Maths Binder 19.12.16

GRADE 2 Maths WB(with answer keys) 2017-2018

Chapter Numbers 3Concept 3.1: Count by Hundreds3.1 I RecallMultiple Choice Questions1) The smallest 2-digit number is: [B] [D](A) 11 (B) 10 (C) 99 (D) 19 [A] (D) 992) The largest 2-digit number is: (D) zero(A) 01 (B) 10 (C) 903) The number name of 2 is: (A) two (B) one (C) three3.1 I Remember and UnderstandMultiple Choice Questions4) 10 tens = ____ hundred [ B] [C] (B) 1 (C) 0 (D) 100 [B] (D) thirty5) The place value of 4 in 243 is ______. (D) 1(A) three (B) four (C) forty6) 50 tens = ________ hundreds. (A) 50 (B) 5 (C) 500

Fill in the Blanks 7) The number name of 346 is three hundred and forty six. 8) 706 = 700 + 0 + 6 9) The expanded form of number 626 is 600 + 20 + 6. Very Short Answer Questions 10) What is the place value of the number 9 in the number 269? Solution: 9 ones 11) What is the number name of 111? Solution: One hundred and eleven 12) What is the expanded form of 673? Solution: 600 + 70 + 3 Short Answer Questions 13) What is expanded form? Write the expanded form of 384. Solution: The form in which a number is expressed as the sum of the place values of its digits is called its expanded form. The expanded form of 384 is 300 + 80 + 4. 14) Write the number names of: a) 425 b) 698 Solution: The number names are – a) Four hundred and twenty five b) Six hundred and ninety eight2

3.1 I ApplyVery Short Answer Question15) Write the number which has 2 in the hundreds place, 1 in the tensplace and 0 in the ones place.Solution: Write the given digits in the place value chart according to theplaces. Hundreds Tens Ones 2 1 0So, the required number is 210.Short Answer Questions16) There are 116 students in Team A, 290 students in Team B, 310 students inTeam C and 400 students in Team D.a) What is the number of students in Team A? Write its number name.b) What is the number of students in Team D? Write its number name.Solution:a) There are 116 students in Team A. The number name of 116 is one hundredand sixteen.b) There are 400 students in Team D. The number name of 400 is four hundred.17)If Ram has 1 note of ` 100 and 1 note of ` 10. How many rupees doeshe have in all?Solution: 1 note of ` 100 = ` 100 1 note of ` 10 = ` 10 So, ` 100 + ` 10 = ` 110 (one hundred and ten) Numbers 3

3.1 I Explore (H.O.T.S)Short Answer Question18) If you add 3 tens and 1 tens and show the answer on an abacus, whichspikes will be empty?Solution: Adding 3 tens and 1 tens, we get 30 + 10 = 40 = 4 tens.So, put 4 green beads on the abacus.Clearly, the hundreds and ones spike on the abacus will beempty.Concept 3.2: Ordinal Numbers 3.2 I RecallMultiple Choice Questions1) The coloured rectangle before red is: [C] (A) black (B) blue (C) orange (D) green2) The coloured rectangle after orange is: [D] (A) blue (B) green (C) orange (D) red3) The coloured rectangle before orange is: [B] (A) green (B) blue (C) orange (D) red4

3.2 I Remember and UnderstandMultiple Choice Questions4) The short form of the ordinal number sixth is: [A](A) 6th (B) six (C) 6 (D) all of the above5) The ordinal number of 9 is: [B](A) nine (B) ninth (C) 9 (D) all of the above6) The ordinal number of 7 is: [C](A) 7 (B) seven (C) seventh (D) all of the aboveFill in the Blanks7) Yellow is in the third position. 58) Grey is in the first position.9) Blue is in the fourth position.Very Short Answer Questions10) What is the short form of the ordinal number eighth?Solution: 8th11) What is the ordinal number for 10?Solution: Tenth12) Which is the number for the ordinal number second?Solution: 2nd Numbers

Short Answer Questions13) What are ordinal numbers? Count the ordinal numbers from one to ten.Solution: The numbers which tell about the position are called ordinal numbers.They are counted as first, second, third, fourth, fifth, sixth, seventh, eighth,ninth and tenth.14) Write the ordinal number and short form of the following numbers. a) 6 b) 9 c) 1 d) 2Solution: The ordinal and short form of the numbers can be written as – Numbers Ordinal Numbers Short Form 6 Sixth 6th 9 Ninth 9th 1 First 1st 2 Second 2nd 3.2 I ApplyVery Short Answer Question15) Which is the second period in your time table today?Solution: Student's responseShort Answer Questions Rohan Mohan Sohan16) Rohan, Mohan and Sohan won a running race.They stood in the positions as given in the picture.a) At which position is Rohan?b) What is Sohan’s position? 2nd 1st 3rd6

