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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
3 Number Knowledge 11
4 Number Knowledge 13
5 Number Knowledge 15
6 Number Knowledge 17
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
17 Multiplication 36
18 Multiplication 38
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
31 Decimal fractions 62
32 Decimal fractions 64
33 Decimal fractions 66
34 Decimal fractions 68
35 Decimal fractions 70
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
42 Preparation of Algebra 86
43 Preparation of Algebra 88
44 Preparation of Algebra 89
45 Practice Test : 3 91
46 Answerkey (Test 1) 94
47 Answerkey (Test 2) 96
48 Answerkey (Test 3) 97
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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
8
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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Student’s Name - Class – 6th
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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Student’s Name - Class – 6th
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)
*Learning outcome/ Now I know-
I understood place value of seven digit numbers and their expanded form.
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Student’s Name - Class – 6th
Area –Number knowledge Topic – Number knowledge
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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Student’s Name - Class – 6th
Area –Number knowledge Topic – Number knowledge
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-
Solve the following examples.
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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Student’s Name - Class – 6th
Area –Number knowledge Topic – Number knowledge
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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Student’s Name - Class – 6th
Area –Number knowledge Topic – Number knowledge
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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Student’s Name - Class – 6th
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.
*Learning outcome/ Now I know-
Can identify prime and coprime numbers.
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Student’s Name - Class – 6th
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.
Solve the following examples.
(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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Student’s Name - Class – 6th
Area –Number operations Topic – Addition
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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Student’s Name - Class – 6th
Area –Number operations Topic – Addition
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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Student’s Name - Class – 6th
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-
Solve the following examples.
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?
28
Student’s Name - Class – 6th
Area –Number operations Topic – Subtraction
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?
29
Student’s Name - Class – 6th
Area –Number operations Topic – Subtraction
Subtopic – Let’s Practice
day - 14
* Concept corner- Subtract.
30
Student’s Name - Class – 6th
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)
31
Student’s Name - Class – 6th
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 ?
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
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 –
Solve the following examples.
(1) 2453÷ 32 (2) 9564 ÷ 87 (3) 3542 ÷ 27
(4) 5789 ÷ 41 (5) 5634 ÷ 43 (6) 63,458 ÷ 26
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - OPERATION ON NUMBERS STANDARD 6TH
TOPIC - DIVISION DAY- TWENTY
Concept Corner - -
Practice Corner -
Challenge 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
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- TWENTY ONE
Concept Corner -
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
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
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - FRACTION STANDARD 6TH
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)
Challenge Corner –
Identify the smaller fraction and encircle it.
1) ;
2) ;
3) ;
4) ;
5) ;
Learning Outcome/ I Understand -
Compare the given fractions.
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - FRACTION STANDARD 6TH
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) – =
Challenge Corner –
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 ?
Learning Outcome/ I Understand -
Add and substract the like fraction.
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - FRACTION STANDARD 6TH
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) – =
Challenge Corner –
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 ?
Learning Outcome/ I Understand -
Add and substract the unlike fractions
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
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
Challenge Corner –
Observe the given diagram and find :
1) Names of angles
2) Vertex of angles :
3) Arms of angles :
Learning Outcome/ I Understand -
Collect information about angles and shapes.
Q R
S
P
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - GEOMETRY STANDARD 6TH
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.
Learning Outcome/ I Understand -
I understand to measure the angle.
Challenge Corner – Find various angles in the given picture and measure
them with protector.
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - GEOMETRY STANDARD 6TH
TOPIC - ANGLE DAY- TWENTY EIGHT
SUB TOPIC - DWAWING AN ANGLE
Let’s Recall -
.
थोडे आठवूया -
Learning Outcome/ I Understand -
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
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - GEOMETRY STANDARD 6TH
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 ?
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
STANDARD 6TH TEST NO 2 MARKS -
15
NAME OF THE STUDENT -
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)
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - FRACTION STANDARD 6TH
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 –
Learning Outcome/ I Understand -
Read and write the fractions in decimal form.
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - FRACTION STANDARD 6TH
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 =
Learning Outcome/ I Understand -
Express the place values of digits in the fraction.
1)दिक्षा अॅप द िंक - https://cutt.ly/unFf3cu
MAHARASHTRA STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING
BRIDGE COURSE MATHEMATICS
NAME OF THE STUDENT -
DOMAIN - FRACTION STANDARD 6TH
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 =
Learning Outcome/ I Understand -
Uses the decimal fractions in daily life.
1)दिक्षा अॅप द िंक - 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
15 minutes past 11 in the morning 30 minutes past 10 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.
40 minutes past 6 in the morning 55 minutes past 2 in the afternoon
10 minutes past 4 in the morning 10 minutes past 4 in the afternoon
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
State Council Of Educational Research And Training
Syllabus of Mathematics Bridge
Std. – Sixth
Name of the student -
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
3) 3 hours 40 minutes + 1 hours 35 minutes 4) 2 hours 10 minutes + 5 hours 55 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 :
1) 3 hours 55 minutes + 5 hours 15 minutes 2) 2 hours 30 minutes + 1 hours 50 minutes
3) 1 hours 25 minutes + 4 hours 45 minutes 4) 4 hours 40 minutes + 2 hours 35 minutes
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
State Council Of Educational Research And Training
Syllabus of Mathematics Bridge
Std. – Sixth
Name of the student -
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
State Council Of Educational Research And Training
Syllabus of Mathematics Bridge
Std. – Sixth
Name of the student -
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
State Council Of Educational Research And Training
Syllabus of Mathematics Bridge
Std. – Sixth
Name of the student -
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
State Council Of Educational Research And Training
Syllabus of Mathematics Bridge
Std. – Sixth
Name of the student -
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
State Council Of Educational Research And Training
Syllabus of Mathematics Bridge
Std. – Sixth
Name of the student -
Name of Sector – Algebra Day- Forty-two
Name of Topic - Preperation for Algebra
......................................................................................................................................................................................................
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
State Council Of Educational Research And Training
Syllabus of Mathematics Bridge
Std. – Sixth
Name of the student -
Name of Sector – Algebra Day- Forty- three
Name of Topic - Preperation for Algebra
…………………………………………………………………………………………………………………………………..
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
State Council Of Educational Research And Training
Syllabus of Mathematics Bridge
Std. – Sixth
Name of the student -
Name of Sector – Algebra Day- Forty- four
Name of Topic - Preperation for Algebra
…………………………………………………………………………………………………………………………………..
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
State Council Of Educational Research And Training
Syllabus of Mathematics Bridge
Std. – Sixth
Test no. 3
Name of the student -
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
Answers Test Number 2
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
Answers Test Number 3
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)