Head Start Workbook G5

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© 2019 Cuemath | Head Start workbook – G5

Get ready for Grade 5 This book contains all the important topics from Grade 4. Many of these topics are foundational to what the student will learn in Grade 5. Some of these also draw from important concepts that were taught in the previous grades. This workbook is created with an objective to help students start their Grade 5 with confidence, by providing practice exercises from on all the prerequisite concepts from Grade 4. It also offers simple explanations to some challenging topics. The students can use this workbook for 10 to 15 minutes each day or spend an hour over the weekend to recall the topics that they learnt in the previous grade, which are foundational to the next grade’s concepts.

Table of Contents What’s coming in Grade 5? ..................................................................................................... 3 Previous Grade dependencies ................................................................................................. 4 Numbers ................................................................................................................................. 5 Arithmetic Operations........................................................................................................... 12 Factors, Multiples and Primes ............................................................................................... 21 Fractions ............................................................................................................................... 29 Decimals ............................................................................................................................... 36 Lines and Angles ................................................................................................................... 42 Measurement ....................................................................................................................... 51

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What’s coming in Grade 5? This table lists out the most common topics covered by CBSE and ICSE boards in Grade 5, as prescribed by NCERT. S. No 1 2 3 4 5 6 7 8 9 10

Topics Numbers and Operations Up to 9 Digits | Arithmetic Operations

Factors, Multiples and Primes Factors, Multiples and Primes | HCF and LCM | Divisibility

Addition and Subtraction of Fractions Equivalent Fractions | The Addition and Subtraction of Fractions

Multiplication and Division of Fractions Fractions and Multiplication | Fractions and Division

Addition and Subtraction of Decimals Consolidation of Basics | Addition and Subtraction of Decimals

Multiplication and Division of Decimals Decimals and Multiplication | Decimals and Division

Applied Math Percentages | Unitary Math

Geometry Lines and Angles | Triangles, Quadrilaterals and Circles

Mensuration Perimeter, Area and Volume

Data Handling Bar Graphs and Pie Charts

Some schools may cover a topic or 2 more than what is listed here while a few schools may drop a couple of topics from this list. Such minor variations are common and expected.

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Previous Grade dependencies To master Grade 5 topics, the student must be fluent with the conceptual knowledge of below topics learnt in the previous grades. S. No

Topics

1

Place Value system, Indian and International Numbering Convention

2

Addition, Subtraction, Multiplication, and Division of small numbers

3

Factors and Multiples

4

Prime and Composite Numbers

5

Visualization of Fractions

6

Visualization of Decimals

7

The Basics of lines and angles

8

The area and perimeter of simple shapes

9

Interpretation and Creation of simple graphs

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Numbers up to 8 digits

Numbers Place Values: The numerical value that a digit represents, by the virtue of its position in a number is referred to as its place value. Example: In the number 768 the face value of the digit in the center is ‘6’ however its numeric value is 60 as it holds a position that has a place value of 10. So, the number 768 can be written as: 7 x 100 + 6 x 10 + 8 x 1 = 700 + 60 + 8

Place values of numbers up to 8 digits: Indian Number System

International Number System

100,00,000

One Crore

10,000,000

Ten Million

10,00,000

Ten Lakhs

1,000,000

One Million

1,00,000

One Lakh

100,000

Hundred Thousands

10,000

Ten Thousands

10,000

Ten Thousands

1,000

Thousands

1,000

Thousands

100

Hundreds

100

Hundreds

10

Tens

10

Tens

1

Ones

1

Ones

Example: 702,845 in International Number System is, 7 X 100,000 + 0 X 10,000 + 2 X 1,000 + 8 X 100 + 4 X 10 + 5 X 1 = 700,000 + 0 + 2,000+ 800 + 40 + 5 Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

7

0

2

8

4

5

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Numbers up to 8 digits Numbers – Practice Exercises I. Find the place value of the highlighted digit in each number: 1. 49,32,081 2. 8,70,421 3. 298,364 4. 1,028,346 5. 17,24,980 II. Observe the following numbers and write the next three numbers by skipping count. 6. 542, 544, 546, ______; ______; ______ 7. 6740, 6745, 6750, _______; ________; ________ 8. 98,125; 98,325; 98,525; _______; ________; ________ 9. 2,32,834; 2,33,834; 2,34,834; _______; ________; ________ 10. 1,120,540; 3,120,540; 5,120,540; _______; ________; ________

III. Write the following in Numeric format. 11. Six million four hundred and eleven thousand two hundred and sixty 12. Sixty-five million one hundred and sixteen thousand five hundred and five 13. Six hundred thousand two hundred and fifteen 14. One hundred and sixteen million One hundred and ten thousand and thirtynine 15. Fifty-five million four hundred and sixty thousand nine hundred and two © 2019 Cuemath | Head Start workbook – G5

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Numbers up to 8 digits IV. Write the following numbers in Indian format. 16. 472,607

17. 1,152,583

18. 198,607

19. 250,832

20. 9,634,227

V. Write the following figures in the Indian System. 21. Fifty thousand two hundred and four

22. Eight lakh ten thousand three hundred and fifteen

23. Forty-three lakhs fifteen thousand eight hundred and five

24. Six crore ten lakh thirteen thousand two hundred and eleven

25. Eighteen crore fifteen lakh nine thousand three hundred and six

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Numbers up to 8 digits VI. Write the following numbers in expanded form. 26. 45,34,248

=_______________________________________

27. 3,48,452

= _______________________________________

28. 389,298

= _______________________________________

29. 2,834,188

= _______________________________________

30. 69,731,569

= _______________________________________

VII. Arrange the following numbers in ascending order 31. 46, 63, 24, 42: _______________________________ 32. 573, 542, 516, 587: _______________________________ 33. 4342, 4567, 4210, 4782: _______________________________ 34. 54326, 54632, 56432, 57436: ______________________________ 35. 107653, 115437, 106987, 107543: _____________________________ VIII. Solve the following 36. Ron had 2 million rupees in his bank account. He deposited 8 lakh rupees more in his account. What is his bank balance now in the Indian system?

37. Sam had 16 million rupees. He invested 18 lakh rupees in his cloth business. How much money is left with him? Write your answer in the Indian system?

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Numbers up to 8 digits 38. David has 5 million 21 thousand in his bank account. What amount does he have in his account in the Indian system?

39. Mike had ₹30 crores in his account. He withdrew ₹20 million from his account. How much money is left in his account? Write your answer using the international system?

40. Jack had ₹2 crores 25 lakhs. He invested ₹95 lakhs in his business and gave 8 million to his younger brother. How much money is left with him? Write your response using Indian system?

41. Jenny has ₹2 crore and Shelly has ₹21 million in their bank accounts. Who has more money in the bank account and by how much?

42. Brad was asked to write the number 230420775 in the Indian system. He wrote 2,30,420,775. Had he expressed the number correctly? If not, write the correct one.

43. Mr. Jones needs 24,36,32,520 for a project. He already has 43,632,520 in his account. How much more money does he need? Write your answer using international system.

