202110719-PERFORM-STUDENT-WORKBOOK-MATHEMATICS-G06-FY_Optimized

5. Understanding Elementary Shapes 5)  Triangular Prism 7) Cylinder − Triangular prism has − It has two circular ends at top triangles as its bases. and bottom. − Looks like Kaleidoscope. − The flat ends are connected − It has 3 rectangular faces by a curved surface. and 2 triangular faces. 8) Sphere − Each rectangular face has 4 − A sphere is a 3-D geometrical edges and each triangular shape that is perfectly round face has 3 edges. and circular - like a ball. − It has 6 corners. Geometrically, a sphere is 6) Cone defined as the set of all points − Cone is a three dimensional equidistant from a single geometric shape that tapers point in space. smoothly from a flat base (circle) to a point called apex / vertex. − It has a circular base and at other end it has a apex/ vertex − It has no flat faces except for the base but has a curved surface. Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET Understanding elementary shapes • Measuring Line segments PS – 1 • Types of Angles • Measurement of angles PS - 2 • Perpendicular lines Self Evaluation Sheet • Classification of triangles • Types of quadrilaterals • Polygons and three dimensional shapes Worksheet for “Understanding Elementary Shapes” Evaluation with Self Check or Peer ---- Check* 37

PRACTICE SHEET - 1 (PS-1) 1. XYZ are the three points on a line such that YZ = 8 cm, ZX = 7 cm & YX= 15 cm. State which point lies between the other two points. 2. Is R, the midpoint of MX ? If not, then mark the midpoint and name it. 3. Find the part of revolution a man turned through, if a man stands facing South and turns anti clockwise facing West. 4. A girl facing West makes 1 3 revolution clockwise. Find the direction to which the girl will be facing after 4 turning. 5. Where will the hour hand of a clock stop if it starts from 5 and turns 1 straight angle and then 1 right angle? 6. Determine the fraction of clockwise revolution made by hour hand of a clock when it turns through i) 7 to 1   ii) 2 to 11. 7. Define the following: i) Acute angle ii) Obtuse angle iii) Reflex angle 8. State whether the statement is true or false. i) While measuring the angles using protractor, the angle is read from 180ᵒ mark coinciding with straight edge. ii) One complete revolution is equal to 360ᵒ 9. Identify the following marked angles. 10. A line segment AB is perpendicular to line segment RS . AB meets RS at point O. Find the measure of ∠AOB and ∠SOA. 11. Fill in the blanks. i) Triangle with two equal sides and two equal angles is _________ triangle. ii) In ∆MNO, ∠MNO = 79ᵒ, ∠MON = 45ᵒ, ∠NMO = 56ᵒ. Thus ∆MNO is a ___________ triangle. iii) An equilateral triangle has ______ equal sides and ______ equal angles. 12. What is a scalene triangle? Illustrate with figure. 14. Identify the following quadrilaterals. 15. Compare rectangle and square. 16. State whether true or false. i) In a rhombus all sides are of equal length and diagonals are also equal to each other. ii)  D iagonals of a square are unequal in length and perpendicular to one another. 17. Fill in the blanks. i) A polygon consisting of six sides is called _________. ii)  O ctagon is a polygon with ___________ number of sides. 38

PRACTICE SHEET - 1 (PS-1) 18. Draw a neat sketch of a square prism showing its salient features. Write the number of vertices in a square prism 19. Give any four real objects examples that resembles. i) Sphere    ii) Cone 20. Answer the following i)  A triangular pramid has _________ faces. ii)  E ach angle of an equilateral triangle is equal to ________. PRACTICE SHEET - 2 (PS-2) I. Choose the correct option. 1. The marked angle between the hands of the given clock is: (A) Obtuse angle (B) Right angle (C) Acute angle (D) Zero angle 2. The number of line segments which are also called edges in the figure is: (A) 4 (B) 6 (C) 8 (D) 12 3. How many mid points does a line segment have? (A) 1 (B) 2 (C) 3 (D) 0 4. Which of the following statements is true pertaining to the given line segments? (A) PQ > AB (B) PQ < AB (C) PQ = AB (D) PQ = 1 AB 5. The measure of a reflex angle is ___________. 2 (A) < 90º (B) > 90º (C) = 180º 6. A pair of parallel lines in the given figure is _____. (D) > 180º (A) BC and FE (B) AB and BC (C) ED and DC (D) AF and ED 7. Raju placed the ruler’s 3 cm mark at one end of the line segment A and found the other end B at 8.8 cm. What is the length of the line segment AB? (A) 8.8 cm (B) 5.8 cm (C) 3 cm (D) 5 cm 8. Lines p and q are perpendicular to the line r. then p and q are ________ lines. (A) Intersecting (B) Perpendicular (C) Parallel (D) Both (A) and (B) 39

