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Contents

1. Large Numbers 7

2. Fractions 11

3. Decimals 15

4. Addition and Subtraction 20

5. Multiplication 25

6. Division 29

7. Money 34

8. Factors and Multiples 38

9. Geometry 42

10. Perimeter and Area 46

11. Measurement 50

12. Time 55

13. Data Handling 60

14. Patterns 64

Comprehensive Test Paper 68

Answers to Worksheets 69

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SuggestedPeriodAllocation

Ch.No. Chapters LearningObjectives

SuggestedNo.ofPeriods

1 Large Numbers zz To understand 5- and 6-digit numberszz To understand face value and place valuezz To understand comparing numberszz To understand forming largest and smallest numberszz To understand Indian and International place value systemszz To read and write Roman numerals

11

2 Fractions zz To understand numerator and denominator in fractionszz To understand equivalent fractionszz To understand fractions in lowest termszz To understand comparison of like and unlike fractionszz To understand proper and improper fractionszz To understand fractions as divisionzz To understand addition and subtraction of like and unlike fractions

12

3 Decimals zz To understand the whole and decimal partszz To understand place value in decimal numberszz To understand conversion of fractions to decimals and vice versazz To understand equivalent decimalszz To understand comparison of decimalszz To understand addition and subtraction of decimals

12

4 Addition and Subtraction

zz To learn addition of 5- and 6-digit numberszz To understand addition of three numberszz To learn to use various properties of additionzz To learn estimation in additionzz To learn subtraction of 5- and 6-digit numberszz To learn to use various properties of subtractionzz To learn estimation in subtractionzz To understand addition and subtraction together

12

5 Multiplication zz To understand properties of multiplicationzz To learn multiplication by 2-digit and 3-digit numberszz To understand multiplication by 10, 100 and 1000zz To learn simplification by DMAS rulezz To learn lattice multiplication of 3-digit numbers

11

6 Division zz To understand division by a 2-digit numberzz To understand properties of divisionzz To understand division by 10, 100 and 1000zz To understand division by a 3-digit numberzz To learn simplification by using DMAS

11

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7 Money zz To understand conversion of money zz To understand addition and subtraction of money zz To understand multiplication and division of money zz To understand unitary method

10

8 Factors and Multiples

zz To understand factors and common factorszz To understand Highest Common Factor (HCF)zz To understand multiples and common multipleszz To understand Lowest Common Multiple (LCM)zz To understand divisibility ruleszz To understand prime and composite numbers

14

9 Geometry zz To understand intersecting and parallel lineszz To understand angleszz To understand interior and exterior of an anglezz To understand open and closed figureszz To understand polygonszz To understand circles

12

10 Perimeter and Area

zz To develop an understanding of perimeter of different shapeszz To find perimeter of various polygonszz To develop an understanding of area of different shapeszz To find the area of various polygons and irregular shapes

12

11 Measurement zz To understand standard units of length, mass and capacity zz To convert various units of length, mass and capacityzz To understand addition and subtraction of measurementszz To understand multiplication and division of measurements

14

12 Time zz To understand reading time up to a minutezz To understand a.m. and p.m.zz To understand 24-hour clockzz To understand calendarzz To understand addition and subtraction of time

10

13 Data Handling zz To understand datazz To understand tally chartzz To understand pictograph and bar graph

10

14 Patterns zz To understand symmetry in different shapes zz To understand lines of symmetryzz To understand various patterns and tiling and tessellations

9

TotalNo.ofPeriods 160

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1 Large Numbers

LearningObjectivesØØ To understand 5- and 6-digit numbersØØ To understand face value and place valueØØ To understand predecessor, successor and skip countingØØ To understand comparing numbersØØ To arrange numbers in ascending and descending ordersØØ To understand forming largest and smallest numbersØØ To round off numbers to the nearest 10, 100 and 1000ØØ To understand Indian and International place value systemsØØ To read and write Roman numerals

Pre-knowledgezz Place value of numbers up to 3 and 4 digitszz Comparing of numberszz Ascending and descending orders of numberszz Basic rules of writing Roman numbers

