NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt

I Explore (H.O.T.S.) Framing story sums for some given numbers would be interesting. Let us see an example. Example 5: Given 32 + 22 = 54, frame a story sum. Solution: Two numbers and their sum are given. We can use some situation to frame the story sum. Step 1: Think of a situation. Here, let us take the number of different fruits such as oranges and apples in a basket. Step 2: Write the story in your words. There were 32 oranges and 22 apples in a fruit basket. How many fruits were there in all? 4.2 Mental Maths Techniques: Addition Mental Maths Let us now learn to add two 2-digit numbers, 53 and 65, mentally. Steps Solved Solve this 53 and 65 38 and 41 Step 1: Add the digits 3+5=8 ______ + ______ = ______ in the ones place mentally. Addition 47 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 51 11/30/2017 4:56:23 PM

Steps Solved Solve this 53 and 65 38 and 41 Step 2: Add the digits The digits in the tens The digits in the tens in the tens place place are 5 and 6. place of the two mentally. Keep 6 in your mind, numbers are ___ and count 5 forward as 7, ____. Keep ____ in your 8, 9, 10 and 11. mind, count ___ forward as ____, ____and ____. 5 + 6 = 11 ____ + ____ = ___ Step 3: Write the sums obtained in steps 1 and 2 together. So, 53 + 65 = 118. So, 38 + 41 = ___. This gives the sum of the given numbers. ? Train My Brain Solve the following mentally: a) 12 + 31 b) 31 + 51 c) 27 + 71 d) 21 + 43 e) 72 + 31 Maths Munchies Let us learn a trick to add 2-digit numbers (55 + 52) quickly. Step 1: Split the numbers such that the ones digit is 0 in both of them. 55 + 52 can be written as 50 + 5 + 50 + 2. Step 2: A dd the 2-digit numbers separately and 1-digit numbers separately. 50 + 50 = 100; 5 + 2 = 7 Step 3: A dd the sums in step 2. Write or tell this as the sum of the given numbers. 100 + 7 = 107 So, 55 + 52 = 107. 48 11/30/2017 4:56:23 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 52

Connect the Dots English Fun Let us read a funny poem about addition. I got a new dog, Addition is his name, He lives in the kitchen, eating is his game. He ate 4 bones, we gave him 4 more. He became so fat, he couldn’t squeeze out the door. He wanted 2 more, so we gave him 3 more. The sum was 11, he was growing more and more! 11 bones are a lot to eat in a day! Now Addition’s so big, it’s just a sad fact. I’ll need a dog, Subtraction, to learn to contract. EVS Fun Count the total number of fingers and toes you have. Also count the same for the other members of your family. Write the total number of fingers and toes that you have counted. Drill Time 4.1 Add 2-digit Numbers and 3-digit Numbers 1) Add 2-digit numbers with regrouping. c) 19 + 35 a) 77 + 13 b) 26 + 35 d) 49 + 12 e) 55 + 25 Addition 49 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 53 11/30/2017 4:56:23 PM

2) Add 3-digit numbers without regrouping. a) 166 + 111 b) 612 + 352 c) 181 + 315 d) 490 + 100 e) 812 + 121 3) Word problems a) Farah has 11 balloons and her friend has 29 balloons. How many balloons do they have in all? b) A khil had 120 beads in one box and 121 beads in another box. How many beads did he have in all? A Note to Parent Take your child to the supermarket. Ask her or him to pick up three types of fruits of their choice. Ask your child to find the total cost of the items. Help them to choose fruits whose rates are without a decimal point. 50 11/30/2017 4:56:23 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 54

Time5Chapter I Will Learn About • the days of the week and the months of the year. • the sequence of events occurring over long periods. 5.1 Read the Clock and Calendar I Think Raj’s mother told him that he can play after 5 o’clock in the evening. Raj looked at the clock. He saw a lot of numbers and two hands on the clock. He couldn’t read the time. From the given clock, can you tell if it is time for Raj to go and play? I Recall We do many activities throughout the day. Certain activities are done during particular parts of the day. NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 55 51 11/30/2017 4:56:23 PM