Solution:a) Rohan is at 2nd position.b) Sohan is at 3rd position.17) If Ram has the following periods in the time table:First Period Second Period Third Period Fourth Period Fifth Period Swimming English Colouring Math Play Timea) Which is the fourth period?b) Which is the third period?Solution:a) Play Time is the fourth period.b) English is the third period. 3.2 I Explore (H.O.T.S.)Short Answer Question18) If the name of the city is BENGALURUa) Which is the third letter?b) Which is the last letter?Solution: In the name of the city is BENGALURUa) The third letter is N.b) The last letter is U. Numbers 7

3.3: Compare and Order 3-digit Numbers 3.3 I RecallMultiple Choice Questions1) A 2-digit number is always greater than: [B] (A) a 3-digit number (C) a 2-digit number (D) a 4-digit number2) What do the following symbols show? >, < [A] (A) The two given numbers are not equal (B) The two given numbers are equal (C) Both the given numbers have the same place value (D) All of the above3) Which of the following symbols do we use to compare the given numbers? (A) +, - (B) < , > (C) +, = (D) - , = [B]8

3.3 I Remember and UnderstandMultiple Choice Questions4) If two 3-digit numbers have same digits in their hundreds and tens places,digits in the________ places should be considered to compare them. [C](A) hundreds (B) tens (C) ones (D) all of the above5) Which of the following signs should we put in the given blank: [A](A) < (B) > (C) = (D) All of the above6) If 320 and 310 are the given numbers, 310 will be the smaller number inthem because: [A](A)The digit in its tens place is less than the digit in the tens place of theother number(B) The digits in the hundreds place of both the numbers are same(C) Both the numbers have zero in their ones place(D) Both of them are three digit numbersFill in the BlanksFill in the blanks with correct sign from those given in the bracket (<, >, =)7) 525 < 5528) 400 = 4009) 354 > 145Very Short Answer Questions10) Which of the numbers 565, 456 is greater in the two? Numbers 9

Solution: 565 11) Which of the numbers 412, 214 is smaller in the two? Solution: 214 12) If 200 and 400 are the given numbers, digits in which place should we consider to compare them? Solution: The hundreds place Short Answer Questions 13) Compare the following numbers using the steps taught to you: 329, 325 Solution: In the hundreds place, 3 = 3; In the tens place, 2 = 2; In the ones places 9 > 5 So, 329 > 325 14) Which of the following numbers is smaller? 576, 367 Solution: In the hundreds place, 5 < 3. So, 367 is smaller than 576. 3.3 I Apply Very Short Answer Question 15) Write the following numbers in the ascending order: 200, 100, 300, 400 Solution: 100, 200, 300, 400 Short Answer Questions 16) There are 179 pages in a Craft book and 263 pages in a Science book. Which of the two books have more number of pages?10

Solution: Number of pages in the Craft book = 179,Number of pages in the Science book = 263Comparing the digits in the hundreds, tens and ones places of the abovenumbers, 263 > 179.So, the Science book has more number of pages.17) Form the largest 3-digit number from the digits given below: 2,6,4Solution: Write the largest of the given digits in the hundreds place.Write thenext larger number in the tens place and place the smallest digit in theones place. So, the number formed is 642. Hundreds Tens Ones 64 2 3.3 I Explore (H.O.T.S.)Short Answer Question18) Form the smallest 3-digit number using only two digits. You can repeatthe digits if required.Solution: Smallest 3-digit number is 100, we can use the digits 1 and 0 to formthe number. Numbers 11

GRADE 3Maths TB2017-2018

Chapter 1 Shapes I will LearnConcepts1.1: Vertices and Diagonals of Two Dimensional ShapesL1_V2_PPS_Math_G3_TB_05112016_V0.indd 1 12/9/2016 9:17:03 PM

Concept 1.1: Vertices and Diagonals of Two Dimensional Shapes I ThinkThere is a paper folding activity in Neena’s class. Her teacher asked thestudents to fold the paper across the vertices of the diagonals. How will Neenafold the paper?To answer this question, we must learn about vertices and diagonals of twodimensional shapes. 1.1 I RecallWe have learnt various shapes formed by straight lines or curved lines. Let us recallthem.AB A BA B Line Line segment Ray (a) (b) (c)Horizontal lines Vertical lines Slant lines Curved lines (d) (e) (f) (g) 2 12/9/2016 9:17:04 PML1_V2_PPS_Math_G3_TB_05112016_V0.indd 2

The straight and the curved lines help us make closed and open figures.Figures which end at the point where they start are called closed figures. Figureswhich do not end at the point where they start are called open figures. Closed figures Open figuresTry this:Write open figure or closed figure in the given blanks:____________ ______________ ____________ ____________Shapes such as rectangle, triangle, square and circle can be laid (or drawn) flat ona piece of paper are called two dimensional shapes. Their outlines are called twodimensional figures. In short, they are called 2D figures.Identify the following shapes and separate them as 1D or 2D shapes. One has beendone for you.Object Shape Name of the shape 1D or 2D Triangle 2D Shapes 3L1_V2_PPS_Math_G3_TB_05112016_V0.indd 3 12/9/2016 9:17:05 PM

