Bridge Course for Std - maa.ac.in

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Bridge Course for Std – 6th Maths

• Promotor : Department of School Education, Government of Maharashtra.

• Publisher : State Council of Educational Research and Training,

Maharashtra, Pune

• Motivation : Hon. Smt. Vandana Krishna, (I.A.S.)

Additional Chief Secretary, Department of School Education and

Sports, Maharashtra.

• Guider : Hon. Shri.Vishal Solanki, (I.A.S.)

Commissioner (Education), Maharashtra, Pune.

Hon. Shri.Rahul Dwivedi (I.A.S.)

State Project Director, Maharshtra Prathamik Shikshan Parishad, Mumbai.

• Editor : Shri.Dinkar Temkar

Director, State Council of Educational Research and Training, Maharashtra, Pune

• Co-Editor : Dr.Vilas Patil

Joint- Director, SCERT, Maharashtra, Pune

• Executive Editor : Shri.Vikas Garad,

I/C Principal, SCERT, Maharashtra, Pune

Dr. Prabhakar Kshirsagar

Senior Lecturer, Department of Mathematics, SCERT, Pune

Smt.Vrushali Gaikwad

Lecturer, Department of Mathematics, SCERT, Pune

• Editing Support : Smt.Vaishali Gadhave and Smt. Bhakti Joshi

Subject Assistant, Department of Mathematics, SCERT, Pune.

• Creative Team:

1. Shri Shailesh Mohanrao Patil, Lecturer, DIET, Jalgaon.

2. Smt. Manisha Rajendra Kurhade, Teacher, Zpps Anandwadi (Narayangaon), Junner, Pune.

3. Shri Sajjan Sridhar Magade, Teacher, Manjri Highschool, Manjri, Tq- Sangola, Dist- Solapur.

4. Shri Gajanan Atmaram Pawar, Subject Assistant, DIET, Buldana.

5. Shri Amit Jivanrao Thokal, Subject Assistant, DIET, Yavatmal.

• Translation Members :

1. Shri Atul Kulkarni, subject Assistant, DIET,Nanded.

2. Shri Umesh Rele, Assistant teacher, Rupnath Vidyalaya, Akola.

3. Shri Anantkumar Suryawanshi, Assistant teacher, zpps Rojkund, Tq. Akkakuwa,

Dist- Nandurbar.

4. Smt. Kavita Patil, Asst. teacher, Shrimant Maisaheb Bawdekar Madhyamaik

Vidyalaya, Kolhapur.

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Instructions for Students

Dear students, due to pandemic situation in the last academic year you

continued your learning and education through online and in various digital modes.

This Bridge Course has been prepared for you with the objective of reviewing the

previous year's syllabus at the beginning of the present academic year and helping you

to prepare for this year's syllabus.

1. The bridge course lasts for a total of 45 days and consists of three tests after a

certain period of time.

2. The bridge course will help you to understand exactly what you have learned in the

previous academic year and to understand the curriculum for the next class.

3. This bridge course should be studied on a day-to-day basis.

4. It consists of day-to-day worksheets. You are expected to solve the worksheet on

your own as per the given plan.

5. Seek the help of a teacher, parent or siblings if you have difficulty solving the

worksheet.

6. The video links are provided to better understand the text and activities given in

each worksheet for reference, try to understand the concept using them.

7. Solve the tests provided along with as planned.

8. Get it checked with the teacher after completing the test.

9. Seek the help of teachers, parents or siblings to understand the part that is not

understood or seems difficult.

Best wishes to you all for the successful completion of this Bridge Course!

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Instructions for Teachers, Parents and Facilitators

As we all are very well aware about the fact that due to pandemic situation, the

schools were formally closed during the last academic year and the actual classroom

teaching and learning could not take place. There is uncertainty even today as to when

schools will restart in the coming academic year. On this background various efforts

have been made by the government in the last academic year to impart education to the

students through online mode. Accordingly, the Bridge Course has been prepared with

the dual objective of reviewing the studies done by the students in the previous academic

year and helping them to learn the curriculum of the present class in this academic year.

1. The bridge course lasts for a total of 45 days and consists of three tests after a

certain period of time.

2. The bridge course is based on the syllabus of previous class and is a link between

the syllabi of previous and the current class.

3. This bridge course has been prepared class wise and subject wise. It is related to the

learning outcomes and basic competencies of the previous class’ textbook and is

based on its components.

4. The bridge course includes component and sub-component wise worksheets. These

worksheets are generally based on learning outcomes and basic competencies.

5. The structure of the worksheet is generally as follows.

Part One - Learning Outcomes/Competency Statements.

Part Two - Instructions for teachers / parents and facilitators

Part Three - Instructions for Students

Part Four - Learning Activity

Part Five - Solved Activity/ Demo

Part Six - Practice

Part Seven - Extension Activity/Parallel Activity/Reinforcement

Part Eight – Evaluation

Part Nine - DIKSHA Video Link/E-Content/QR Code

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Part Ten - My Take Away/ Today I Learnt

6. This bridge course will be very important from the point of view to revise and

reinforce the learning of the students from the previous class and pave the way to

make their learning happen in the next class.

7. Teachers/parents and facilitators should help their children to complete this bridge

course as per day wise plan.

8. Teachers/parents and facilitators should pay attention to the fact that the student will

solve each worksheet on his/her own, help them where necessary.

9. The teacher should conduct the tests from the students after the stipulated time

period, assess the test papers and keep a record of the same.

10. Having checked the test papers, teachers should provide additional supplementary

help to the students who are lagged behind.

Best wishes to all the children for the successful completion of this Bridge Course!

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Index

Sr.no. Topice Page No.

1 Roman Numerals 07

2 Number Knowledge 09





7 Multiples and factors 19

8 Multiples and factors 21

9 Addition 23

10 Addition 25

11 Addition 27

12 Subtraction 28

13 Subtraction 30

14 Addition and Subtraction 32

15 Practice test : 1 33

16 Multiplication 34



19 Division 39

20 Division 41

21 Division 42

22 Decimal fractions 43

23 Fractions 46

24 Fractions 49

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25 Fractions 51

26 Angles 53

27 Angles 55

28 Angles 57

29 Circle 59

30 Practice test : 2 61






36 Measuring Time 72

37 Measuring Time 75

38 Problems on measurement 78

39 Problems on measurement 80

40 Pictographs 83

41 Preparation of Algebra 85




45 Practice Test : 3 91

46 Answerkey (Test 1) 94



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Student’s Name - Class – 6th

Area –Number knowledge Topic – Roman Numerals

Subtopic – Multiplying a number by a number up to 3 digits

day – 1

*LET’S RECALL –

Some watches have different numbers than international numbers. You know these are Roman numerals.

I =1 ,V =5 ,X =10

*CONCEPT CORNER –

Roman numerals are written as following.

2=II ,20 =XX, 6 =VI ,12 =XII ,15 =XV ,4 =IV ,9 =IX ,24 =XXIV

*PRACTICE CORNER

Q.1 - Write appropriate numbers in blank places.

International

numerals

7 14 28

Roman numerals IX

XXXV

*Challenge corner-

Q.1 - Write down where you see Roman numerals used.

Q.2 - Write in international and Roman numerals as shown below.

Roman Numerals

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Numbers Fifty

Forty Thirty

Eight

Twety four Twenty

Nine

International

numerals

50

Roman

numerals

L

*Learning Outcomes/ I understood it all -

Understood how international numbers are written in Roman numerals.

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Area –Number knowledge Topic – Numbers

Subtopic – Seven digit numbers – introduction, reading and writing

day – 2

*Let’s recall –

We have learnt to read and write seven digit numbers. So let's read the numbers as shown below.

*Concept Corner –

Fill in the empty boxes given below.

*Practice corner

Q.1 - Using each digit only once from the each flower make different seven digit numbers.

E.g.1)12,34,567 2) 3) 4) 5)

6) 7) 8) 9) 10)

Devnagari

Numerals

International

Numerals

Reading the Numbers

५,७४६ 5,746

Five thousand seven hundred and forty

six

२,७८,९३२ 2,78,932

Two lakh seventy eight thousand nine

hundred and thirty two

६२,४७,५१२ 62,47,512

Sixty two lakh forty seven thousand

five hundred and twelve

Sr.no. International

numbers

Numbers in word

1 32,19,876

Thirty two lakh Nineteen thousand eight

hundred seventy six

2

Sixty five thousand seven hundred twenty three

3 5,00,000

4

Nineteen lakh seven

5 86,37,954

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*challenge corner –

Q. 1 )

Write seven digit largest and smallest numbers using digits in the above given balloons only once.

