Government of Karnataka Mathematics Work Book

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Government of Karnataka

Mathematics Work BookPart - 1

6Sixth Standard

_________________________2020-21

Name : ...........................................................

Name of the School : ..................................................

..................................................

Dept. of State Council of Education Research and Training

100 Feet road, Banashankari 3rd State, Bengaluru-560085

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Contents

Sl.No. Contents Page No.

Preface ii

Learning Outcomes iii

Contents iv

1. Knowing Numbers 1 - 13

2. Whole Numbers 14 - 22

3. Playing with numbers 23 - 36

4. Basic Concepts of Geometry 37 - 46

5. Understanding Elementary Shapes 47 - 53

6. Integers 54 - 64

Part - 1

Students to follow

Practice one page of the workbook every day.

Only after completing a page, move on to next page.

If you fi nd any diffi culties to understand take the help of friends/teachers.

In self evaluation Page mark ‘’ for your favourite activity, ‘’ for par-tially liked and ‘’ code for unwelcome activity.

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Learning Outcomes

• Can Solve the verbal Problems by using basic operations on bigger numbers.

• Can do basic operations on Natural numbers, Whole numbers and integers, using Number Line.

• Can Solve Problems on LCM and HCF.

• Can Solve the problems on money, length, weight and temperature by using the operations on Fractions and decimals.

• Can solve the problems of daily life related to ratio proportion and unitary method.

• Can identify basic geometrical shapes like line, segment,angle, circle, triangle, quadrilateral in our surrounding environment.

• Can classify the triangle and quadrilateral based on angles.

• Can identify symmetrical objects and their line of symmetry in nature.

• Can Construct angles using scale and compasses and circle of given radius.

• Can differentiate the area and perimeter of closed fi gures.

• Can form albebraic expressions by using variables and constants.

• Can solve problems of daily life by organising, analysing and explaining the data.

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1. Knowing Numbers - 1/13

1. KNOWING NUMBERS

I. Answer the following questions in the box provided :

1. How many digits are present in the following numbers

25 -

409 -

345 - 7892 -

2. Which is the smallest three digit Number?

3. Which is the largest four digit Number?

4. Which number should be added to the given number to get the largest

four digit number? 8888 + =

5. Which number should be subtracted from the smallest six digit number

to get the largest fi ve digit nuber? 1,00,000 − =

II. Choose the correct answer from the given options and write its an-swer code in the given box.

1. The Place value of 8 in 86,93,04,600 is

a) Eight Crore b) Sixty Eight Crore

c) Eighty Crore d) Eight Six Crore

2. 2143 in Roman number system a) MMCXLIII b) MMCLIII

c) MMCXLII d) MMDXLIII

3. The difference of place values of 3 in 31,16,365

a) 29,99,700 b) 30,00,700

c) 29,90,700 d) 30,00,300

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4. Appropriately derived Roman number

a) VVI b) LLXX

c) MDDL d) XXI

5. In a class there are 27 boys and 19 girls. The total number of admitted students in Roman number is.

a) XCV b) XLIV c) XLVI d) XLVII

6. 498 in Roman number system

a) CDCXVIII b) CDCXIV

c) CDXCVIII d) CDXCVII

7. Raju's age is 22 years and Ramu's age is 19 years. The difference of their ages written in Roman number.

a) III b) XXDI

c) XXXLII d) XXXLL

8. The product of 1768 x 25 is

a) 44,100 b) 44,200

c) 44,300 d) 44,400

9. The correct form of descending order of 85868788, 85888687, 85878688 is

a) 85868788 > 85878688 > 85888687

b) 85878688 > 85868788 > 85888688

c) 85868788 > 85888687 > 85878688

d) 85888687 > 85878688 > 85868788

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2.

16,79,481 +

3.

83,24,680 +

IV. In the given pairs of Whole numbers, write the number, which comes fi rst on the number line.

Sl. No. First Number Second Number Answer

1. 263 236

2. 108 118

3. 4095 4056

4. 12199 12991

5. 877689 877681

V. Solve the following.

[Remember: By using the rule solve one step at once

1. (3 + 2 × 3) × 2=

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10. When the number 648340021 is written using comma in International number system

a) 648,340,021 b) 6, 4, 8, 3, 0, 0, 2, 1

c) 64, 83, 40, 02, 1 d) 64,83,40,02

11. The Proper ascending order of the folloing number

(i) 6392 (ii) 6782 (iii) 6784 (iv) 6654

a) (i) < (iii) < (ii) < (iv) b) (ii) < (iv) < (iii) < (i)

c) (i) < (iv) < (ii) < (iii) d) (ii) < (iii) < (i) < (iv)

III. Do as shown in the model.

50,000

800

50,80056,829 +

Instruction : The place value of 5 is 50,000 and the place value of 8 is 800, sum of those two numbers is written as 50,800.

1.