Object Shape Name of the shape 1D or 2D1.1 I Remember and UnderstandAs we have already learnt various shapes, let us now learnhow to name their parts. Consider a rectangle ABCD asshown.In the given rectangle, AB, BC, CD and DA are called itssides. There are lines joining A to C and B to D. These linesnamed AC and BD are called diagonals.Points A, B, C and D where two sides ofthe rectangle meet are called vertices. Vertex: The point where at least twoA square too has all these parts. sides of a figure meet is called aNote: A triangle and a circle do not vertex. The plural of vertex is vertices.have any diagonal. Diagonal: A straight line inside a shapeTry this: that joins the opposite vertices is called a diagonal.Fill the given table with vertices, sides anddiagonals of the different shapes. One has been done for you.Shapes Vertices Sides DiagonalsDC A, B, C, D AB, BC, CD, DA AC, BDAB 4 12/9/2016 9:17:06 PML1_V2_PPS_Math_G3_TB_05112016_V0.indd 4

Shapes Vertices Sides Diagonals ___, ___, ___, ___ ___, ___, ___, ___ _____, _____ Y Z X ___, ___, ___, ___ ___, ___, ___, ___ _____, _____ W Train my brainName the given figures and find the number of their vertices anddiagonals. a) b) c)1.1 I ApplyWe know that a 2D shape has length and breadth. Let us now learn to find thenumber of sides of a 2D shape. Consider a triangle as shown. AThe given triangle has 3 sides named as AB, BC and CA. We canalso name them as BA, CB and AC.The different number of small lines on the sides of the triangle show C Bthat the lengths of all the 3 sides are different.The same number of small lines on the sides of the triangle show that the lengths ofall the 3 sides are the same. Shapes 5L1_V2_PPS_Math_G3_TB_05112016_V0.indd 5 12/9/2016 9:17:06 PM

Let us now learn to find the number of sides of a few 2D shapes and name them.Shape Name of the shape Number of sides Names of sides Square 4 PQ, QR, RS, SP (All sides are equal) 4 Rectangle (Opposite sides AB, BC, CD, DA are equal) Triangle 3 AB, BC, CA (All sides equal in this case)We find many shapes in the objects around us.Fill in the following table by writing the basic shapes of these given objects, numberof their vertices and diagonals.Objects Basic shape Number of vertices Number of diagonals 6 12/9/2016 9:17:07 PML1_V2_PPS_Math_G3_TB_05112016_V0.indd 6

A tangram is a Chinese geometrical puzzle consisting of asquare cut into seven pieces. These pieces can be arrangedin different ways to make various shapes.To create different shapes, we arrange these tangram pieceswith their sides touching one beside the other another.We may also arrange these shapes with their verticestouching each other.Make your own tangramMaterial needed:1) A square sheet of paper2) A pair of scissors3) A ruler (Optional)Procedure: Steps FigureStep 1: Fold the square sheet of paperas shown.Step 2: Cut the square into two Atriangles, across the fold. BStep 3: Cut one of the trianglesobtained in step 2, into two equal parts.We get two smaller triangles as shown. Shapes 7L1_V2_PPS_Math_G3_TB_05112016_V0.indd 7 12/9/2016 9:17:07 PM

Steps FigureStep 4: Fold the other big triangle asshown.Step 5: Unfold this piece and cut itacross the fold. We get one moretriangle.Step 6: Fold the boat-shaped piece fromone end as shown. We get a triangleagain on cutting at the fold.Step 7: Fold the remaining part ofthe paper again as shown. We get asquare on cutting at the fold.Step 8: Fold the remaining paper again.We now get one more triangle on cuttingat the fold.From all these cuts, we get 7 pieces ofthe tangram.Step 9: Colour these shapes using different colours. You can use these tangrampieces to make different shapes. 8 12/9/2016 9:17:07 PML1_V2_PPS_Math_G3_TB_05112016_V0.indd 8

1.1 I Explore (H.O.T.S.)Observe the object in the given figure. It looks like a box. Each sideof the box is a square.In the figure, AB is the length and BF is the breadth of the box. AD is Cubecalled the height of the box. So, this shape has three dimensions -length, breadth and height.Such shapes are called three-dimensional shapes or 3D shapes or solid shapes.In the figure,• The points A, B, C, D, E, F, G and H are called vertices.• The lines AB, BC, CD, DA, BF, FE, EA, CG, GH, HD, HE and GF are called edges.• The squares ABCD, ABFE, BFGC, GCDH, EFGH and AEHD are called faces.Solid shapes with all flat square faces are called cubes.Let us learn how to draw a cube in a few simple steps. Steps FigureStep 1: Draw a square ABCD.Step 2: Draw another square EFGHcutting square ABCD as shown. Shapes 9L1_V2_PPS_Math_G3_TB_05112016_V0.indd 9 12/9/2016 9:17:07 PM