Activity1:PlaceValuesObjective: To understand and reinforce the concept of place value. The students will also be able to identify the value of numerals through 6-digit numbers.MaterialsRequired: Number cards (flash cards) – the number cards can be made by cutting out a chart paper into equal-sized squares and writing one number on each card; blackboard; chalk; paper; pencil; eraser; connecting cubes or various countersProcedure:The teacher will recall the place values of 3-digit and 4-digit numbers through a few examples. And then extend to the place values of 5- and 6-digit numbers. The teacher may also explain the concept of how the place values have been used in Indian number system and in International number system.The students are then asked to identify the (place) values of underlined numerals in 5-digit, 6-digit numbers (20 sums). For example, 43218. The digit which is underlined is located in the thousands place. So the students should be able to say the place value of 3 in 43218 is 3000. They can also be asked to represent them through cubes or counters in the given table.

Thousands Hundreds Tens Ones

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The students will form groups of 5 and 6 in each and will be given number cards from 0 to 9.

0

1

2

3

4

5

6

7

8

9

The teacher will call out a number. The students will line up in the order of their place values holding their number cards. For example, the teacher calls out the number four thousand one hundred and thirty-two (4132). The first group of four students who line up in order from right to left using thousands, hundreds, tens and ones wins. The first student holds the number card 4 (which represents thousands place, i.e., 4000), the second student holds the number card 1 (which represents hundreds place, i.e., 100), the third student holds the number card 3 (which represents tens place, i.e., 30) and the fourth student holds the number card 2 (which represents ones place, i.e., 2).

4

1

3

2

Assessment:zz Students will be able to identify place values of the underlined digits in a given number.zz Students will be able to form up to 6-digit numbers using number cards.zz Students will be able to appreciate cooperative learning through the activities.

Activity2:RomanNumeralsObjective: To reinforce the concept of Roman numerals using matchsticks.MaterialsRequired: A4 sheets, matchsticks and glue stickStep1: The teacher will divide the class into groups of 5 children in each group.Step2: The teacher will write a statement or an equation on the whiteboard. The students will write the same statement or the equation on a sheet of paper using matchsticks and glue.Step3: Once the teacher says ‘go’, they will reposition just one matchstick to make the equation valid. Then, the teacher may ask more question on this for the students to reposition a matchstick and make the equations valid.Forexample:(a) (b)

(c) (d)

(e) (f)

(g)

Answers: (a) V – III = II (b) IV + I = V (c) VIII + I = IX (d) XI – X = I (e) X – V = V (f) XI = XX – IX (g) VII – V = I + IThe team that finishes all the parts correctly or maximum sums correctly wins.

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Worksheet 1A 1. Write the place value and the face value of the underlined digits. (a) 12598 (b) 25894 (c) 122098 (d) 401713

2. Write the numbers in expanded form. (a) 9231 (b) 80104 (c) 450917 (d) 291789

3. Make the largest number using all the digits once. (a) 4, 1, 9, 5, 0 (b) 1, 5, 8, 9, 3, 2 (c) 1, 0, 4, 3, 9, 8

4. Make the smallest number using all the digits once. (a) 3, 5, 1, 7, 9 (b) 2, 8, 0, 4, 6 (c) 2, 9, 0, 3, 1, 6

5. Write the next five numbers by skip counting: (a) by 40s starting from 10,400 , , , , (b) by 100s starting from 20,300 , , , , (c) by 2000s starting from 2,45,789 , , , ,

6. Rewrite the numbers in Indian and International systems. Write them in words. (a) 67900 (b) 194209 (c) 780952 (d) 8340941

7. Write the numbers in figures in Indian and International systems, placing commas at the right places.

(a) Eighty-nine thousand nine hundred twenty-two (b) Seventy-five lakh ninety-three thousand seven (c) Two million three hundred twenty-nine thousand nine hundred nine

(d) Four million one hundred thousand one (e) Fifty-five lakh twenty-nine thousand eight hundred six

8. Fill in the blanks with preceding and succeeding numbers.

Predecessor Number Successor29,0124,57,1009,99,9992,67,980

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Worksheet 1B 1. Compare the numbers and fill in the blanks with >, < or =. (a) 4,54,879 4,45,978 (b) 23,978 32,789

