by classklapTM MATHEMATICS 1 TEXTBOOK - PART ALPINE SERIES Enhanced Edition 1 Name: ___________________________________ Section: ________________ Roll No.: _________ School: __________________________________ NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 1 12/24/2018 2:37:19 PM
Preface IMAX Program partners with schools, supporting them with learning materials and processes that are all crafted to work together as an interconnected system to drive learning. IMAX Program presents the latest version of this series – updated and revised after considering the perceptive feedback and comments shared by our experienced reviewers and users. This series endeavours to be faithful to the spirit of the prescribed board curriculum. Our books strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. The books are split into two parts to manage the bag weight. The larger aim of the curriculum regarding Mathematics teaching is to develop the abilities of a student to think and reason mathematically, pursue assumptions to their logical conclusion and handle abstraction. The Mathematics textbooks and workbooks offer the following features: Structured as per Bloom’s taxonomy to help organise the learning process according to the different levels involved S tudent engagement through simple, age-appropriate language S upported learning through visually appealing images, especially for grades 1 and 2 Increasing rigour in sub-questions for every question in order to scaffold learning for students Word problems based on real-life scenarios, which help students to relate Mathematics to their everyday experiences Mental Maths to inculcate level-appropriate mental calculation skills Stepwise breakdown of solutions to provide an easier premise for learning of problem-solving skills Overall, the IMAX Mathematics textbooks, workbooks and teacher companion books aim to enhance logical reasoning and critical thinking skills that are at the heart of Mathematics teaching and learning. – The Authors NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 2 12/24/2018 2:37:19 PM
Textbook Features Let Us Learn About Think Contains the list of learning objectives Introduces the concept and to be covered in the chapter arouses curiosity among students Recall Discusses the prerequisite knowledge for the concept from the previous academic year/chapter/ concept/term Remembering and Understanding Explains the elements in detail that form the Application basis of the concept Ensures that students are engaged in learning throughout Connects the concept to real-life situations by enabling students to apply what has been learnt through the practice questions Higher Order Thinking Skills (H.O.T.S.) Encourages students to extend the concept learnt to advanced scenarios Drill Time Additional practice questions at the end of every chapter NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 3 12/24/2018 2:37:19 PM
Contents 1Class 1 Shapes 1.1 Understand Spatial Words�������������������������������������������������������������������������������� 1 2 Patterns 2.1 Patterns in Surrounding������������������������������������������������������������������������������������12 3 Numbers 3.1 Count in Ones and Tens ��������������������������������������������������������������������������������� 22 3.2 Compare 2-digit Numbers����������������������������������������������������������������������������� 31 4 Addition 4.1 A dd 1-digit and 2-digit Numbers ������������������������������������������������������������������� 38 4.2 Add Two 1-digit Numbers Mentally���������������������������������������������������������������� 46 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 4 12/24/2018 2:37:20 PM
Chapter Shapes 1 Let Us Learn About • basic flat and solid figures. • corners and sides of objects/ figures. • outlines of the bases of the objects. Concept 1.1: Understand Spatial Words Think Bantei has a glass, a book, a die and a birthday hat. He drew the outlines of their bases. He has three shapes as shown. Do you know what these shapes are called? NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 5 1 12/24/2018 2:37:20 PM
Recall Look at the positions of the cat with respect to the ball in these pictures. on under above below far near 12/24/2018 2:37:20 PM 2 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 6