Steps FigureStep 3: Join DH, AE, BF and CG.A few other such 3-dimensional shapes are cuboids and cones. CuboidSolid shapes with flat rectangular faces are called cuboids. A solid shape with a circular base and a curved surface is called a cone.ConeTry this:Draw a cuboid and a cone showing the formation of the figure in steps.Shapes Step 1 Step 2 Train My BrSateipn3CuboidCone 10 12/9/2016 9:17:08 PML1_V2_PPS_Math_G3_TB_05112016_V0.indd 10

Maths munchiesWe can use tangrams to make many shapes such as: 213 Boat Candle RocketCan you make a house with the following tangrams?You can use the same shape twice. Connect the DotsSocial fun We can see 2D shapes such as rectangles, squares, circles and 3D shapes such as cubes and cuboids in the buildings in our neighbourhood. Shapes 11L1_V2_PPS_Math_G3_TB_05112016_V0.indd 11 12/9/2016 9:17:09 PM

English fun Try drawing a square while reciting the rhyme. From the bottom to the top, Straight across right and then you stop. Straight down to the bottom again, Across left and stop where you began. If the lines are the same size, Then a square is formed for you a surprise. A Note to ParentTake your child to public places like hospitals, markets, religious places like temples,mosques and churches and so on. Help them name the 3D shapes that are commonlyseen on these structures. 12 12/9/2016 9:17:10 PML1_V2_PPS_Math_G3_TB_05112016_V0.indd 12

Drill time Concept 1.1 Vertices and Diagonals of Two Dimensional Shapes Find the number of vertices and diagonals of the following shapes:Shapes Vertices Diagonals Shapes 13L1_V2_PPS_Math_G3_TB_05112016_V0.indd 13 12/9/2016 9:17:10 PM

GRADE 3 Maths WB(with answer keys) 2017-2018

Chapter Shapes 1Concept 1.1: Vertices and Diagonals of Two Dimensional Shapes I RecallMultiple Choice Questions1) The shape of is: [A ] (D) Triangle(A) Circle (B) Square (C) Rectangle (C) 2D [ D ]2) A triangle is a _________ figure. (D) Both (B) and (C)(A) open (B) closed3) The shape of is: [B ] (A) Square (B) Rectangle (C) Triangle (D) Circle I Remember and UnderstandMultiple Choice Questions4) The point where at least two sides of a figure meet is called a/an ________. [ C ](A) line (B) diagonal (C) vertex (D) edgeMaths_G3_L03_Shapes_WB.indd 1 Shapes 1 12/9/2016 9:23:38 PM

5) A straight line that joins the opposite vertices of a closed figure is called a/an _________. [ B ](A) vertex (B) diagonal (C) line (D) edge DC6) The diagonals in A B are: [C](A) AB, BC (B) AD, CB (C) AC, BD (D) AB, DCFill in the Blanks7) A triangle has no diagonals.8) A circle has no vertices.9) A square and a rectangle have four vertices.Very Short Answer Questions10) What is the unique feature of a square?Solution: It has 4 equal sides.11) How many vertices does a triangle have?Solution: 312) How many diagonals does a circle have?Solution: 0Short Answer Questions13) Complete the following table: Shape Vertices Diagonals PR, QS P, Q, R, S 2 12/9/2016 9:23:39 PMMaths_G3_L03_Shapes_WB.indd 2

14) Complete the following table: Shape Vertices Diagonals AC, BD A, B, C, DLong Answer Questions A B E c15) Look at the figure and answer the following questions: Da) How many vertices does it have? Name them. Fb) How many diagonals does it have from A? Name them.Solution: a) It has 6 vertices. A, B, C, D, E, and F. b) It has 3 diagonals from A. AC, AD and AE.16) Draw a square WXYZ and answer the following questions: a) Name the vertices. b) Name the diagonals.Soluti on: a) The vertices are W, X, Y and Z. b) The diagonals are WY and XZ.Maths_G3_L03_Shapes_WB.indd 3 Shapes 3 12/9/2016 9:23:39 PM

I ApplyShort Answer Questions17) Complete the following table:Shapes Number of vertices Number of diagonals 4 2 42 6918) Complete the following table: Number of Number of Shapes vertices diagonals 55 42 12/9/2016 9:23:39 PM Long Answer Questions 19) Look at the picture given and answer the following questions: a) What is the shape of this object? b) How many sides does it have? c) How many diagonals does it have? d) How many vertices does it have? 4Maths_G3_L03_Shapes_WB.indd 4

