CO MPASS SERIES mathematics textbook part -2 3 Name: Learn@Home Sec�on: Roll No.: School:
Preface C ass ap partners with schools, supporting them with learning materials and processes that are all crafted to work together as an interconnected system to drive learning. Our books strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. C ass ap presents the Compass s s s sp a o m ms o the new curriculum released in November 2016 by the Council for the Indian School C a am a o s C C Guiding principles: CC m s a s o o as a o s p p so Mathematics teaching: Develop mathematical thinking and problem-solving skills and apply these skills to formulate and solve problems. ssa ma ma a o p s a s s o a and for continuous learning in Mathematics and related disciplines. Recognise and use connections among mathematical ideas and between Mathematics and other disciplines. Reason logically, communicate mathematically and learn cooperatively and independently. a o s p p s so a s sp C ass ap oo s workbooks and teacher companion books have been designed. The C ass ap team o p a o p s as a o a s mapp so a a am o as o CC mo m Key features of C ass ap Compass series: Theme-based content that holistically addresses all the learning outcomes sp CC m oo s a o oo s a s as p oom s a o om o help organise the learning process according to the different levels involved. Student engagement through simple, age-appropriate content with a p a a o o s ps Learning is supported through visually appealing images, especially for Grades 1 and 2. as s soso so p a o a s p o as p C C m All in all, the Compass Mathematics books aim to develop problem-solving and aso s s as as om a p a ma ma a skills as appropriate to the primary level. – The Authors
Textbook Features I Will Learn About I Think Contains the list of concepts to be covered oss s s in the chapter along with the learning objectives curiosity before introducing the concept I Recall I RUenmdeermsbtearndand Pin-Up-Note Recapitulates the as as Highlights the key points or os p so o elements that form the the concept learnt previously basis of the concept ? Train My Brain I Apply I Explore(H.O.T.S.) Checks for learning to gauge Connects the concept oa s s o the understanding level of the to real-life situations by op a student providing an opportunity a os to apply what the student o mo omp s has learnt Maths Munchies Connect the Dots Drill Time Aims at improving speed of Aims at integrating Revises the concepts with calculation and problem Mathematical concepts pa s o sa solving with interesting facts, with other subjects end of the chapter tips or tricks A Note to Parent a s pa oo classroom learning of their child
Contents 6 Subtraction 6.1 Subtract 2-digit Numbers and 3-digit Numbers ........................................... 1 6.2 Mental Maths Techniques: Subtraction......................................................... 6 7 Money 7.1 Add and Subtract Money without Conversion ............................................10 8 Multiplication 8.1 Repeated Addition and Skip Counting........................................................17 9 Division 9.1 Repeated Subtraction ...................................................................................30 10 Measurement 10.1 Measure Lengths Using Non-standard Units ..............................................40 10.2 Comparing Mass and Volume by Estimation ...........................................47 11 Data Handling 11.1 Pictographs..................................................................................................62
6Chapter Subtraction I Will Learn About s a oo a ms p o ms so a s s ao m a as 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. o aa m oa s m oo I Recall ass a a os a s a m a a so o a a so o s a o s pa a a s so oo o a o pos a o 1
Co as a ms os a) b) c) d) 2
I Remember and Understand Subtraction of 2-digit numbers with regrouping pa a so s m sa s sa m s a a s begin from a o s om m s s a amp s the ones place. s op s s som oo pa s Example 1: a om op Solution: m sa mo Steps Solved Solve these a os Step 1: TO TO s a os a om o op s 6 s s 8 38 os Step 2: o o so om s o s so s a om s p a as o sa om TO TO o spa 6 98 8 39 o o a os a om o o 8 m s o o om pa s a o amp o s a om o a o sa om o oo om spa o o oa o Step 3: a s TO TO as s 8 pa 5 o 48 27 08 Subtraction 3