39,20,868 +

50,000 + 800 50,800

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2. (2 × 3 + 4) ×5 =

3. (6 – 2 × 2) × 9 =

4. (4 + 2 × 3) ÷ 5 =

5. 12 ÷ (2 + 2 × 1)=

6. 7 × (3 + 48 ÷ 8)=

7. 3 × (9 + 2 × 2)=

8. (22 – 3 × 4) ÷ 2=

9. (7 × 1 + 3) × 4 =

10. 33 ÷ (4 + 5 × 1 + 2)=

11. 15 × (3 + 1 × 1)=

VI. Estimate the following numbers to the nearest tens, hndreds and thousands.

Sl.No. Number Nearest 10 Nearest 100 Nearest 1000

a. 875

b. 77,318

c. 1,99,560

d. 2,568

e. 4,760

f. 51,555

g. 43,090

h. 28,902

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i 2,99,960

j 1,48,451

k 98,99,789

l 73,950

m. 84,101

n. 1,20,480

VII. Think and answer the following:

1. Write the given numbers in words in Indian number system by using comma.

a) 86391:_____________________________________________

b) 903512: ____________________________________________

c) 2854709: ___________________________________________

2. Write the given numbers in descending order.

a) 97,654, 98,000, 96,999 ______________________________

b) 10,56,783, 9,99,999, 12,00,101 ________________________

3. Write the place value and face value of the underlined number

a) 372814 ____________________________________________

b) 56082431 __________________________________________

4. Write the smallest and largest 6 digit number without repeating any digit from 3, 7, 2, 0, 6 and 4.

Smallest number : _________________________

Largest number : ________________________

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5. Find the sum of the largest 6 digit number and the smallest 4 digit number.

6. Insert commas suitably according to Indian system of numeration.

a) 246813579 : _________________________________________

b) 136857099 : _________________________________________

7. Insert commas suitably according to International system of numeration

a) 2453190876 : ________________________________________

b) 5400958203 : ________________________________________

8. Write the following in Numerical form.

a) Four crore twenty lakh three hundred and six :__________________

b) Seventy nine lakh eight : __________________________

9. Write your date of birth in the box given below Date Month Year

a) Write the above date of birth in the systems given below

Indian Number system

International Number system

Roman Number system

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10. Find the difference of 74,582 and 65,382 by rounding off to nearest thousands and compare the difference to the actual answer.

11. Match the numbers with their place value of 4.

a) 14,50,916 4,000b) 48,02,357 4,00,000c) 3,32,34,901 40,00,000

12. Arrange the following numbers in ascending and descending order

100101, 100001, 100011, 10001

Ascending Order :

Descending Order :

13. Find the Difference of the place values of seven in 78,65,49,756.

14. A Steel wire of length 100 m is divided into 8 equal parts. Find the length of each part?

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BRAIN TEASERSVIII. Answer the following:

1. There are 4 strips of antiboiotic tablets in a box. There are 9 tablets in each strip and each tablet contains 250 mg of medicine. Find the total weight of medicine in grams present in 50 boxes.

2. 6003 marbel tiles are required to cover the fl oor of an auditorium. There are 9 marbel tails in a pack. How many packs are to be purchased by the civil contractor to complete the fl ooring work?

3. Merchant Raveesh has ` 78,592 . He wishes to purchase 39 Radios of cost of ` 1,234 each? After purchase how much amount is left with him?

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4. The capacity of a water tank is 1000l. The Capacity of the Bucket which is used to fi ll the tank is 12500ml. How many buckets are to be used to fi ll the tank.

5. 1m 30cm of cloth is required to stitch a pant. How many pants can be stitched in 15 m of cloth? And fi nd the length of the remaining cloth?

6. There are 2,75,67,890 bags of wheat in the Godown of Food Corporation of India. At the time of drought in Odissa and Assam States, FCI sent 87,89,045 and 96,73,500 bags of wheat. Then how many bags of wheat are remained in FCI ?

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7. The population of the town is 9,75,689. In fi rst year the population is increased by 4563. By the next year the population is decreased by 8976. Then what would be the population in last two years?

8. A School has purchased 70 black boards and 40 chairs. Cost of each black board and chair is ` 450 and ` 225 respectively. What is the total amount that school has spent to purchase these?

9. In the number 9,87,964 subtract the face value of 7 from its place value.

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10. Record the temperature of any fi ve days of a week. Find the difference of maximum and minium temperature.

Days Maximum Minimun DifferenceDay 1Day 2Day3Day 4Day 5

11. Answer the following questions with the help of the tabel given below:Fruits Price/Kg Apple ` 40.00Orange ` 30.00Grapes ` 20.00Papaya ` 20.00Gauva ` 15.00

a) What is the cost of 2 kg of Papaya?

b) Which fruit costs `10 less than the apple'?

c) Which fruit costs double that of grapes?

d) What is the total cost of 2 kg of Papaya?

e) Whats is the cost of 1 Kg of apple and one Kg of Grapes?

f) Which fruit has the highest price?

g) Which fruit has the lowest price ?

h) Which fruits have the same price?

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IX. Identify the numbers. Write the numbers in Roman number system and show the exit to Bhumika. ?

MMMCDXXI

DXCIV

453

Student Self Evaluation

Sl.No.

Learning Outcomes

1. I understood to identify the biggest number, formation of numbers, place value and face value of numbers.

2. I understood putting comma in different number system- reading, writing numberts, Roman Number system.

3. I learnt estimating numbers, usage of brackets, operations on numbers.

4. I learnt to do operations on bigger numbers which come across in day to day situations.

Teachers Opinion

Excel-lent

Good Aver-age

EXIT

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2. Whole Numbers - 1/9

2. Whole Numbers

I. Choose the correct answer from the given options and write its an-swer code in the given box.

1. The predecessor of 1998a) 1997 b) 1996 c) 1995 d) 1994

2. The Successor of 1999a) 1998 b) 2000 c) 2001 d) 2002

3. Use the proper symbol in 540 ________ 504a) > b) < c) = d) ≥

4. The proper symbol to be used to complete the statement 78654 _____ 87654

a) > b) < c) = d) ≤

II. Fill in the blanks with the correct answer :1) The smallest whole number is ________

2) The predecessor of 10049 is ________

3) The Natural number that doesn't has any predecessor is ________

4) Additive identity of whole numbers is ________

5) (7 + 8) + 3 = 7 + (8 + 3) shows ________ rule of addition.