Name the parts of the day when these activities are done. Activity Go to school Do homework Brush teeth Part of the day Activity Have lunch Wake up Play Part of the day I Remember and Understand We can also tell the time at which we are doing an activity. We use a clock to find the time. Numbers from 1 to 12 are written on the face of a clock. A clock has two hands: 1) the short hand is called the ‘hour hand’, and 2) the long hand is called the ‘minute hand’. 52 11/30/2017 4:56:23 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 56

Minute Hand For each complete round Hour Hand of the minute hand, the hour hand moves to the next number. This shows the completion of one hour. Reading a clock 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. 8 o’clock or 8:00 Let us see an example. Example 1: Read the time shown by these clocks. One is done for you. a) The minute hand is at 12 and the hour hand is at 4. The time is 4 o’clock or 4:00. b) c) d) Time 53 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 57 11/30/2017 4:56:23 PM

Reading a calender We have already learnt about a clock. Let us now learn about a calendar. We see the days and months of a year in a calendar. Observe the given calendar. January 2018 February 2018 March 2018 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1 2 3 456 123 123 7 8 9 10 11 12 13 4 5 6 7 8 9 10 4 5 6 7 8 9 10 14 15 16 17 18 19 20 11 12 13 14 15 16 17 11 12 13 14 15 16 17 21 22 23 24 25 26 27 18 19 20 21 22 23 24 18 19 20 21 22 23 24 28 29 30 31 25 26 27 28 25 26 27 28 29 30 31 April 2018 May 2018 June 2018 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1 2 3 4 567 1 2 345 12 8 9 10 11 12 13 14 6 7 8 9 10 11 12 3 4 5 6 789 15 16 17 18 19 20 21 13 14 15 16 17 18 19 10 11 12 13 14 15 16 22 23 24 25 26 27 28 20 21 22 23 24 25 26 17 18 19 20 21 22 23 29 30 27 28 29 30 31 24 25 26 27 28 29 30 July 2018 August 2018 September 2018 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1 2 3 4 567 1 234 1 8 9 10 11 12 13 14 5 6 7 8 9 10 11 2 3 4 5 678 15 16 17 18 19 20 21 12 13 14 15 16 17 18 9 10 11 12 13 14 15 22 23 24 25 26 27 28 19 20 21 22 23 24 25 16 17 18 19 20 21 22 29 30 31 26 27 28 29 30 31 23 24 25 26 27 28 29 30 October 2018 November 2018 December 2018 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1 2 3 456 123 1 7 8 9 10 11 12 13 4 5 6 7 8 9 10 2 3 4 5 678 14 15 16 17 18 19 20 11 12 13 14 15 16 17 9 10 11 12 13 14 15 21 22 23 24 25 26 27 18 19 20 21 22 23 24 16 17 18 19 20 21 22 28 29 30 31 25 26 27 28 29 30 23 24 25 26 27 28 29 30 31 Week • T here are seven days in a week. They are: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday. 54 11/30/2017 4:56:23 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 58

Month • A month has 30 or 31 days. • February is the 2nd month of the 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. 30Februa3ry 1DaysApril eptemb January August erS DecembOerctober June Novem ber March May July Days 28 29OR Using a calendar, we can find the day and the date. Example 2: Answer the following. One is done for you. a) Which day comes after Sunday? Monday b) Which day comes before Thursday? __________________ c) Which month comes between May and July? ___________ d) Which month comes before November? _______________ Time 55 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 59 11/30/2017 4:56:23 PM

? Train My Brain Read the time shown by these clocks. a) b) c) I Apply We have learnt to read time from a clock. Let us now write a few activities in sequence. Example 3: Look at the clocks and mention the time. One is done for you. a) I wake up at b) I have my breakfast at 7 o’clock in the morning. _______ o’clock in the morning. c) I reach school at d) I have my lunch at _______ o’clock in the morning. _______ o’clock in the afternoon. 56 11/30/2017 4:56:23 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 60

e) I do my homework at f) I go to play at _______ o’clock in the afternoon. _______ o’clock in the evening. g) I have m y dinner at h) I go to b ed at _______ o’clock in the night. _______ o’clock in the night. Let us now learn to draw the hands of a clock to show the given time. Example 4: Draw the hands of the clock to show the time given. One is done for you. b) c) a) 2 o’clock 12 o’clock 10 o’clock Time 57 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 61 11/30/2017 4:56:23 PM