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Numbers up to 8 digits 44. The amount of ₹2 crores 60 lakhs was to be collected for a relief fund. The first collection made was 96,42,500 and the second one was 9,983,500. How much is yet to be collected?

45. Shane had ₹6 million. He purchased a plot for ₹12 lakhs and a car for 8 lakhs. How much is left with him?

46. Kate had ₹30 lakhs. She spent ₹3 million. How much is left with her?

47. The annual income of a company is ₹8 crores. They spend ₹2 million. What is the annual profit of the company?

48. Write two numbers more after 2,00,000 by skipping 10000.

49. Write four numbers more after 17,350,100 by skipping 2,000,000?

50. What number has 6-ten thousands, 2 fewer thousands than ten thousands, no hundreds, 2 more tens than ten thousands, and 8 more ones than hundreds?

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Numbers up to 8 digits

Solutions: I. Place values 1. Thousand 2. Ten 3. Hundred thousand 4. One million 5. Ten lakhs II. Skip counted numbers 6. 548, 550, 552 7. 6755, 6760, 6765 8. 98,725, 98,925, 99,125 9. 2,35,834; 2,36,834; 2,37,834 10. 7,120,540; 9,120,540; 11,120,540 III. Numeric Format 11. 6,411,260 12. 65,116,505 13. 600,215 14. 116,110,039 15. 55,460,902 IV. Indian Format 16. 4,72,607 17. 11,53,583 28. 1,98,607 19. 2,50,832 20. 96,34,227 V. Indian System 21. 50,204 22. 8,10,315 23. 43,15,805 24. 6,10,13,211 25. 18,15,09,306

VI. Expanded form 26. Forty five lakh thirty four thousand two hundred and forty eight 27. Three lakh forty eight thousand four hundred and fifty two 28. Three hundred eighty nine thousand two hundred and ninety eight 29. Two million eight hundred thirty four thousand one hundred and eighty eight 30. Sixty nine million seven hundred thirty one thousand five hundred and sixty nine VII. Ascending Order 31. 24, 42, 46, 63 32. 516, 542, 573, 587 33. 4210, 4342, 4567, 4782 34. 54326, 54632, 56432, 57436 35. 106987, 107543, 107653, 115437 VIII. Word Problems 36. 28 Lakhs 37. 1 Crore 42 Lakhs 38. 50 Lakhs 21 Thousand 39. 280 Million 40. 50 Lakhs 41. Shelly. One Million more. 42. No. 23,04,20,775 43. 200 Million or 200,000,000 44. 63,74,000 or 6,374,000 45. 40 Lakhs or 4 Million 46. Nothing. 30 Lakhs = 3 Million 47. 78 Million or 7.8 Crores 48. 2,10,000; 2,20,000 49. 17,550,100; 17,750,100; 17,950,100; 18,150,100 50. 64,088

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Arithmetic Operations

Arithmetic Operations Addition Addition is finding the total of two different values by adding them together. The numbers that get added are called ‘Addends’ and the total value obtained is known as ‘Sum’ While working on addition of values that have multiple digits, it is important to add the digits from the same place value. For an error free process, we line up the numbers in a way that their place values match. Example: If you are adding 243 to 656 here’s how the operation would look like Hundreds 2 6

Tens 4 5

Ones 3 6

8

9

9

→ Addend → Addend → Sum

Subtraction Subtraction is the process of taking away a certain value from another. The resulting value is called ‘Difference’. Similar to addition, we need to ensure that we are completing the operation using the correct place values. So, lining them up makes it easier to work out an error free solution. Example: If you remove 173 from 786, it would Hundreds Tens Ones 7 8 6 -1 7 3 6

1

3

→ Difference

Multiplication The process of repeatedly adding a number to itself a given number of times is known as multiplication. For example, 5 X 3 = 15 where 5 is added three times. © 2019 Cuemath | Head Start workbook – G5

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Arithmetic Operations The terms ‘Multiplicand’ and ‘Multiplier’ are used to refer to the numbers that are being multiplied and the resulting number is referred to as “Product’ 5

x

3

= 15

↓

↓

↓

Multiplicand

Multiplier

Product

Division A process of repeatedly subtracting a value from another is called division. Or it could be the process of dividing a number into multiple groups of equal size. For example, if you are attempting to calculate 30 ÷ 6 then you can repeatedly subtract 6 until there is nothing left from the 30. ‘Dividend’ and ‘Divisor’ are the terms used for the numbers used in this operation. The answer to a division operation, is known as ‘Quotient’. 30

÷

6

=5

↓

↓

↓

Dividend

Divisor

Quotient

In some cases, it is not possible to completely divide a number. For instance, you cannot divide 37 into 7 equal groups. But you can divide 35 into 7 equal groups. The additional 2 which is left over is referred to as ‘Remainder’ 37

÷

7

=5

2

↓

↓

↓

↓

Dividend

Divisor

Quotient

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Remainder

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Arithmetic Operations

Arithmetic Operations – Practice Exercises I.

Solve

1. Round off 42, 97 and 359 to their nearest tens

2. Add the rounded of numbers from question 1

3. Round off the answer from question 2 to its nearest hundred

II. Solve 4. Round off 642 and 273 to the nearest tens

5. Find the difference between the rounded off numbers from Question 4

6. Round of the difference from question 2 to its nearest hundred

III.

Find the number which is

7. 53,172 more than 64,278: __________________ 8. 53,172 less than 64,278: ___________________ 9. 1,872 more than 23,265: ___________________ 10. 1,872 less than 23,265: ____________________

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Arithmetic Operations IV.

Evaluate.

11. 3 4 1 5 + 2 6 3 7 – 4 5 2 3: _____________________ 12. 3 6 3 7 – 2 4 5 2 + 1 3 1 5: ______________________ 13. 5 8 3 7 + 3 0 3 4 – 4 4 1 3: ______________________ 14. 3 8 3 7 – 5 4 1 3 + 3 0 5 3: ______________________ 15. 5 2 0 0 3 – 4 3 7 – 5 1 8: _______________________ V.

Fill in the blanks.

16. 20 ÷ 1 = ______ 17. 0 ÷ 20 = ______ 18. 20 ÷ 20 = ______ 19. ______ ÷ 1 = 35 VI.

Write if the statements below are true or false.

20. 24 ÷ 2 = 2 ÷ 24 __________ 21. 59 ÷ 59 = 59 ____________ 22. 69 = 6 ÷ 9 _____________ 23. 45 ÷ 9 = 5 _____________ 24. 8 - 2 - 2 - 2 - 2 = 0, so 8 ÷ 4 = 2 ____________

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Arithmetic Operations VII.

Find the product of

25. 57 × 29 ___________________ 26. 407 × 19 __________________ 27. 284 × 32__________________ VIII.

Write in Columns and add.

28. 72,956 and 62,450

29. 310572 and 576296

30. 76531 and 63275

31. 56879 and 632957

IX.

