camp at 2 o’clock 7 o’clock in the night in the afternoon The order in which the events happened is: b) c) e) a) d) Now, you try it yourself. Look at the clocks and write the time. Then, arrange the events. a) I drink milk and b) I eat snacks and c) I watch TV at have my breakfast at do homework at _____ o’clock in the _____ o’clock in the _____ o’clock at night. f) I have dinner at morning. evening. d) I go to bed at e) I reach school at _____ o’clock at _____ o’clock in the _____ o’clock at night. night. morning. g) I go to play at h) I have lunch at i) I come home from school at _____ o’clock in the _____ o’clock in the _____ o’clock in the afternoon. afternoon. evening. Time 8 04/08/2023 5:29:24 PM Ascend_G2_Maths_TB2_V1.indb 8
Reflection Time! 1) At what time does your school get over? Draw it on the clock by placing the hour hand and the minute hand on the correct numbers. 2) We have seen that a clock has an hour hand and a minute hand. But it also has a third hand. Do you know what the third hand in a clock denotes? Ask your parents or teachers to find out. Drill Time 6.2: Sequence Events Over Longer Periods 1) Read the time shown by the clocks given below. a) b) c) d) e) f) Time 9 Ascend_G2_Maths_TB2_V1.indb 9 04/08/2023 5:29:29 PM
Drill Time 2) Reorder the pictures in the correct sequence. Begin with 1 for the first activity. Maths Munchies 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 min- 5 10 15 20 25 30 35 40 45 50 55 60 utes 10 Time Ascend_G2_Maths_TB2_V1.indb 10 04/08/2023 5:29:43 PM
Connect the Dots English Fun Let us read a funny poem on calendar. 30 days make 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 on a sunny day and observe your shadow in the morning, noon and evening. Is there any change in the length of the shadow? 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 11 Ascend_G2_Maths_TB2_V1.indb 11 04/08/2023 5:29:45 PM
7 Money I Will Learn adding amounts without conversion About subtracting amounts without conversion 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. 12 04/08/2023 5:29:48 PM Ascend_G2_Maths_TB2_V1.indb 12
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 minimum 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 this Step 1: Add the paise. `p `p Write the sum in the paise 45 . 50 11 . 11 column. +32 . 20 +22 . 22 70 Money 13 Ascend_G2_Maths_TB2_V1.indb 13 04/08/2023 5:29:50 PM
Steps Solved Solve this 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 Step 1: Subtract the paise. `p `p Write the difference in the 75 . 60 45 . 45 paise column. –25 . 40 –12 . 12 20 Step 2: Subtract the rupees. `p `p Write the difference in the 75 . 60 98 . 43 rupees column. –25 . 40 –46 . 22 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. 14 Money Ascend_G2_Maths_TB2_V1.indb 14 04/08/2023 5:29:51 PM
Example 3: Five bananas cost `20 and two pencils cost ` 12. What is their total Solution: 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 return? Solution: The amount Veer gave 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 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. Money 15 Ascend_G2_Maths_TB2_V1.indb 15 04/08/2023 5:29:53 PM
A few of the possible combinations are: Combination 2 Combination 1 `100 `250 `150 `100 `350 Combination 3 Combination 4 `150 `350 `250 `200 Drill Time 7.1: Add and Subtract Money without Conversion 1) Add: a) `27.17 + `12.12 b) `35.88 + `12.11 c) `46.37 + `10.10 d) `87.22 + `12.77 e) `11.11 + `22.22 f) `64.35 + `32.41 2) Subtract: a) `99.99 – `11.11 b) `45.23 – `11.13 c) `76.43 – `15.20 d) `39.28 – `27.10 e) `65.65 – `35.35 f) `84.76 – `42.13 3) Word problems. a) Abdul has `52 and Shama has `15. How much money do they have in all? b) Sam bought chocolates for `41. Rehan bought some chocolates for `24. How much money did they spend in all? 16 Money Ascend_G2_Maths_TB2_V1.indb 16 04/08/2023 5:29:56 PM