in front of behind inside outside Look at the picture given below. The mouse, the cat and the woollen ball are in a line. The mouse is before the cat. The cat is between the mouse and the woollen ball. The woollen ball is after the cat. Shapes 3 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 7 12/24/2018 2:37:20 PM
Let us recall the concept of position. Choose the correct word to fill the blanks. One is done for you. a) The jug is on the table. (on/in) b) The ball is ___________________ the box. (outside/inside) c) The butterfly is ____________________ the dog. (above/under) d) The cat is ____________________ the table. (above/under) e) The dog is ____________________ the table. (far away from/near) f) The teddy bear is _____________________ the jug. (behind/in front of) & Remembering and Understanding Let us learn about shapes through an example. Example 1: Join the dots in order and name the shapes formed. a) b) c) d) 4 12/24/2018 2:37:20 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 8
Solution: a) Triangle b) Square c) Rectangle d) Circle Figures such as triangle, square, rectangle and circle are called flat figures. Let us learn more about flat figures. Study the following table. Flat figure Features Object Corner • 3 sides Side • 3 corners Corner • 4 equal sides Side • 4 corners Corner • 4 sides Side • 4 corners • O pposite sides are equal • No sides • No corners Shapes 5 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 9 12/24/2018 2:37:20 PM
Example 2: W rite the number of corners of the given figures. One is done for you. Figure Number of corners 3 Application Objects such as (cube), (cuboid), (cone) and (sphere) are called solid objects. Their figures drawn using straight or curved lines are called solid figures. Observe the solid figure shown here. Cube Cuboid Cone Cylinder Sphere 6 12/24/2018 2:37:20 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 10
Example 3: Some objects are given here. Draw and name the outlines of their bases. Object Outline of the base Circle Triangle Rectangle Circle Square Higher Order Thinking Skills (H.O.T.S.) Let us try to identify the different solids through an example. Example 4: Observe the given picture and answer the questions that follow. a) How many cubes are there? Colour them blue. b) How many cuboids are there? Colour them red. Shapes 7 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 11 12/24/2018 2:37:20 PM
c) How many cones are there? Colour them yellow. d) Name the solid figure shown: Colour them brown. e) H ow many are there in the given picture? Colour them Solution: green. c) 2 d) Cylinder e) 2 a) 3 b) 4 Drill Time Concept 1.1: Understand Spatial Words 1) Where is the dragon with respect to the box in the given pictures? a) b) c) d) 8 12/24/2018 2:37:20 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 12
e) f) 2) Complete the following table. Name of the solid figure Object Shapes 9 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 13 12/24/2018 2:37:20 PM
3) Circle the words that tell the position of the cat with respect to the ball. One is done for you. h y pmy z d x i c z c j y f l gmh i k x eqbe l own a b o v e wm s x f f ebp t d j g s r e h o y wp z l mo m i nmew j f z n on z pegqc k t ed l unde r do h t r h j ad t a f 4) Complete the following table. Object Shape of the base Name of the figure formed 10 12/24/2018 2:37:20 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 14
Object Shape of the base Name of the figure formed Shapes 11 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 15 12/24/2018 2:37:20 PM
Chapter Patterns 2 Let Us Learn About • patterns in shapes. • patterns in numbers. Concept 2.1: Patterns in Surrounding Think Bantei found paper cuttings of different shapes and sizes. He arranged the pieces in different ways and made many designs. Do you know how to make a design? Recall We see many things around us. They all have different sizes, shapes and colours. 12 12/24/2018 2:37:20 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 16
Recall the flat and solid shapes that we have already learnt. Different shapes are given in this table. Write their names. One is done for you. Figure Name Example Triangle Patterns 13 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 17 12/24/2018 2:37:20 PM