PRACTICE SHEET - 2 (PS-2) 9. Identify the statement that is NOT true of the following statements. (A) A rectangle is a special parallelogram (B) A square is not a quadrilateral (C) A square is a special rhombus (D) A parallelogram has equal opposite sides 10. Identify the statement that is true among the given statements. (A) Parallel lines can also be intersecting lines (B) Perpendicular lines can also be parallel (C) Intersecting lines can also be perpendicular (D) Parallel lines make an acute angle II. Short answer questions. 1. Compare the given pairs of line segments and write the name of the smaller line segement. (a) (b) 2. Identify the type of angles marked in the given figures. 3. Intersecting lines can also be perpendicular. Justify. III. Long answer questions. 1. Name the given angles. (a) (b) (c) (d) 2. Write your name in capital letters and identify the different types of angles formed. 40

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Name the polygons shown in the figure. (2 Marks) ii) ii)     (1 Mark) 2. Give reasons: Reflex angle cannot be formed in a triangle. 3. Sketch a triangular prism and shade the bases. (1 Mark) 4. Match the following: (2 Marks) a) Diagonals are equal and bisect i) Quadrilateral each other. b) All angles and all sides of a ii) Right angle tester triangle are equal. c) Polygon with 4 sides. iii) Square d) Instrument used to compare iv) Equilateral triangle angles with right angle. 5. AB is perpendicular to XY and meets XY at B. What is the condition for AB to act as a perpendicular bisector of XY. (2 Marks) 6. Fill in the blanks. i)  39.9⁰ = _____________ angle ii)  3 of revolution = _________ ⁰ 4 41

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 7. State whether true or false. i) A square is also a parallelogram. ii) All the angles of a rhombus are equal to 90⁰. iii) In an obtuse angles isosceles triangle two sides are equal and two angles are greater than 90⁰  (3 Marks) 8. State the important properties of an equilateral triangle with a neat sketch. (2 Marks) 9. If Kishore is facing North and turns anti clockwise by 3 right angles, then he will be facing ________. (1 Mark) 10. Draw a neat labeled figure of cone with circular base. (1 Mark) 42

6. Integers Learning Outcome • Perform addition of integers both manually and on the number line By the end of this chapter, a student will be able to: • Define integers and represent integers on number • Explain additive inverse of integers • Carry out subtraction of integers line • Understand the concept of ordering of integers Concept Map Key Points zero. Zero, is a non–negative and non–positive integer. • Negative Numbers • Representation of Integers on a Number Line The numbers which are less than zero and with a o Draw a line and make some points at equal negative sign are called negative numbers. A minus sign (−) is attached with negative numbers. intervals / distance on it. Example: o Mark a point on the line as zero, (0) –1, –2, –3, –50, …. etc. o Points to the left of zero are negative integers Profit is tagged with ‘+’ sign and loss with ‘–‘ sign. Earnings or income can be tagged with ‘+’ sign and and are marked as –1, –2, –3,.. .etc. expenditure or spending can be represented with o Points to the right of zero are positive integers ‘–‘ sign. and are marked as +1, +2, +3, … etc or simply Temperature above 0⁰ C can be denoted with ‘+’ 1, 2, 3,… etc. sign and below 0⁰ C with ‘–‘ sign. • Ordering of Integers • Integers Consider the number line shown in the figure Integers is the collection of numbers that include above. whole numbers and negative numbers, i.e., 0, 1, 2, It can be observed that the number increases as we 3, ……., –1, –2, –3, –4, ……. move to the right and the number decreases as we Collection of 1, 2, 3, 4, …. i.e., numbers greater than 43 zero are called positive integers and –1, –2, –3, ….. are called negative integers, i.e., numbers less than