Find the Quotient and Remainder.

32. 2151 ÷ 2 ______________ and _____________ 33. 4050 ÷ 3 ______________ and _____________ © 2019 Cuemath | Head Start workbook – G5

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Arithmetic Operations 34. 4152 ÷ 4 ______________ and _____________ 35. 4198 ÷ 5 ______________ and _____________ X.

Solve the below word problems.

36. The population of a town is 198,568. Out of them 45,312 are men and 35,678 are women. Find the number of children in the town.

37. A shopkeeper has 2,425 boxes of 24 pencils each. How many pencils do all the boxes have in total?

38. Linda bought a coat for ₹2265 and a saree for ₹2150. She gave 5000 rupees to the shopkeeper. How much money should the shopkeeper return to her?

39. The cost of 21 TV sets is ₹95,844. Find the cost of one TV set.

40. A factory produces 24,532 bulbs in a month. What is its annual production?

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Arithmetic Operations 41. There are 145,968 bags of sugar, 236,487 bags of wheat and some bags of rice in a godown. It the total number of bags in the godown is 450,000, find the number of bags of rice.

42. A factory manufactured 483,685 toys in three weeks. The production in first week was 146,345 toys and in second week 138,152 toys. Find the production in the third week.

43. The cost of a sofa set is ₹9372. How much will 124 sofa sets cost?

44. There are 86 rooms in a school. 4,386 students study there. If the number of students is sitting in each room is equal, how many students are sitting in each room?

45. 1575 students of a school want to go to Agra by bus. If one bus can carry 75 students, how many buses are required to carry all the students?

46. The cost of a radio set is ₹1475. What is the cost of 35 radio sets?

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Arithmetic Operations 47. In a town election, 52,496 people voted for Ron, 44,929 people for Jon and 36,824 people for Mike. If everyone voted in the town, what is the total number of voters?

48. Maria bought 96 toys priced equally for ₹12,960. The amount of 1015 rupees is still left with her. Find the cost of each toy and the amount she had.

49. A carton holds 24 packets of biscuits. Each packet has 12 biscuits. How many biscuits can be packed in 45 cartons?

50. If 950 kg of wheat is packed in 95 bags, how much wheat will each bag contain?

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Arithmetic Operations

Solutions I. Solve 1. 40, 100, 360 2. 500 3. 500 II. Solve 4. 640, 270 5. 370 6. 400 III. Find the number 7. 117,450 8. 11,106 9. 25, 173 10. 21393 Vi. Evaluate 11. 1529 12. 2500 13. 4458 14. 1477 15. 51048 V. Fill in the blanks 16. 20 17. 0 18. 1 19. 35 VI. True or False 20. False 21. False 22. False 23. True 24. True

VII. Find the product 25. 1653 26. 7733 27. 9088 VIII. Add in columns 28. 135,406 29. 886,868 30. 139,806 31. 689,836 IX. Quotient and remainder 32. 1075 and 1 33. 1350 and 0 34. 1038 and 0 35. 839 and 4 X. Word problems 36. 117,578 37. 58,200 38. Rs. 585 39. Rs. 4564 40. 294,384 41. 67545 42. 199,188 43. 1,162,128 44. 51 45. 21 46. 51,625 47. 134,249 48. Rs 135 and Rs. 13,975 49. 12960 50. 10 KG

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Factors, Multiples and Primes

Factors, Multiples and Primes You should understand the definition of Natural and Whole numbers before we explore Factors, Multiples and Primes Natural Numbers: Numbers from 1, 2, 3, 4, and so on till infinity Whole Numbers: Numbers from 0, 1, 2, 3, 4, and so on till infinity

Factors A number or quantity that when multiplied with another produces a given number or expression. For example, 3 can divide 15 without leaving a remainder. So, 3 is a factor of 15. But at the same time 5 can also divide 15 without leaving a remainder. So, 5 too is a factor of 15. Similarly, the numbers 1 and 15 are also factors of 15.

Multiples When 2 or more whole numbers are multiplied, the resulting product is a multiple of those numbers. Example: 2 X 3 = 6. In this case 6 is the multiple of both 2 and 3. Now, consider multiplying 2 with each of the natural numbers in a sequence. We get 2 X 1 = 2, 2 X 2= 4, 2 X 3 = 6, 2 X 4 = 8 and so on. In this case 2, 4, 6, 8 are all multiples of 2. The list of multiples of 2 will be endless as you continue multiplying 2 with each natural number. By this logic, all the natural numbers from 1 to infinity are multiples of 1.

Prime Numbers A number with only 2 factors one and the number itself is called a prime number. For example, 7, 11 and 13 are the numbers that have only One and those numbers themselves as factors. So, they are prime numbers. Alternatively, it can be defined as a number which is the multiple of only 2 numbers. The number itself and the number One.

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Factors, Multiples and Primes

Prime Factorization Expressing a number as a multiple of only prime numbers is called prime factorization. Examples: 15 can be expressed as 3 X 5 where both 3 and 5 are prime numbers. 14 can be expressed as 2 X 7 where both 2 and 7 are prime numbers 18 can be expressed as 2 X 3 X 3 where 2 and 3 are prime numbers There are 2 methods of identifying prime factors of a number: Division Method: a. Divide the number using the smallest prime number b. Divide the quotient using another small prime number c. Repeat the process until the quotient is a prime number Example: Write 36 using prime factors 2

36 2

Factor tree method: a. Write the number as the root at the top b. Write it as a product of 2 of its factors c. Branch out from the factors by writing them down as a product of 2 of their factors d. Continue until the last set of factors are prime numbers Example: Find out the prime factors of 54 54

18 3

9

3

3

So, number 36 can be written as 2 X 2 X 3 X 3 or 22 X 32

X

18

2

X

9

3

X

3

So, number 54 can be written as 3 X 2 X 3 X3 or 2 X 33

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Factors, Multiples and Primes

Factors, Multiples and Primes – Practice Exercises I. Solve: 1. Underline all the even numbers from the below list 27, 36, 48, 125, 360, 453, 518, 423, 54, 58, 917, 186, 423, 928, 358

2. Underline all the odd numbers from the below list 10, 45, 78, 146, 347, 543, 495, 638, 497, 968, 729, 427, 624, 572

II. Write all the factors of the following numbers 3. 27: _______________________________ 4. 32 _______________________________ 5. 18 _______________________________ 6. 45 _______________________________ 7. 25 _______________________________ III. Write the first 5 multiples of the following numbers 8. 4 _______________________________ 9. 3 _______________________________ 10. 7 _______________________________ 11. 9 _______________________________ 12. 5 _______________________________

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Factors, Multiples and Primes IV. Find the missing factors. 13. 7 × _____ = 56 14. 5 × _____ = 30 15. _____ × 3 = 24 16. ___ __× 9 = 72 17. 6 × _____= 48 18. 8 × _____ = 72 V. Write all the prime numbers between the following: 19. 31 and 50 ________________________________________ 20. 50 and 90 ________________________________________ 21. 61 and 80 ________________________________________ 22. 91 and 100 ________________________________________ VI. Write all the composite numbers between the following: 23. 40 and 50 ________________________________________ 24. 75 and 90 ________________________________________ 25. 25 and 35 ________________________________________ 26. 50 and 70 ________________________________________

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Factors, Multiples and Primes VII. Find the number using the prime factorization given below 27. 2 × 5 × 7 = ___________________ 28. 3 × 7 × 7 = _____________________ 29. 2 × 7 × 13 = _____________________ 30. 2 × 2 × 3 × 5 = ___________________ 31. 7 × 11 × 11 = _____________________ VIII. Determine the prime factorization by any method you like. 32. 2 33. 86 34. 50 35. 68 IX. Solve these word problems 36. Write the multiples of 6 which are greater than 20 and less than 50.