Figure Name Example & Remembering and Understanding Observe the following pictures. a) b) c) d) From the given pictures, we observe that: a) same shapes of different sizes and colours are arranged alternately. b) different shapes of different colours are arranged alternately. c) and d) same shapes of the same size but of different colours are arranged as a group. 14 12/24/2018 2:37:20 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 18
In all these, we observe that the groups repeat many times. Repetition of basic shapes is called a pattern. Let us see a few examples of patterns. Example 1: Observe the colours of the balloons and complete the pattern. Solution: T here are balloons of two colours: pink and purple. They are arranged alternately. So, the pattern formed by these balloons is shown below. Example 2: Complete the following patterns. One is done for you. a) b) c) d) Patterns 15 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 19 12/24/2018 2:37:20 PM
Try this! Colour the given pictures according to the pattern. a) b) c) Application Let us now see some more patterns. Example 3: Tick the picture that comes next in these patterns. One is done for you. Pattern Next picture 16 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 20 12/24/2018 2:37:20 PM
Pattern Next picture Example 4: Circle the figure that does not belong to each of the patterns given. One is done for you. a) b) c) d) Patterns 17 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 21 12/24/2018 2:37:20 PM
Patterns can also be seen in numbers as shown. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Higher Order Thinking Skills (H.O.T.S.) We see patterns on roofs of buildings and monuments. We also see them on floor tiles, saree borders, dresses, grills and so on. Patterns on floor tiles Patterns on roofs of monuments Patterns on saree borders 18 12/24/2018 2:37:20 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 22
Patterns on doors Patterns on grills Example 5: Complete the given patterns. One is done for you. a) 10 20 30 40 50 60 70 b) 2 4 6 8 _____ 12 ____ c) 14 13 12 ____ 10 _____ 8 Patterns 19 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 23 12/24/2018 2:37:20 PM
Drill Time Concept 2.1: Patterns in Surrounding 1) Observe these patterns. Colour the pictures to complete them. a) b) c) d) 2) Observe and complete these patterns. a) _________ _________ _________ b) ________ _________ ________ c) _______ _______ _______ d) _______ _______ ______ 20 12/24/2018 2:37:20 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 24
3) Continue the pattern by colouring the correct boxes. 9 10 12345678 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Patterns 21 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 25 12/24/2018 2:37:20 PM
Chapter Numbers 3 Let Us Learn About • the concept of zero. • the sequence of numbers up to 99. • place value and face value of numbers. • writing number names. • comparing, ordering and forming numbers. Concept 3.1: Count in Ones and Tens Think Bantei has five sticks. He counted them one by one. His father gave him more sticks to count. Is it easy to count them one by one? Is there an easier way? Recall We have learnt to count objects and write their numbers. 22 12/24/2018 2:37:20 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 26
Counting by 1s The numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 are called 1-digit numbers. They are also called single digit numbers. Colour the picture given. Use the colours as given for the numbers. 1 (One) 2 (Two) 3 (Three) 4 (Four) 5 (Five) 6 (Six) 7 (Seven) 8 (Eight) 9 (Nine) Numbers 23 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 27 12/24/2018 2:37:20 PM
& Remembering and Understanding There are 5 ducks in a pond. They flew away one by one. At last, there are no ducks in the pond. Let us learn to represent this using a number. Introducing ‘0’ 1 duck flew away. 2 ducks flew away. 4 ducks are in the pond. 3 ducks are in the pond. 3 ducks flew away. 4 ducks flew away. 2 ducks are in the pond. 1 duck is in the pond. All ducks flew away. So, there are ‘zero’ ducks in the No ducks are in the pond. pond. 24 If there are no objects, we write it as zero (0). NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 28 12/24/2018 2:37:21 PM