d) e) f) 7 o’clock 4 o’clock 3 o’clock g) h) i) 5 o’clock 8 o’clock 9 o’clock I Explore (H.O.T.S.) We can find the time a few hours before or after a given time. We can also find how many hours a given time is less than or more than some other given time. Example 5: Answer the questions given. One is done for you. a) W hat time is 5 hours before 8 o’clock? 3 o’clock b) W hat time is 3 hours after 4 o’clock? ______________________ c) H ow many hours after 3 o’clock is 9 o’clock? ______________________ d) H ow many hours before 8 o’clock is 6 o’clock? ______________________ 58 11/30/2017 4:56:23 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 62

Maths Munchies 12 o’clock 6 o’clock The hour hand and the minute hand are on the same number at 12 o’clock. They are on the opposite ends at 6 o’clock. Connect the Dots EVS Fun Observe your shadow in the morning, noon and evening. Is there any change in the length of your shadow? English Fun Let us read a funny poem on calendars. 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. Time 59 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 63 11/30/2017 4:56:24 PM

Drill Time 5.1 Read the Clock and Calendar 1) Read the time shown by the clocks given below. a) b) c) d) e) f) 2) Answer the following questions. a) Which day comes after Tuesday? b) Which day comes before Saturday? c) Which month comes after September? d) Which month comes in between February and April? 3) Draw the hands of the clock to show the time given. a) b) c) 6 o’clock 1 o’clock 11 o’clock A Note to Parent Help your child make his or her own clock using a paper plate for the face and straws of paper for the hands of a clock. Explain how the hands of the clock move from 4 o’clock to 5 o’clock. 60 11/30/2017 4:56:24 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 64

6Chapter Subtraction I Will Learn About • subtraction of 2-digit and 3-digit numbers. • solving daily-life problems with subtraction. • mental Maths techniques. 6.1 Subtract 2-digit Numbers and 3-digit Numbers I Think Raj has got 83 candies from his parents for his birthday. He gives 27 candies to his friend Neha. How can Raj find the number of candies left with him without counting? I Recall In class 1 we have learnt to subtract using a number line and also by counting. We have also done subtraction using the place value chart. Let us solve the following to recall the concept of subtraction. NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 65 61 11/30/2017 4:56:24 PM

Count, write and subtract the numbers in the boxes. a) b) c) d) 62 11/30/2017 4:56:24 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 66

I Remember and Understand Subtraction of 2-digit numbers with regrouping The place values of digits in 2-digit numbers are tens While subtracting, and ones. Sometimes, subtracting 2-digit numbers always begin from needs regrouping. Let us see some examples. the ones place. Example 1: Subtract 48 from 56. Solution: Write the numbers according to their places. Write the bigger number on the top. Steps Solved Solve these Step 1: Subtract the ones. TO TO As 8 > 6, we cannot subtract 8 56 44 from 6. So, regroup the tens. −4 8 −3 8 5 tens = 4 tens + 1 ten (1 ten = 10 ones) Step 2: Add 1 ten to the ones. So, TO TO it becomes 16 ones. Also, subtract 4 16 1 ten from the tens place (that is, 56 98 5 – 1 = 4). Now, subtract 8 from 16; −4 8 −3 9 16 – 8 = 8. Write the difference in the ones place. 8 Step 3: Subtract the tens. TO TO 4 16 That is, 4 – 4 = 0. Write the 56 86 difference in the tens place. −4 8 −2 7 08 So, 56 – 48 = 8. Subtraction 63 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 67 11/30/2017 4:56:24 PM