6) The largest 3 digit even number is ________.

7) Multiplicative identity of the whole numbers is ________

8) The division of whole numbers by ________ is not defi ned.

9) ________ + 2417 = 2417

10) In division, if the divident, the divisor and the quotient are same, then the no. is ________

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11) 6678 = 63 ( _______ + ________ )

12) The value of 13 × 0 is _______

13) The whole number which has no predecessor _______

14) The whole numbers are closed under _______ & _______.

15) The smallest natural number is _______

16) The successor of 99,999 is ___________

17) The whole number has _______ as its predecessor.

18) The total number of whole numbers between 53 and 75 is _______

19) The total number of Natural numbers between 86 and 100 is _______

20) Successor of 4,10,739 is _______

21) The Predecessor of 3,15,619 is _______

22) The number to be added to get the successor of any Natural number is _______

23) When '1' is subtracted from any number (Except Zero), we get _____

24) The smallest two digit whole number is _______

25) The biggest three digit Natural number is _______

26) 1 Million = ________ Thousands

27) 1 Crore = ________ Lakhs

28) 1 km = ________ m

29) 1 g = ________ mg

30) 1 l = ________ ml

III. Say whether True or False :1) All natural numbers are whole numbers. 2) Whole numbers are closed under division.

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IV. Brain Teasers :Solve the following :

1. How many times does 4 comes in unit place of Natural numbers upto 100?

2. How many whole numbers are there till 80?

3. The price of a meal and a cup of milk is `47 and `19 respectively. Then how much money is spent for these in 5 days ?

4. You are travelling in a bus with the constant velocity of 55 km/h from Bangalore to Dharwad. How much time is required to travel a distance of 220 km?

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5. In a Hostel, 32 Students can stay in a room. Then how many students can stay in 5 such Rooms?

6. A general knowledge book has 365 pages. Now you are reading 123rd page. Then how many pages still you have to read?

7. The product of two numbers is 3,75,200. If one of the number is 160, then which is another number?

8. When 4,56,789 is divided by a number, we get 1952 as quotient and 21 as reminder. Then fi nd the divisor?

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9. When 4 digit biggest number is divided by 2 digit biggest number, what Quotient and reminder you get?

10. In a school, the annual fee of a 6th Standard Student is `135 and 7th standard student is `165. Then what is the total amount collected, if there are 235 students in 6th Standard and 169 students are in 7th standard?

11. Find the divisor, when 43,621 is divided by a number to get the quo-tient 1246 and the reminder 11.

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12. The Product of two numbers is 118275. If one of the number is 1425, then which is the other number?

13. A Merchant sells 155 Radios on Monday, 245 Radios on Tuesday. If the cost of one Radio is `3050, then what is the total amount collect-ed by the merchant?

14. Sheela scored 49 marks in Maths, 39 in English and 51 in Science. John Scored 62 marks in Maths, 32 in English and 54 in Science. Then whats is the total marks scored by them?

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15. A School has 25 Students in each section. If ` 812 is collected from each student as monthly fee. If the school has 40 sections, How much fee is collected for a month ?

16. A bouquet has 7 roses and 8 Lily fl owers. Then how many fl owers are there in 9 such bouquet? Write the mathematical expression for the statement?

17. A hotel has fi xed ` 55 for lunch and ` 45 for dinner to John. Then, what is the total amount paid to the hotel at the end of 7 days?

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V. Four bags fi lled with numbers are given. Choose any 10 numbers from the bags so as to get 1554 as their sum.

37 37 3737 37

373737

37

111 111111111

111111

185 185185185

185 185

259259259

259 259

VI. Every shapes has a distinct value. Find their values.

+ + = 24

+ = 25

− = 8

+ + = ?

22


VII. RIDDLES1. I'm a 4 digit number between 5000 and 6000. My face valuein units place is half the face value of tens place. My face value in hundreds place is thrice the face value of tens place. Then which number am I?

2. I'm an odd number(I'm less than 25 and more than 11 and also a factor of 39. Who am I?

2. I'm more than 6x5 and less than 5x7, I'm nor an even number, neither 31, then Who am I?

VIII. Draw a circle inside a Square, a triangle inside the circle and a circle inside the triangle. Write your age inside the circle.

Students Self Evaluation

Sl.No. Learning Indicators 1. I understood natural numbers, whole numbers,

predecessor and successors.

2. I understood the properties of the whole num-bers, comutative propery of addition and mul-tiplication, associative property and Identity element.

3 I understood the operations on whole numbers..

Teachers Opinion

Excel-lent

Good Aver-age

23

3. Playing with Numbers - 1/14

3. Playing with Numbers

I. In the given numbers

If a number is completely divisible by 2 put mark.If a number is completely divisible by 3 put mark.If a number is completely divisible by 5 put mark.If a number is completely divisible by 9 put mark.