(c) 4,09,007 4,90,070 (d) 76,45,012 76,54,120

2. Write the smallest number and the largest number. (a) 1,90,657; 56,82,965; 10,87,908; 8,89,345; 56,098

(b) 10,76,945; 10,87,567; 28,98,012; 28,10,111; 34,87,012

(c) 1,09,901; 1,90,109; 1,09,910; 1,90,190; 1,90,009

(d) 9,11,110; 9,10,111; 9,11,010; 9,01,111; 9,00,111

3. Round off the following numbers to the nearest 1000. (a) 56,980 (b) 12,52,813 (c) 6,09,721 (d) 2,87,123

4. Rewrite the numbers using Indian and International number systems. (a) 712356 (b) 5098723 (c) 4209876 (d) 318745

5. Write the Hindu-Arabic numbers for the following Roman numbers. (a) LXXXVIII (b) XXXVI (c) D (d) XVIII (e) LXII

6. Write the Roman numbers for the following numbers. (a) 800 (b) 70 (c) 900 (d) 40 (e) 1000

7. Make the largest and the smallest (a) 6-digit numbers using 6, 0, 3 and 1, and using 6 three times.

(b) 5-digit numbers using 2, 4, 6 and 8, and using 2 two times.

8. Write the next 5 numbers that follow:

(a) 4,09,812(b) 98,670(c) 11,119(d) 45,09,807

9. Write the numbers in figures in International system. (a) Eighty-six lakh twenty thousand three hundred four

(b) Five lakh two thousand two

(c) Fifteen lakh twenty-nine thousand five hundred five

(d) Sixteen lakh nine thousand two hundred one

(e) Twenty-seven thousand three hundred ten

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2

LearningObjectivesØØ To understand numerator and denominator in fractionsØØ To understand different types of fractionsØØ To understand equivalent fractionsØØ To understand fractions in lowest termsØØ To understand comparison of like and unlike fractionsØØ To understand proper and improper fractionsØØ To understand fractions as divisionØØ To understand addition of like and unlike fractionsØØ To understand subtraction of like and unlike fractions

Pre-knowledgezz Understand whole numbers and four operations thoroughlyzz Recognise the meaning of a wholezz Recognise a fraction as equal parts of a wholezz Understand the meaning of fraction: as part of a whole and part of a collectionzz Understand numerator and denominator in a fraction

Activity:FractionsonNumberLineUse a chart paper (a strip of cardboard or an ice-cream stick) to prepare a strip of paper. Draw a number line along one edge of the strip. Divide each number into 10 equal parts. Put a rubber band on the strip of paper such that it can slide on the number line. The rubber band will act as a pointer on the number line to show different numbers. The teacher can place the rubber band at different places to show the fractions on the number line. Explain the concept of whole number and fraction of a number by placing the rubber band at different places.

0 110

210

310

410

510

610

710

810

910

1

0 12 1

0 16

26

36

46

56

1

0 13

23

1

Fractions

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Examples: Move the rubber band to show these numbers on the number strip.

(a) 110

(b) 210

(c) 710

(d) 310

(e)1 110

(f) 2 910

0 1 2 3 4

0 1 2 3 4

0 1 2 3 4

0 1 2 3 4

0 1 2 3 4

0 1 2 3 4

Represent the following fractions on the number line.

(a) 15

(b) 1310

(c) 2610

0 1 2 3 4

0 1 2 3 4

0 1 2 3 4

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Worksheet 2A 1. Each figure represents a fraction. Write the fractions. Which figures represent the

same fractions? (a) (b)

(c) (d)

2. Fractions with different denominators are called (a) like fractions (b) unlike fractions

(c) equivalent fractions (d) proper fractions

3. 99

is .

(a) eight ninths (b) a whole

(c) four ninths (d) four parts of a whole

4. Which of these fractions are equal?

(a) 15

(b) 210

(c) 525

(d) 840

5. Express 3696

in the simplest form.

6. Aditya cut two cakes on his birthday: a chocolate cake and a pineapple cake. In the

party, 815

of the chocolate cake and 1315

of the pineapple cake were eaten. Which cake

was consumed more, and by how much more?

7. Two pizzas of same size were cut into 8 equal slices each. Five slices of the first pizza were eaten by Rajesh and two slices were eaten by Shreya. Renu ate four slices of the second pizza. How many slices of the two pizzas are left? Write them in fractions.