Solutio n: a) Rectangle b) 4 c) 2 d) 420) Look at the picture and answer the following: a) What is the shape of this object? b) How many sides does it have? c) How many diagonals does it have? d) How many vertices does it have?Solution: a) Triangle b) 3 c) 0 d) 3 I Explore (H.O.T.S.) Shapes 5 Short Answer Question 12/9/2016 9:23:39 PM 21) Name a 3-dimensional figure that has the following: a) A circular base. b) A rectangular base. c) A square base.Maths_G3_L03_Shapes_WB.indd 5

Solution: a) Cone b) Cuboid c) CubeLong Answer Question22) Look at the figure and answer the following questions a) Name the vertices. b) Name the edges. c) Name the faces.Solution: a) The vertices are A, B, C, D, E, F, G and H. b) The edges are AB, BC, CD, DA, BE, FE, GH, HE, DG, AH and GF. c) The faces are ABCD, BCFE, EFGH, ADGH, ABEH and CDGF. 6 12/9/2016 9:23:39 PMMaths_G3_L03_Shapes_WB.indd 6

GRADE 4Maths TB 2017- 2018

Chapter 3 Numbers I will LearnConcepts3.1: Count by Ten Thousands3.2: Compare and Order 5-digit Numbers3.3: Round off Numbers Numbers 1L01_V2_PPS_Maths_G4_TB.indd 1 12/9/2016 3:27:56 PM

Concept 3.1: Count by Ten Thousands I Think Surbhi’s father bought a TV and the bill read as ` 55,515. Surbhi read it as five thousand five hundred and fifty one and one more five. Her father told her that she was wrong and asked her to learn the correct way of saying 5-digit numbers in words. Can you read such big numbers? To read such numbers, we must learn to count into ten thousands. 3.1 I RecallWe know that 10 ones make a ten, 10 tens make a hundred and 10 hundreds makea thousand.Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80, 90Counting by 100s: 100, 200, 300, 400, 500, 600, 700, 800, 900Counting by 1000s: 1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000Let us read the number names for the following numbers:80 – Eighty800 – Eight hundred8000 – Eight thousand888 – Eight hundred and eighty eight 2 12/9/2016 3:27:56 PML01_V2_PPS_Maths_G4_TB.indd 2

Let us recall the smallest and the largest 2-digit, 3-digit and 4-digit numbers andname them.Number of Digits Smallest Largest 2 10 (Ten) 99 (Ninety nine) 3 100 (Hundred) 999 (Nine hundred and ninety nine) 4 1000 9999 (Nine thousand nine hundred and (Thousand) ninety nine)There are numbers greater than 9999. Let us learn about them.3.1 I Remember and UnderstandRemember, the number after the greatest 3-digit number is the smallest 4-digitnumber: 999 + 1 = 1000.Similarly, the smallest 5-digit number comes just after(successor of) the largest 4-digit number. Th H TO The smallest 5-digit 1 1 1 number = 10000 9 + 9 99 The largest 5-digit 1 0 0 1 number = 99999 00We get a new place in the place value chart. It is calledthe ten thousands place. In short, we write it as T Th. T Th Th H T O 111 9999 +1 1000010000 in words is ten thousand. It is the smallest 5-digit number. Numbers 3L01_V2_PPS_Maths_G4_TB.indd 3 12/9/2016 3:27:57 PM

Count a few numbers in ones after ten thousand and write their number names: 10000 + 1 = 10001 = Ten thousand and one 10000 + 2 = 10002 = Ten thousand and two 10000 + 9 = 10009 = Ten thousand and nineSimilarly, let us count a few numbers in tens after ten thousand and write their numbernames. 10000 + 10 = 10010 = Ten thousand and ten 10000 + 90 = 10090 = Ten thousand and ninetyNow, let us count a few numbers in hundreds after ten thousand and write theirnumber names. 10000 + 100 = 10100 = Ten thousand one hundred 10000 + 900 = 10900 = Ten thousand nine hundredNow, let us count a few numbers in thousands after ten thousand and write theirnumber names. 10000 + 1000 = 11000 = Eleven thousand 10000 + 5000 = 15000 = Fifteen thousandLet us count a few numbers in ten thousands and write their number names. 10000 = 1 ten thousand = Ten thousand 20000 = 2 ten thousand = Twenty thousand 30000 = 3 ten thousand = Thirty thousand 40000 = 4 ten thousand = Forty thousand 50000 = 5 ten thousand = Fifty thousand 60000 = 6 ten thousand = Sixty thousand 70000 = 7 ten thousand = Seventy thousand 80000 = 8 ten thousand = Eighty thousand 90000 = 9 ten thousand = Ninety thousand 4 12/9/2016 3:27:57 PML01_V2_PPS_Maths_G4_TB.indd 4