Subtraction of 3-digit numbers without regrouping s sa o os a m s o som amp s Example 2: a om Solution: a m sa o o pa a s Steps Solved Solve these Step 1: a os HT O HT O 9 3 9 2 the difference in the ones 1 2 2 pa a s Step 2: a s HT O HT O 94 3 3 the difference in the tens 3 4 pa a s 02 Step 3: a s HT O HT O 93 8 s pa 1 82 2 as o Properties of subtraction 1) Zero property: sa om a m s ms om a so o o amp 2) Before numbers property: sa om a m m so a so o o amp s aa m 3) Subtracting a number from itself: a so o ss o amp 4
? Train My Brain om s a a om a a s a m ss a I Apply s o p o s a o o so som a s a o s ss a amp s Example 3: as s a s oo mo m s s a s o ma o sa s oo Solution: m os s s oo HTO mos 39 m o os 2 oa os s oo Example 4: a a s aa C a p as o ma a sa a Solution: m o a s aa TO m o a sa a 2 m oa s a 37 o a as I Explore (H.O.T.S.) s o a o am a s o s m as o s a o Subtraction 5
Example 5: am a s o s m Solution: o m sa a as som s a o o am so s m Step 1: o as a o o amp am a s som o o a s o s oo o s a ss a o s o oa ss o given away. Step 2: so o o s am a s o o a s o s oo o s a sa s o o a s amo s assma s o ma o oa sa m 6.2 Mental Maths Techniques: Subtraction Mental Maths s o a os a m sm a a om m a Solve this Steps Solved 69 – 35 76 – 52 Step 1: a The digits in the tens o sm a The digits in the tens pa a a pa a a Step 2: a sm a o ma a ____. s a op o ma a ma os s a op o m Co ma os ma m o o m Co s a a op ma m o s a a op 6
Steps Solved Solve this 76 – 52 69 – 35 Step 3: o o differences obtained in s ps a as difference of the given ms ? Train My Brain o oo m a a Maths Munchies a oo m s om from 9 Co s amp a om ps as s amp as om a om s ss a aos Connect the Dots EVS Fun oa p op o ma o s so so o aa o s s o pa s a a pa s a a so s pa a a am m m s o ma s s ma Subtraction 7
English Fun s a a po m a o s a o Away a part, away a part, Here we go subtracting numbers, Subtracting numbers, subtracting Next you take away a part, numbers o Here we go subtracting numbers, oa o o pa o o pa o pa s o sa o oa o o pa oo as s o sa o o Next you take away a part, Drill Time 6.1 Subtract 2-digit Numbers and 3-digit Numbers 1) Subtract the following with regrouping. a 2) Subtract the following without regrouping. a 3) Word problems as as ps a o s o moa a pa o s o ma ps a s a as a s a a o as o ma a sa 8
A Note to Parent o a o s o p a a am a o o oo s a so o s o oo m oo s a remain. so o oo o mo oo m o o s a ma so o o m so o sa as o ma a Subtraction 9
7Chapter Money I Will Learn About addition and subtraction of an amount up to ` 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. 10
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 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. a pa s 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 11
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. `p Write the difference in the `p paise column. 75 . 60 45 . 45 –25 . 40 –12 . 12 Step 2: Subtract the rupees. Write the 20 `p difference in the rupees 98 . 43 column. `p –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. 12
Solution: Cos o p s ` 20 `p 20 . 00 Example 4: Cos o o p s ` 12.50 +12 . 50 Solution: 32 . 50 s m ` 20 + ` 12.50 pa s So, the total cost of pens and pencils is ` os s o p sa Veer bought a ball for ` 12.50 and gave the shopkeeper ` 15.50. How much change did the shopkeeper give Veer? amo pa s op p ` 15.50 `p Cos o a ` 12.50 amo s ` 15.50 – ` 12.50 1 5 . 5 0 So, the shopkeeper gave Veer ` 3. – 12 . 50 I Explore (H.O.T.S.) 3 . 00 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 13
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. 14
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 and get money from there anytime! 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 Money 15
3) Word problems a) Ram has ` 52.50. He gave ` 40.00 to Shama. How much money does Ram have left? b) Soham 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. 16
8Chapter Multiplication I Will Learn About repeated addition. skip counting. m p a o a so and 5. 8.1 Repeated Addition and Skip Counting I Think Raj wants to buy toffees for his birthday. His mother asks him to get 3 toffees for each of his friends. He as so a a o o many toffees he has to buy? I Recall aa o o oa o s o sa sam o oo s Multiplication 17