37. Write all the prime numbers between 1 and 15.

38. Write all the composite numbers between 1 and 30.

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Factors, Multiples and Primes 39. 12 fire engines were sent to put out the fire. Each fire engine carried 7 people. How many people helped put out the fire?

40. 72 books were arranged equally on 8 shelves. How many books are there on each shelf?

41. If you were asked to arrange the seats of 36 children in a classroom in rows and columns, what would be the different ways in which you can arrange them?

42. A gardener planted 7 rose bushes in the first garden and added 7 more rose bushes in the next garden and then 7 more in the third garden. He repeated this until the 10th garden. How many bushes did he plant in total?

43. Rachael has 8 sweets. She has same number of children in her class. How many sweets will she give each child?

44. Every number is a factor of itself. Why?

45. Do you think a number that has 8 as a factor will have 4 as a factor?

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Factors, Multiples and Primes 46. Do you think a number that has 3 as a factor will have 6 as a factor?

47. Write the 1st, 2nd and 3rd multiples of 8.

48. Write the multiples of 6 until the 5th multiple and then arrange them in descending order.

49. Write the multiples of 10, 100, 1000 till the 5ᵗʰ place. Can you discover any pattern?

50. Make a chart of numbers from 1 to 50 o Color the multiple of 3 in red. o Find the common multiples of 3 and 9. o Circle the multiples of 9 in green. o Are all multiples of 3 multiples of 9?

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Factors, Multiples and Primes

Solutions I. Solve 1. 36, 48, 360, 518, 54, 58, 186, 928, 358 2. 45, 347, 543, 495, 497, 729, 427, 572 II. Factors 3. 1, 3, 9, 27 4. 1, 2, 4, 8. 16, 32 5. 1, 2, 3, 6, 9, 18 6. 1, 5, 9, 45 7. 1, 5, 25 III. Multiples 8. 4, 8, 16, 20, 24 9. 3, 6, 9, 12, 15 10. 7, 14, 21, 28, 35 11. 9, 18, 27, 36, 45 12. 5, 10, 15, 20, 25 IV. Missing Factors 13. 8 14. 6 15. 8 16. 8 17. 8 18. 9 V. Prime Numbers 19. 37, 41, 43, 47 20. 53, 59, 61, 67, 71, 73, 79, 83, 89 21. 61, 67, 71, 73, 79 22. 97 VI. Composite Numbers 23. 42, 44, 45, 46, 48, 49 24. 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88 25. 26, 27, 28, 30, 32, 33, 34

26. 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69 VII. Find the number 27. 70 28. 147 29. 182 30. 60 31. 847 VIII. Prime factors 32. 2 33. 2 × 43 34. 2 × 5 × 5 35. 2 × 2 × 17 IX. Word problems 36. 24, 30, 36, 42, 48 37. 2, 3, 5, 7, 11, 13 38. 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28 39. 84 people 40. 9 books 41. 1 × 36; 3 × 12; 4 × 9 42. 70 43. 1 44. Because it can divide itself 45. Yes 46. No. Examples 9, 27 47. 8, 16, 24 48. 30, 24, 18, 12, 6 49. 10, 20, 30, 40, 50; 100, 200, 300, 400, 500; 1000, 2000, 3000, 4000, 5000 50. Common multiples of 3 and 9: 9, 18, 27, 36, 45

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Fractions

Fractions Fraction is a part of a whole. While writing fractions it is written as one number upon another, separated by a line. The number written on the top is known as the ‘Numerator’, which represents the part of the whole while the number written at the bottom is known as ‘Denominator’, which represents the whole. You should divide the whole into equally sized parts to represent a fraction.

𝟏 𝟑

𝟏 𝟑

𝟏 𝟑

𝟐

𝟑

The space shaded in red is represented a

When represented together: I. All fractions that have the same denominator are called like fractions 1 2 3 4 5 6 , , , , , are all like fractions 5 5 5 5 5 5 II. Fractions with different denominators are called unlike fractions 3 5 1 4 9 , , , , are unlike fractions 4 6 3 7 9 While comparing like fractions, the fraction with a higher value in numerator is the fraction with greater value For example, of the fractions

: <

, , and

>

the last one is the fraction with ; ; ; highest value as 6 is the highest of the numerators in the given options.

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Fractions

Fractions – Practice Exercises I. Write the fraction for the objects in the shaded part of the closed figure as a part of the whole collection.

1.

2.

3.

II. Write the following fractions in words: 4. 5/9 _______________________________ 5. 3/7 _______________________________ 6. 2/11 _______________________________ 7. 4/7 _______________________________ 8. 7/14 _______________________________ 9. 9/13 _______________________________

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Fractions III. Fill in the blanks For

10

Two parts of seven

11

Four parts of five

12

13

What we say?

What do we write

Nine parts out of seventeen Three parts out of six

IV. Draw pictures to show the following 14. Five eighth of a collection

15. Four ninth of a rectangle

16. Five twelfth of a collection

17. Three fourth of a square

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Fractions 18. Separate the like and the unlike fractions from the below list: 𝟒 𝟓 𝟏 𝟑 𝟗 𝟏𝟏 𝟏𝟑 𝟒 𝟏𝟏 𝟐 𝟐 𝟒 𝟒 , , , , , , , , , , , , 𝟕 𝟗 𝟓 𝟕 𝟓 𝟗 𝟕 𝟗 𝟓 𝟗 𝟓 𝟏𝟏 𝟓 Like fractions:

Unlike Fractions:

V. There are some groups of like fractions. Write three more like fractions 𝟐 𝟓 𝟕 19. , , 𝟗 𝟗 𝟗 𝟏 𝟑 𝟒 20. , , 𝟕 𝟕 𝟕 𝟑 𝟓 𝟕 21. , , 𝟖 𝟖 𝟖 22.

𝟐 𝟒 𝟔 , , 𝟏𝟏 𝟏𝟏 𝟏𝟏

VI. Fill in the blanks with the symbol < or >: 23. 7/8 _____7/5 24. 4/7 _____ 5/7 25. 7/18 _____ 11/18 26. 11/16 _____ 11/15 27. 3/8 _____ 3/11 28. 9/14 _____ 11/14

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Fractions VII. Write three like fractions with the denominator: 29. 8 30. 12 VIII. Arrange the fractions in ascending order 1 5 3 7 31. , , , 8 8 8 8 2 4 7 5 32. , , , 9 9 9 9 33.