Drill Time c) Ria has `42. Her mother gives her `13. How much money does she have in total? d) F our pens costs `20 and two erasers costs `10. What is their total cost? e) R ashi has `64. She gives her friend `20. How much money is left with Rashi? f) T ilak bought a notebook for `30 and gave the shopkeeper `50. How much change did the shopkeeper return? Maths Munchies Presently we have 500, 200, 100, 50, 20, and 10 rupee notes. The new `500 notes were introduced in November 2016 and `200 notes were introduced in August 2017. They look like this: The old `500 notes, `1000 notes and `2000 notes looked like this: These notes are no longer used. 17 Money 04/08/2023 5:30:00 PM Ascend_G2_Maths_TB2_V1.indb 17
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 to them at any time and get money! English Fun Think of at least three rhyming words for ‘money’. 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 about money. 18 Money Ascend_G2_Maths_TB2_V1.indb 18 04/08/2023 5:30:01 PM
8 Multiplication I Will Learn repeated addition About skip counting multiplication tables from 2 to 6 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 out the total number of legs? 8.1 I Recall 19 We already know how to add some objects by counting. Let us recall the same through the following exercise. 04/08/2023 5:30:03 PM Ascend_G2_Maths_TB2_V1.indb 19
Count, add and write the number of objects. Multiplication a) 04/08/2023 5:30:06 PM Number of honey bees = _____________ b) Number of trees = ___________ c) Number of birds = ___________ d) Number of windows = ___________ 20 Ascend_G2_Maths_TB2_V1.indb 20
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. 21 04/08/2023 5:30:08 PM Solution: Number of groups = 4 Number of equal 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 objects in each group = 4 Total number of objects = 4 + 4 + 4 = 12 We read it as, 3 groups of 4 is 12. Multiplication Ascend_G2_Maths_TB2_V1.indb 21
Train My Brain Identify the number of equal 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 3 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 is 12. Therefore, 3 dogs have 12 legs altogether. 22 Multiplication Ascend_G2_Maths_TB2_V1.indb 22 04/08/2023 5:30:43 PM
Example 4: A star has 5 corners. How many corners will 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 Let us see an example based on repeated addition. Example 5: Sudha wanted to buy beads to make necklaces for her daughter and herself. To make each necklace, she needs 25 beads. How many beads are needed to make necklaces for both of them? Solution: Number of necklaces (groups) = 2 Number of beads (objects) for each necklace (group) = 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. Drill Time 8.1: Concept of Repeated Addition 1) Count and add. a) Multiplication 23 Ascend_G2_Maths_TB2_V1.indb 23 04/08/2023 5:30:45 PM
Drill Time b) c) d) 2) Word problems. a) Seeta observed that there were 4 cars parked in a row. What was the total number of wheels that she could count? b) A farm has 6 hens. How many legs do these hens have in all? 24 Multiplication Ascend_G2_Maths_TB2_V1.indb 24 04/08/2023 5:31:03 PM
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? 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 [] 25 Multiplication 04/08/2023 5:31:07 PM Ascend_G2_Maths_TB2_V1.indb 25
8.2 I Remember and Understand Skip counting helps you Skip counting is • to count many things quickly. counting by a • to learn multiplication tables. number that is not 1. Count by 2s In counting by 2s, we begin with the given number and count every alternate number. Example 6: Help the frog find its way to the snail. You can do so using skip counting by 2. Write the numbers on which the frog jumps. One is already done for you. a) b) c) 26 Multiplication Ascend_G2_Maths_TB2_V1.indb 26 04/08/2023 5:31:10 PM
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 given boxes. One is done for you. a) 9 b) 16 c) 36 Multiplication Table 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. There are two groups of 1 star. So, we see that 2 groups of 1 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. 27 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’. 04/08/2023 5:31:11 PM We read it as, ‘2 twos are 4’ Multiplication Ascend_G2_Maths_TB2_V1.indb 27