Example 1: Count the number of animals. Write the numbers in the boxes. One is done for you. Animals Numbers 4 Counting by 10s Let us say shows 1. Ten such boxes show a 10. So, = 10 ones = 1 ten Counting is easy if we group things into bundles of ten. We can make such collections of 10 with different things. 1 ten of balls 1 ten of books 1 ten of logs NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 29 Numbers 25 12/24/2018 2:37:21 PM
Suppose we are given 34 logs of wood to count. First, we count 10 logs and make a bundle. So, one bundle has ten wooden logs. With 34 logs, we can make 3 bundles. 3 tens (written as 30) 4 ones Thus, 4 logs of wood remain. We count these remaining logs in ones. The total number of wooden logs can be written as 3 tens and 4 ones. The number 34 has two digits. So, we use the Place Value Chart tens (T) and the ones (O) places for two digits. Thus, we write the number 34 in a place value Places Tens (T) Ones (O) chart as shown. Values 3 4 Each digit has its place and place value in the place value chart. Abacus counting We can show 2-digit numbers using an abacus. Let us show the number 9 using a spike abacus. TO TO TO One shows the We show a digit in the number 1. ones place with a blue bead. See Fig. (a). Nine in the ones spike show the 9 blue beads show 9 in number 9. the ones place. Each spike of an abacus can One shows the have only 9 beads. number 10. Fig. (a) Fig. (b) See Fig. (b). To show the number 10, we remove all the blue beads. We then put 1 green bead in the tens spike. The tens spike represents the tens place. Let us show the number 34 using a spike abacus. We put 3 green beads in the tens spike. We then put 4 blue beads in the ones spike. In the same way, we can show the numbers 46 and 99 on the abacus. So, 34 is 3 tens and 4 ones, 46 is 4 tens and 6 ones and 99 is 9 tens and 9 ones. 26 12/24/2018 2:37:21 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 30
TO TO TO shows 34 shows 46 shows 99 Number names Let us now learn the number names from 10 to 99. 10 ― Ten 20 ― Twenty 30 ― Thirty 11 ― Eleven 21 ― Twenty-one 31 ― Thirty-one 12 ― Twelve 22 ― Twenty-two 32 ― Thirty-two 13 ― Thirteen 23 ― Twenty-three 33 ― Thirty-three 14 ― Fourteen 24 ― Twenty-four 34 ― Thirty-four 15 ― Fifteen 25 ― Twenty-five 35 ― Thirty-five 16 ― Sixteen 26 ― Twenty-six 36 ― Thirty-six 17 ― Seventeen 27 ― Twenty-seven 37 ― Thirty-seven 18 ― Eighteen 28 ― Twenty-eight 38 ― Thirty-eight 19 ― Nineteen 29 ― Twenty-nine 39 ― Thirty-nine 40 ― Forty 50 ― Fifty 60 ― Sixty 41 ― Forty-one 51 ― Fifty-one 61 ― Sixty-one 42 ― Forty-two 52 ― Fifty-two 62 ― Sixty-two 43 ― Forty-three 53 ― Fifty-three 63 ― Sixty-three 44 ― Forty-four 54 ― Fifty-four 64 ― Sixty-four 45 ― Forty-five 55 ― Fifty-five 65 ― Sixty-five 46 ― Forty-six 56 ― Fifty-six 66 ― Sixty-six 47 ― Forty-seven 57 ― Fifty-seven 67 ― Sixty-seven 48 ― Forty-eight 58 ― Fifty-eight 68 ― Sixty-eight 49 ― Forty-nine 59 ― Fifty-nine 69 ― Sixty-nine Numbers 27 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 31 12/24/2018 2:37:21 PM
70 ― Seventy 80 ― Eighty 90 ― Ninety 71 ― Seventy-one 81 ― Eighty-one 91 ― Ninety-one 72 ― Seventy-two 82 ― Eighty-two 92 ― Ninety-two 73 ― Seventy-three 83 ― Eighty-three 93 ― Ninety-three 74 ― Seventy-four 84 ― Eighty-four 94 ― Ninety-four 75 ― Seventy-five 85 ― Eighty-five 95 ― Ninety-five 76 ― Seventy-six 86 ― Eighty-six 96 ― Ninety-six 77 ― Seventy-seven 87 ― Eighty-seven 97 ― Ninety-seven 78 ― Seventy-eight 88 ― Eighty-eight 98 ― Ninety-eight 79 ― Seventy-nine 89 ― Eighty-nine 99 ― Ninety-nine Let us see a few examples. Example 2: Count the number of objects. Write the number and its number name. Solution: The numbers and the number names of the objects are: Objects Number and number name 32 a) Thirty-two 17 b) Seventeen 61 c) Sixty-one 28 12/24/2018 2:37:21 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 32
Example 3: Write the places for each of the given numbers. Then, show them on a spike abacus. a) 13 b) 29 c) 64 Solution: Number T O a) 13 1 3 b) 29 2 9 c) 64 6 4 TO TO TO a) 13 b) 29 c) 64 Application We can form a number when the place values of its digits are given. Let us see a few examples. Example 4: A number has 1 in the tens place and 4 in the ones place. What is the number? Solution: Write the given digits in the place value chart as T O shown. 14 So, the number is 14. Example 5: Form using the following numbers. a) 3 in the tens place; 7 in the ones place b) 6 in the tens place; 0 in the ones place Solution: To form the numbers, write the digits in the place value chart as shown. a) T O b) T O 37 60 So, the numbers are 37 and 60. Numbers 29 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 33 12/24/2018 2:37:21 PM