1 2

3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

● 4 numbers which are completely divisible by 2 ____ ____ ____ ____


● 4 numbers which are completely divisible by 2 & 3 ___ ____ ____ ____



24


II. If the given numbers are divisible by the following number mark 'If not mark `’ in the given place.a) 42 b) 237 c) 1620

by 2 ........ by 2 ........ by 2 ........

by 3 ........ by 3 ........ by 5 ........

by 4 ........ by 6 ........ by 10 ........

by 6 ........ by 7 ........ by 9 .........

III. Mark the factors of the remaining numbers as shown in the table.

Num

bers →

10

9

8

7

6

5

4

3

2

1

1 2 3 4 5 6 7 8 9 10Factors →

25


I. Four answers are given to the following questions. Choose the correct answer and write the answer code in the given box.

1. The biggest of the consecutive composite number between any 2 prime numbers from 1 to 11. a) 7 b) 8 c) 9 d) 10

2. The pair of Co-prime numbers : a) 6 and 8 b) 18 and 35

c) 7 and 35 d) 35 and 15

3. Express the number 14 as the Sum of Two prime numbers.a) 3 + 11 b) 7 + 7 c) 5 + 9 d) 1 + 3

4. The sum of prime numbers between 60 and 80 are completely divisible by. a) 2 b) 5 c) 3 d) 4

5. The LCM of two numbers is 504. Which of the following is not their HCF? a) 9 b) 5 c) 11 d) 4

6. If a number is divisible by two co-prime numbers, then number is divisible by its .......... a) Sum b) Difference c) Product d) Division

7. The number has 7 as remainder on dividig it by 15 or 20 isa) 307 b) 68 c) 601 d) 157

8. Prime factors of 266 area) 2, 7, 19 b) 2, 3, 7 c) 5, 2, 3 d) 7, 3, 11

9. If a number divisible by 4, then its .... (a) last digit should be 4 (b) Last digit should be zero (c) last digit divisible by 4 (d) last digit shoule be 8.

26


10. A number having 1 as the common factor.

a) Even Number b) Odd number

c) Prime Number d) Composite Number

11. The HCF of 343 and 70 is

a) 7 b) 10 c) 3 d) None of these.

12. The greatest 4 digit number which is completely divisible by 6

a) 9999 b) 9992 c) 9997 d) 9996

13. If 5*84 is divisible by 3, Then the smallest number inplace of *

a) 2 b) 3 c) 1 d) 0

14. Write the missing number

30

15 2

? 5

a) 1 b) 2

c) 3 d) 4

15. To examine divisibility of 2, 5, 10 We have to observe

a) Sum of the digits b) Last digit

c) Last two digits d) last 3 digits

16. 4 = 2 × 2, 15 = 3 × 5, therefore the H.C.F. of 4 and 15 is

a) 0 b) 1 c) 2 d) 3

17. If a number is completely divisible by 5 and 3, then that number is also divisible by

a) 6 b) 15 c) 4 d) 8

27


18. The common factor of Coprime numbers

a) 0 b) 1 c) 2 d) 3

19. In series 5, 7, 11, 13 the next number isa) 15 b) 17 c) 9 d) 19

20. The smallest number which is divisible by 6, 15, 18 after dividing that number always gives the remainder 5. The number is

a) 90 b) 180 c) 95 d) 185 II. Complete the following factor-trees.

a)

50

b)

68

c)150

d)80

28


e)

92

46

2

f) 180

2

5

2

III. Match A with B.

A B1 45 Multiple of 12 15 Factor of 403 24 Multiple of 74 20 Factor of 305 35 Multiple of 9

IV. By using the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9, fi ll the blanked boxes. The sum should be 100 (digits can be repeated)

+

+

+

10 0

29


V. Group Activity : ● Divide the students of the class into 8 teams. For each team give one

prime numbers and named those numbers as 2,3,5,7,11,13,17 and 19 like that.

● Prepare the slips containing composite numbers in large quantity.

● Folding the prepared slips, keep in bowl. Then teacher take one slip and write the number shown in the slip on the blackboard. which team who got factors of that nmber , they will get 10 marks.

● Like this continue the game by taking the slips.

● After 20 minutes highest scored team will win.

VI. Which of the following statements are true? If it is true tick, `’ If not tick `’.

1) 1 is a composite number

2) All prime numbers are odd numbers.

3) Any composite numbers have at least 3 factors.

4) Every number has its own highest facror.

5) 1 is the factor of every number `

6) The multiples of any number are infi nite.

7) Prime number is always an even numbers.

8) Every multiple of a number is completely

divisible by that numbers..

9) 18, 24 and 30, are the multiples of `3’

30


VII. Activity:

Note : Answer the following questions. determine/decide whether the number. If it is prime number circle the given letter 'P' or If it is a composite number circle the letter 'C' and write the factors of that number,

1) From how many years you have been attending the School ................ P or C.

2) So far how many books have you read? ________ P or C

3) Which are the last two digits of your year of birth ? _____ P or C

4) If you write your name in English, how many letters are there in your name ________ P or C

5) Which is your favourite colour? The number of letters in that colour ________ P or C

6) How many uncle and Aunts you have ________ P or C

7) Write your date of birth and month in numbrs and add them, then the sum is ________ P or C

8) The sum of the last 4 digits of your telephone number______ P or C

VI. Activity : Tests for divisibility of a numbers.

A box containing 1 to 9 digits of slips. Each of the student picks 2, 3 or 4 slips and write that number in given space. By using divisibility test. Fill the blanks. (Mention YES or NO)

No. Is divisible by this number?