These are 2 groups with 3 stars in each. We write it as, 3 + 3 = 6 and read it as, 2 groups of 3 is 6. This can also 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. 28 Multiplication Ascend_G2_Maths_TB2_V1.indb 28 04/08/2023 5:31:12 PM
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 Multiplication 29 Ascend_G2_Maths_TB2_V1.indb 29 04/08/2023 5:31:12 PM
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 30 Multiplication Ascend_G2_Maths_TB2_V1.indb 30 04/08/2023 5:31:13 PM
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. Multiplication 31 Ascend_G2_Maths_TB2_V1.indb 31 04/08/2023 5:31:17 PM
8.2 I Explore Let us see another example of skip counting. Example 10: Complete the wheel of skip counting by 3 and 5. Solution: Using skip counting by 3 and 5: Drill Time 8.2: Skip Counting 1) Skip count and fill in the blanks. a) Skip count by 2 2 8 b) Skip count by 3 15 3 32 Multiplication Ascend_G2_Maths_TB2_V1.indb 32 04/08/2023 5:31:18 PM
Drill Time c) Skip count by 4 4 24 d) Skip count by 5 5 45 2) Word problems. a) Harry counts the flowers below using skip counting by 5. How many flowers does he count altogether? b) Saket counts the sheep below using skip counting by 4. How many sheep does he count altogether? Multiplication 33 Ascend_G2_Maths_TB2_V1.indb 33 04/08/2023 5:31:24 PM
Maths Munchies a) The result when any number is multiplied by zero is always zero. b) The result when any number is multiplied by one is always the number itself. Connect the Dots English Fun Read and make interesting poems like the one 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. EVS Fun 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. A Note to Parent Make your child practice multiplication tables regularly. Knowing tables by heart is important, as it helps children to do mental calculations faster. 34 Multiplication Ascend_G2_Maths_TB2_V1.indb 34 04/08/2023 5:31:25 PM
9 Division Readiness I Will Learn equal grouping and sharing About repeated subtraction and division facts 9.1: Division as Equal Grouping I Think Farida and her brother Piyush got a chocolate bar with 14 pieces for Christmas. Piyush divided it and gave Farida 6 pieces. Do you think Farida got an equal share? How can we find out? 9.1 I Recall In the previous chapter, we have learnt multiplication. Multiplication is finding the total number of objects that have been grouped equally. Let us use this to distribute objects equally in groups. Consider 12 bars of chocolate. The different ways in which they can be distributed are(shown on the next page): Ascend_G2_Maths_TB2_V1.indb 35 35 04/08/2023 5:31:28 PM
Distributing in 1 group: 1 × 12 = 12 Distributing in 2 groups: 2 × 6 = 12 Distributing in 3 groups: 3 × 4 = 12 Distributing in 4 groups: 4 × 3 = 12 Distributing in 6 groups: 6 × 2 = 12 Distributing in 12 groups: 12 × 1 = 12 Distributing a given number of objects into equal groups is called division. We can understand division better by using equal sharing and equal grouping. 9.1 I Remember and Understand Equal sharing means having equal number of objects or things in a group. We use division to find the number of things in a group and the number of groups. 36 Divison Readiness Ascend_G2_Maths_TB2_V1.indb 36 04/08/2023 5:31:30 PM
Suppose 9 balloons are to be shared 1st round: 1 balloon is taken by each equally among 3 friends. Let us use friend. repeated subtraction to distribute the balloons. 9 – 3 = 6. So, 6 balloons remain. 2nd round: From the remaining 6 balloons, 3rd round: From the remaining 3 balloons, 1 more balloon is taken by each friend. 1 more balloon is taken by each friend. Now, each of them has 3 balloons. Now, each friend has 2 balloons. 3 – 3 = 0. So, 0 balloons remain. Each friend gets 3 balloons. 6 – 3 = 3. So, 3 balloons remain. We can write it as 9 divided by 3 equals 3. The symbol for ‘is divided by’ is ÷. 9 divided by 3 equals 3 is written as ↓ ↓ ↓ Total Number of Number of number of objects in each groups objects group Quotient Dividend Divisor Divison Readiness 37 Ascend_G2_Maths_TB2_V1.indb 37 04/08/2023 5:31:43 PM