8. An adult human being has 32 teeth, 16 in the lower jaw and 16 in the upper jaw. In each jaw there are 4 incisors, 2 canines, 4 premolars and 6 molars. What fraction of all the teeth are (a) incisors (b) canines (c) premolars (d) molars (e) All teeth in the lower jaw?

9. Varun buys 28 balls. 37

of them are green and the rest are red. How many red balls does he buy?

10. What is the fraction of numbers which have a zero at the units place for numbers from 1 to 100 (100 is included)?

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Worksheet 2B 1. Write the fraction of the shaded and unshaded squares in each of the following. (a) (b) (c)

2. In the given figure, what fraction represents the coloured part?

3. (a) Colour 38

of the tomatoes. How many tomatoes are coloured?

(b) Colour 12

of the apples. How many apples are coloured?

4. How many more triangles have to be coloured if 34

of the triangles need to be coloured?

5. Find four equivalent fractions of 25

.

6. Find an equivalent fraction of 4554

by division.

7. Arrange in descending order: 710

, 110

, 310

, 610

, 410

.

8. Ayesha has a bouquet of flowers, which has 7 stems. Each stem has 5 flowers. While putting the bouquet in a vase, Ayesha observed that 3 flowers had wilted. What fraction of the flowers is wilted?

9. A bar of chocolate had 12 squares. If Golu ate 2 squares, Esha ate 3, Nandini ate 6 and Ambica ate one square. Name all children who ate less than half of the chocolate?

10. A rainbow consists of seven colours. They are violet, indigo, blue, green, yellow, orange and red. What fraction of the rainbow is the colour red?

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3

LearningObjectivesØØ To understand decimal numbersØØ To understand the whole and decimal partsØØ To understand place value in decimal numbersØØ To understand conversion of fractions to decimalsØØ To understand conversion of decimals to fractionsØØ To understand equivalent decimalsØØ To understand comparison of decimalsØØ To understand addition and subtraction of decimals

Pre-knowledgezz Understand place and face values in whole numberszz Understand comparing whole numbers using place valuezz Understand the operations on whole numberszz Understand the basics of fractionszz Understand numerator and denominator in fractions

Activity1:BuildingDecimalsObjective: To form decimal numbers and writing them in place value chart.MaterialsRequired: Spinner, place value chart, base 10 blocks, paper sheets, pencil, eraserMethod:

zz Take a spinner with 10 divisions with numbers 0–9 written on it. It can also be created by cutting out a cardboard. Draw a circle and divide it into 10 equal parts and write numbers from 0 up to 9.

zz Spin the spinner twice, thrice or four times to make a 2-digit, 3-digit or 4-digit number respectively. It has to be decided by the teacher beforehand.

zz Provide the students base 10 blocks (or cardboard cut outs of base 10 blocks can be used).

012

345

678

9

Decimals

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DecimalPlaceValueChart

Thousands

Hundreds

Tens

Ones

Decim

alpoint

Tenths

Hundredths

Thousandths

00

.

.52

25

zz The teacher can ask the students to form groups of 2 each. Each team will build numbers using the spinner, base 10 blocks and place value chart.

zz For example, the teacher asks the students to form a decimal number with two decimal places. Spin the spinner twice to have two digits to form the decimal number; we get the numbers, say, 2 and 5.

Then build the number 0.52 or 0.25. Now write the number in place value chart and represent the number using base 10 blocks.

0.52 0.25

zz Then the teacher can ask each team to generate numbers and model solutions, taking turns determining the decimal and whole numbers.

Activity2:DecimalNumberLines:TenthsandHundredthsDraw a number line on a strip of cloth or chart paper. Mark 0, 1, 2, 3, … on it.

Divide the part between 0 and 1 into 10 equal parts. Mark 110

, 210

, 310

, 410

, 510

, …, corresponding to the decimals on the number line.

0 110

210

310

410

510

610

710

810

910

1

This is same as (the fractions have been converted into decimals):

0 10.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

This is a number line that shows the tenths. The numbers are between 0 and 1.