Example 6: There are four groups for a drama competition. Each group has a few students as shown. Group A Group B Group C Group D a) C ount the number of students in Group B. Write its number name. b) Count the number of students in Group C. Write its number Solution: name. a) There are 10 students in Group B. Its number name is ten. b) There are 19 students in Group C. Its number name is nineteen. Higher Order Thinking Skills (H.O.T.S.) Let us see a few examples of 2-digit numbers on an abacus. Example 7: Write the numbers shown on the abacuses. a) b) c) TO TO TO 30 12/24/2018 2:37:21 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 34
Solution: Count the number of beads T O Number in each spike. Write it in the Example 8: a) 3 2 32 Solution: place value chart. Put a 0 in b) 3 0 30 the places where there are no c) 2 3 23 beads. Draw beads on abacus to show the given numbers. a) 78 b) 25 c) 39 a) T O b) 7 8 Write the digits in the place value chart. c) 2 5 3 9 Draw as many green beads as the tens digit. Draw as many blue beads as the ones digit. a) b) c) TO TO TO Concept 3.2: Compare 2-digit Numbers Think Bantei has 59 marbles and his sister has 95 marbles. How will they know who has more marbles? Numbers 31 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 35 12/24/2018 2:37:21 PM
Recall Observe the given picture. It shows cars of different colours. The red car is before The blue car is The black car is the blue car. between the red and after the blue car. the black cars. The words before, after and between give the positions of a car. In the same way, we can identify the numbers before and after a number. Look at these numbers. We see that 4 is before 5 and 5 is after 4. 1 2 3 4 5 6 7 8 9 10 11 12 20 19 18 17 16 15 14 13 Fill in the blanks with before, between or after numbers. a) _____ is before 14. b) 15 is after _____. c) 7 is between 6 and _____. & Remembering and Understanding Comparing 2-digit numbers is similar to comparing 1-digit numbers. We can order the numbers after comparing them. Let us learn this concept. 32 12/24/2018 2:37:21 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 36
Before and after numbers Read the following: a) 11 comes before 12; 12 comes after 11. b) 9 comes before 10 and after 8. So, 9 lies between 8 and 10. c) 15 comes before 16 and after 14. So, 15 lies between 14 and 16. Example 9: Write the numbers that come before and after: a) 96 b) 31 c) 49 d) 55 e) 60 Solution: The numbers before and after the given numbers are: Number Before Number After Number 96 95 97 31 30 32 49 48 50 55 54 56 60 59 61 Compare numbers We use the concept of more and less to find the greater and the lesser numbers. The symbols for greater than, less than and equal to are is >, < and =. Observe the following picture. The crocodile’s mouth is open The crocodile’s mouth is closed where there are more fish. where there are less fish. 4 is more than 1 or 4 is greater than 1. 2 is less than 3. We write it as 4 > 1. 2 is smaller than 3 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 37 We write it as 2 < 3. Numbers 33 12/24/2018 2:37:21 PM
When both the numbers are the same, we say that both are equal to each other. We write as 4 = 4. Let us see a few examples of using the symbols <, > and =. Example 10: Fill in the blanks with the correct symbols (<, > or = ). a) 23 ______ 21 b) 99 ______ 98 c) 54 ______ 74 d) 13 ______ 13 e) 4 _______ 7 Solution: a) > b) > c) < d) = e) < Application Order 2-digit numbers We can compare more than two numbers. For that, we have to arrange them in order. There are two ways to do this: Ascending order: Writing the numbers from the smallest to the largest Descending order: Writing the numbers from the largest to the smallest Example 11: Write the numbers 26, 29 and 25 in ascending order. Solution: The given numbers are 26, 29 and 25. All the three numbers have 2 in their tens place, 2 6, 2 9, 2 5. So, let us compare the digits in their ones place, 2 6 , 2 9, 2 5. As 5 < 6 < 9, 25 < 26 < 29. So, the ascending order of the numbers is 25, 26, 29. Example 12: Write the numbers 34, 38 and 30 in descending order. Solution: The given numbers are 34, 38 and 30. All the numbers have 3 in their tens place, 3 4, 3 8, 3 0. So, let us compare the digits in their ones place, 3 4 , 3 8 , 3 0. 34 12/24/2018 2:37:21 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 38