7 5 2 9 , , , 11 11 11 11

33.

7 5 2 9 , , , 11 11 11 11

5 5 5 5 34. , , , 6 9 8 11 2 3 1 6 35. , , , 7 7 7 7 IX. Arrange the fractions in descending order 36.

7 2 5 3 , , , 11 11 11 11

37.

16 11 15 13 , , , 17 17 17 17

38.

5 5 5 5 , , , 12 8 6 14

39.

7 7 7 7 , , , 11 10 15 8

3 3 3 3 40. , , , 4 13 7 5

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Fractions X.

Solve the below word problems

41. In a fraction 2/7, into how many parts is the whole divided into?

42. In the fraction 3/8, how many parts are taken from the whole?

43. The larger fraction of 1/6, 1/7, 1/5 is ___________

44. The improper fraction in the group 5/7, 1/7, 7/3 is ____________.

45. Simplify the fraction 38/54.

46. The fraction 23/5 expressed as a mixed number is ____________.

47. If 8 is the numerator of an improper fraction, what is the denominator?

48. What is the whole number for 13/13?

49. How many quarters are there in a whole?

50. A ribbon is 30 cm long. What is it as a fraction of a meter?

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Fractions

Solutions I. Write Fractions 1. 6/15 or 2/5 2. 8/14 or 4/7 3. 6/15 or 2/5 II. In words 4. five ninth 5. three seventh 6. two eleventh 7. four seventh 8. seven fourteenth 9. nine thirteenth III. Fill in the blanks 10. two seventh, 2/7 11. four fifth, 4/5 12. nine seventeenth, 9/17 13. three sixth, 3/6 III. Draw an image 14. 5/8 15. 5/12 16. 4/9 17. 3/4 18. Like Fractions: 1/5, 11/5, 4/5; 4/7, 3/7, 13/7; 5/9, 11/9, 4/9, 2/9 Unlike fraction: 4/11 V. Like fractions: 19. Any fractions with denominator 9 20. Any fractions with denominator 7 21. Any fractions with denominator 8 22. Any fractions with denominator 11

24. 4/7 > 5/7 25. 7/18 < 11/18 26. 11/16 < 11/15 27. 3/8 > 3/11 28. 9/14 < 11/14 VII. Three like fractions 29. Any fractions with denominator 8 30. Any fractions with denominator 12 VIII. Ascending order 31. 1/8, 3/8, 5/8, 7/8 32. 2/9, 4/9, 5/9, 7/9 33. 2/11, 5/11, 7/11, 9/11 34. 5/11, 5/9, 5/8, 5/6 35. 1/7, 2/7, 3/7, 6/7 IX. Descending order 36. 7/11, 5/11, 3/11, 2/11 37. 16/17, 15/17, 113/17, 11/17 38. 5/6, 5/8, 5/9, 5/12 39. 7/8, 7/10, 7/11, 7/15 40. 3/4, 3/5, 3/7, 3/13 X. Word problems 41. 7 42. 3 43. 1/5 44. 7/3 45. 19/27 46. 4 3/5 47. any number less than 8 48. 13 49. 4 50. 3/10

VI: Fill in the blanks: 23. 7/8 < 7/5 24. 4/7 > 5/7 7/18 < 11/18 | Head Start workbook – G5 © 25. 2019 Cuemath 26. 11/16 < 11/15 27. 3/8 > 3/11

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Decimals

Decimals Decimal is derived from the Latin word ‘decem’ which means 10. Remember, 10 is the base of the decimal system. A decimal number has two parts - A whole number and a decimal fraction, separated by a decimal point. It is denoted by a dot (.)and is called point. We have already studied about fractions. Fractions can also be expressed as decimal Fractions. 1/10 = 0.1 2/100 = 0.02 3/1000 = 0.003 The dot (.) in 0.1, 0.02, 0.003 is called a decimal point or point.

Place values: We are aware that the place values are increased in value, 10 times as we move from right to left. Ones, Tens, Hundreds and so on. If we extended the place value chart to its right, the place values will reduce in value, one-tenths at time. Thousands Hundreds Tens Ones 1000

100

10

1

One

One

One

tenths hundredths thousandths 0.1

0.01

0.001

Converting Money using decimals 1 Rupee = 100 Paisa 1 Paisa = 1/100 of Rupee 1 Paisa = 0.01 Rupee

Converting time 1 Hour = 60 Minutes 1/2 hour = 30 Minutes 30 Minutes = 0.5 hours

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Decimals

Decimals – Practice Exercises I. Express the decimals in words: 1. 0.6 2. 2.05 3. 14.308 4. 29.007 5. 14.25 II. Express in numerals: 6. Three point three eight 7. Zero point nine eight 8. Twenty-three point one eight six 9. One hundred three point zero seven one 10. Three hundred nine point four zero nine III. Express as fractions: 11. 9.8 12. 23.58 13. 50.09 14. 1.004 15. 15.325

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Decimals IV. Express in expanded form: 16. 0.35 17. 1.358 18. 87.496 19. 825.249 20. 59.56 V. Express in short form: 21. 40 + 5 + 0.2 + 0.05 22. 100 + 50 + 6 + 0.6 + 0.08 + 0.002 23. 200 + 30 + 5 + 0.3 + 0.05 + 0.001 24. 500 + 80 + 9 + 0.7 + 0.009 25. 800 + 40 + 6 + 0.9 + 0.002 VI. Express as decimals: 26. 9 tenths + 2 hundredths 27. 4 tenths + 1 hundredth + 2 thousandths 28. 8 hundredths + 5 thousandths 29. 6 tenths + 7 thousandths 30. 2 tenths + 9 thousandths

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Decimals VII. Arrange in ascending order: 31. 1.23, 1.32, 1.03, 1.2, 1.02 32. 6.34, 6.43, 6.13, 6.40, 6.48 33. 3.96, 3.09, 3.609, 3.906 34. 24.316, 24.613, 23.136, 32.621 35. 20.04, 20.841, 20.149, 20.914 VIII. Solve the below word problems 36. Convert 6085 paisa into rupees and paisa.

37. Convert ₹57.50 into paisa.

38. Add ₹12.65, ₹0.95 and ₹136.65

39. Subtract ₹30.57 from ₹75.30.

40. Ram and Sam have ₹360.45 and ₹638.95 respectively. If, Luis has an amount equal to the sum of the money that they have, how much is it?

41. How many paisa are there ₹7.00? How many 25-paisa coins make ₹7?

42. Three pairs of slippers cost ₹366. What is the cost of one pair of slippers?

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Decimals 43. A pack of biscuits cost ₹15.50. What is cost of 6 packs?