Q. 2)

Write seven digit largest even number.

Q. 3)

Write seven digit smallest odd number.

*Learning outcome/ Now I know-

I can identify,read and write seven digit numbers.

Let’s have friendship

with numbers

Frame

largest seven

digit and

smallest

seven digit

numbers

using given

digits

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Area –Number knowledge Topic – Number knowledge

Subtopic – Seven digit numbers – Place Value and expanded form

day - 3

*Let’s Recall -

We can read and write seven digit numbers. Let us tell the place value of a given digit

in a number.

65,23,504 - Write place value of each digit in this given number.

Digit

6 5 2 3 5 0 4

Place

Ten lakh Lakh Ten

Thousand

Thousand Hundred Tens Unit

Place value of

digit

60,00,000 5,00,000 20,000 3,000 500 0 4

*Concept Corner

Q. 1) Write place and place value of each digit in given numbers below.

Place value of

digit

Number

Ten lakh Lakh Ten

Thousand

Thousand Hundred Tens Unit

7,28,549

82,69,657

90,475

Q. 2) Write the number in expanded form as shown below.

1)96,34,587 = 90,00,000 + 6,00,000 + 30,000 + 4,000 + 500 + 80 + 7

2)14,95,210 =

3)88,88,888 =

Practice Corner-

Q. 1) Write the number using their expanded form.

1) 80,00,000 + 5,00,000 + 70,000 + 3,000 + 200 + 40 + 6 = 85,73,246

2) 60,00,000 + 9,00,000 + 30,000 + 4,000 + 500 + 80 + 7 =

3) 90,00,000 + 0 + 50,000 + 4,000 + 0 + 90 + 0 =

Challenge corner

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Frame seven digit numbers and write their expanded form using the following digits only once.

One example has done for you.

- 1 (7654321 =70,00,000 + 6,00,000 + 50,000 + 4,000 + 300 + 20 + 1

2)

3)

4)

5)


I understood place value of seven digit numbers and their expanded form.

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Subtopic – Seven digit numbers – Comparison

day - 4

Let us Recall –

You can compare numbers. Let us understand again.

6,794 ˃ 16,794

65,39,874 ˂ 53,64,789

99,999 ˃ 99,99,999

35,88,276 ˂ 35,80,726

*Concept corner –

Write sign out of <, >, = in the following boxes.

35,970 53,790

80,00,808 88,888

4,00,000 04014,00,

35,23,302 30235,32,

2004,80, 0004,88,

*practice corner –

Q.1 – Cirlce the smaller number.

7052,35, ; 46899,

0105,75, ; 1005,75,

0490,00, ; 1919,99,9

Q.2) Underline the larger number.

0013,27, ; 7,23,100

76845,62, ; 57,987

(00080,00, ; 00880,00,

Challenge corner

Solve the following examples.

1) Primary school children in Aurangabad district collected 3,27,800 seeds, while children in Pune district

collected 5,82,900 seeds.

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2) In an exhibition, Swayamsiddha Mahila Bachat Gat sold items worth Rs 4,15,700. Adishakti Mahila Bachat

Gat sold items worth Rs. 5,00,900 .Srijan Mahila Bachat Gat sold items worth Rs. 2,85,000.

(i) which women's Bachat Gat did the most sales?

(ii) which women's Bachat Gat did the least sales?

Learning outcomes/ Now I know-

I understood comparison between seven digit numbers.

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Subtopic – Seven digit numbers – Ascending and Descending order day - 5

*Let us Recall – We can identify smaller and bigger numbers. Let us understand again.

Sr.no. Numbers

Smallest number Biggest number

1 35,742 ; 4,18,976 ; 6,087

6,087 4,18,976

2 26,00,549 ; 47,982 ; 89,96,005

47,982 89,96,005

*Concept Corner- Going from smaller to bigger numbers is called ascending order and going from

bigger to smaller numbers is called descending order.

Q.1- Arrange in ascending and descending order as shown below.

Sr.

no.

Numbers

Ascending order Descending order

1 55,555 ; 5,555 ; 5,55,555

5,555 ; 55,555 ; 5,55,555 5,55,555 ; 55,555 ; 5,555

2 43,07,854 ; 85,72,416 ; 25,79,868

3 7,82,899 ; 92,32,992 ; 35,705

Practice Corner - Arrange in Ascending and descending order as shown below.Challenge Corner-


1) Annapurna Mahila Bachat Gat made 3,45,750 papads. Nirman Bachat Gat made 5,70,400 papads. Srijan

Mahilagata produced 4,50,800 papads. Then –

Sr.

no.

Numbers

Ascending order Descending order

1 9,00,786 ; 74,26,614 ; 30,98,786

2 43,07,854 ; 85,72,416 ; 25,79,868

3 80,432 ; 5,329 ; 4,55,008

4 70,00,700 ; 8,88,790 ; 22,74,705

5 76,54,369 ; 24,12,636 ; 47,528

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A) Which Bachat Gat produced the most number of papads?

B) Which Bachat Gat produced the least number of papads?

C) Write the papads prepared by the three Bachat Gat in descending order.

D) Write the papads prepared by the three Bachat Gat in ascending order.

Learning outcome/ Now I know-

I understood the ascending and descending order of Seven digit numbers.

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Subtopic – (Introduction of Crore) Reading and Writing of Eight and Nine digit Numbers

day - 6

*Let Us Recall -

We have learnt to read and write seven digit numbers. Let us read the numbers as shown below.

International Numbers Reading of Numbers

15,746 Fifteen thousand seven hundred and forty six

25,78,932 Twenty five lakh seventy eight thousand nine hundred and thirty

two

70,47,512 Seventy lakh forty seven thousand five hundred and twelve

*Concept corner-

*संबोध कोपरा –

99,99,999 is the largest seven digit number. If 1 is added in this number then we get 1,00,00,000 which is the

smallest eight digit number. This number is read as 'one crore'.

Fill in the following empty boxes.

Sr.

no.

International numbers Writing number in words

1 32,19,876 Thirty two lakh nineteen thousand eight hundred and seventy six

2 Sixty five lakh eighty four thousand seven hundred and twenty three

3 7,59,00,000

4 Twenty eight crore twenty nine lakh four hundred and seven

5 86,37,95,496

Practice corner-

Question 1) Read the following numbers and write in letters.

1) 62,41,76,519 - Sixty two crore forty one lakh seventy five thousand twenty nine

2) 5,68,00,486 -

3) 99,00,55,999 -

4) 10,00,72,010 -

5) 62,09,00,216 -

Challenge corner-

Question 1) Write the following numbers in numbers.

1) Sixty seven crore Ninteen lakh fifteen thousand four hundred and seven -67,19,15,407

2) Eight crore forty five lakh twelve thousand seven hundred and thirty four -

3) Ninety nine crore ninety nine lakh ninety nine thousand nine hundred ninety nine -

4) Four crore and four -

5) Seventy Six crore fourteen lakh eight hundred –

*Learning Outcome/ Now I know-

I can read and write eight and nine digit numbers.

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Subtopic – Divisibility Tests

day - 7

*Let Us Recall -

We have learnt to read and write seven digit numbers. Let us read the numbers as shown below.

• Dividing a number by a given number leaves nothing, that is, zero then that number is completely

divisible by the given number.

For example, let us see which numbers divide completely to12.

• The number 12 is divisible by all the numbers 1,2,3,4,6,12, so these numbers are all called divisors or

factors of 12.

• When the divisor divides the number and leaves zero, the number is called dividend.

• E.g. the numbers 1,2,4,6,12,24 divide 24 and so 24 is said to be divisible by 1,2,4,6,12 and 24.

• The numbers in table of 3 are divisible by 3.

*Concept Corner-

*Divisibility Test of 2 - If any one of the numbers with digit at unit place has 0,2,4,6,8, it is divisible by 2.