2 3 4 5 6 8 9 10 11Yes No Yes No No Yes No No No

31


IX. Either Prime number or Composite number?(Dise Play) Every players roll two dise and write the number shown in the dise in

the given suitable square boxes. Mltiply these two numbers and write the product in the suitable place. Identify whether the product is prime or composite number. The player who scored highest will won.

Player Dise-1 Dise-2 Prod-uct

Prime/Composite

1 × =2 × =1 × =2 × =1 × =2 × =1 × =2 × =1 × =2 × =1 × =2 × =1 × =2 × =1 × =2 × =

32


X. 1. Find the H.C.F. for the following.a) 12 and 30

b) 150 and 210

c) 140, 150 and 210

d) 90, 120 and 150

33


2. Find the L.C.M. for the following.a) 25 and 40

b) 16 and 50

c) 55, 70 and 77

d) 15, 20 and 35

34


XI. Solve the following.1. Three Tankers containing 527 liters, 646 liters and 748 liters of water

respectively. Find the maximum capacity of a container that can measure the water of the three containers exact number of times.

2. The length of two rods are 6m, 75 cm and 15m, 50 cm respectively. In order to measure these rods fi nd the maximum length of the tape .

3. The traffi c lights in a Circle-A, Circle-B, Circle-C change after 48,72,108 seconds respectively. These three signal lights show green colour at 8:20:00, Then at what time will they again show green colour.

35


4. 40 girls and 32 boys of 6th Standard are willing to participate in interschool debate competition.

a) Make teams having equal number of girls and boys. Find the number of boys and girls in each team?

b). How many teams can be formed maximum?

5. What is the smallest 4-digit number which is divisible by 21?

Students Self Evaluation

Sl.No.

Learning Indicators

1. Understood Multiples, Dividents, Factors, Prime numbers, Composite numbers, Co-prime numbers.

2. Know Divisibility rule of numbers

36


3 To fi nd HCF and LCM of given Numbers(Know)

Teacher's Opinion

Excel-lent

Good Aver-age

Small TestI. Answwer the following questions and fi ll in the given space.

1. What is the number added to the following number to become greatest

4-digit number? 7777 + =

2. To complete the following statement, use suitable symbol 98654 _____ 77654

a) > b) < c) = d) ≥

3. In the series 8, 11, 14, the next number isa) 15 b) 17 c) 9 d) 19

II. If the given numbers are divisible by the following numbers, put `’mark , If not put `’ mark a) 84 b) 537 c) 1640 By 2 ........ By 7 ........ By 4 .......

4. Harish had ` 48000 with him. He placed an order for purchasing 30 speakers at ` 1200 each. How much money will remain with him after the purchase?

5. In the students canteen everyday Cost ` 37 for meal and ` 11 for 1 glass milk will be taken. Then how much money was spend by the students for 7 days?

37

4. Basic Concepts of Geometry - 1/10

4. BASIC GEOMETRICAL IDEAS

I. NOTE : Four answers are given to each question. Write the correct answer's letter in the given 'box'.

1. In the following fi gures, the polygon

a) b) c) d)

2. The angles made by short and long hand of the Clock at 9'O' clock a) 90O, 300O b) 270O, 90O

c) 75O, 225O d) 30O, 300O

3. In the given fi gure, we represent the angle made by B asA

B D C

a) ACB b) ABC

c) ABC d) BAC

4. Among the following this has the specifi c measurement

a) Paint b) Ray

c) Line d) Line Segment

5. In the following fi gure, number of triangles are

a) 10 b) 12

c) 13 d) 14

38


6. In the given fi gure, DE represents A

B

D

C

E F

G

a) Ray b) Angle

c) Line Segment d) Line

7. Number of lines passing through a point

a) one b) Infi nite

c) two d) Zero

8. In a plane, two non-parallel lines intersects each other at

a) one point b) two points

c) 3-points d) Infi nite points

9. In the following fi gures, odd one is.

a) b)

c) d)

10. Which of the following not representing the plane? a) Foot Ball b) Black Board c) Wall d) Surface of the book

11. Which of the following statement is correct?

a) A line segment has no length.

b) A line segment has one end point.

c) A line segment has length.

d) None of the above.

39


II. State whether the following statements are true (T) or false (F), If the statement is false make it correct:

1. A four sided polygon has two diagonals.

2. A Circle has vertices.

3. A point has measure, because point can be seen as big (bulk) dot on the pages.

4. The surface of the swimming pool (without any waves) represents a plane..

5. The highest intersecting points of two lines are three.

6. Only one line can be drawn through a given point.

7. In a circle the diameter is twice its radius.

8. Two lines, which do not intersects each other called parallel lines.

9. The line is greater than the line segment.

III. a) Draw the following shapes and fi ll your favourite colours.

a) b)

c) d)

40


IV. Observe the following fi gure, based on the fi gure answer the questions.

C B

A

T

P

N

M

O 1. Three angles made at the vertex ‘O’

a) b) c)

2. Three angles made at the vertex ‘T’ a) b) c)3. Three angles having common side as ‘OP’ a) b) c)

4. ‘Three angles having common side as ‘TA’

a) b) c)

5. An angle with vertex ‘O’.

6. An angle without the vertex ‘T’

V. Name the angle made by the following digit numbers.

Number

Angle À

VI. Which of the following is the example for a) Point b) Line Segment c) Plane ?

1. Edge of the Wall

2. Tip of the Pen

3. Floor of the house

41


4. Edge of the Table

5. Wall of the Room

6. Locate the cities in the map

7. Edge of the Match Box

VII. With the help of given fi gure, Name the following :

1. Chord __________F

2. Diameter __________

3. Radius __________

4. Semicircle __________

5. Major Segment __________

6. Minor Segment __________

7.Fill 'Red' colour to major segment

8.Fill 'Blue' colour to minor segment

VIII. Complete the fi gure by connecting all the given paints, Name the

fi gure and complete the given data.