Subtraction of 3-digit numbers without regrouping Let us understand how to subtract 3-digit numbers through some examples. Example 2: Subtract 141 from 943. Solution: Arrange the numbers according to their place values. Steps Solved Solve these Step 1: Subtract the ones. Write H T O H T O the difference in the ones 9 4 3 4 9 6 place. That is, 3 – 1 = 2. −1 4 1 −2 6 2 2 Step 2: Subtract the tens. Write H T O H T O the difference in the tens 9 4 3 6 3 6 place. That is, 4 – 4 = 0. −1 4 1 −1 3 0 0 2 Step 3: Subtract the hundreds. H T O H T O Write the difference in the 9 4 3 8 4 6 hundreds place. −1 4 1 −4 2 0 That is, 9 − 1= 8. 8 0 2 So, 943 – 141 = 802. Properties of subtraction 1) Zero property: When we subtract 0 from a number, the difference is the number itself. F or example, 12 – 0 = 12; 28 – 0 = 28 and so on. 2) Before numbers property: When we subtract 1 from a number, we get the number just before it. For example, 35 – 1 = 34; 59 – 1 = 58 and so on. 3) S ubtracting a number from itself: When we subtract a number from itself, the difference is 0. For example, 35 – 35 = 0; 62 – 62 = 0 and so on. 64 11/30/2017 4:56:24 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 68

? Train My Brain a) Subtract 0 from 12. b) Find the difference between 50 and 1. c) W hat is the difference when a number is subtracted from itself? I Apply We use the concept of subtraction to solve some real-life situations. Let us see a few examples. Example 3: There are 390 students in a school. Among them,150 students are girls. How many boys are there in the school? Solution: Number of students in the school = 390 HTO Number of girls = 150 Number of boys = 390 – 150 39 0 So, there are 240 boys in the school. −15 0 24 0 Example 4: There are 52 candies in a jar. Children ate up 37 candies. How many candies are left in the jar? Solution: Number of candies in a jar = 52 TO Number of candies eaten by children = 37 Number of candies left in the jar = 52 – 37 4 12 So, there are 15 candies left in the jar. 52 −3 7 15 I Explore (H.O.T.S.) Let us now learn to frame a story sum based on subtraction. Subtraction 65 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 69 11/30/2017 4:56:24 PM

Example 5: Given 163 −120 = 43, frame a story sum. Solution: Two numbers and their difference are given. We can use some situation to frame the story sum. Step 1: Think of a situation. For example- Shyam takes some chocolates to school on his birthday. Since it is subtraction, these chocolates should be given away. Step 2: Write the story in your words. Shyam takes 163 chocolates to school on his birthday. He shares 120 chocolates among his classmates. How many chocolates are left with him? 6.2 Mental Maths Techniques: Subtraction Mental Maths Let us now learn to subtract 2-digit numbers mentally. Subtract 52 from 76 mentally. Steps Solved Solve this 76 – 52 69 – 35 Step 1: Subtract the ones mentally. 6–2=4 ______ – ______ = ______ Step 2: Subtract the tens mentally. The digits in the tens The digits in the tens place are 7 and 5. place are ___ and ____. So, imagine that 7 So, imagine that ____ fingers are open. fingers are open. Then imagine closing Then imagine closing 5 of them. Count the of them. Count the remaining number of remaining number of fingers that are open. fingers that are open. 7–5=2 ____ – ____ = ____ 66 11/30/2017 4:56:24 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 70

Steps Solved Solve this 76 – 52 69 – 35 Step 3: Write the So, 69 – 35 = ____. differences obtained in the steps 1 and 2 as the So, 76 – 52 = 24. difference of the given numbers. ? Train My Brain Solve the following mentally: a) 53 – 31 b) 65 – 23 c) 65 – 14 d) 29 – 19 e) 81 – 11 Maths Munchies 1 0 0 − 8 6 from 9 = 1 4 from 10 Subtraction of 2-digit numbers from 100: Consider the example 100 – 86. In this example, we have subtracted 8 from 9 and then 6 from 10 which results in 14. This trick helps in faster calculations. Connect the Dots EVS Fun You have invited 15 people. Six of them are your friends. Also, there is one uncle, one aunt and three cousins. Your parents and grandparents are also there. If we separate all the extended family members, how many guests will remain? Subtraction 67 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 71 11/30/2017 4:56:24 PM