*Divisibility Test of 5 - Numbers having digits 0 or 5 at their unit place are divisible by 5.

*Divisibility Test of 10 - Numbers having digits 0 at their unit place are divisible by 10.

* Question 1) Write the divisors of the given numbers as shown below.

1) 10 - 1,2,5,10

2) 32 -

3) 14 -

*Question 2) Write the answers to the given questions as shown below.

A) Write three-digit five numbers divisible by 5 - 100, 105, 200,250, 315

B) Write three digit five numbers divisible by 10.

C) Write three digit five numbers divisible by 2.

*Practice Corner-

Tick √ if the number is completely divisible by the given numbers and ‘X’ if it is not divisible.

*आव्हानात्मक

कोपरा –

*Challenge

Corner-

Sr. No. Numbers

Divisors/factors

1) 8

1, 2, 4, 8

2) 16

1, 2, 4, 8, 16

3) 25

1, 5, 25

divisor

number

2 5 10

25

50

18

40

19

Question-

1) There is a rope 6 meters long. Can it be cut into 50 cm lengths? Write the reason.

2) There is a ribbon 8 meters long. She wants 11 pieces of 90 cm length, so how long will the ribbon be

short?

*Learning outcome/ Now I know –

Understood the divisors of number and divisibility tests.

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Area –Number knowledge Topic – Dividend and divisors

Subtopic – Prime and Coprime numbers

day - 8

*Let Us Recall -

1) A number which has only two divisors, 1 and that number itself, is called prime number.

2) A number which has more than two divisors is a composite number.

3) 1 is neither a composite nor prime.

*Concept Corner - 2 is the smallest prime number.

Coprime numbers -

• Two numbers that have only 1 as their common divisor are called coprime numbers. For example, 10

and 21 have 1 as their only in common, so 10 and 21 are coprime numbers.

* Look carefully at the prime and composite numbers from 2 to 10 in the table below. There are 4 prime

numbers from 2 to 10.

Numbers Divisors Prime/ composite

2 1,2

Prime number

3 1,3 Prime number

4 1,2,4 Composite number

5 1,5 Prime number

6 1,2,3,6 Composite number

7 1,7 Prime number

8 1,2,4,8 Composite number

9 1,3,9 Composite number

10 1,2,5,10

Composite number

Q. 1) Write prime numbers from 11 to 30.

Q. 2) How many prime numbers are there between 1 to 50 and write them.

*Practice corner-

Q. 1) Circle the prime numbers from the given numbers.

24 , 31 , 49 , 12 , 23 , 48 , 59 , 74 , 79 ,10 ,91

Q. 2) Determine whether the numbers in given pairs are coprime or not.

1) 14 ; 21 -

2) 13 ; 17 -

21

3) 10 ; 30 -

4) 50 ; 52 –

5) 15 ; 16 –

*Challenge corner-

Write the numbers from 1 to 100 in the box.

A) Circle the numbers divisible by 2 in red colour.

B) Draw a blue box around the numbers divisible by 5.

C) Circle the prime numbers from 1 to 100.


Can identify prime and coprime numbers.

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Area –Number operations Topic – Addition

Subtopic – Addition of six and seven digit numbers

day - 9

* Concept corner- : - In the previous class we have seen how to add numbers up to five digits.

Let us study this example as a review.

e.g. (1) 2,38,097 + 6,58,304

L TTH TH H T U

1 1 1

2

6

3

5

8

8

0

3

9

0

7

4

8 9 6 4 0 1

e.g. (2) 49,67,049 + 8,57,167

TL L TTH TH H T U

1 1 1 1 1

4

9

8

6

5

7

7

0

1

4

6

9

7

5 8 2 4 2 1 6

* Practice corner- : - Solve the following example.


(1) 8,24,578 + 645 + 67,627 (2) 47,02,609 + 824 + 98,53,743

* Challenge corner :- solve the following examples.

1) 63,47,048 women and 64,29,638 men cast their votes in the Assembly elections. What is the total number of

votes cast?

L TTH TH H T U

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2) What is the sum of the smallest seven digit number and the largest six digit number?

*Solve the following example.

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Subtopic – Word problems

day - 10

* Concept corner- : -

A farmer sold farm produce worth Rs 34,596 on the first day and Rs 47,348 on the second day, what is

the total value of the farm produce sold?

3 4 5 9 6

+ 4 7 3 4 8

8 1 9 4 4

In the same way, numbers with more than five digits can be added.

See the following example.

* Practice corner- : -

Solve the following example.

* Challenge corner-

1) If Sahebrao bought a tractor worth Rs 9,13,557 and a threshing machine worth Rs 32,068, how much

did he spend in total?

2)38,60,049 boys and 47,08,204 girls appeared in the secondary examination, how many students

appeared for the examination?

L TTH TH H T U

4 6 9 0 8 7

+ 2 7 6 9 3 5

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Subtopic – Let’s Practice

day - 11

* Concept corner- : -

Add.

1) 13,47,048 women and 14,29,638 men cast their vote in an election. The total no. of vote cast is?

2) What is the sum of six digit smallest and six digit greatest numbers?

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Area –Number operations Topic – Subtraction

Subtopic – Subtraction of six and seven digit numbers

day - 12

* Concept corner-

In the previous class we have seen how to subtract numbers up to five digits.

If a trader bought farm produce worth Rs 34,506 on the first day and Rs 54,937 on the second day, how

much more did he buy on the second day than on the first day?

5 4 9 3 7

3 4 5 0 6

2 0 4 3 1

The same method can be used to subtract numbers with more than five digits.

Study the following examples.

example . (1) 16,38,097 - 2,58,304

Example - (2) 64,31,254 – 17,42,207

6

1

4

7

3

4

1

2

2

2

5

0

4

7

4 6 8 9 0 4 7

Try to carry out examples taking borrow in mind.

* Concept corner-

Subtract-

.

(1) 13,17,519 – 10,07,423 (2) 70,12,345 – 28,64,547

1

1

3

0

1

0

7

7

5

4

1

2

9

3

0 3 1 0 0 9 6

12 17

5 2 7 10

1

6

2

3

5

8

8

0

3

9

0

7

4

1 3 7 9 7 9 3

27

7

2

0

8

1

6

2

4

3

5

4

4

5

7

4 1 4 7 7 9 8

* challenge corner-


1) Sandesh wants to buy a laptop worth Rs 27,459. He has Rs 24,575, so how much more will he need to

buy a laptop?

2) In the first year, a sugar factory produced 26,37,356 bags of sugar, while in the second year, 34,92,978

bags of sugar were produced. So how many bags of sugar did the factory produce in the second year?

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Subtopic – Subtraction of six and seven digit numbers

day - 13

* Concept corner-

* Practice corner-

* Challenge corner-

1) If the organization with a deposit of Rs. 24,13,758 donated Rs. 29,25,807 to the corona patients, how

much would the organization have collected?

2) Frame an example of subtraction with the numbers 15,249 and 17,726?

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Subtopic – Let’s Practice

day - 14

* Concept corner- Subtract.

30


Area –Number operations Topic – Addition and subtraction

Subtopic – Addition and Subtraction

day – 15

Test No. 1

Marks – 15

Instructions: 1. All questions are compulsory.

2. The numbers in right parentheses indicate marks.

Q.1 A) Read the numbers given below and write in letters. (2)

1) 95,71,628 –

2) 70,00,010 –

B) Write the expanded form of the numbers given below. (2)

1) 88,35,721 =

2) 5,60,007 =

Q.2 - Arrange in ascending and descending order. (2)

Sr.no. Numbers Ascending order

Descending order

1 9,28,995 ; 29,93,872 ; 53,670

2 74,09,854 ; 18,72,864 ;

25,96,768

B) Write all the divisors of the following numbers. (2)

1) Divisors of 36 =

3) Divisors of 65 =

Q.3- Solve the following examples.

A) A textile factory produced 24,17,839 meters of cloth last year. If 32,47,560 meters of cloth was

produced this year, how many meters of cloth were produced in both the years? (2)

B) The number of males in a city is 18,73,568 and the number of females is 17,98,989. How much less is

the number of females than males? (2)

Q.4- For a cricket match, 23,495 tickets were sold on the first day, 19,005 on the second day and some

on the third day. 50,875 tickets were sold in three days, how many tickets were sold on the third

day? (3)

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Area –Number operations Topic – Multiplication

Subtopic – Multiplying a number by a number up to 3 digits

day – 16

* Concept corner-

We have already studied that repeated addition of numbers is multiplication. Let us see following example.