Co a a m oo s a) Number of honey bees = _____________ b) Number of trees = ___________ c) Number of birds = ___________ d) Number of windows = ___________ I Remember and Understand s a ao pa a o a sp o 18
Repeated addition Repeated addition is adding the same number In repeated again and again. addition p the objects into ss a amp s equal groups to Example 1: s p a a o o oa oa number of houses. Solution: m o o ps m oo sa op om s oa m o o s o a oss a a as o ps o Skip counting ‘Skip Counting’ is counting by a number other than 1. ps o o a o ma s a m p ao a s Multiplication 19
Count by 2s o s am a o aa number. Example 2: p o o s a o s a o a o so s sp o is done for you. m so mps a) b) c) Count by 3s so m om m amp o m ao s ss a ms os so oo Example 3: a) 20
b) c) ? Train My Brain Identify the number of groups. Write the number of items present in each group. a) b) c) I Apply so a o os m p a o a s o m s om o Multiplication 21
s oo sa o po sas o s a o po s as mas ms s sm o s s om p ao s a as m s a as o s a a o ps sas a as a a as o ps o s a a so as mas ms s a as os a sa o ps sas a as a a as o ps o s sa as mas ms s a as sa sa a om m p a o a o Forming the multiplication table of 2 ms s ms s 22
ms s ms s ms s ms s ms s ms s ms s ms s Multiplication 23
oo a m p a o a so a a mao 2 5 34 s o app o po p a a o a m p ao Example 4: s as p o s o ma s o s os a ao Solution: s as p os o m o o ps s a o as so m o ao s a o ps o o ps o s a a so s m p ao a o m os s a os sa o p os a sa o 24
I Explore (H.O.T.S.) ss a o amp o s p o Example 5: Comp s m o os p o and 5. Solution: a omp s sp o a as shown. Maths Munchies s a sa o m p a o o a m a p am sa o amp × × a so o p am s sam m o amp × × a so o Multiplication 25
Connect the Dots EVS Fun a as o a aso a s s a sm p o a o m ma o a s s o as big tree growing with many branches. English Fun a a ma s po ms as One and two climb a tree. m a o o oo ms s o Drill Time 8.1 Repeated Addition and Skip Counting 1) Count, add and write the total number. a) 26
b) c) d) po a as a po 8 2 Multiplication 27
b) Skip count by 3 15 3 po 4 24 d) Skip count by 5 5 3) Word problems a ao s a a s pa ao o ma s o s oo as 28
b) Hari counts some pens using skip counting by 3. How many pens o s o ao A Note to Parent ao pa s m p a o a s a o as o a a as a s mpo a as ma s as o o Multiplication 29
Division9Chapter I Will Learn About equal sharing and equal op pa s a o so s a m 9.1 Repeated Subtraction I Think Raj wants to distribute 20 craft papers equally among 4 of s s o ma pap s o ma a pap s o you think each of them would get? I Recall p o s ap a a ao m p ao p ao oo saa op a s oa m a o ps s s s so s o 30
Co s a so o oa as a s a as o o s 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 op Division 31
as a mas a a am oo s a op s so sa op a a so o mo mo o ps s so Suppose 9 balloons are to be 1st round: 1 balloon is taken by a s a a amo s o a oo s ma s s pa s a o os a oo s 2nd round: From the remaining 6 3rd round: From the remaining 3 balloons, 1 more balloon is taken balloons, 1 more balloon is taken a a oa as a oo s o a o m as a oo s o a oo s ma o a oo s ma a s a oo s sa sam m aa a aa s s o as repeated subtraction amo sa s a oo s a oo s a 32
We can write it as 9 divided by 3 equals 3 s s m o o so write it as follows: sm o for ‘is divided by s Total Number of Number of number of objects in each groups objects group s s a s o a amp Example 1: 20 pencils are to be equally distributed in a few pencil s a s a s a a o p s o ma s a s be needed? Solution: s pa s a o o s p sa a a s a as p s ss p p s o sa p sp s p s ma om ma p sp p s a o sa Division 33
p sp s ps p s ma om ma p sp p s a o sa ps p s p sp s remain ps p s p sp s remain s o mo p sa sa s o a sp sa sa s p sa a as oa m o p s m o p s a sa m o sa s 34
Division using a number line as m os o p a s a o Co a mps o a s s a amp a a s a ma ÷3 Example 2: s am a (2) (1) Solution: a (5) (4) (3) a om mp a a s ps o a a mps as s o ao s o a as (6) (5) (4) (3) (2) (1) a om mp a a s s ps o a a mps as s o ao s o a as ? Train My Brain oo s so s m o as s s Division 35