English Fun Let us read a poem about subtraction. Here we go subtracting numbers, Away a part, away a part, Subtracting numbers, subtracting Next you take away a part, numbers To find the difference Here we go subtracting numbers, You have found the other part, To find the difference The other part, the other part, First you start with the whole, You have found the other part, With the whole, with the whole, That is the difference. First you start with the whole, To find the difference Next you take away a part, Drill Time 6.1 Subtract 2-digit Numbers and 3-digit Numbers 1) Subtract the following with regrouping. c) 48 – 19 a) 25 – 18 b) 37 – 29 d) 56 – 27 e) 90 – 25 2) Subtract the following without regrouping. a) 356 – 256 b) 197 – 106 c) 786 – 122 d) 476 – 111 e) 854 – 221 3) Word problems a) V ishu has 33 cups in a box. He used 17 of them for a birthday party. How many cups are left in the box? 68 11/30/2017 4:56:24 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 72

b) N isha has 41 handkerchiefs with her. She gave 24 handkerchiefs for washing. How many handkerchiefs are left with her? A Note to Parent Give your child a few toffees. Now play a game according to the following rules: a) A sk for 0 toffees. Then tell your child to count the number of toffees that remain. b) Ask your child to give you one toffee. Tell him or her child to count the number of toffees that remain. c) Ask your child to give you different numbers of toffees and then ask how many are left. Subtraction 69 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 73 11/30/2017 4:56:24 PM

7Chapter Money I Will Learn About • addition and subtraction of an amount upto ` 100 without conversion. • estimation of money. 7.1 Add and Subtract Money without Conversion I Think Raj and his mother bought a few items from a shop. When Raj’s mother paid the bill, the shopkeeper gave her some change. Raj wondered why the shopkeeper gave his mother some money. Do you know why? I Recall We add or subtract numbers by writing them one below the other. This method of addition or subtraction is called the column method. 70 11/30/2017 4:56:24 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 74

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 21 1 ` 47 ` 23 ` 35 ` 78 ` 99 I Remember and Understand Money is written in rupees and paise, In the column method, we write rupees under separated by a dot. rupees. Then we write paise under paise, exactly one below the other. When paise is not given, For example, ` 3.50 is we put 00 in the paise column. Then we add or read as three rupees subtract as usual. and fifty paise. Addition of money Let us understand the addition of money 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. Write the sum in the `p `p paise column. 45 . 50 11 . 11 +32 . 20 +22 . 22 70 Money 71 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 75 11/30/2017 4:56:24 PM

Steps Solved Solve these Step 2: Add the rupees. Write the sum in the `p `p rupees column. 45 . 50 20 . 19 +32 . 20 +32 . 20 77 . 70 Subtraction of money Let us understand the subtraction of money 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. Write the difference in the `p `p paise column. 75 . 60 45 . 45 Step 2: Subtract the –25 . 40 –12 . 12 rupees. Write the difference in the rupees 20 `p column. `p 98 . 43 –46 . 22 75 . 60 –25 . 40 50 . 20 ? Train My Brain c) ` 76.24 – ` 12.10 Solve the following: a) ` 34.33 – ` 24.22 b) ` 21.25 + ` 42.23 I Apply Let us see some real-life examples of addition and subtraction of money. Example 3: Five pens cost ` 20 and two pencils cost ` 12.50. What is their total cost? Write in words. 72 11/30/2017 4:56:24 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 76

Solution: Cost of five pens = ` 20 `p Cost of two pencils = ` 12.50 20 . 00 Their sum = ` 20 + ` 12.50 +12 . 50 So, the total cost of pens and pencils is ` 32 . 50 32.50. In words, it is thirty-two rupees and fifty paise. Example 4: Veer bought a ball for ` 12.50 and gave the shopkeeper ` 15.50. How much change did the shopkeeper give Veer? Solution: The amount Veer paid the shopkeeper = ` 15.50 Cost of the ball = ` 12.50 ` p 50 Difference in the amounts = ` 15.50 – ` 12.50 1 5. 50 00 So, the shopkeeper gave Veer ` 3. – 1 2. I Explore (H.O.T.S.) 3. Let us see a few more 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) Combination 1 b) Combination 2 ` 100 ` 250 ` 150 ` 100 ` 350 Money 73 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 77 11/30/2017 4:56:24 PM

c) Combination 3 d) Combination 4 ` 150 ` 350 ` 250 ` 200 Maths Munchies 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. Connect the Dots 11/30/2017 4:56:25 PM EVS Fun Have you seen ATMs in your city or town? ATM stands for ‘Automated Teller Machine’. Every bank has its an ATM. Most ATMs work for 24 hours. We can go and get money from there anytime! 74 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 78