For example- 1) There are 376 students in our school. The cost of uniform of one student is Rs. 195, what

is the total cost of uniform of all students ?.

3 7 6

5

3 7 6 1 8 8 0 3 7 6

1 9 5 9 0

1 8 8 0 ......5 multiplying by ones 3 3 8 4 0

3 3 8 4 0 .......9 multiplying by tens

3 7 6 0 0 ......1 multiplying by hundreds 3 7 6

7 3 3 2 0 1 0 0

3 7 6 0 0

The total cost of the uniform will be Rs 73,320.

In this example, 376 is a multiple, 195 is a multiplier, and 73320 is a multiplication.

Remember-

We can solve this example by taking the number 376 for 195 times and adding them, but by multiplying

the same answer is obtained in less time and with less effort.

* Practice corner-

1) 6157 × 408 =?

32

6 1 5 7

8

6 1 5 7 4 9 2 5 6 6 1 5 7

4 0 8 0

4 9 2 5 6 ......8 multiplying by ones 0 0 0 0

0 0 0 0 .......0 multiplying by tens

2 4 6 2 8 ......4 multiplying by hundreds 6 1 5 7

7 3 8 8 4 4 0 0

2 4 6 2 8

* Challenge corner-

Multiply –

1) If the price of one mobile is Rs. 21,687 then calculate the price of 65 such mobiles.

MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING

BRIDGE COURSE MATHEMATICS

NAME OF THE STUDENT -

DOMAIN - OPERATION ON NUMBERS STANDARD 6TH

TOPIC - LETS PRACTICE DAY- EIGHTEEN

Concept Corner - -

1. Multipy

(1) 327 × 92 (2) 807 × 126 (3) 567 × 890 (4) 4317 × 824

(5) 6092 × 203 (6) 1177 × 99 (7) 456 × 187 (8) 6543 × 79

(9) 2306 × 832 (10) 6429 × 509 (11) 4321 × 678 (12) 20304 × 87

2. How many paper bags are made overall, if 745 students made 25 paper bags

each during ‘avoid plastic’ mission ?

3. In 132 rows, 215 herbs are planted in the forest land. What are the total number

of herbs planted in the forest land ?

4. Cost of a computer is 27,540 Rs. Calculate the total cost of 18 computers.

5. Under ‘Inspired Award’ scheme, every student get offerd 5,000 Rs to purchase

the Scirntific project material. If 154 students are benefited by scheme in a tahsil.

What is the total grant sanctioned for whole tahsil ?

6. A two-wheeler cost is Rs 53,670. what will be the cost of such 35 vehicles ?

7. An hour is consists of 3600 seconds. How many seconds are there in 365

hours ?




DOMAIN - OPERATIONS OF NUMBERS STANDARD 6TH

TOPIC - DIVISION DAY- NINETEEN

SUB TOPIC - TO UNDERSTAND THE CONCEPT

Concept Corner - -

You have learnt some things about division. For example, we know that division means making equal parts of a given number, or, subtracting a number repeatedly from a given number.

Also, we get two divisions from one multiplication. For example, from 7 × 8 = 56, we

get the divisions 56 ÷ 7 = 8 आणि 56 ÷ 8 = 7.

Lets study the examples shown below.......

Example (1) 0 1 8 9

27 5 1 0 9 27

× 1 = 27

2 7

27 × 2 = 54

2 4 0

27 × 3 = 81

2 1 6

27 × 4 = 108

0 2 4 9 27

× 5 = 135

2 4 3 27

× 6 = 162 0 0 0 6

27 × 7 =

189

27 × 8 = 216 ( Quotient 189, Remainder 6)

27 × 9 = 243

Example (2)

1 1 8 5

42 × 1 = 42 42 4 9 7 8 5

42 × 2 = 84

4 2

42 × 3 = 126

0 7 7

42 × 4 = 168

4 2

42 × 5 = 210

3 5 8

42 × 6 = 252

3 3 6

42 × 7 = 294

0 2 2 5

42 × 8 = 336

2 1 0

0 0 1 5

( Quotient 1185, Remainder 15)

In the above example, we may divide the number just by guessing the quotient

instead making the table of 42.

Practice Corner - Solve the following examples by guessing the qoutient where the divisor is greater

than 30.

Examples : (1) 7584 ÷ 37 (2) 8959 ÷ 53

Challenge Corner –


(1) 2453÷ 32 (2) 9564 ÷ 87 (3) 3542 ÷ 27

(4) 5789 ÷ 41 (5) 5634 ÷ 43 (6) 63,458 ÷ 26





TOPIC - DIVISION DAY- TWENTY

Concept Corner - -

Practice Corner -


Solve the following examples of division.

(1) 2485÷ 38 (2) 4164 ÷ 27 (3) 3642 ÷ 17

(4) 2547 ÷ 37 (5) 5875 ÷ 44 (6) 63,854 ÷ 49

Divident Divisior





TOPIC - LETS PRACTICE DAY- TWENTY ONE

Concept Corner -




DOMAIN - FRACTION STANDARD 6TH

TOPIC - READING AND WRITING OF FRACTION DAY- TWENTY TWO

Let’s Recall -

We are well known about numerator and denominator in the fraction.

While writing fraction, the number of equal pieces of thing we divided are witten

below the line is known as denominator.

Number of pieces taken from all pieces are known as numerator.

If one bhakari is equally divided between two people, everyone gets 1 off 2 parts.

And is written as 1∕2.

If bhakari is divded into 4 equal parts, and shared between 2 people, everyone gets

2 off 4 parts. It means everyone gets half of bhakari. And its written as 2∕4.

If 6 equal parts of bhakari are shared between 2 people, everyone gets 3 off 6 parts.

And is written as 3∕6. Again, its half of bhakari.

It means that half of whole are written in different ways such as…. 1∕2, 2∕4, 3∕6.

And value of all these fraction is equal.

1/2 = 2/4 = 3/6

Such fractions of equal value are known as ‘Equivalent fractions’

Concept Corner -

‘Equivalent fractions’ -

= , = and

= It means, numerator and denominator of a

fraction are multiples of numerators and denominators onother fractions

respectively.

When numerator and denominator of

a fraction are multiplied by same non

zero integer, we get a fraction is

equivalent to the given fraction. .

numerator and denominator of fracton are divisible by 3.Iif we

devide both of them by 3, we get .

Therefore… =

If numerator and denominator have

common divisor, and the fraction we get on

deviding them by the divisor then the

fraction we get is equivalent to the given

fraction.

= = ;

= =

* Like Fractions -

The fractions whose denominators are equal are known as ‘Like Fractions’. Ex.

. , ,

* Unlike fractions -

The fractions whose denominators are not equal are known as ‘Like Fractions. Ex.

, ,

* Converting unlike fractions into like fractions -

Ex. Make a common denominator of and .

At first, lets find the common multiple of 4 and 3.

Multiples of 4 : 4,8,12,16,20,24,28 ,..........

Multiples of 3 : 3,6,9,12,15,18,21,24,27,...........

Here, 24 is a common multiple of both numbers. So lets make denominator of both

fractions be 24.

= = ;

= =

So, and both having common denominator.

व are Like fractions.

Practice Corner-

Q 1) Write appropriate number at question mark.

=

=

Q 2) Find equivalent and like fractions with deonominator 30, of all fractions given

below.

, , , ,

Q 3) Convert all given fractions into like fractions.

1) ,

2) ,

Challenge Corner – Q 1) Find two equivalent fractions for each of the following fraction.

1) =

2) =

3) =

Q 2) Conver the given fractions into like fractions.

1) ,

2) ,

Learning Outcome/ I Understand -

Ifdentifies equivalent fractions and converts unlike fractions into like fractions.