44. A bus leaves for Rampur at 4:30 p.m. It takes 1 hr. 25 min. to reach there. At what time will it reach Rampur?

45. The duration of a movie is 3 hr. 15 min. It starts at 6:30 p.m. When will it end?

46.The Punjab Mail arrived at Lucknow at 11:55 a.m. It reached Lucknow 1 hr. 25 minutes. late. When was the train originally scheduled to arrive?

47. Rex attended a fashion show. He stayed there for 2 hr. 30 min. If he reached the fashion show at 8:45 p.m. when did he leave for his home?

48.Max travelled for 2 hr 45 mins by bus and 4 hr. 45 mins. by train. Calculate the time he spent in travelling.

49. David left home at 4:30 p.m. to meet his friend. He came back after 3 hr. 25 min. What time did he return?

50. The difference between two decimals is 68.09. The smaller one is 353.48. Find the other one.

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Decimals

Solutions I. In words 1. zero point six 2. two point zero five 3. fourteen point three zero eight 4. twenty-nine point zero zero seven 5. fourteen point two five I. In Numerals 6. 3.38 7. 0.98 8. 23.186 9. 103.071 10. 309.409 III. In Fractions 11. 98/100 12. 2358/100 13. 5009/100 14. 1004/1000 15. 15325/1000 IV. Expanded form 16. .3+.05 17. 1 + .3 + .05 + .008 18. 80 + 7 + .4 + .09 + .006 19. 800 + 20 + 5 + .2 + .04 + .009 20. 50 + 9 + .5 + .06 V. Short form 21. 45.25 22. 156.682 23. 235.351 24. 589.709 25. 846.902

VI. In decimals 26. .92 27. .412 28. .085 29. .607 30. .209 VII. Ascending order 31. 1.02, 1.03, 1.2, 1.23, 1.32 32. 6.13, 6.34, 6.40, 6.43, 6.48 33. 3.09, 3.609, 3.906, 3.96 34. 24.136, 24.316, 24.613, 32.621 35. 20.04 20.149, 20.841, 20.914 VIII. Word Problems 36. 60.85 37. 5750 38. 150.25 39. 44.73 40. 999.4 41. 700,28 42. 122 43. 93 44. 5:55pm 45. 9:45pm 46. 10:30am 47. 11:15pm 48. 7 hours and 30 minutes 49. 7:55pm 50. 421.57

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Lines and Angles

Lines and Angles Open and Close Curves The shape which is not enclosed by a line segment or a curve is called an open curve. Here are some examples of an open curve.

Simple shapes that are closed by a line segment or a curve are called as closed curves. Triangles, Quadrilateral, Circle etc. are examples of closed Curves.

Line Segment, Ray and Line Line: A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions Line Segment: In geometry, a line segment is a part of a line that is bounded by two distinct endpoints and contains every point on the line between its endpoints.

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Lines and Angles Ray: A geometrical ray is considered a special kind of line which starts from a fixed point and goes to any distance to the other direction of the starting point.

Angles: When two rays meet at a point, they form an angle. In the given figure, OA and OB are rays. They meet at a common point O and form an angle named AOB. An angle is represented by the symbol (∠AOB). A

O

B

The inside space between the arms in known as the interior of the angle. The outside space is called the exterior of the angle

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Lines and Angles

Lines and Angles – Practice Exercises I. Use the figure to name:

1. Five points: ____________________ 2. A Line: ________________________ 3. Four Rays: ______________________ 4. Five Line segments: ________________ II. Use the figure to name:

5. Line containing point E. ____________________ 6. Line passing through A. ____________________ 7. Line on which O lies _______________________ 8. Two pairs of intersecting lines ________________ III. How many lines can pass through? 9. one given point: _______________________ 10. two given points: _______________________

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Lines and Angles

IV. In the given figure, points A, B, C, D and E are collinear such that AB = BC = CD = DE.

Fill in the blanks using the above information: 11. AD = AB + ____________ 12. AD = AC +____________ 13. mid-point of AE is ____________ 14. mid-point of CE is ____________ 15. AE = ____________ × AB. V. State true or false: 16. A horizontal line and a vertical line always intersect at right angles.

17. If the arms of an angle on the paper are increased, the angle increases.

18. If the arms of an angle on the paper are decreased, the angle decreases.

19. If line PQ || line m, then line segment PQ || m

20. Two parallel lines meet each other at some point.

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Lines and Angles VI. Draw rough diagrams of two angles such that they have: 21. One point in common.

22. Two points in common.

23. Three points in common.

24. Four points in common.

25. One ray in common.

VII. Name the following angles of the given figure, using three letters:

26. ∠1 ____________________ 27. ∠2 ____________________ 28. ∠3 ____________________ 29. ∠1 + ∠2 ____________________ 30. ∠2 + ∠3 ____________________

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Lines and Angles VIII. Classify the following curves as (i) Open or (ii) Closed. 31.

___________________

32.

___________________

33.

___________________

34.

___________________

35.

___________________

IX. Draw rough diagrams to illustrate: 36. Open Curve

37. Closed Curve

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Lines and Angles X. Draw rough diagrams to illustrate the following, if they are possible: 38. A closed curve that is not a polygon

39. An open curve made up entirely of line segments

40. A polygon with 2 sides

XI. Answer questions 41 to 44 using the below figure:

41. What is AE + EC? _____________________ 42. What is AC – EC? _____________________ 43. What is BD – BE? _____________________ 44. What is BD – DE? _____________________ XII. Fill in the blanks 45. An angle greater than 180° and less than 360° is called _______. 46.The number of right angles in a straight angle is __________ and that in a complete angle is ____________

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Lines and Angles 47. What has only one endpoint and can be extended endlessly in the other direction?

48. What do we call the part of a line that has two distinct end points?

49. Draw two acute angles and one obtuse angle without using a protractor. Estimate the measures of the angles. Measure them with the help of a protractor and see how accurate is your estimate?

50. If two rays intersect, will their point of intersection be the vertex of an angle of which the rays are the two sides?

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Lines and Angles

Solutions I. Figure 1 1. B, C, D, E, O 2. DB 3. ED, OC, OB, OD 4. DE, EO, OB, OC II. Figure 2 5. AE 6. AE 7. CO

30. ∠ABD VIII. Open or closed curves? 31. Open 32. Open 33. Close 34. Close 35. Close IX. Draw

8. CO, AE

36 to 37. Drawing activity.