English Fun Think of at least three rhyming words for ‘money’. Drill Time 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) R am has ` 52.50. He gave ` 40.00 to Shama. How much money does Ram have left? b) S oham bought some chocolates for ` 41.00. Rehan bought some chocolates for ` 24.50. How much amount did they spend in all? A Note to Parent Take your child for grocery shopping on a weekend. Ask him or her to count the coins and notes before paying the shopkeeper. Such hands-on experiences will strengthen your child’s understanding of the uses of money. Money 75 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 79 11/30/2017 4:56:25 PM

8Chapter Multiplication I Will Learn About • repeated addition. • skip counting. • multiplication tables of 2, 3, 4 and 5. 8.1 Repeated Addition and Skip Counting 11/30/2017 4:56:25 PM I Think Raj wants to buy toffees for his birthday. His mother asks him to get 3 toffees for each of his friends. He has 7 friends. How can Raj find out quickly how many toffees he has to buy? I Recall We already know how to add objects by counting. Let us recall the same through the following exercise. 76 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 80

Count, add and write the number of objects. a) Number of honey bees = _____________ b) Number of trees = ___________ c) Number of birds = ___________ d) Number of windows = ___________ I Remember and Understand Let us learn about repeated addition and skip counting. Multiplication 77 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 81 11/30/2017 4:56:25 PM

Repeated addition In repeated addition, we put Repeated addition is adding the same number the objects into again and again. equal groups to find their total. Let us see a few examples. Example 1: Use repeated addition to find the total number of houses. Number of groups = 4 Solution: 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 becomes 8. Skip counting ‘Skip Counting’ is counting by a number other than 1. It helps you to: a) count many things quickly. b) learn multiplication tables. 78 11/30/2017 4:56:25 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 82

Count by 2s In counting by 2s, we begin with a number and count every alternate number. Example 2: 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. Let us see an example. Example 3: Begin with the given number and count by 3s. Write the numbers in the boxes given. One is done for you. a) Multiplication 79 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 83 11/30/2017 4:56:25 PM

b) c) ? Train My Brain Identify the number of groups. Write the number of items present in each group. a) b) c) I Apply Let us now learn to construct the multiplication tables of numbers from 2 to 5. 80 11/30/2017 4:56:25 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 84

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. 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 2 2 times 1 is 2. 2×2=4 2 + 2 2 times 2 is 4. Multiplication 81 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 85 11/30/2017 4:56:25 PM

2×3=6 2 + 2 + 2 2 times 3 is 6. 2×4=8 2 + 2 + 2 + 2 2 times 4 is 8. 2 × 5 = 10 2 + 2 + 2 + 2 + 2 2 times 5 is 10. 2 × 6 = 12 2 + 2 + 2 + 2 + 2 + 2 2 times 6 is 12. 2 × 7 = 14 2 + 2 + 2 + 2 + 2 + 2 + 2 2 times 7 is 14. 2 × 8 = 16 2 times 8 is 16. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 2 × 9 = 18 2 times 9 is 18. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 2 × 10 = 20 2 times 10 is 20. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 82 11/30/2017 4:56:25 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 86

The following are the multiplication tables of 2, 3, 4 and 5. Read them aloud. 2 3 4 5 2×1=2 3×1=3 4×1=4 5×1=5 2×2=4 3×2=6 4×2=8 5 × 2 = 10 2×3=6 3×3=9 4 × 3 = 12 5 × 3 = 15 2×4=8 3 × 4 = 12 4 × 4 = 16 5 × 4 = 20 2 × 5 = 10 3 × 5 = 15 4 × 5 = 20 5 × 5 = 25 2 × 6 = 12 3 × 6 = 18 4 × 6 = 24 5 × 6 = 30 2 × 7 = 14 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35 2 × 8 = 16 3 × 8 = 24 4 × 8 = 32 5 × 8 = 40 2 × 9 = 18 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45 2 × 10 = 20 3 × 10 = 30 4 × 10 = 40 5 × 10 = 50 Let us now apply the concept of repeated addition and multiplication. Example 4: 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. We can also use the multiplication table to find the number of legs. As there are 3 dogs with 4 legs each, we write 3 × 4 = 12. So, the three pet dogs have 12 legs altogether. Multiplication 83 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 87 11/30/2017 4:56:25 PM