E

A

B

D

C

1. This is Polygon.

2. Name the completed fi gure

3. Five Vertices = a) b) c)

d) e)

4. Five Diagonals = a) b) c)

d) e)

42


5. Five Triangles a) b) c)

d) e)

IX. Name the vertices, Angles and sides in the following fi gures.

Figure Vertices Angles Sides

1.

Q

P R

P QPR QP, PR

2.

A

B C

D

3.

A Q

O

R

S

4. Q

P

TS

R

43


X. Complete as for the following examples.

Shape Name of the Shape

Verti-ces Sides Angles

1.

ExampleA

CB

∆ABC A, B, CAB BC AC

A OR BAC

B OR ABC

C OR ACB

2.

3.

4.

P

RQ

M

PN

X

Y

Z

44


IX. Observe the following fi gure. With the help of this, name at least 10 vertices, 10 line segments, 10 angles, two pair of parallel lines and 3-polygons.

1. 10 Vertices ____, _____, _____, _____, _____,

____, _____, _____, _____, _____ .

2. 10 Line Segments ____, _____, _____, _____, _____,

____, _____, _____, _____, _____ .

3. 10 Angles ____, _____, _____, _____, _____,

____, _____, _____, _____, _____ .

4. Two pairs of parallel lines _____________ , ____________ .

5. Three polygons __________ , __________ , __________ .

45


X. Construct the circle of radius 3cm . Draw diameter AB, Name point C on the circumference and join AC and BC and measure them.

AC = _______ cm

BC = _______ cm

XI. Observe the following fi gure and write the answer.

A

D E

H

R

G

FC

B

PQ

1. 3 - Quadrilaterals _________, __________, _________ .

2. 6 - Diagonals _______, _______, ______, ______, _______, _______ .

3. 2 - Quadrilaterals having common sides

_______ and _________ quadrilateral ____________ Common side.

_______ and _________ quadrilateral ____________ Common side.

4. Pair of Quadrilaterals having common vertex

_______, _______, _________, ________ .

5. Quadrilateral having common vertex

_______, _______, _________, ________ .

6. 3 - pairs of _________ and _________, _________ and_________, _________ and _________ .

46


XII. Using the following letters given in the box, Try to Identify the En-glish words belongs to Geometry. [circle, line, angle, point, like this learn the remaining words with your teacher]

T T S R O U S E R DR S Q H I R T R C II V U T O M A E V AA T A O N I O C L MN C R S C H O L D EG I E N W S E I V TL R P A P O I N T EE C O N E P I E E RC L R A D I U S R UH E X A R C N E R E

Example : (CIRCLE)

XIII. Construct the following :

1) Simple curved Line

2) Opened curved line

3) Closed curved line Student's Self Evaluation

Sl.No. Learning Indicators

1. Understood, Point, line, line segment, Ray and other basic Geometrical ideas.

2.Naming and identifying types of curved lines, name of the angles, quadrilateral, triangles, polygons, circle.

3. Know plane, parallel-line, Radius segments..

Teachers's opinion

Excel-lent

Good Average

47

5. Understanding Elementary Shapes - 1/7

5. Understanding Elementary Shapes

I. There are four alternatives for each question. Write the alphabet of the correct answer in the box:

1. We name the angle which is greater than 1800 and less than 2700 as

a) Right Angle b) Refl ex angle

c) Straight angle d) Zero angle

2. The regular polygon having 3 sides is called as

a) Isosceles triangle b) Equilateral triangle

c) Scalene triangle d) Right angled triangle

3. Number of right angled triangles formed in the given

fi gure

a) 1 b) 2 c) 3 d) 4

4. Number of plane surfaces formed in the given fi gure.

a) 1 b) 2 c) 3 d) 4

5. The solid fi gure which has no edge

a) Pyramid b) Cuboid c) Sphere d) None of these

6. A bicycle wheel has 36 spokes. The measure of angle between two spokes is a) 3600 b) 10 c) 100 d) 150

7. The angle made by a ray having no revolution

a) Refl ex angle b) Acute Angle

c) Obtuse angle d) Zero angle

48


8. The fi gure which has line segments only is

a) b) c) d)

9. In the given fi gure a pair of non parallel line segments

a) PQ, SR b) PT , UR

c) QT, US d) PS , SR

10. The geometrical concept which is not shown in the given fi gure

a) Point b) Line Segment

c) Straight line d) Ray

II. Measure all the angles in the given fi gure.

Angle Measurement Type

A B

E D

C

O50O

AOBAOEAOCBODEOD

BOE

III. Name the angle between the directions given below.N

SW

NE

W E

SSE

NWa) East and Westb) East and Northc) North and North Eastd) North East and West

49


IV. Compare the facts in the list A with the correct facts in the list B. Then write the option number in the box which is correct.