1)दिक्षा अॅप द िंक - https://youtu.be/YDxvbBvCrsc

https://youtu.be/9WQitQWqe5M

https://youtu.be/YDxvbBvCrsc

https://youtu.be/9WQitQWqe5M





TOPIC - FRACTION DAY- TWENTY THREE

SUB TOPIC - COMPARISON OF FRACTIONS

Let’s Recall -

We have studied equivalent fractions, like fractions and conversion of unlike

fraction into like fractions.

are equivalent fractios.

, , are like fractions.

Concept Corner -

Comparing like fractions :

1) >

2) <

Of two fractios with equal numerator, the

fraction with smaller denominator is greater

fraction.

Ex.

1)

2)

In like fractions, fraction with greaer

numerator is greater fraction.

3)

From above figure,

> >

Ex Compare these fractions : व

.

At first, lets conert both unlike fractions into unlike ones.

=

=

= =

>

Therefore… > Practice Corner -

Fill the blanks with <, > or = these signs, to compare the given fractions. .

1)

2)

3)

4)

To compare unlike fractions, we convert them into

their equivalent fractions with common denominator.

By comparing thier numerators.

5)


Identify the smaller fraction and encircle it.

1) ;

2) ;

3) ;

4) ;

5) ;


Compare the given fractions.





TOPIC - FRACTION DAY- TWENTY FOUR

SUB TOPIC - ADDITION AND SUBSTRACTION OF LIKE FRACTIONS

Let’s Recall -

We have learnt, to compare the given fractions. Ex.

1) < ;

2) > ; 3)

,

= =

= =

< , therefore…. <

Concept Corner -

Ex. 1) + =

1) + =

Ex. 1) – =

2) – =

While adding like fractions, we add numerators of

the fractions and write the denominator as it is.

While substracting a fraction from onother like

fraction, we write the difference between

numerators at numerator and write the denominator

as it is.

Practice Corner -

Q 1) Add fractions :

1) + =

2) + =

3) + +

=

Q 2) Substract fractions :

1) – =

2) – =

3) – =


Q 1) portion of sweater is knitted by mother

and potion is knitted by sister. What portionof

the sweater needs to be knitted?

Q 2) part of mellon is eaten by children, what portion

of mellon is remaining ?


Add and substract the like fraction.





TOPIC - FRACTION DAY- TWENTY FIVE

SUB TOPIC - ADDITION AND SUBSTRACTION OF UNLIKE FRACTIONS

Let’s Recall -

We have learnt to add and substract the like fractions. Lets revise it…

Ex. 1) + = ;

2) – =

Concept Corner -

Addition and substraction of unlike fractions While adding and substracting the unlike fractions, we have to convert them into

like fractions and the add/sustract them.

*Add :

1) + = ?

= =

= =

+ =

Therefore, + =

*Substract :

1) – = ?

= =

= =

– =

Therfore, – =

Practice Corner –

Q 1) Add :

1) + =

2) + =

3) + =

Q 2) Substract :

1) – =

2) – =

3) – =


1) Rajiv eaten portion of gauva he having. Sanjiv eaten

portion of gauva he having. What portion did both have

eaten altogether ?

2) Rupali painted portion of painting, and dipali painted

portion of painting. How much part rupali paintd more than

dipali ?


Add and substract the unlike fractions




DOMAIN - GEOMETRY STANDARD 6TH

TOPIC - ANGLE DAY- TWENTY SIX

SUB TOPIC - COMPONENTS OF ANGLE AND NAMING OF ANGLE.

Let’s Recall -

Practice Corner – Lets complete the table given below :

Sr

No.

Diagram

Name of angle

Vertex of angle

Arms of angle

1)

A

B

C

2)

P

Q

R

3)

x

Y

Z

We have learnt about angle and its components such as.. vertex, arms of thr angles. The angle

also have name. So that we can read the angle by its name. Ex. In the figure below,

• Name of angle is : ∠ABC / ∠CBA

• Vertex of angle is :B

• Arms of angles are : AB and BC

A

B

C


Observe the given diagram and find :

1) Names of angles

2) Vertex of angles :

3) Arms of angles :


Collect information about angles and shapes.

Q R

S

P





TOPIC - ANGLE DAY- TWENTY SEVEN

SUB TOPIC - MEASURING AND DWAWING AN ANGLE

Let’s Recall -

Practice Corner –

In previous standard, we have studied to measure the angle. Lets recall it once again….

Lets see, what Ravi has taken various actions to measure the angle :

Measure the following angle and wite the measure.

Centre ू Baseline

A

B C

P

Q

R

X

Y Z

1)First, put the centre of protector at

the vertex of the angle.

2)Place the baseline of protector at

one of the arm of angle.

3)The angle is measured,starting from

the zero from the side of vertex on

which arm of the angle liess.


I understand to measure the angle.

Challenge Corner – Find various angles in the given picture and measure

them with protector.





TOPIC - ANGLE DAY- TWENTY EIGHT

SUB TOPIC - DWAWING AN ANGLE

Let’s Recall -

.

थोडे आठवूया -


I understand to draw the angle of given measure.

As we use the protector to measure the angle. Same way its also use to draw angle.

Rakesh is drawing tha angle of 50 degrees. Lets see, what are the actions he is performing….

M

1) Draw the segment MN using scale.

2) Put the centre of protector at point .

3) Place protector so that the baseline

lies on seg MN.

4) Count the divisions from zero near

pont N. Mark a point L at the

division shows 50°

5) Lift the protector. Draw a ray from

point M to the marked point. Name

it as ‘ L ’

N

M

L

N

Practice Corner - Now we are going to draw the angles as Rakesh drow. Lets name them too.

1) 40° 2) 110° 3) 50° 4) 90°

Challenge Corner - ◼ Is ther exist an angle of 240° ?

◼ Is it possible to draw it using the aids in your campass box ?

CENTRE BASELINE





TOPIC - CIRCLE DAY- TWENTY NINE

SUB TOPIC - DRAWING A CIRCLE

Concept Corner -

Practice Corner - Draw the circles of given lenth of radius.

1) 3 cm. 2) 4 cm. 3) 2 cm.

Dear students, we have drown the circle using something like coins, bangle, plate, dish

etc.

Now we are going to draw a circle of certin radius, using campass.

1) First fix the pencil of suitable

length to the campass. Allign the

metal tip with the point of

pencil.

2) Take a convenient distance

between the pencil point and a

metal tip, as shown in the figure

beside

3) Take any point on paper. Hold

the metal tip steady on paper and

turnthe pencil point around it.

The shape created by pencil

point is a circle.

Challenge/Activities -

Activities 1 : We have to prepare the ground to play one leg hop. Is is possible to

draw using campass ?

If not, what the aid be used ?

Prepare the ground with the help of your teacher.

Activities 2 : Cut the circles drown using differnt dish and plates. Fold those

paper circles and show radius, diameter and chords.

Measure the length of radius and diameters of various circles you cut.

What is co-relation between them ?



STANDARD 6TH TEST NO 2 MARKS -

15


Instructions : All questions are compulsory.

Numbers in the brackets to the right indicates marks.

Q 1) Solve the follwing exam

A) Multiply. (2)

(1) 384 × 74 (2) 7385 × 126

B) Divide (2)

(1) 3264 ÷ 32 (2) 3537 ÷ 27

Q 2) Identtify the smaller fraction and encrcle it.

1) ;

2) ;

3) ;

4) ;

Q 3) Solve the follwing examples. (2 marks each)

1) Yesterday I read 6/11th part of a book. Today I read 2/11th part of the book. What

portion of the book is remained to read?

2) 3/8th poart of mellon is eaten by children and 2/8th part is eaten by grandmother.

What is the fraction of remaining portion of water mellon ?

3) Multiply four digit biggest and and three digit smallest number.

4) 46 papers are needed to make bind a notebook. What would be the total number of

notebooks bounded from such 5,750 papers ?

Q 4) Draw an angle ABC of 40°. (1)





TOPIC -DECIMAL FRACTION DAY- THIRTY ONE

SUB TOPIC - READING AND WRITING OF DECIMAL FRACTION

Let’s Recall -

We have studied decimal fractions. Lets understand something more about them…

A fraction whose denominator is 10, 100 or 1000 or any other multiple of 10, such

fraction is decimal fraction.

Ex. , ,

Concept corner -

Decimal Place -

1 unit is devided into 10 equal parts,each part is . For

it, a place made up to the right of unit place. The place is called one tenth

place. means ‘one upon ten’ is ‘one-tenth’ or one

part of ten.