In a division, the number that is divided is called the dividend. The number that divides is called the divisor. The answer is called the quotient. The number (part of the dividend) that remains is called the remainder. 9 ÷ 3 = 3 is called a division fact. In this, 9 is the dividend, 3 is the divisor and 3 is the quotient. Note: Representing the dividend, divisor and quotient using the symbols ÷ and = is called a division fact. We use multiplication tables to find the quotient in a division. We find the factor which when multiplied by the divisor gives the dividend. Let us understand this through a few examples. Example 1: 18 pens are to be shared equally by 3 children. How many pens does each of them get? Solution: Total number of pens = 18 Number of children = 3 Number of pens each child gets = 18 ÷ 3 = 6 (since 6 × 3 = 18) Therefore, each child gets 6 pens. Example 2: 10 flowers are put in some vases. If each vase has 2 flowers, how many vases are used? Solution: Number of flowers = 10 Number of flowers in each vase = 2 Number of vases used = 10 ÷ 2 = 5 (since 5 × 2 = 10) Therefore, 5 vases are used to put 10 flowers. 38 Divison Readiness Ascend_G2_Maths_TB2_V1.indb 38 04/08/2023 5:31:43 PM
We get two division facts from a multiplication fact. The divisor and the quotient are the factors of the dividend. Observe the following table: Dividend ÷ Divisor = Quotient Multiplicand × Multiplier = Product 6 × 3 = 18 18 ÷ 6 = 3 ↓↓ ↓ ↓↓ ↓ Divisor Quotient Dividend Product Factor Factor (Multiplicand) (Multiplier) From the multiplication fact 6 × 3 = 18, we can write two division facts: a) 18 ÷ 3 = 6 and b) 18 ÷ 6 = 3 Multiplication and division are reverse operations. Let us now understand this through an activity. We can show a multiplication fact on the number line. For example, 5 × 3 = 15 means 5 times 3 is 15. To show 5 times 3 on the number line, we take steps of 3 for 5 times. We go forward from 0 to 15. Similarly, we can show the division fact 15 ÷ 3 = 5 on the number line. To show 15 divided by 3 on the number line, we take steps of 3 for 5 times. We go backward from 15 to 0 as shown. Divison Readiness 39 Ascend_G2_Maths_TB2_V1.indb 39 04/08/2023 5:31:45 PM
Train My Brain Write two multiplication facts for each of the following division facts. a) 20 ÷ 5 = 4 b) 49 ÷ 7 = 7 c) 10 ÷ 2 = 5 9.1 I Apply Equal sharing and equal grouping are used in some real-life situations. Consider the following situations. Example 3: 25 buttons are to be stitched on 5 shirts. If each shirt has the same number of buttons, how many buttons are there on each shirt? Solution: Total number of buttons = 25 Number of shirts = 5 The division fact for 25 buttons distributed among 5 shirts = 25 ÷ 5 = 5 Therefore, each shirt has 5 buttons on it. Example 4: 24 marbles are to be divided equally among 4 friends. How many marbles will each friend get? Solution: Total number of marbles = 24 Number of friends = 4 Number of marbles each friend will get = 24 ÷ 4 = 6 Therefore, each friend will get 6 marbles. 9.1 I Explore Division is used in many situations in our day-to-day lives. Let us see some examples. Example 5: Aman spends 14 hours a week for tennis practice. He spends 21 hours a week for doing homework and 48 hours a week at school. If he spends the same amount of time for each activity each day, how much time does he spend in a day for these activities? (Hint: 1 week = 7 days. The school works for 6 days a week.) Solution: Time spent for tennis practice per day = 14 hours ÷ 7 = 2 hours Time spent for doing homework per day = 21 hours ÷ 7 = 3 hours 40 Divison Readiness Ascend_G2_Maths_TB2_V1.indb 40 04/08/2023 5:31:45 PM