A BA If all the sides of a triangle are

of different measurei) Rectangle

B The parallelogram which has each angle 900

ii) Equilateral Triangle

C The triangle which has all the sides equal

iii) Parallelogram

D The quadrilateral with two pairs of parallel lines which has no right angles

iv) Scalene Triangle

1) A – i ; B – iv ; C – iii ; D - ii2) A – iv ; B – i ; C – ii ; D – iii3) A – iii ; B – ii ; C – i ; D – iv4) A – ii ; B – iii ; C – iv ; D – i

V. Draw the fi gures of the specifi ed solid shapes and fi ll the table by following the pattern

Sl. No. Solid Figure Faces Vertices Edges

1.

i) ABCDii) EFGHiii) BCFGiv) ADEHv) CDEFvi) ABGH

A, B, C, D, E, F, G, H

AB, BC, CD, AD, EF, FG, GH, HE, AH, BG, DE, CF

2. Cuboid

3. Square based Pyramid

4. Triangle based Prism

50


5. Square based Prism

6. Triangle based Pyramid

VI. A square is formed by arranging match sticks. Make 5 squares by removing only 4 - match sticks.

VII. Verify that the following statements are True or False.

1. The angle between the north and the South directions is a right angle.

2. If angle is twice that of an acute angle, then it is an obtuse angle

3. The fi gure which has fi ve sides is called pentagon.

4. The opposite sides of a trapezium are equal.

5. It two angles are acute, then their measurements are equal.

6. The diagonals of a parallelogram are equal.

7. A triangle having angles 700, 600, 500 is a regular polygon.

51


VIII.In the adjacent fi gure, at what angle that the pointer has to move with respect to the following questions.

1. Clockwise motion from warm to Cool

_______

2. Anticlockwise motion from hot to very Hot

_______

3. Clockwise motion from Cold to Warm

_______

4. Clockwise motion from Cold to Hot _______

5. Anticlockwise motion from very hot to Normal

_______

IX. In the following fi gures, write the measurement of angle formed between the hands of the clock (Except Refl ex angle).

52


X. Observe the following fi gure, and answer the following with respect to triangles formed as shown in the patterna) Isosceless triangle = KLM

b) Equilateral triangle =

c) Obtuse angle triangle =

d) Acute angle triangle =

e) Right angle triangle =

f) Scalene triangle =

XI. Name any 10 Line segments by observing the given fi gure.

a) __________ e) __________

B C

H G

S P

R Q

A D

T UM

QN

EK

Lb) __________ f) __________c) __________ g) __________d) __________ h) __________

XII. Write the geometrical shapes of the given fi gures.

Sl.No. Objects Geometrical shapes

Sl.No.

Objects Geometrical shapes

1. 5.

2. 6.

3. 7.

4. 8.

53


XIII. You need to draw a 4-sided shape on Geo board. Elephant has made one of them as model. Try the rest.

Model

One model is done for you

XIV. The following fi gure of train has triangle, rectangle and circles. Colour the triangles in blue, circles in brown, rectangles in red, Semi circles in green colour. And Enjoy by seeing the coloured fi gure.

Suggest a name to the Train

......................................................

Self Evaluation By StudentSl.No. Learning Indicators

1. I will name the angles based on their measurement and mea-sure the angles exactly.

2. I will identify and name the types of triangles.

3 I will understand the basic facts of simple geometrical fi gures.

4. I can name the solid shapes, also identify and name the faces, vertices and Edges.

Teacher Opinion Excellent Good Average

54

6. Integers - 1/11

6. Integers

● Set of Integers is denoted by Z or I ● Set of Integers Z or I = {......−3, −2, −1, 0, 1, 2, 3 ......}

I. Do the following :1. Write the successor of these numbers.

a) −2 .........................b) 3 ........................ e) 12 ........................c) 0 ........................ f) -18 ........................d) −7 ........................ g) 34 ........................

2. Write the predecessors of these numbers.a) 3 ........................ e) 6 ........................b) −4 ........................ f) 7 ........................c) 2 ......................... g) -10 ........................d) 0 ........................ h) -23 ........................

3. Represent the following numbers on the number linea) 5 b) −3 c) 0 d) −6

II. What the following number line indicates ?

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 31.

2. The integer which indicates the level of a ball, when it falls 12 cm below from the ground level..

3. Write the position of the student on the number line.

-6 -5 -4 -3 -2 -1 0 +6 2 3 4 5 6

Zero Standing

649 650 648

4. Suppose Ramu is on the 649the Staircase, if he moves 35 steps up and 19 steps down, what is his present po-sition (In which step is he now?)

-3 -2 -1 0 +1 +2 +3Observe

55

6. Integers - 2/11

5. Suppose you are on the 100th Step below the ground level, what is your position, if you move one step down?

6. Teacher asked Kavitha to classify the following Integer cards as positive integer, negative integer, and the integers which are neither positive NOR negative. Write in the table that how she classifi ed.-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 Positive Integer Neither Positive nor

negative integerNegative integer

7. In a game of card Manasa distribute some cards having values neigher positive nor negative, positive and negative to her students. Then she instruct the student to stand who is having the number next to the num-ber she called. Now she calls the numbers as follows :

56

6. Integers - 3/11

Sl. No. Value of a Card Succeding Number1 -702 103 -7054 -15 0

8. The above game is played by Kavitha teacher related to number cards and also exchanging them. She also instructs that she will call the pre-ceeding number and the students should identifi es the correct number now kavitha calls the numbers listed below.

Sl.No. Preceding number Value of a Card1 -702 103 -7054 -15 0

(Write your answer in the space given)9. An open tank is fi lled with water due to hot

weather the level of watr evaporates and 3cm of water level comes down. If this is so then how many centimetres of water decreases (comes down) after 3 days.?