Decimal point -

Decimal places are used to write fraction. A dot (.) is writtten at the after the

unit place of whole number, to indicate the ending of whole part of that

number. This dot (.) is known as decimal point.

Using decimal point the fraction 8 is written as

8.4. And its read as ‘Eight point four’.

Hundredths –

Ten equal parts of gives us

. It is ‘one hundredth’.

A frction is written in decimal form as 0.14 And is

read as ‘zero point one four’.

Que - Complete the table as directed.

Fractions Tens Units Tenths Hundredths Decimal fractions

in figurs

Decimal fraction in

words

9

9 5 9.5 Nine point five

7 7 0 7.09 Seven point zero

nine

0 3 6 0.36 Zero point three six

54

Practice Corner -

Write the following fractions in decimal form and read them aloud.

1) –

2) 6 -

3) 4 -

4) -

5) 7 -

Challenge -

Write the following fractions in mixed as well as decimal form.

1) Zero point four six –

2) Five point two nine –

3) Fourty seven point six eight –

4) Zero point zero three five –

5) Seventy eight point four one –


Read and write the fractions in decimal form.





TOPIC -DECIMAL FRACTION DAY- THIRTY TWO

SUB TOPIC - PLACE VALUE OF DECIMAL FRACTION

Let’s Recall -

We have studied decimal fractions. Lets understand something more about them…

Read the following fractions written in both mixed and decimal form.

1) – zero point zero eight

2) 6 – six point nine

3) 4 – four point three five

Concept corner -

As we determine the place value of whole numbers, in the same way we determine the

place value of decimal numbers also.

Ex. Place value of each digit in 375.28 is as shown in table :

Digit

3

7 5 2 8

Place Hundreds Tens Units Tenths Hundredths

Place value 3×100 = 300

7×10 = 70 5×1 = 5 2×1/10 = 0.2 8×1/100 = 0.08

Que - Write the place value of all digits in the fractions given below.

1) 52.17 –

2) 4.8 –

3) 137.65 –

Practice Corner - Read all the fractions alloud and write the place value of ech digits in them,

1) 13.8 –

2) 84.09 –

3) 27.54 –

4) 0.95 –

5) 763.42 –

Challenge Corner -

Write the fraction from the place value of digits given below :

1) 5×10 + 8×1 + 4 + 7 =

2) 9×100 + 6×10 + 8×1 + 4 +

7 =

3) 2×10 + 5×1 + 9 + 7 =


Express the place values of digits in the fraction.

1)दिक्षा अॅप द िंक - https://cutt.ly/unFf3cu

https://cutt.ly/unFf3cu





TOPIC -DECIMAL FRACTION DAY- THIRTY THREE

SUB TOPIC - USES OF DECIMAL FRACTION

Let’s Recall - We have We can read and write decimal fractions. We can also write the place

values of digits in decimal fractions. Lets learn the following example once again…

1) 84.75 - eighty four point seven five = 8×10 + 4 ×1 + 7 × +

5×

Concept corner -

Lets learn, how the decimal fractions are used in daily life :

Lets understand, how 54.50 rupees are equal to 54 rupees 50 paisa.

100 paise equal to 1 rupee. So, 1 paisa is equal to 1 hundredth rupee and 50 paise are

equal to 50 hundredths rupee.

Therefore, 54.50 rupees are equal to 54 rupees 50 paisa.

As same, we can consider the reading and writing of meter and centimeters.

100 CM are equal to 1 meter.

Therfore, 75 CM are 0.75 meters.

Also, we can conclude for centimeters and millimeters.

10 MM are equal to 1 CM.

So, 6 MM = 0.6 CM.

Complete the following table as directed :

100 pase = 1 rupee 100 centimeters = 1 meter

1 paisa = rupee = 0.01 rupee

1 cm = meter = 0.01 meter

50 paise = rupee= 0.50 rupee

25 cm = meter = 0.25 meter

1.5 rupees =9 rupees 50 paise

4.35 meter = 4 meter 35 cm

75 paise = 60 cm =

57.50 rupees =

35.9 meter =

Practice Corner -

Que - Write how may meters and how may centimeters.

1) 36.75 meter. =

2) 0.90 meter. =

3) 91.40 meter. =

Que - Write how may meters in decimal form.

1) 8.7 cm =

2) 50.4 cm =

3) 0.3 cm =

Challenge Corner -

Que 1) Write how may rupees in decimal form.

1) 16 rupees 50paise =

2) 38 rupees 4paise =

3) 650paise =

Que 2) Write how may meters in decimal form.

1) 60 meter 40 cm =

2) 8 meter 95 cm =

3) 347 cm =

Que 3) Write how may centimeters in decimal form.

1) 8 cm 2 meter =

2) 56 mm =

3) 495 mm =


Uses the decimal fractions in daily life.

1)दिक्षा अॅप द िंक - https://cutt.ly/unFf3cu

https://cutt.ly/unFf3cu

1

State Council Of Educational Research And Training

Syllabus of Mathematics Bridge

Std. – Sixth

Name of the student -

Name of Sector – Measurement Day- Thirty-sixth

Name of Topic - Measuring Time Subtopic -24 hour clock

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

Let’s recall : .

Last year, we have studied 12 hour clock. But, in this year we will study 24 hour clock necessary for

journey of plans , boats, trains and buses.

Concept corner :

25 minutes past 1 in the afternoon 45 minutes past 9 in the morning

12 hour clock : 01: 25 24 hour clock : 13 : 25 12 hour clock : 09: 45 24 hour clock : 09 : 45

Practice corner :

1. The time below is given by the 12 hour clock. Write the same by the 24 hour clock.

10 minutes past 8 in the morning 35 minutes past 4 in the afternoon


2

2 during night time

12 hour clock : 24 hour clock :

Challanging corner :

1. The time below is given by the 12 hour clock. Write the same by the 24 hour clock.



04 minutes past 8 in the afternoon

12 hour clock : 24 hour clock :

3

Now I know!

1. ..71.0805 Reads and writes time in 12 hour clock and 24 hour clock.

2 . By understanding the concept of ‘ before and after noon’, measures the time .

4



Std. – Sixth


Name of Sector – Measurement Day- Thirty-seventh

Name of Topic - Measuring Time Subtopic – Problems on measuring time

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

Let’s recall : .

In the previous topic, we have studied 24 hour clock and practiced reading and writing . We

understood the concept of before and after noon measuring the time .

Concept corner :

Example (1) Add. Example (2) Subtract

5 hours 20 minutes + 3 hours 45 minutes 4 hours 10 minutes - 2 hours 35 minutes

65 Min. = 1 Hour 05 Min. 53 minutes cannot be subtracted

from 10 minutes. Therefore, 1 hour

is converted into 60 minutes .

Ex3. Manjary highschool, Manjary, Ta. Sangola opens at 10:30 am in the morning and closes at

4:45 pm in the evening. How long is the school open ?

Method : By 24 hour clock in the morning 10:30 and evening 4: 45 means 16:

45

Manjary highschool, Manjary, Ta. Sangola school remains open about 6 hour 15 min.

Hr Min 5

+ 3 20 45

8 65 9 05

Hr Min 3 60 + 10

4 - 2

10 35

1 35

Hr Min 16

- 10 45 30

6 15

5

Practice corner :

Example (1) Add :

1) 6 hours 25 minutes + 4 hours 55 minutes 2) 1 hours 50 minutes + 2 hours 15 minutes


Example (2) Subtract :

1) 5 hours 15 minutes - 2 hours 45 minutes 2) 3 hours 10 minutes - 2 hours 25 minutes

3)4 hours 30 minutes - 1 hours 55 minutes 4) 2 hours 20 minutes - 1 hours 30 minutes

Ex 3) Online lecture of Abhay was for 2 hours and 20 minutes in the morning and 1 hour and 30

minutes in the evening. How long was his total online lecture ?

Ex 4) During lockdown, If grocery shops are open from 7:30 am in the morning and forced

to close at 1:15 pm in the afternoon then how long are the shops open ?