As 8 > 4 > 0, 38 > 34 > 30. So, the descending order of the numbers is 38, 34, 30. Form 2-digit numbers Let us learn to form the greatest and the smallest 2-digit numbers. Example 13: F orm the greatest and the smallest 2-digit numbers using 2 and 4 (without repeating the digits). Solution: To form the greatest number: TO 42 Write the bigger digit in the tens place and the smaller digit in the ones place. So, the greatest 2-digit number that can be formed is 42. To form the smallest number: W rite the smaller digit in the tens place and the TO bigger digit in the ones place. 24 So, the smallest 2-digit number that can be formed is 24. Example 14: Form the greatest and the smallest 2-digit numbers using 5 and 7 (by repeating the digits). Solution: To form the greatest number: TO 77 Find the larger digit. Here, it is 7. P lace the same digit in both the places in the place value chart. So, the greatest number is 77. To form the smallest number: TO Find the smaller digit. Here, it is 5. 55 Place the same digit in both the places in the place value chart. So, the smallest number is 55. Numbers 35 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 39 12/24/2018 2:37:21 PM
Higher Order Thinking Skills (H.O.T.S.) Let us see another example. Example 15: Some children are in a row as shown. Observe the picture and answer the questions that follow. Suma Ravi Rahul Salman Rita Amy Solution: a) Which two boys are just after Suma? 12/24/2018 2:37:21 PM b) Between which two children is Salman? c) Who is at the right end? d) Who is just before Rahul? a) Ravi and Rahul are just after Suma. b) Salman is between Rahul and Rita. c) Amy is at the right end. d) Ravi is just before Rahul. Drill Time Concept 3.1: Count in Ones and Tens 1) Write the numbers in the place value chart. a) 51 b) 90 c) 16 d) 72 e) 39 2) Write the number names of the given numbers. a) 49 b) 31 c) 94 d) 10 e) 32 36 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 40
3) Form numbers which have: a) 4 in the tens place and 1 in the ones place b) 9 in the tens place and 2 in the ones place c) 7 in the tens place and 3 in the ones place d) 8 in the tens place and 6 in the ones place e) 3 in the tens place and 8 in the ones place Concept 3.2: Compare 2-digit Numbers 4) FiIl in the blanks with before, after or between numbers. a) _____, 45 b) 98, _____ c) 19, ______, 21 d) 87, _____ e) ______, 32 5) Write the symbols >, < or = in the following. a) 34 ____ 30 b) 20 ____ 12 c) 17 ____ 60 d) 84 ____ 84 e) 56 ____ 90 6) Write the greater and the smaller numbers in each of these pairs. a) 39, 19 b) 87, 12 c) 65, 10 d) 45, 41 e) 76, 70 7) Arrange the numbers in ascending and descending orders. a) 87, 98, 80 b) 19, 17, 30 c) 40, 50, 19 d) 28, 19, 85 e) 34, 10, 99 8) Form the greatest and the smallest 2-digit numbers using the given digits. Do not repeat the digits. a) 3, 2 b) 9, 8 c) 1, 7 d) 4, 6 e) 7, 9 Numbers 37 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 41 12/24/2018 2:37:21 PM
Chapter Addition 4 Let Us Learn About • adding numbers up to 99 without regrouping. • adding two 1-digit numbers mentally. • different methods of adding numbers. Concept 4.1: Add 1-digit and 2-digit Numbers Think Bantei can count and add the number of his toys. His father asks him to add 35 and 22. He does not have that many objects to count and add. How can he add these numbers? 38 12/24/2018 2:37:21 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 42
Recall Let us recall counting of objects. Look at the vegetables given. Count and write their numbers in the boxes. Vegetables Number a) b) c) d) e) Addition 39 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 43 12/24/2018 2:37:21 PM