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HundredthsNumberLineNow divide the part between 0 and 1 on the number line into hundred equal parts. That means, divide each part into 10 equal parts, i.e., divide the part between 0 and 0.1 into 10 equal parts, part between 0.1 and 0.2 into 10 equal parts, and so on.

0 0.10.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

This is a number line that shows the hundredths. The numbers are between 0 and 0.1. Similarly, we can show the other parts as follows:

0.1 0.20.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19

0.2 0.30.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29

0.3 0.40.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39

0.4 0.50.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49

0.5 0.60.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59

0.6 0.70.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69

0.7 0.80.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79

0.8 0.90.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89

0.9 10.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99

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Worksheet 3A 1. What part of the square is coloured? Express it in fraction and decimal. (a) (b)

2. Which is greater: 4.7 + 2.3 or 3.45 + 3.55?

3. Arrange in ascending order: 4.3, 4.333, 4.003, 4.033, 4.303, 4.030

4. Write 13.795 in expanded notation.

5. Write as a decimal number:

2 × 10 + 1 × 1 + 3 × 110

+ 5 × 1100 + 8 ×

11000

6. What should be added to 5.85 to get 10.435?

7. Fill in the blanks.

2.75, 2.80, 2.85, 2.90, , , , ,

8. Convert the following fractions into decimals.

(a) 3110

(b) 567100

9. Convert the following decimals into fractions. (a) 0.261

(b) 8.65

10. Add or subtract. (a) 0.34 + 1.53

(b) 2.965 + 5.357

(c) 16.62 – 4.31

(d) 53.231 – 13.485

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1. Fill in the blanks.

(a) Decimal form of 25

is (b) 56.75 – = 35.67

(c) 23.75 + = 75.00

2. Which decimal number is equivalent to 9100

?

3. Write 25.973 in expanded form.

4. Write as a decimal number: 1 × 100 + 4 × 1 + 5 × 110

+ 7 × 1100

+ 9 × 1

1000

5. Write in ascending order: 1.050, 1.500, 1.005, 1.550, 1.055, 1.505

6. Write the number name: (a) 0.32 (b) 45.864

7. Represent 0.7 in the figure. How many parts in the circle did you colour?

8. Represent 0.78 in the figure. How many parts did you colour?

9. Represent the shaded portion as a decimal number.

10. Represent the shaded portion as a decimal number.

11. What is the difference in the face value and the place value of 9 in the number 2.089?

12. What is the sum of the place value and the face value of 6 in the number 5.067?

Worksheet 3B

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LearningObjectivesØØ To learn addition of 5- and 6-digit numbers: without and with regroupingØØ To understand addition of three numbersØØ To learn to use various properties of additionØØ To learn estimation in additionØØ To understand solving word problems on additionØØ To learn subtraction of 5- and 6-digit numbers: without and with regroupingØØ To learn to use various properties of subtractionØØ To learn estimation in subtractionØØ To understand solving word problems on subtractionØØ To understand addition and subtraction together

Pre-knowledgezz Place value of numbers up to 6 digitszz Addition and subtraction of up to 4-digit numberszz Regrouping numbers in addition and subtraction

Activity1:AdditionandSubtractionofNumbersObjective: To reinforce the concept of addition and subtraction.MaterialsRequired: Paper, pencil, a bag, counters with numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 written on them.

0

1

2

3

4

5

6

7

8

9

Steps: 1. The teacher will divide the students into groups of four children in each. Each team will select or

choose their leader. 2. The counters are put in the bag and kept on the teacher’s table. The teacher will ask the groups to

pick out 3, 4, 5 or 6 counters depending on the number of digits they are going to add or subtract in that round.

3. The team leader from each team will pick out any 4 counters (say) randomly from the bag and go back to the team to work out with the team members.

4. Using the counters they will form the largest and the smallest possible numbers, write if they are even or odd numbers, work out and write their sum and difference.

5. Then they will fill in the details as given in the table. For example, if one team takes out counters 8, 2, 6 and 0 from the bag, they will form the largest

possible number as 8620, which is even and the smallest possible number as 2068, which is also even. Now they add 8620 + 2068 and subtract 2068 from 8620 and will fill in the columns of the table.

4 Addition and Subtraction

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S.N.