Now, let us understand the place value chart for 5-digit numbers.Place Ten thousands Thousands Hundreds Tens OnesValue T Th Th H T O 10000 1000 100 10 1In this chart, we see that, as we move towards the left from the ones place, thevalue of the place becomes 10 times more than the value of the current place.Let us place the number 25436 in the place value chart below:Place Ten thousands Thousands Hundreds Tens OnesValue T Th Th H T O 2 5 4 3 6 2 ten thousands = 20,000; 5 thousands = 5,000; 4 hundreds = 400; 3 tens = 30; 6 ones = 6 Thus, 25436 = 20000 + 5000 + 400 + 30 + 6.We read it as twenty five thousand four hundred and thirty six.Let us now name some 5-digit numbers, by looking at the digits and the places theyoccupy. S.No. Ten thousands Thousands Hundreds Tens Ones 1) 3 6 3 46 2) Thirty six thousand three hundred and forty six 8 1 4 23 3) Eighty one thousand four hundred and twenty three 4) 6 4 7 21 Sixty four thousand seven hundred and twenty one 4 1 3 11 Forty one thousand three hundred and eleven Numbers 5L01_V2_PPS_Maths_G4_TB.indd 5 12/9/2016 3:27:57 PM

Place value and face value:Let us write the place value of '4' in each of the following numbers:Numbers Place Value of '4'36346 4 is in tens place. So, its place value is forty.81423 4 is in hundreds place. So, its place value is four hundred.64721 4 is in thousands place. So, its place value is four thousand.41311 4 is in ten thousands place. So, its place value is forty thousand.From this, we can see that the value of 4 changes according to its place in a number.Place value: Every digit in a number occupies a place in the place value chart. Each digit gets its value from the place it occupies. This value is called its place value.Face value: The face value of a number is the number itself. It does not depend on the place it occupies in the place value chart. The face value of 4 in each of the above numbers is 4.Writing numbers using periods:We can also show a 5-digit number in a place value chart, by dividing it into twoparts called periods. The two periods are:• the ones period which has three places = H, T and O• the thousands period which has two places = T Th and ThLet us write 65274 and 92658 in the place value chart. T Th Th H T OTo show the periods, separate the digit using commas. 6 5 2 7 4So, 65,274 is sixty five thousand, two hundred and 9 2 6 5 8seventy four. 6 12/9/2016 3:27:57 PML01_V2_PPS_Maths_G4_TB.indd 6

Place the commas at the appropriate places and write the number names of thefollowing numbers:1) 82558 − 82,558; Eighty two thousand, five hundred and fifty eight2) 66756 − 66,756 ; Sixty six thousand seven hundred and fifty sixExpanded form:Once we understand the concept of place values, we can write the expandedforms of numbers.A number is said to be written in its expanded form, when it is expressed as a sum ofplace values of its digits.Note: The place of the digit 0 is ignored.Example 1: Expand the number 53842. T Th Th H T OSolution: First, we find the place value of each 5 3 8 4 2 digit. 2 × 1 = 2; 4 × 10 = 40; 8 × 100 = 800; 3 × 1000 = 3000; 5 × 10000 = 50000 Hence, the expanded form of 53842 is 5 × 10000 + 3 × 1000 + 8 × 100 + 4 × 10 + 2 × 1 = 50000 + 3000 + 800 + 40 + 2Example 2: Write 60257 in expanded form and write its number name.Solution: 60,257 = 6 × 10000 + 2 × 100 + 5 × 10 + 7 × 1 = 60000 + 200 + 50 + 7 = Sixty thousand two hundred and fifty sevenTrain my brainSay the number names of the following:a) 10024 b) 20010 c) 60600 Numbers 7L01_V2_PPS_Maths_G4_TB.indd 7 12/9/2016 3:27:57 PM

3.1 I ApplyLet us see some real life examples where we can use the knowledge of 5-digitnumbers.Example 3: How many rupees do the following make in all? 10 notes of ` 2000, 8 notes of ` 100 and 15 notes of ` 10Solution: 10 notes of ` 2000 = 10 × ` 2000 = 20,000 8 notes of ` 100 = 8 × ` 100 = ` 800 15 notes of ` 10 = 15 × ` 10 = ` 150 So, ` 20,000 + ` 800 + ` 150 = ` 20,950 Therefore, the given notes make ` 20,950 in all.Example 4: The names of some places and their populations are given below. Use this information to answer the questions that follow: Chennai: 99,256 Velhe: 54,497 Morwada: 85,890 a) What is the population of Velhe? Write it in words. b) What is the population of Vashi? Write it in words. c) Which place, Sunam or Moregaon, has more population?Solution: a) The population of Velhe is fifty four thousand four hundred and ninety seven. b) The population of Vashi is ninety two thousand one hundred and seventy three. c) Sunam has more population. 8 12/9/2016 3:27:57 PML01_V2_PPS_Maths_G4_TB.indd 8