III. How many lines 9. Infinite

X. Is it possible: 38. Not possible

10. One

39. Possible 40. Not possible

IV. Figure 3 11. BD 12. CD 13. C 14. D 15. 4 V. True or False 16. True 17. False 18. False 19. True 20. False VI. Draw 21 to 25. Drawing activity

XI. Figure 5 41. AC 42. AE 43. ED 44. BE XII. Blanks/Word problems 45. Reflex angle 46. 2 and 4 47. ray 48. Line segment 49. Drawing activity 50. Yes

VII. Figure 4 26. ∠DBC 27. ∠EBD 28. ∠ABE 29. ∠EBC © 2019 Cuemath | Head Start workbook – G5

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Measurement

Measurement Perimeter Perimeter is the measurement of the outline of a shape.

a

b

a l Look at the above square and rectangle. IF you want to calculate the perimeter of the square or the rectangle given, you simply have to add the measurement of all the sides. ∴ Perimeter of the square = a + a + a + a = 4a Perimeter of the rectangle = l + b + l + b = 2l + 2b = 2(l + b)

Area Area of a closed figure is the size of its surface. It is the amount of space inside the boundary of a flat (2-dimensional) object such as a square, rectangle, triangle or circle. It is calculated in square units as if the entire figure had been divided into unit squares like below:

∴ Area of the square is the product of 2 of its sides = a x a = a2 Sq. Units Area of the rectangle is the product of its length & breadth = l x b = lb Sq. Units

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Measurement

Measurement – Practice exercises I. Find the perimeter of the following figures

1

_______________

2

_______________

3

_______________

4

_______________

5

_______________

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Measurement II. Find the perimeter and are of the rectangles with the following dimensions 6. Length=7cm, breadth=5cm: P =_____________; A = ____________ 7. Length=3cm, breadth=2cm: P =_____________; A = ____________ 8. Length=12m, breadth=10m: P =_____________; A = ____________ 9. Length=25m, breadth=15m: P =_____________; A = ____________ 10. Length=15m, breath=10m: P =_____________; A = ____________ III. Find the perimeter and are of the square with the sides measuring: 11. 5cm: P =_____________; A = ____________ 12. 14m: P =_____________; A = ____________ 13. 12m: P =_____________; A = ____________ 14. 7cm: P =_____________; A = ____________ 15. 9cm: P =_____________; A = ____________ IV. Fill in the blanks 16. Length x breadth gives the _________ of a rectangle. 17. 4 x side gives the _________________ of a square. 18. The perimeter of a square of side 2cm is__________ 19. The area of a square of side 2cm is______________ 20. All sides of a square are _______________in length.

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Measurement V. Calculate the areas of the rectangles with the below dimensions. Identify the smallest and the largest rectangles, in area 21. l =9 m and b = 6 m 22. l = 17 m and b = 3 m 23. b = 4 m and l = 14 m The area of the largest rectangle is _____________ and the smallest rectangle is _____________ VI. State whether the following statements are true or false: 24. If the length of a rectangle is halved and breadth is doubled then the area of the rectangle obtained remains the same. 25. Area of a square is doubled if the side of the square is doubled. 26. Perimeter of a regular octagon of side 6cm is 36cm. 27. A farmer who wants to fence his field, must find the perimeter of the field. 28. An engineer who plans to build a compound wall on all sides of a house must find the area of the compound. 29. To find the cost of painting a wall we need to find the perimeter of the wall. 30. To find the cost of a frame of a picture, we need to find the perimeter of the picture

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Measurement VII. In the given figure, each square is of length One unit. Find:

31. What is the perimeter of the rectangle ABCD?

32. What is the area of the rectangle ABCD?

33. Two equal parts of the rectangle are shaded. What is the area of the shaded region?

34. Can you divide the remaining area into 8 equal parts and shade it with different colors?

35. Find the perimeter of each of the areas that you shaded? Are they equal?

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Measurement VIII. Solve the below word problems 36. A rectangular park, 50 m long and 25 m wide. An athlete ran 10 rounds around the park. Find the total distance covered by him.

37.

Parmindar walks around a square park once and covers 800m. What is the area of this park?

38. The side of a square is 5cm. How many times does the area increase, if the side of the square is doubled?

39.

Amit wants to make rectangular cards measuring 8cm × 5cm. She has a square chart paper of side 60cm. How many cards can she make?

40.

Length of a rectangular field is 6 times its breadth. If the length of the field is 120cm, find the breadth and perimeter of the field.

41.

Anmol has a chart paper measuring 90cm × 40cm, and Abhishek has one which measures 50cm × 70cm. Who has the larger chart paper and how much larger is it?

42. The perimeter of a rectangle is 230 cm. If the length of the rectangle is 70 cm, find its breadth and area.

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Measurement 43. The area of a rectangle is 96 cm². If the breadth of the rectangle is 8 cm, find its length and perimeter.

44. The area of a square field is 100 Sq. meters. Find its perimeter.

45. A rectangular room has a length of 520cm and breadth of 140cm. How many tiles with measuring 13cm in length and 7cm in breadth are needed to cover the floor of the said room?

46. Find the dimensions of the rectangle with 38 Sq. cm as area? Find the perimeter of the rectangle.

47. The length of a rectangular wooden board is thrice its width. If the width of the board is 120 cm, find the cost of framing it @ 5 rupees for 20 sq. cm.

48. Find the perimeter of a square whose area is 625 cm².

49. Find the area of the square whose perimeter is 440 cm.

50. A square and rectangle are equal area. If the square’s side is 20 cm and the rectangle’s breadth is 10 cm, Find the rectangle’s length and perimeter.

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Measurement

Solutions I. Perimeter 1. 18 CM 2. 13 CM 3. 20 CM 4. 28 CM 5. 27 CM II. Rectangle Dimensions 6. A=35, P=24 7. A=6, P=10 8. A=120, P=44 9. A=375, P=80 10. A=150, P=50 III. Square Dimensions 11. A=25, P=20 12. A=196, P=56 13. A=144, P=48 14. A=49, P=28 15. A=81, P=36 IV. Blanks 16. Area 17. perimeter 18. 8cm 19. 4 cm2. 20. equal V. Areas 21. Middle 22. Smallest 23. Largest

26. false 27. true 28. false 29. false 30. true VII. Figure 1 31. 32 32. 60 33 to 35. Activity. VIII. Word Problems 36. 1500 37. 40000 38. 4 times 39. 90 40. 20, 280 41. Anmol’s by 100cm2
42. 45, 3150 Sq. CM 43.12, 40 44. 40 45. 800 46. length=19, breadth=2, 76cm 47. 240 48. 100 49. 12100 50. l=40, 100

VI. True or False 24. true 25. false © 2019 Cuemath | Head Start workbook – G5

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Data handling - Graphs

Graphs Data is a collection of numbers gathered to provide crucial information. Data can be arranged in various formats to offer quick and easy understanding. Here are some of the formats that are widely used

Tally marks: Tally marks are a quick way of keeping track of numbers in groups of five. One vertical line is made for each of the first four numbers; the fifth number is represented by a diagonal line across the previous four.

Pictographs A pictograph represents data in the form of pictures, objects or parts of objects.

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Data handling - Graphs

Bar graphs Bars of equal width are drawn with uniform spacing between them, where length of the bar visually represents the size of the data.