& Remembering and Understanding A pencil stand has 3 pencils as shown in Fig. (a). Another pencil stand has 4 pencils as shown in Fig. (b). We count the pencils in the two stands continuously. The Fig. (a) Fig. (b) last number gives the total number of pencils. Counting the number of objects together is called addition. The answer in addition is called the sum. The words add, total, together, in all, altogether and sum are some words used in addition. We use the symbol ‘+’ (read as plus) for addition. Example 1: Count and write the correct number of objects. One is done for you. a) 1 89 b) 40 12/24/2018 2:37:21 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 44
c) Methods of addition: 1) Addition using fingers 2) Addition using the number line 3) Vertical or column addition Let us understand these methods. Addition using fingers Observe these fingers. Each of them shows the number given. Addition 41 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 45 12/24/2018 2:37:21 PM
Let us learn to add two numbers using fingers. Example 2: Add using fingers: a) 4 and 3 b) 1 and 5 c) 5 and 5 Solution: a) 4 + 3 += Open 4 fingers on one hand. Open 3 fingers on the other. B egin counting the fingers on one hand. Continue to count the fingers on the other hand. The number counted for the last finger is the sum or total. So, 4 + 3 = 7. b) 1 + 5 += So, 1 + 5 = 6. c) 5 + 5 += So, 5 + 5 = 10. 12/24/2018 2:37:21 PM Addition using the number line A line marked with numbers is called the number line. We use it to add numbers. Let us see an example. 42 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 46
Example 3: Add using the number line: a) 2 and 3 b) 4 and 4 c) 3 and 4 Solution: a) L et us find 2 + 3 using the number line. Draw an arrow from 0 to 2. To add 3 to 2, we move 3 steps to the right of 2. Draw arrows for each step as shown. The number at which the steps end is 5. So, 2 + 3 = 5. b) 4 + 4 So, 4 + 4 = 8. c) 3 + 4 So, 3 + 4 = 7. Vertical or column addition We can add numbers by writing them one below the other. This is called vertical addition or column addition. Let us see a few examples. Addition 43 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 47 12/24/2018 2:37:21 PM
Addition of 1-digit numbers Example 4: Add 6 and 2 by writing the numbers in columns. Solution: Write the numbers under the ones place, as shown. O 6 +2 8 Addition of 2-digit numbers Example 5: Add the following by writing the numbers in columns. 23 + 32 Solution: Step 1: Add the ones Step 2: Add the tens TO TO 23 23 +32 +32 5 5 5 Solve these TO TO TO 41 14 78 +2 8 +3 3 +2 1 Application We now know how to add numbers. Let us see some real-life examples of addition of numbers. Example 6: Madhu has 5 kites and Sita has 4 kites. How many kites do they have in all? 44 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 48 12/24/2018 2:37:21 PM
Solution: Write the numbers one below the other. Add them and write the sum as shown. O 5 +4 9 So, Madhu and Sita have 9 kites in all. Example 7: Ram had 14 marbles. Shyam gave him 15 marbles. How many Solution: marbles does Ram have altogether? TO Write the numbers one below the other. Add them 14 and write the sum as shown. So, Ram has 29 marbles altogether. + 15 29 Higher Order Thinking Skills (H.O.T.S.) We have learnt how to add two 1-digit and 2-digit numbers. Let us now learn to add three 1-digit and 2-digit numbers. Example 8: Sunita bought 2 mangoes, 3 apples and 4 bananas. How many fruits did she buy altogether? Solution: Write the numbers under the ones place and add. O 2 +3 +4 9 So, Sunita bought 9 fruits. Example 9: There are 14 students in Row 1. Row 2 has 15 students. Row 3 has 10 students. How many students are there altogether? Addition 45 NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 49 12/24/2018 2:37:21 PM
Solution: Write the numbers one below the other. Step 1: Add the ones Step 2: Add the tens T O TO 14 14 + 15 + 10 + 15 39 + 10 9 So, there are 39 students altogether. Concept 4.2: Add Two 1-digit Numbers Mentally Think Bantei had 4 chocolates. His sister gave him 2 more. Bantei could tell the total number of chocolates he has. But he did not use a paper and a pencil. Can you try to find the total mentally? Recall To add numbers mentally, first we must know the correct order of numbers. Let us practise the correct order of numbers. Write the numbers in the blanks given. a) 1 to 20 1 ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 20 ___ ___ ___ ___ ___ ___ ___ 46 12/24/2018 2:37:21 PM NR_BGM_9789388751797 ALPINE G01 MATHS TEXTBOOK PART 1_Text.pdf 50
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