I Explore (H.O.T.S.) Let us see another example of skip counting. Example 5: C omplete the wheel using the method of skip counting by 3 and 5. Solution: We can complete the wheel using skip counting by 3 and 5 as shown. Maths Munchies Interesting facts about multiplication of a number by 0 and 1. Multiplying a number by 0, gives a 0. For example, 3 × 0 = 0; 58 × 0 = 0 and so on. Multiplying a number by 1 gives the same number. For example, 24 × 1 = 24; 18 × 1 = 18 and so on. Connect the Dots 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. 84 11/30/2017 4:56:25 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 88

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. Drill Time 8.1 Repeated Addition and Skip Counting 1) Count, add and write the total number. a) b) c) Multiplication 85 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 89 11/30/2017 4:56:25 PM

d) 2) Skip count and fill in the blanks. a) Skip count by 2 8 2 b) Skip count by 3 15 3 c) Skip count by 4 4 24 86 11/30/2017 4:56:25 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 90

d) Skip count by 5 45 5 3) Word problems a) Seeta observed that there were 4 cars parked in a row. How many wheels could she count on the cars? b) H ari counts some pens using skip counting by 3. How many pens does he count altogether? A Note to Parent Make your child practise multiplication tables regularly. Knowing tables by heart is important, as it makes it easier for your child to calculate faster. Multiplication 87 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 91 11/30/2017 4:56:25 PM

Division9Chapter I Will Learn About • equal sharing and equal grouping. • repeated subtraction. • division using a number line. 9.1 Repeated Subtraction I Think Raj wants to distribute 20 craft papers equally among 4 of his friends to make paper figures. How many craft papers do you think each of them would get? I Recall In the previous chapter, we have learnt about multiplication. Multiplication is finding the total number of objects that have been grouped equally. Let us use this to distribute objects equally in groups. 88 11/30/2017 4:56:25 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 92

Consider 12 bars of chocolate. The different ways in which they can be distributed are as follows. 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 I Remember and Understand Distributing a given number of objects into equal groups is called division. We can understand division better by using equal sharing and equal grouping. Division 89 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 93 11/30/2017 4:56:25 PM

Equal sharing means having an equal number of objects in a group. We use division to find the number of things in a group. We can also find the number of groups by using division. Suppose 9 balloons are to be 1st round: 1 balloon is taken by shared equally among 3 friends. each friend. Let us use repeated subtraction to distribute the balloons. 9 – 3 = 6. So, 6 balloons remain. 2nd round: From the remaining 6 3rd round: From the remaining 3 balloons, 1 more balloon is taken balloons, 1 more balloon is taken by each friend. by each friend. Now, each friend has 2 balloons. Now, each of them has 3 balloons. 6 – 3 = 3. So, 3 balloons remain. 3 – 3 = 0. So, 0 balloons remain. Each friend gets 3 balloons. Here we subtracted the same number again and again. This is known as repeated subtraction. When 9 balloons are divided among 3 friends, each friend gets 3 balloons. 90 11/30/2017 4:56:26 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 94

We can write it as 9 divided by 3 equals 3. Using the symbol of division, we write it as follows: ↓ ↓ ↓ The symbol for ‘is divided Number of by’ is ÷. groups Total Number of number of objects in each objects group Let us understand this through an example. Example 1: 2 0 pencils are to be equally distributed in a few pencil stands. Each stand can hold 5 pencils. How many stands will be needed? Solution: We use repeated subtraction to distribute 20 pencils equally. Given that each stand has 5 pencils, let us first put 5 pencils in one stand. 20 pencils – 5 pencils = 15 pencils remain From the remaining 15 pencils, put 5 pencils in another stand. Division 91 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 95 11/30/2017 4:56:26 PM