Challenging corner :

Example (1) Add :



Example (2) Subtract :

1) 4 hours 35 minutes - 1 hours 55 minutes 2 ) 3 hours 40 minutes - 2 hours 45 minutes

3) 5 hours 10 minutes - 3 hours 25 minutes 4) 6 hours 15 minutes - 2 hours 50 minutes

Ex.3) Pramod practiced batting for 3hr.25min. and balling for 2hr.10 min. then how much

total time did he practice?

Ex.4) A bus leaving from Pandharpur at 9:35 , arrives at Mumbai at 19:10. How long is

the journey of bus from Pandharpur to Mumbai ?

6

Now I know !

1) 05.71.08 Solves examples of addition and substraction of measuring time properly.

2) Solves by understanding the word problems of measuring time. :

7



Std. – Sixth


Name of Sector – Measurement Day- Thirty-eighth

Name of Topic - Measuring unit Subtopic – Problems on measuring Time

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

Let’s recall :

We use the units metre, gram and litre every day to measure length, mass and capacity

respectively. While shopping, we use the units rupees and paise.

Concept corner :

Example (1) Add. Example (2) Subtract.

23 km 150 m + 17 km 650 m 28 kg 340 g - 13 kg 630 g

41 km 200 m 14 kg 710 g

(450+750=1200 1200m=1km+200m)

Example (1) Add. Example (2) Subtract.

32 𝒍 510 𝒎𝒍 + 25 𝒍 250 𝒎𝒍 ₹ 70 , 50 paise - ₹ 42, 80 paise

57 𝒍 760 𝒎𝒍 ₹ 27 , 70 paise

km m 11

23 + 17

450 750

41 200

kg g 27 1340

28 - 13

340 630

14 710

𝒍 𝒎𝒍 32

+ 25 510 250

57 760

₹ paise 69 150

70 - 42

50 80

27 70

8

Challenge corner :

Example (1) Add.

1) ₹ 44 , 20 paise + ₹ 28, 60 paise 2) 61 𝒍 750 𝒎𝒍 + 21 𝒍 950 𝒎𝒍

3) 49 kg 340 g + 11 kg 500 g 4) 35 km 850 m + 46 km 630 m

Example (2) Subtract.

1) 37 𝒍 250 𝒎𝒍 - 19 𝒍 500 𝒎𝒍 2) ₹ 50 , 30 paise - ₹ 38, 20 paise

3) 98 km 720 m - 41 km 960 m 3) 76 kg 250 g - 55 kg 750 g

Now I know !

1) 05.71.08 Solves by arranging the examples of addition and subtraction in measurement

2) By understanding all concept solves examples in measurement

9



Std. – Sixth


Name of Sector – Measurement Day- Thirty-ninth

Name of Topic - Measuring unit Subtopic – Word Problems

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

Let’s recall :

In daily life , we use the units metre, gram and litre every day to measure length, mass and

capacity respectively. We studied addition and subtraction on it .We learn many related

concepts while shopping .

.

Concept corner :

Ex. 1 For his birthday, Sagar gave 17 kg 500 g Laddoo and 12 kg 250 g Chivada to the children

in an Ashramshala . How much snacks did Sagar donate ?

Method :

Sagar donated 29 kg 750 g of snacks to the children in an Ashramshala

Ex. 2 A shopkeeper made basundi from 120 𝒍 850 𝒎𝒍 of milk out of 275 𝒍 500 𝒎𝒍

milk. How much milk did he had now?

Method :

Shopkeeper had 154 𝒍 650 𝒎𝒍 milk now.

kg g 17

+ 12 500 250

29 750

𝒍 𝒎𝒍 274 1500

275 - 120

500 850

154 650

10

Ex. 3 If one notebook costs 18 rupees 50 paise , how much will 15 notbook cost ?

Method :

₹ Paise

18 50

× 15 ( 750 paise = 7 rupees 50 paise )

450 750

Cost of 15 notebook is 457rupees 50 paise

Ex. 4 If a wire that is 6 m 40 cm long is cut into pieces of 4 cm each, how many

pieces will be made ?

Method :

6 m 40 cm = 640 cm

160

4 640

- 4

24

- 24

000

- 0

0

160 pieces will be made.

Challanging corner :

Ex. 1 If in the school one student gets 11kg 400g rice from the Government

then, how much rice does the school get for 17 students from the gornment?

Ex. 2 If Vijay spends 680 rupees 90 paise out of 912 rupees 50 paise for

medicines then , how much money does he have left ?

Ex. 3 If buffaloes of a farmer gives 63 𝒍 340 𝒎𝒍 milk in the morning and

51 𝒍 870 𝒎𝒍 milk in the evening per day then, how much total milk is

produced per day?

Ex. 4 To construct one pillar of 7m it takes 1 sack of cement then how many

pillars can be construct by 266 sacks of cement?

)

11

Now I know !

1) 05.71.08 Solves word problem of addition, subtraction, multiplication and division in

measurement by proper arrangement.

2) Understands concept of differents units and solves word problems meaningfully.

12



Std. – Sixth


Name of Sector – magement of information Day- Forty

Name of Topic - Graph Subtopic – Pictograph

Let’s recall :

Dear students, it is necessary to classify the stastical information. The aim of pictographs is to make

numerical information easier to understand. It helps to understand most things by only observation.

Ex. Number of farmers growing crops in the village named Varud.

Number Crops Number of farmers

1 cotton 20

2 Soyabean 35

3 Tur 25

4 Jowar 10

Now, let’s draw pictograph of above information. It is easier to use an appropriate scale for the

numbers in the information . Here all four numbers in the given data are divisible by 5. So, using one

picture for 5 farmers.

Scale : 1 picture = 5 farmers

Number Crops Number of farmers

1 cotton

2 Soyabean

3 Tur

4 Jowar

13

Practice corner :-

Challenge/Activity :-

Now I know ! -

1) In daily life , collect various information,classify it and draw pictograph.

Information of number of students using various mediums for travelling to school is

given. Draw a pictograph using the iformation.

Number Type of vehical Number

1 Bicycles 16

2 schoolbus 24

3 Auto 12

Collect the information of sport students in your class like to play using it .

Draw a pictograph. ( Kabaddi , Langadi, Kho-Kho, Cricket )

14



Std. – Sixth


Name of Sector – Algebra Day- Forty-one

Name of Topic - Preperation for Algebra

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

Concept corner -

Revesion - Algebra consists of the use of numbers and letters to state and solve problem

(5+5) , (13-3) , (5 X 2) , (20÷5 ) Each arrangement is called as expressions .

The value of each of these expressions is 10, which means all these expressions are equal to

each other.

(5+5( = )13-3) An expression as is called an ‘equality’.

To represent ‘not equal expresssion’, the symbol ‘≠’ is used. .

Ex. ( .4+5 ) ≠ (4 x 9 )

Practice corner -

1. Using brackets, write three pairs of numbers whose sum is 15. Use them to write three equalities.

Challanging corner -

1 .Find four pairs of numbers, one for each of addition, subtraction, multiplication and division that make

the number 22. .

2. Write a number in the box that will make this statement correct.

(26÷2) > (5+ □(

(29-8) < (3 x□)

Now I know! -

Arrangenment and comparison of expression.

15



Std. – Sixth


Name of Sector – Algebra Day- Forty-two


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

Concept corner -

The values of expressions are not equal,then it is known as inequality .

Ex .

(9+5) ≠ (15 ÷ 3)

If two expressions are not equal, one of them is greater or smaller than the other.

To show greater or lesser values, we use , .

1. (7+5) < (7X5)

2. (16X3) > (4×11)

In first example, value of left expression is smaller than the value of right expression. In second

example, value of left expression is greater than the value of right expression. .

Observe the signs .

Practice corner -

1. Fill in the boxes between the expressions with the right symbol from <, = or > .

1) (9+6) □ (5×7)

2) (15+9) □ (8×3)

3) (16-5) □ (26÷2)

4) (24÷2) □ (17-6)

5) (7×5) □ (6×6)

16

2. Say whether right or wrong and write it .

1) (27+5) = (5+27) -----------------

2) (9+4) > (12) -----------------

3) (32 ÷ 4) > (15-7) -----------------

4) (4X7) = (30-3) -----------------

Challenging corner -

Let’s solve.