I Apply a s pa s a o som a s a o s aa amp s Example 3: as a s a s o ma a a as a ma o ma a sa Solution: oa m o a s Number of beads in each necklace = 6 mo as o a ma as Example 4: a so as o ps o ma feathers will be there in each group? Solution: oa m o a s Number of groups = 6 m o a s a op 36
o a s a op I Explore (H.O.T.S.) so a m p ao a s op a o s s sa s ppos a os a oa a mo s s Number of toys on each shelf = 12 ÷ 4 = 3 o o so a s a o so s s a o a m o o s as Division 37
o a sa a s o a m p a o a s op a o s Similarly, 3 × 4 = 12 Maths Munchies Interesting facts about division: am s ms a so o o amp a so o am ss o amp Connect the Dots English Fun o sa p s os RGAD I V I S I ON B S R EDBDB G F K AA I EQ A G N O A S GD R N W Y E WWG R O I NGAGBW QR I ER N WI CD O K AA YGA R Q S A E CNV DJ E J W OE YD DDX E YDV I V 38
EVS Fun so m a as a ss o o oo a am s oo o o as s o am m m s o a am s a What kind of division of work do you see in your neighbourhood? Drill Time 9.1 Repeated Subtraction 1) Find using repeated subtraction. a 2) Find using a number line. a 3) Word problems as sa o op a o ps o ma o ma students will be there in each group? p sm s s a amo pens will each child get? A Note to Parent Engage your child in the activities that involve division in day-to-day life a om o amp apa s amo s a o a a splitting pocket money or some chocolates with his or her siblings, putting o s as s a so o Division 39
10Chapter Measurement I Will Learn About measurement of length and distance using uniform units. comparison of two or more objects by their weights. use of the simple balance to compare weights. the order of containers based on their capacities. 10.1 Measure Lengths Using Non-standard Units I Think Raj and his mother decided to measure the length of a table. They measured using their cubits. Do you think that they will get the same number of cubits? I Recall We have learnt to compare the lengths of objects. Let us recall the same. 40
Tick the tallest tree and cross the shortest. Tick the longest insect and cross the shortest. We have also learnt to measure the lengths of objects using hand span. Measurement 41
Complete the given table. Measuring the length of Number of hand Object the objects spans I Remember and Understand We can also use our palm, foot and Hand span and cubit are used to pace to measure lengths. measure small lengths. Foot and pace are used to measure longer lengths. 42
Hand span Cubit Foot Pace Example 1: Measure these objects with the help of cubits. Write the number of cubits. One is done for you. Object Measuring the length Number of cubits 3 Measurement 43
We can measure the lengths of long objects using some shorter objects. Example 2: Measure these objects with the given smaller object. One is done for you. a) The paint brush is 6 paper clips long. b) The notebook is _________ erasers long. c) The chocolate bar is _________ sharpeners long. d) The pen is _________ crayons long. ? Train My Brain Write the lengths of the objects using the given smaller objects. a) b) c) 44
I Apply We measure the lengths of various objects in our daily life. Let us see a few examples. Example 3: Measure the lengths of the objects as directed. Write the measurement values in this table. Object Measure a) Length of a textbook Measured using Length of a TV stand hand span Length of a window b) Length of a table Height of a table Measured using Edge of a chair cubit Length of a rack c) Length of a mat Width of a mat Measured using Length of a blanket foot Width of a blanket Measured using pace d) Length of your class room Width of your class room Measurement 45
Example 4: Tick the most suitable non-standard unit to measure the lengths of the following objects. One is done for you. Object Hand span Cubit Book Blackboard Laptop Bed I Explore (H.O.T.S.) Estimation of lengths and distances Sometimes, we need not know the exact length of an object. A value closer to the actual value will be enough. In such cases, we guess the lengths and distances. To guess the values is called estimation. Let us now understand estimation of lengths. Example 5: Estimate the lengths of the given objects using your hands and feet. Write the values in a table. Check if your guess is close to the actual measure. a) Maths textbook b) Lunch box c) Water bottle d) Desk e) Duster f) Teacher’s table g) Class cupboard h) Height of your classroom door 46
Search