Time spent at school per day = 48 hours ÷ 6 = 8 hours (School works for 6 days a week) Thus, the total time spent by Aman in a day for all the activities = (2 + 3 + 8) hours = 13 hours (except Sunday) Example 6: Deepa shares 15 lollipops equally among 5 of her friends. Instead, if she shares the lollipops among only 3 of them, how many more lollipops does each of them get? Solution: Number of lollipops = 15 If Deepa shares the lollipops equally among 5 of her friends, the number of lollipops each of them would get = 15 ÷ 5 = 3 If Deepa shares the lollipops equally among only 3 of them, the number of lollipops each of them gets = 15 ÷ 3 = 5 Difference in the number of lollipops = 5 – 3 = 2 Therefore, her friends would get 2 more lollipops. Drill Time 9.1: Division as Equal Grouping 1) Divide the number in equal groups. a) 16 in 4 equal groups b) 18 in 9 equal groups c) 20 in 5 equal groups d) 32 in 8 equal groups e) 10 in 2 equal groups f) 42 in 7 equal groups 2) Word Problems a) 26 students are to be divided equally into 2 groups. How many students will be there in each group? b) 14 pencils must be distributed equally among 7 children. How many pencils will each student receive? c) 1 6 cakes are to be packed equally in 2 boxes. How many cakes will be packed in each box? Divison Readiness 41 Ascend_G2_Maths_TB2_V1.indb 41 04/08/2023 5:31:46 PM
Maths Munchies Why is division of a number by 0 not possible? We know that division and multiplication are related. If we have to find 6 ÷ 3, we get the answer 2, because 2 × 3 = 6. Similarly, if we have to find 6 ÷ 0, what would be the answer? We must get a number which when multiplied by 0 gives 6. But any number when multiplied by 0 results in 0. Therefore, 6 ÷ 0 is not possible. Connect the Dots English Fun Let us read a funny poem on division. Each time I want to divide and equally share the things that I have, two dots and a line will help my mind to avoid mistakes and always be fair! EVS Fun Human beings have one large single stomach. On the other hand, the stomach of sheep, goats, and cattle is divided into four compartments. A Note to Parent Engage your child in the activities that involve division in day-to-day life. Ask your child to distribute food made by you like rotis, puris and dosas equally among their siblings. Make this a habit. 42 Divison Readiness Ascend_G2_Maths_TB2_V1.indb 42 04/08/2023 5:31:47 PM
10 Measurements I Will Learn measuring lengths and distances using standard units About comparing weights of two or more objects u sing simple balance to compare weights ordering containers based on their capacities 10.1: Measure Lengths Using Standard Units We have learnt 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. Can you think of some body parts using which we can measure objects? We can measure objects using our hands, palm, feet and so on. 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. So, measures such as handspan, cubit, foot, and leg span are called non-standard units. Ascend_G2_Maths_TB2_V1.indb 43 43 04/08/2023 5:31:49 PM
What are the standard units to measure length? The standard unit of measurement of length is called a Comparison between metre. It is used to measure the length of a room, the units of length. width of a room, the height of a building and so on. We also measure the amount of cloth needed to make a 1 km > 1 m > 1 cm dress in metres. The unit ‘metre’ is written in short as ‘m’. To measure lengths smaller than a metre, we use another unit called centimetre. Centimetre is used to measure a line, the length of a ribbon and so on. We write the unit ‘centimetre’ in short as ‘cm’. To measure lengths greater than a metre, we use a larger unit called the kilometre. It is written in short as ‘km’. It is used to measure the length of a road, the distance between two places, lengths of bridges, tunnels and so on. 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. How can we measure objects using a ruler? A ruler is made of plastic, wood or metal. It has two scales, one on each side, as shown in the picture. One side has the centimetre scale, while the other side has the inch scale. An inch is another standard unit of measurement. 1 inch = 2.54 cm We can measure lengths of small objects such as chalk, duster, sketch pen, pencil, pencil box and so on using any of these scales. The distance between 0 and the number on a ruler at the other end of the object is the length of that object. 44 Measurements Ascend_G2_Maths_TB2_V1.indb 44 04/08/2023 5:31:54 PM
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