Counterspickedup

Largestnumber

Odd/even

Smallestnumber

Odd/even

Sumoflargest&smallestnumbers

Differencebetweenlargest&smallestnumbers

1 8, 2, 6, 0 8620 Even 2068 Even 10,688 65522345

6. The game can be played five times in each round and for 3–4 rounds with different number of digits each time. For each round they have to take a new table and fill in the details in the table. Whichever team completes filling up the table first and correctly will be the winner.

Activity2:ReinforcementofAdditionandSubtractionObjectives: To reinforce the concept of addition and subtraction of two numbers with and without regrouping.MaterialsRequired:Place value chart, dice, cut out circles of different colours, paper, pencil, eraserProcedure:The teacher will divide the class into groups of 2 or 4 children in each. Provide each group place value charts and different coloured counters with numbers 1, 10, 100, 1000, 10,000 written on them or cut out circles of different coloured papers with numbers 1, 10, 100, 1000, 10000 written on them. Use as many colours as the number of digits you want to reinforce – for example, use red coloured paper for ones, blue for tens, yellow for hundreds, green for thousands, purple for ten thousands, and so on.

1 10 100 1000 10000

Each group throws the dice in turn for 4 times for a 4-digit number and form the numbers to be added. They will represent the number in the place value chart using the coloured circles. At the same time of modelling and solving the problems, have a student showing on another sheet abstractly what is being done as it is being shown concretely on the chart. This will enable the students to transfer what they see concretely to the abstract. Also this will explain how we go abstract from concrete in mathematics. Be sure to stress that the largest digit each place value can have is a 9 and that exchanges must be made for numbers larger than 9.For example, 3122 + 2112

Th H T O

1000 1000 1000 100 10

10 1

1

+ 1000 1000 100 10 1

1

1000 1000 1000 1000 1000 100

100 10

10

10 1

1

1

1

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Abstractly, 3 1 2 2 + 2 1 1 2 5 2 3 4

Similarly, the process of subtraction can be explained.Th H T O

1000 1000 1000 100

100 10

10

10 1

– 1000 1000 100 10

10 1

1000 100 10

Abstractly, 3 2 3 1 – 2 1 2 1 1 1 1 0

AdditionalActivities 1. In groups of 2 or 4, give each group an envelope with papers having a problem and four clues

written on it. The group discusses the problem and the four clues. The first group that solves the problem and can explain how the solution was obtained wins.

For example: Q: How many mangoes are there in the tree? Clue1: The number uses the digits 1, 2, 7 and 5, not in that order. Clue2: Each digit is used once. The 2 is not in the ones place. Clue3: The smallest digit is in the hundreds place. Clue4: The largest digit is in the tens place. Ans: 2175 mangoes 2. Write a story sum that you can solve using the number sentence: 1035 + 3167 = ? 3. On a piece of paper, students make 4 square boxes and directly below that 4 more square boxes in

preparation for adding two 4-digit numbers. A cube or die is rolled. The number appearing on the cube or die is put on one of the 8 boxes. The cube or die is rolled again and the second number is placed in one of the remaining blank boxes. The process is repeated until all the 8 boxes are filled in. The two numbers are then added, and the student with the largest sum is the winner.

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1. Arrange the numbers in columns and add. (a) 56,879 + 25,718 (b) 19,034 + 43,823

(c) 2,72,879 + 1,23,098 (d) 34,781 + 45,871 + 1099

2. Fill in the blanks. (a) 54,089 + = 41,094 +

(b) + 45,098 = 45,098

(c) 34,999 + = 35,000

(d) + 87,097 = 87,097 + 32,098

(e) 67,098 + (45,009 + 12,678) = (67,098 + 45,009) +

3. Round off the numbers to the nearest 10 and add. (a) 67,098 + 31,765 (b) 34,096 + 45,123

(c) 34,768 + 45,900 (d) 12,845 + 456

4. Round off the numbers to the nearest 100 and add. (a) 21,567 + 30,987 (b) 4509 + 7897

(c) 12,876 + 92,045 (d) 10,978 + 31,034

5. Round off the numbers to the nearest 1000 and add. (a) 78,412 + 56,023 (b) 34,987 + 45,067

(c) 4987 + 56,098 (d) 34,826 + 1,29,045

6. In a school, the number of boys is 2305, the number of girls is 2758 and the number of teachers is 254. What is the total number of students and teachers in the school?