We can also form a number using the given digits. Let us see some examples:Example 5: Form a number with 8 in ten thousands place, 6 in thousands place, 5 in hundreds place, 1 in tens place and 4 in ones place.Solution: Let us write the given numbers in the place value chart according to their places. Ten thousands Thousands Hundreds Tens Ones 8 65 1 4 So, the number is 86,514.3.1 I Explore (H.O.T.S.)Let us see some more examples using 5-digit numbers.Example 6: Find the difference between the face value and place value of the digit in bold, for each of the following: a) 50572 b) 84395Solution: a) 50572: Face value = 5; Place value = 500, Difference = 500 – 5 = 495 b) 84395: Face value = 3; Place value = 300, Difference = 300 – 3 = 297Example 7: Write the number from the clues given below: a) T  he only digit in 67891 with the same place value and face value. b) A few 5-digit numbers which have the same digit in all the five places.Solution: a) 1 b) 99,999; 11,111; 66,666; 44,444 and so on. Maths munchies 213 8 × 1 = 8 8 × 10 = 80 8 × 100 = 800 8 × 1000 = 8000 8 × 10000 = 80000You can see that any number multiplied by ‘1’ followed by zeros, is thenumber followed by those many of zeroes. Numbers 9L01_V2_PPS_Maths_G4_TB.indd 9 12/9/2016 3:27:58 PM

Concept 3.2: Compare and Order 5-digit Numbers I Think Surbhi’s father said that his smartphone costs ` 15,456 and the washing machine costs ` 15,567. How will Surbhi find which one costs more? To answer this, let us learn about the comparison of 5-digit numbers. 3.2 I RecallGiven any two numbers, we can compare them to find out the greater or the smallerof the two.The knowledge of place value of numbers helps us compare them.Let us revise these points:1) The number with fewer digits is always the smaller one. For example, of the numbers 6789 and 678, 678 is the smaller one as it is has fewer digits.2) To compare two numbers with the same number of digits, we start comparing the digits in the highest place.To compare 4566 and 4673, the largest place is the thousands place and the digit inthis place is equal in both the numbers, that is 4.So, compare the digits in the hundreds place.5 hundred is smaller than 6 hundred.Hence, 4566 < 4673. 10 12/9/2016 3:27:58 PML01_V2_PPS_Maths_G4_TB.indd 10

3.2 I Remember and UnderstandLet us understand the comparison of 5-digit numbers through some examples.Example 8: Compare 16,626 and 24,846.Solution: To compare two 5-digit numbers, follow these steps:Step 1: Arrange the given numbers in the Rules forcomparing numbers:Step 2: place value chart: 1) Lesser number of digits T Th Th H TO means it is the smaller 16 6 26 number. 24 8 46 2) Start comparing the numbers from the highest Compare the digits in the ten place value. thousands place. 1 ten thousand is less than 2 ten thousands. Thus, 16,626 < 24,846.Compare ten Compare Compare Compare Comparethousands, thousands, hundreds, tens, ones.if digits in the if digits in the if digits in the if digits inten thousands thousands hundreds the tensplace are place are place are place aresame. same. same. same.Example 9: Compare 57163 and 52196 and find the greater number.Solution: As the digits in ten thousands place are the same, compare the digits in thousands place. Here, 7 thousands > 2 thousands. Thus, 57163 > 52196.L01_V2_PPS_Maths_G4_TB.indd 11 Numbers 11 12/9/2016 3:27:58 PM

Example 10: Compare 81742 and 81859 and find the lesser number.Solution: The digits in ten thousands place and thousands place are the same. So, compare the digits in the hundreds place. Here, 7 hundreds < 8 hundreds. Thus, 81742 < 81859.Train my brainFill in the blanks with the greater/lesser sign:a) 23650 _____ 23891 b) 12434 _____ 12325 c) 30064 _____ 30604 3.2 I ApplyWe can apply the place value concept to:1) compare and arrange numbers in ascending and descending orders2) form the greatest and the smallest numbers from a given set of digits1) Ascending and descending orders:We know that to arrange numbers in the ascending and descending orders, weneed to compare them.Ascending order:Numbers arranged from the smallest to the greatest are said to be in increasingorder or ascending order. For example, 4, 10, 500 and 1478 are in ascending order.Descending order:Numbers arranged from the greatest to the smallest are said to be in decreasingorder or descending order. For example, 1478, 500, 10 and 4 are in descendingorder. 12 12/9/2016 3:27:59 PML01_V2_PPS_Maths_G4_TB.indd 12