Choosing a Scale Representing the data using bar graphs or pictographs requires us to choose a scale. For example, each smiley in pictograph represents 1 vote. We can choose to represent 10 or even 100 votes with one smiley if the data is large. Similarly, each unit of the bar graph above represents one million gallons of oil reserve that each country has. Choosing the right scale helps you represent the data

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Data handling - Graphs

Graphs – Practice Exercises I. Solve the following questions using tally marks 1. Following are the choice of games of 40 students of class IV. football, cricket, football, kho-kho, hockey, cricket, hockey, kho-kho, tennis, tennis, cricket, football, football, hockey, kho-kho, football, cricket, tennis, football, hockey, kho-kho, football, cricket, cricket, football, hockey, kho-kho, tennis, football, hockey, cricket, football, hockey, cricket, football, kho-kho, football, cricket, hockey, football. Represent the above data using tally marks Name of the sport

Tally Marks

Total

2. Which is the most participated sport as per the above tally marks table? 3. Which is the last participated sport as per the above tally marks table? 4. Below are the grades scored by 30 students in a class. Represent this data using tally marks: B, C, C, E, A, C, B, B, D, D, D, D, B, C, C, C, A, C, B, E, A, D, C, B, E, C, B, E, C, D Name of the sport

Tally Marks

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Total

61

Data handling - Graphs 5. The number of two wheelers owned individually by each of 50 families are listed below. Make a table using tally marks. 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 0, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 1, 4, 1, 3, 1, 1, 2, 1, 1, 1, 1, 2, 3, 2, 1, 1 Number of 2wheelers

Tally Marks

Total

What is the total number of families with 2 or more 2-wheelers?

6. The lengths in centimeters (to the nearest centimeter) of 30 carrots are given as follows: 15, 22, 21, 20, 22,15, 15, 20, 20,15, 20, 18, 20, 22, 21, 20, 21, 18, 21, 18, 20, 18, 21, 18, 22, 20, 15, 21, 18, 20 Length of carrots

Tally Marks

Total

How many carrots have a length of 20 cm or more? 7. Use the above table to identify the: Number of carrots with maximum length ____________ Number of carrots with minimum length _____________

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Data handling - Graphs 8. Thirty students were interviewed to find out what they want to be in future. Their responses are listed as below: doctor, engineer, doctor, pilot, officer, doctor, engineer, doctor, pilot, officer, pilot, engineer, officer, pilot, doctor, engineer, pilot, officer, doctor, officer, doctor, pilot, engineer, doctor, pilot, officer, doctor, pilot, doctor, engineer Populate the below table with tally marks using this data Profession

Tally Marks

Total

II. Following pictograph represents some surnames of people listed in the telephone directory of a city. Observe the pictograph and answer the questions from 9 to 12:

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Data handling - Graphs 9. How many people have surname ‘Roy’?

10. Which surname appears the maximum number of times in the telephone directory?

11. Which surname appears the least number of times in the directory?

12. Which two surnames appear an equal number of times? III. Students of Class VI in a school were given a task to count the number of articles made of different materials in the school. Use this pictograph to answer questions from 13 to 16:

13. Which material is used in maximum number of articles? 14. Which material is used in minimum number of articles? 15. Which material is used in exactly half the number of articles as those made up of metal?

16. What is the total number of articles counted by the students?

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Data handling - Graphs IV. The number of scouts in a school is depicted by the following pictograph. Observe the pictograph and answer the questions from 17 to 21:

17. Which class has the minimum number of scouts?’ ______________ 18. Which class has the maximum number of scouts? _______________ 19. How many scouts are there in Class VI? ______________________ 20. Which class has exactly four times the scouts of Class X? __________ 21. What is the total number of scouts in the Classes VI to X? __________ V. The following pictograph depicts the information about the areas in Sq. KM (to nearest hundred) of some districts of Chhattisgarh State.

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Data handling - Graphs 22. What is the area of Koria district? ________________________ 23. Which two districts have the same area? ___________________ 24. How many districts have area more than 5000 Sq. KM? __________ 25. Below table has the data of cool drink sales in a retail store for 6 consecutive days. Prepare a pictograph with this data, where each picture of a cool drink bottle represents 50 units sold.

Day of the week

Bottles

= 50

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Data handling - Graphs 26. The following table provides information about the circulation of daily newspapers in a town, in 5 languages. Use this data to create a pictograph with a symbol of your choice. Each symbol should represent 1000 units.

Language

Circulation

VI. The following bar graph shows the number of houses (out of 100) in a town using different types of fuels for cooking.

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Data handling - Graphs Answer the below questions using the bar graph: 27. Which fuel is used in maximum number of houses?

28. How many houses are using coal as fuel?

29. Suppose that the total number of houses in the town is 1 lakh. From the above graph estimate the number of houses using electricity.

VII. The following bar graph represents the data for different sizes of shoes worn by the students in a school. Read the graph and answer the following questions.

30. Find the number of students whose shoe sizes have been collected.

31. What is the number of students wearing shoe size 6?

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Data handling - Graphs 32. What are the different sizes of the shoes worn by the students?

33. Which shoe size is worn by the maximum number of students?

34. Which shoe size is worn by minimum number of students?

35. State whether true or false: The total number of students wearing shoe sizes 5 and 8 is the same as the number of students wearing shoe size 6. VIII. The following graph gives the information about the number of railway tickets sold for different cities at a ticket counter between 6.00 am to 10.00 am. Read the bar graph and answer the following questions

36. How many tickets were sold in all?

37. For which city were the maximum number of tickets sold?

38. For which city were the minimum number of tickets sold?

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Data handling - Graphs 39. Name the cities for which the number of tickets sold is more than 20.

40. Tickets sold for Delhi and Jaipur together exceed the total number of tickets sold for Patna and Chennai by:

IX. Draw a bar graph 41. The lengths in km (rounded to nearest hundred) of some major rivers of India is given below. Draw a bar graph showing this information.

Bar Graph:

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Data handling - Graphs 42. The number of ATMs of different banks in a city is shown below. Draw a bar graph showing this information with a scale of your choice.

Bar Graph:

43. Number of mobile phone users in various age groups in a city is listed below. Draw a bar graph with a scale of 1 = 1,000

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Data handling - Graphs Bar Graph:

X. Read the bar graph given below and answer the following questions:

44. The bar graph shows the information about ___________________ 45. Number of students is maximum in the year ___________________ 46. Number of students is twice that of 2002-03 in the year ___________ 47. ________ saw a decrease in the students’ number from the previous 48. ________ year has the maximum increase in students’ number

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Data handling - Graphs XI. Following is the choice of sweets of 30 students of Class IV. Ladoo, Barfi, Ladoo, Jalebi, Ladoo, Rasgulla, Jalebi, Ladoo, Barfi, Rasgulla, Ladoo, Jalebi, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo, Rasgulla, Ladoo, Ladoo, Barfi, Rasgulla, Rasgulla, Jalebi, Rasgulla, Ladoo, Rasgulla, Jalebi, Ladoo. 49. Arrange the names of sweets in a table using tally marks. Profession

Tally Marks

Total

50. Which sweet is preferred by most of the students?

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Data handling - Graphs

Solution Almost all the questions are activity based. The teachers/ parents who are correcting this section are requested to exercise their judgement for identifying the correct answers.

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