7. In the school library, there are 12,035 fiction books and 21,555 non-fiction books. Find the total number of books in the library.

8. The population of three towns are 34,876; 23,098 and 65,067. What is the total population of the three towns?

9. An ice-cream company sells 24,978 ice-cream bricks in the month of April, 34,987 ice-cream bricks in the month of May, and 1,98,067 ice-cream bricks in the month of June. What is the total number of ice-cream bricks the company sells in these three months?

10. In a family, the monthly salary of Mr John is ` 76,900; Mrs John is ` 34,890, that of their son is ` 23,258 and daughter is ` 10,561. What is the total monthly salary of the four members of the family?

Worksheet 4A

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Worksheet 4B 1. Arrange the numbers in columns and subtract. (a) 45,342 – 16,653 (b) 31,016 – 14,138 (c) 61,024 – 42,755

(d) 50,241 – 35,406 (e) 1,43,112 – 55,235

2. Fill in the blanks. (a) 32,110 – = 32,110

(b) – 14,213 = 0

(c) 24,535 – = 24,534

(d) 15,321 – = 15,221

(e) 37,100 – = 36,100

3. Round off the numbers to the nearest 10 and subtract. (a) 15,586 – 12,367 (b) 14,772 – 11,125

(c) 32,312 – 12,601 (d) 41,235 – 10,627

4. Round off the numbers to the nearest 100 and subtract. (a) 40,971 – 29,615 (b) 25,805 – 20,251

(c) 80,602 – 61,104 (d) 91,034 – 14,555

5. Round off the numbers to the nearest 1000 and subtract. (a) 25,023 – 16,198 (b) 78,413 – 45,207

(c) 51,611 – 23,906 (d) 2,04,879 – 1,25,045

6. Solve. (a) 34,205 + 2208 – 21,612 (b) 72,345 – 25,219 + 1134

(c) 14,734 + 5789 – 17,999 (d) 57,250 – 24,121 + 3295

(e) 12,980 + 6067 – 1034 – 4507 + 2908

7. In a school, there are 3056 people, which includes children and staff members. If there are 205 staff members and 1879 boys, find the number of girls in the school.

8. A family spends ` 10,900 on grocery, ` 4500 on entertainment, ` 15,000 on transportation and saves the remaining. If the total income of the family is ` 50,000, find the savings of the family.

9. What is 1 lakh more than the sum of 45,872 and 17,908?

10. Ms Verma wants to buy a car worth ` 6,49,000. She has saved ` 4,89,460. How much more money does she need so that she can buy the car?

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LearningObjectivesØØ To understand properties of multiplicationØØ To learn multiplication by 2-digit and 3-digit numbersØØ To understand multiplication by 10, 100 and 1000ØØ To understand multiplication tablesØØ To learn simplification by DMAS ruleØØ To solve word problems involving multiplicationØØ To learn estimation in multiplicationØØ To learn lattice multiplication of 3-digit numbers

Pre-knowledgezz Skip counting and equal groupingzz Multiplication by 1-digit and 2-digit numberszz Multiplication of 3-digit numbers by 2-digit numberszz Lattice multiplication of 2-digit numbers

Activity:MultiplicationbyBreakingupMultiplicandandMultiplierObjective: To learn and master multiplication by breaking up numbers as per their place values.Procedure:

zz Explain to the students that they need to apply their understanding of place value in multiplication.zz It will be helpful if the teacher spends a few minutes reviewing place value before getting into the

actual lesson. Before starting the topic, questions the teacher could ask are: (a) What is place value? (b) How is understanding place value helpful while solving various sums?

zz Write a 2-digit number on the board, such as 85. Ask the students how they could break this number down by place value or expanded notation. Remind students that expanded notation means writing a number to show the value of each digit in a number.

zz Write the 2-digit number in expanded form: 85 = 80 + 5. Make sure the students understand that these numbers came from identifying the total of tens and ones in the number.

zz Follow the same process for a few more increasingly larger numbers, such as: 97, 345, 1375, etc.zz Explain that the focus of the lesson is on solving multiplication sums involving 2-digit and 3-digit

numbers.zz Explain to the students that while larger multiplication sums can look scary, this lesson will teach

them a very helpful strategy for solving them.zz Explain to the students that the strategy they will be using to solve multiplication sums will be

multiplication by breaking the multiplicand and the multiplier which uses the concept of place value.

zz For example, let us multiply 346 by 74.