Example 11: Arrange these numbers in ascending order: 32156, 22940, 85218, 87216.Solution: Write the numbers in a place value chart as shown: T Th Th H T O In ten thousands place, 8 > 3 > 2. 32156 22940 In thousands place, 7 > 5 > 2. 85218 87216 So, 22940 < 32156 < 85218 < 87216. Thus, the ascending order of the given numbers is 22940, 32156, 85218, 87216. Also 87216 > 85218 > 32156 > 22940. The same numbers can be written in descending order as: 87216, 85218, 32156, 22940.2) Forming numbers:Applying the concept of ascending and descending orders, we can make the smallestor the largest number from a given set of digits, when the digits are not repeated:• In order to write the largest number, we write the given digits in descending order, without a comma between them.• In order to write the smallest number, we write the digits in ascending order without a comma between them. We do not write 0 as the left-most digit.Example 12: Form the smallest and the largest numbers using each of the digits 6, 5, 4, 1 and 7 just once.Solution: The largest number: Arrange the given digits in descending order. 7, 6, 5, 4, 1 The required largest number is 76541. The smallest number: Arrange the given digits in ascending order. 1, 4, 5, 6, 7 The required smallest number is 14567.L01_V2_PPS_Maths_G4_TB.indd 13 Numbers 13 12/9/2016 3:27:59 PM

3.2 I Explore (H.O.T.S.)Let us now see some more examples involving forming numbers.Example 13: I am a 5-digit number. If my digits are reversed, I become a 4-digit number. What is the digit in my ones place?Solution: The digit in the ones place of the number should be 0. This is because a number cannot begin with a zero, and so we get a 4-digit number.Example 14: What is the difference between the greatest and the smallest 5-digit numbers that can be formed using the digits 0, 7, 0, 8 and 9?Solution: To form 5-digit numbers only 7, 8 or 9 can be placed in the ten thousands place. The largest 5-digit number that can be formed = 98700 The smallest 5-digit number = 70089 Their difference = 98700 − 70089 = 28611 Maths munchiesNagesh goes swimming four days a week. Here is the data of how long heswam in a particular week: Day Time in Seconds Saturday 10042 Sunday 10402 Monday 12004 Tuesday 10204Arrange the days in ascending order, based 213on how long Nagesh spent in the swimming pool. 14 12/9/2016 3:27:59 PML01_V2_PPS_Maths_G4_TB.indd 14

Concept 3.3: Round off Numbers I ThinkThere is a birthday party at Surbhi's house. 48 children were invited. Her motherordered 50 bars of chocolate. Surbhi asks her mother why she has ordered 50bars of chocolate. Can you help Surbhi?To answer this question, let us learn about rounding off numbers. 3.3 I RecallLet us revise comparing 1-digit, 2-digit and 3-digit numbers through examples.1) Fill in the blanks using > or <: a) 4 ____ 9 b) 42 ____ 52 c) 195 ____ 105 d) 23 ____ 12 e) 100 ____ 200 3.3 I Remember and UnderstandMany times, we do not need to know the exact number. Just to get an idea of therequired number, we round off a given number. For example, if we have ` 993, Iwould generally say that we have about ` 1000. This rounding off may be to thenearest tens, hundreds, thousands, ten thousands and so on.Rounding off a number to the nearest tens:• If the digit in the ones place is 0, 1, 2, 3 or 4 (less than 5), then the digit in ones place is replaced with a 0.• If the digit in the ones place is 5, 6, 7, 8 or 9 (more than or equal to 5), then the digit in ones place is replaced with a 0 and 1 is added to the digit in the tens place. Numbers 15L01_V2_PPS_Maths_G4_TB.indd 15 12/9/2016 3:28:00 PM

Example 15: Round off 16768 to the nearest 10.Solution: In 16768, the digit in the ones place is 8, which is greater than 5. So, we round off 16768 to 16770.Rounding off a number to the nearest 100:• If the digit in the tens place is 0, 1, 2, 3 or 4, we replace the digits in the tens and ones place with zeros (0).• If the digit in the tens place is 5 or more, that is 6, 7, 8, or 9; we replace the digits in the ones and tens places with 0 and increase the digit in the hundreds place by 1.Example 16: Round off the following numbers to the nearest 100. a) 1745 b) 21750Solution: a) In 1745, the digit in the tens place is 4 which is less than 5; so, it is rounded off to 1700. b) In 21750, the digit in the tens place is 5. So, it is rounded off to 21800.Rounding off a number to the nearest 1000:• If the digit in the hundreds place is 0, 1, 2, 3 or 4; we replace the digits in the hundreds, tens and ones places with zero.• If the digit in hundreds place is 5, 6, 7, 8 or 9; we replace the digits in the hundreds, tens and ones places by zeros and increase the digit in the thousands place by 1.Example 17: Round off the following numbers to the nearest 1000. a) 24190 b) 54729Solution: The digits in the hundreds place, we have: a) 1 < 5. Therefore, 24190 is rounded off to 24000. b) 7 > 5. Therefore, 54729 is rounded off to 55000. 16 12/9/2016 3:28:00 PML01_V2_PPS_Maths_G4_TB.indd 16