1. Write a number in the box that will make this statement correct .

1) (2X6) = (15 - □)

2) (5X7) > (8 × □)

3) (48÷3) < (□ × 6)

4) (1+0) > (22 × □)

5) (27-9) = (36 ÷□)

17



Std. – Sixth


Name of Sector – Algebra Day- Forty- three


…………………………………………………………………………………………………………………………………..

Concept corner -

Symbols are frequently used in mathematical writing. Letters can be used like symbols to make our

writing short and simple.

Resivion -

Ex .1) 4+5 = 9 and 2) 5+4 = 9

We learn from above example, The sum of any two numbers and the sum obtained by reversing

the order of the two numbers is the same.

Let’s write this rule by using letters ., use a and b to represent any two numbers.

(a+b) = (b+a)

Practice corner -

1. Is the product of any two numbers and the product obtained after changing the order

of those numbers is the same? Solve some examples and use letters for it .

Challanging corner -

Write the following properties in words .

1. a × 0 = 0

2. b ÷ 1 = b

Now I know! -

Like signs use of letters in mathematical writing .

18



Std. – Sixth


Name of Sector – Algebra Day- Forty- four


…………………………………………………………………………………………………………………………………..

Concept corner -

Let’s practice.

1. Using brackets, write three pairs of numbers whose sum is 32. Use them to write three equalities .

2. Fill in the boxes between the expressions with <, = or > .

1) (9+4) □ (6×7) 2) (15+13) □ (8×4)

3) (16+13) □ (66÷3) 4) (52-18) □ (17×2)

5) (8×9) □ (54+6)

3. Write a number in the box that will make this statement correct .

1) (8X6) = (25 + □)

2) (12X7) > (14 X □)

3) (48÷6) < (□ X 2)

4) (33÷1) > (7 X □)

5) (27+9) = (36 ÷□)

19



Std. – Sixth

Test no. 3


Day : forty-five Marks :30

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

Instructions : 1 . All questions are compulsory

2. Numbers in right bracket indicates marks.

Q .1. Encircle the smaller between given two numbers. ( 4 )

1 )2,35,705 ;99,468

2 )5,75,010 ;5,75,100

3) 53,64,789 ;9,99,9194

4 )04920,90, ;19,99,919

.2Q . Write the proper symbol, ‘=’ ‘<’ or ‘>’ in the box. ( 4 )

1) (9+ 8 ) □ (5×4)

2) (7× 4 ) □ (5 ×6)

3) (18 -12 ) □ (25 ÷5 )

4) (54 ÷9 ) □ (15 -9 )

Q.3. Find four pairs of numbers, one for each of addition, subtraction, multiplication and

division that make the number 16. .)2(

Q .4 Write following numbers in figures (1 )

1) Sixty seven crore ninteen lakh fourteen thousand eight hundred and seven -

20

2) Eight crore forty-five lakh twelve thousand fourteen –

Q.4 Read the numbers and write them in words. ( 1 ) 1) 10,42,55,999– 2) 5,38,00,485 -

Q .5 . Solve following subquestions.

a) Convert the given fractions into like fractions. )1) 1) 4

5 , 9

15

b ) Find equivalent fraction for given fraction. )1) a.

5

9 =

c) Solve. )2) a.

8

15 +

11

15 =

b. 9

12 –

4

12 =

ड ) Solve following examples by proper meaning of given signs . )2) 1) 47,02,609 + 87,53, 356 2 ) 70,32 ,345 – 28,99 ,547

इ ) Solve following examples by proper meaning of given signs. )2) 1) 954 × 27 2) 9656 ÷17

Q .6. Solve following word problems (each for 2 marks) )8)

1. Kishor purchased a laptop for rupees 43,550 and a printer for rupees 14,990. Then how

many rupees did he spend?

2. Mohasin sold his old four wheeler for rupees 2,27,450 and bought new vehical of rupees

8,68,775 from the same shop. Then how much cost did he pay ?

3. Cost of one computer purchasing for school is rupees 29,680 . What is the cost of such 15

computers?

4. The 18 passout student contributed rupees 9,00,018 to construct a science lab for school.

What is the contribution of each student if they contributed equally ?

21

Q.6 Complete the following table. (3)

No.

Diagram

Name of the

angle

Vertex

Arms of an angle

1)

A

B

C

Q.4 Draw a circle of radius 7cm. (1)

22

Answers Test Number 1

Std :Six Subject :Maths Marks :15

Q 1 a) 1) Fifty five lakh seventy one thousand six hundred and twenty eight.

2) Seventy lakh ten

b) 1) 88,35,721 =80,00,000 + 8,00,000 + 30,000 + 5,000 +700 + 20 + 1 2) 5,60,007 = 5,00,000 + 60,000 + 0 + 0 + 0 + 7 Q 2 a)

S.

No.

Number

Ascending order of numbers Decending order of numbers

1 9,28,995 ; 29,93,872 ;

53,670

53,670 ; 9,28,995 ; 29,93,872 29,93,872 ; 9,28,995 ; 53,670

2 74,09,854 ; 18,72,864 ;

25,96,768 18,72,864 ; 25,96,768 ;

74,09,854 74,09,854 ; 25,96,768 ;18,72,864

b) 1) Divisors of 36 = 1,2,3,4,6,9,12,18,36 .

2) Divisors of 65 = 1,5,13,65 . Q 3 a)

11

2417839 + 32 47560

Cloth produced in last year Cloth produced in this year

5665399 Total cloth produced in two year

Total cloth produced in two years is 56,65,399 m

1873568 - 1798989

Number of men city Number of women city

0074579 Less no. of women than men

Number of women are less by 74,579 then men city .

23

Q 4 )

1

23495 + 19005

Tickets sold on first day Tickets sold on second day

42500 Tickets sold on both two days

50875

- 42500

Total tickets sold on three days Tickets sold on both two days

08 375 Tickets sold on third day

8375 tickets were sold on third day of cricket match.

24


Std :Six Subject :Maths Marks 15

:…………………………………………………………………………………………………………………

.

Q .1 .

a( (1) 28416 (2) 930510 (b( (1) 102 (2) 131

Q.2 . 1)

6

13

2) 12

17

3) 7

8

4) 2

14

Q.3.

1) 3

11

2) 5

8

3) 99,89,001

4) 125

Q.4. Draw angle ABC of measure 60 degree. (1)

25


Std :Six Subject :Maths Marks 30:

………………………………………………………………………………………………………………….

Q .1 .

1 )99,468

2 )0105,75,

3) 53,64,789

4( 19,99,919

Q .2 .

1) (9+ 8 ) ˂ (5×4)

2) (7× 4 ) ˂ (5 ×6)

3) (18 -12 ) ˃ (25 ÷5 )

4) (54 ÷9 ) = (15 -9 )

Q.3 . )28 -12 ) , (3 2 ÷2 ), ) (9+ 7 ), (4 ×4) various answer like this .

Q 4 a Write following numbers in figure. (1 )

1)Sixty seven crore nineteen lakh fourteen thousand eight hundred and

seven – 67,19,14,807

2) Eight crore fourty five lakh twelve thousand and fourteen –8,45,12 014

Q 4 b) Read the numbers and write them in words. (1) 1) 10,42,55,999– Ten crore fourty two lakh fifty five thousand nine hundred and ninty nine

2) 5,38,00,485 – Five crore thirty eight lakh four hundred and eighty five Q .5 . Solve following subquestions.

a) Convert the given fractions into like fractions. )1) 1) 12

15 , 9

15

26

b ) Find two equivalent fractions for each of the following fraction. )1) 1)

5

9 , 10

18 , 15

27 various answer like this.

c) Solve. )2)

a. 19

15

b. 5

12

d ) Solve following examples by proper meaning of given signs. )2) 1) 1,34,55,965 2 ) 41,32,798

e ) Solve following examples by proper meaning of given signs. )2) 1) 25,758 2) 568

Q .6. Solve following word problem ) each 2 marks ) 8 )

1. 58,540

2. 6,41,325

3. 4,45,200

4. 50,001

Q .7. Complete the following table . ) 3)

s.no.

figure

Type of angle

Vertex of angle

Side of angle

1)

A

B

C

Obtuse angle

vertex B

sideAB, side BC

प्रश्न क्र . 4 Draw a circle of radius of 7cm . )1)

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