5 Multiplication

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Make a table as follows and break the numbers as per their place values.

346

× 300 40 6 Answer

7470 21000 2800 420

4 1200 160 24

22200 2960 444 25604

346 × 74 = 22200 + 2960 + 444 = 25604 Let us now cross-check the multiplication by normal method: 3 4 6 × 7 4 1 3 8 4 + 2 4 2 2 0 2 5 6 0 4As both the methods give the same result our method is correct.

SomeImportantPointsfortheTeacherzz The students will now be able to solve multiplication sums using this strategy independently. If

you feel some students need extra support, split the class into pairs of students so each person has a partner to work with.

zz As students work, walk around to make sure they are breaking the numbers correctly. Provide assistance to those who need extra support.

zz Challenge advanced students to try multiplication problems with 4-digit and bigger numbers.zz Keep track of student participation during the whole activity and modify instructions as needed

and assess students’ understanding.zz Before the end of the lesson review the concept once. Call on student volunteers to explain each

step of the strategy.zz Write some sample problems on the board for the students to solve at home using the strategy.

(a) 497 × 42 (b) 519 × 264 (c) 946 × 129 (d) 916 × 37

Teacher’s Sign: © Headword Publishing Company Pvt. Ltd

1. Multiply and find the product. (a) 13 × 9 = (b) 17 × 8 =

(c) 16 × 9 = (d) 15 × 6 =

(e) 20 × 7 = (f) 12 × 8 =

2. Multiply mentally using grouping property. (a) 20 × 78 × 5 = (b) 10 × 106 × 10 =

(c) 4 × 543 × 25 = (d) 426 × 2 × 50 =

3. Fill in the blanks. (a) 23 × 45 = 45 ×

(b) 12 × (56 × 23) = (12 × 23) ×

(c) 534 × = 534

(d) 3789 × = 0

(e) 13 × (4 + 5) = 13 × 4 + ×

4. Multiply.(a) 5 2 3

× 1 8 7

(b) 4 5 1

× 3 2 1

(c) 5 9 0

× 3 1 7

5. Simplify. (a) 18 × 9 + 16 × 9 – 45

(b) 79 – 43 + 11 × 8 – 54 + 100

(c) 500 × 20 – 390 × 2 + 7 × 25

6. Multiply using lattice multiplication method and cross-check. (a) 312 × 45 (b) 529 × 76 (c) 521× 701

(d) 491 × 312 (e) 831 × 410 (f) 4189 × 42

7. In a school there are 12 classes each having 7 sections. If the number of children in each section is 51, find the total number of students in the school.

8. Find the number of hours in 5 years? (Consider all of them as non-leap years.)

Worksheet 5A

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1. Multiply and write the product. (a) 429 × 10 =

(b) 539 × 100 =

(c) 309 × 1000 =

(d) 423 × 20 =

(e) 519 × 30 =

(f) 910 × 500 =

(g) 31 × 2000 =

(h) 186 × 40 =

2. Fill in the blanks with >, < or =. (a) 12 × 15 13 × 10

(b) 21 × 5 6 × 20

(c) 23 × 6 32 × 4

(d) 34 × 12 10 × 36

(e) 42 × 5 7 × 39

(f) 20 × 5 50 × 2

3. Multiply.(a) 4 0 8

× 1 9 8

(b) 3 9 7 6

× 2 3 1

(c) 5 1 0

× 1 1 2

4. Simplify. (a) 17 × 8 + 15 × 7 – 8 × 12

(b) 14 × 5 – 9 × 4 – 2 × 12

(c) 213 × 8 – 50 × 7 + 23 × 178

5. A table costs ` 500 and a chair costs ` 230. Find the cost of 45 tables and 90 chairs.

6. In one trip a bus can carry 55 people. If the bus makes 167 trips, how many people have used the services of the bus?

Worksheet 5B