10. The government has ordered to compulsory install rain water harvesting to all newly built houses. Based on this a newly constructed house has a tank (base-ment) which is under the ground level. During rainy season a picture is shown to see the level of water in 3 consecutive days. Tell us how much of water level is raised? ( in cms)

57

6. Integers - 4/11

11. Imagine you are standing on a multistored building which is 97 feet above the ground level. If you drop your bag down and it falls 43 feet per minute then how much high is the bag from the ground level in the same one minute.

12. Rachana is daughter of a milkman during holi-days. She accompanies her father and sells 200 li-tres, 180 litres and 210 litres milk in 3 consecutive days. If one litre is Rs. 40 then prepare a chart of the milk sold and the money she got below.

13 In a game of cards, teacher gave some cards the value of cards as follows:

Group A −1010

Group B −563

58

6. Integers - 5/11

Largest Integer Smallest IntegerGroup AGroup B

Both Group A & Group B

1. Find the distance between the largest and the smallest integers in the group A.

2. Find the sum of the smallest integers of group A and group B.14. A Peacock was sitting on a Tree. It used to sit

daily on the same tree. Rohan student if 6th Stan-dard decided to vacate the bird from that place. So he identifi ed the place a plane.

He pasted a number slit to that tree. But still the bird sat on the same tree as usual the next morn-ing. As he tried to reach near peacock. It used to perch on the next branches. And as he went back the bird also used to return to the same place.

Rohan used to write the number on which the bird Sat. Related to this try to fi ll the tabular column and answer the questions below..

Attempts 1 2 3 4

Above 220

milimeter

Below110

milimeter

Below440

milimeter

Above 380

milimeterIntegers

Successors

a) Which number is generally negative?

59

6. Integers - 6/11

b) Find the sum of integers above 380 milimeters and below 110 mili-meters.

c) Write all the above 8 integers in ascending order.

d) Write the predeccessors of the integers from the above data.

15. Raju and srujan are playing Snake and Ladder game. This game begins with number - 400 and ends with -300.

The game begins and Raju in his First attempt climbs the ladder by getting - 380. But in his second attempt he is caught in Snake's mouth and falls to -395. Then how many steps does Raju fall or come back.

Find out the sum of lowest and the highest place in the chart (The num-bers shown in the fi gure shown here have no resemblance to the given numbers.

60

6. Integers - 7/11

16. Answer the following questions and evaluate yourself.

22 − 33 ____ 67 − 19 ____

26 − 3 ____ 67 − 99 ____

The sum of answers of the problem given in the above Stares ______________.

17. There are 10 questions in a quiz question paper. There is a5 marks for each question + 5marks for every right answer and -3 marks for every wrong answer.a) Ramesh answers all questions. In that 6 answers right and 4 answers

are wrong. Manju answers for 8 questions, in which 5 are correct and remaining are wrong. Who is the winner?

Sum

61

6. Integers - 8/11

18. Integers addition table

0 41 29 38 48 58 66 71−12−29−31−48−51

19. Integers subtraction Table. Subtract the numbers in the given column.

22 −54 63 5511

−110

−1

20. Complete the following magic Square.

−4 = −15−5 = −15−1 = −15

= −15 = −15 = −15 = −15

21. Complete the following pyramid. In this pyramid the sum of the num-bers in the two rectangles is same as the integers of the above rectangle.

6 5 −126

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6. Integers - 9/11

22. Solve the problem.

224 + = 112

+ =

− 600 =

−

−100

=

212

− 350 =

−

50

=

300

+ = − 400

23. Construct and solve the problem in your own method. (As in the above problem)

Student Self EvaluationSl.No. Learning Indicators

1. I can identify positive Integers and Negative

Integers.2. I am able to represent the Integers on the

number line.3. I can compare Integers by using the symbols

=, >, < 4. I am able to write the given integers in Ascend-

ing and Descending order.5. I can show the fundamental operations related

to Integers on the number line

Teacher Opinion Excellent Good Average

63

6. Integers - 10/11

Unit TestI. Four alternatives are given for each of the following questions. Write

the alphabet of the correct answer in the box.1. The shape which has edges.

a) Cuboid b) Circle c) Sphere d) Semisphere

2. The triangle which has 2 sides equal is

a) Isosceles triangle b) Equilateral Triangle

c) Scalene Triangle d) Right angle Triangle

II. State True or false. If false write the correct statement.

1. The 4 sided Polygon has only two diagonals.

2. Circle has no vertices.

3. Infi nite number of lines can be drawn through a given point.

4. Diameter of a circle is 4 times its radius.

5. Two intersecting lines are called parallel lines.

6. Line is shorter than a line segment.

III. Construct the following.

1. Straight line

2. Line Segment

IV. What can you observe from the following number lines.

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 31.

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6. Integers - 11/11

2.

-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

V. Solve the problems given below :1. Suppose Sarita is on the 349th Stair Case. If she climbs the 25 Stairs and

goes down the 18 Stair. What is her present position? (In which staircase she is now)

2. Complete the table (Subtract the given numbers in the column.)

44 −44 54 −543310054

3. Vandana is the daughter of a fl ower seller. During the holidays she went with her mother. She sale 150 Kg, 200 Kg and 250 Kg fl ower in three days at Rs. 30 per Kg, Create a table detailing the fl owers that she sales and the money she earned.

Government of Karnataka Mathematics Work Book

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