15 pencils – 5 pencils = 20 – 5 – 5 pencils = 10 pencils remain From the remaining 10 pencils, put 5 pencils in another stand. 10 pencils – 5 pencils = 20 – 5 – 5 – 5 pencils = 5 pencils remain 5 pencils – 5 pencils = 20 – 5 – 5 – 5 – 5 pencils = 0 pencils remain As no more pencils are left, we need 4 stands. So, we can distribute 20 pencils equally in 4 stands with 5 pencils in each. We can write it as 20 ÷ 5 = 4. (Total number of pencils) ÷ (Number of pencils in each stand) = (Number of stands needed) 92 11/30/2017 4:56:26 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 96

Division using a number line We can use the number line to show repeated subtraction. Count backwards and make equal jumps to reach 0. Let us see an example. Example 2: Divide using a number line: a) 10 ÷ 2 b) 18 ÷ 3 Solution: a) 10 ÷ 2 (5) (4) (3) (2) (1) Starting from 10, jump backward in steps of 2. We reach 0 after 5 jumps as shown by the arrows. So, 10 – 2 – 2 – 2 – 2 – 2 = 0. We can write it as 10 ÷ 2 = 5. b) 18 ÷ 3 (6) (5) (4) (3) (2) (1) Starting from 18, jump backwards in steps of 3. We reach 0 after 6 jumps as shown by the arrows. So, 18 – 3 – 3 – 3 – 3 – 3 – 3 = 0. We can write it as 18 ÷ 3 = 6. ? Train My Brain Write the following using the division symbol. a) 21 divided by 3 gives 7 b) 42 divided by 7 gives 6 c) 32 divided by 8 gives 4 Division 93 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 97 11/30/2017 4:56:26 PM

I Apply We can use repeated subtraction in some real-life situations. Here are a few examples. Example 3: Sunil has 18 beads. He wants to make a necklace with 6 beads each. How many necklaces can he make? Solution: Total number of beads = 18 Number of beads in each necklace = 6 Number of necklaces = 18 ÷ 6 = 3 So, Sunil can make 3 necklaces. Example 4: Renu wants to divide 30 feathers in 6 groups. How many feathers will be there in each group? Solution: Total number of feathers = 30 Number of groups = 6 Number of feathers in each group = 30 ÷ 6 = 5 94 11/30/2017 4:56:26 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 98

So, there will be 5 feathers in each group. I Explore (H.O.T.S.) Division and multiplication are reverse operations. Let us understand this. Suppose there are 12 toys. We want to arrange them on 4 shelves. Number of toys on each shelf = 12 ÷ 4 = 3 So, there will be 3 toys on each shelf. If there are 3 toys on 4 shelves, we can find the total number of toys as 4 × 3 = 12. Division 95 NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 99 11/30/2017 4:56:26 PM

So, we can say that division and multiplication are reverse operations. If 12 ÷ 4 = 3, then 4 × 3 = 12. Similarly, 3 × 4 = 12 Maths Munchies Interesting facts about division: Dividing a number by 1, gives the number itself. For example, 21 ÷ 1 = 21; 46 ÷ 1 = 46 and so on. Dividing a number by itself gives 1. For example, 39 ÷ 39 = 1; 18 ÷ 18 = 1 and so on. Connect the Dots EVS Fun Division mean equal sharing. It exists in our neighbourhood and families too. The members of a family share the work or tasks of the family. What kind of division of work do you see in your neighbourhood? English Fun RGAD I V I S I ON B S H R T E D B D B H UGH T F K Find these words in the T AA I EQUA L UGH T N word search puzzle. O L A S PGD R N LWU Y E WWG R O U P I N G A G B W DIVISION Q R P I E R H N MW I U C D T O L K AA YGA R T Q S L EQUAL H T A E C N V L D J E J MW OE YDHDDX E YDV I V SHARING GROUPING 96 11/30/2017 4:56:26 PM NR_BGM_Traveller-G2-Textbook-Maths-FY_Txt.pdf 100