6. Integers move to the left from any given number. First move 4 steps to the right of zero to reach 4, 5 > 2 as 5 is to the right of 2 then move 2 steps to the left of 4 to reach 2. –5 < 0 as –5 is to the left of 0 So (+4) + (–2) = +2 −6 < −5 < −4 < −3 < −2 < −1 < 0 < 1 < 2 < 3 < 4 < 5 < 6 iv.  Add –4 and +2 on the number line. So the collection of integers can be written as First move 4 steps to the left of 0 to reach –4, then ……− 6,−5,−4,−3,−2,−1,0,1,2,3,4,5,6,……. move 2 steps to the right of –4 to reach –2. So, (–4) + (+2) = –2. • Addition of Integers • When a positive integer is added to an integer, the When addition of two positive integers is considered resulting number is greater than the given integer. we just add them. Example: –7 + (+3) = –4, –4 > – 7 Example: 8 + 9 = 17  (or) (+8) + (+9) = (+17) • When a negative integer is added to an integer, the Note that +8 or +9 can be denoted as just 8 or 9. resulting integer is smaller than the given integer. When addition of two negative integers is Example: – 7 + (–3) = –10, –10 < –7 considered, then we have to add the two numbers • Additive Inverse and the denote the answer with a minus sign. Numbers such as –5 and +5, –7 and +7 etc, when Example: (–8) + (–9) = –(8+9) = –17 added to each other results in zero sum. They are Note: when 2 integers of the same are added and the same sign is also retained in the answer. When addition of one positive and one negative integer is considered, we need to subtract and answer will take the sign of the bigger integer (ignoring the signs of numbers, decide which is bigger). Example: (+12) + (–5) = +7      (–12) + (+5) = –7 • Addition of Integers on a Number Line i.  Add 6 and 3 on the Number Line. called additive inverse of each other. −5 + 5 = 0 + 7 + (−7) = 0 On the number line, first move 6 steps to the right • Subtraction of Integers with the help of Number from 0 to reach 6; then to add 3, move 3 steps to the Line right of 6 to reach 9. Subtract 3 from 5 on a number line. So, 6 + 3 = 9 ii.  Add –6 and –3 on the number line. On the number line first move 6 steps to the left 5 – 3 is equivalent to 5 + (–3), i.e., adding –3 to 5. We from 0 to reach –6, then move 3 steps to left of –6 move 3 steps to the left from 5 to reach 2. to reach –9. So 5 – 3 = 5 + (–3) = 2 So (–6) + (–3) = –9 Note that –3 is the additive inverse of +3. Sum of two positive integers is positive and sum of Now subtract 5 – (–3) on a number line. two negative integers is negative. iii.  Add +4 and –2 on the number line. 44

6. Integers First find the additive inverse of –3, i.e., +3. We write 5 – (–3) = 5 + 3. Now move 3 steps to the right of 5 to reach 8 on the number line. • When a negative integer is subtracted we get a greater integer. • Subtraction of an integer from another integer is equivalent to the addition of additive inverse of the integer that is being subtracted to the other integer. Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET Integers • Negative numbers PS – 1 • Introduction to integers • Number line of integers PS - 2 • Ordering of integers Self Evaluation Sheet • Addition of integers • Additive inverse of integers • Subtraction of integers Worksheet for “Integers” Evaluation with Self Check –––– or Peer Check* 45

PRACTICE SHEET - 1 (PS-1) 1. Define integers and draw number line of integers. 2. Write the following as integer with proper signs. i) Vijay spends rupees five thousand from his salary. ii) The temperature of Antarctica is 28o C below 0o C. 3. Fill in the blanks with >, < or = sign. i) –37 ------ –25 ii) 0 ------ –1 4. Find the predecessor of –1289. 5. Write two negative integers greater than –998 and two negative integers less than –998. 6. Draw a number line and answer the following. i) How many moves are needed to reach 4 from –7? ii) To reach –6 from –1, in which direction should we move? iii) Write all the integers between –3 and +3. 7. Using the number line, write the integer which is i) 5 more than –1 ii) 7 less than 4. 8. Find (–8) + 9 + (–3) using number line. 9. Find the value of –756 + (–296) + 1299. 10. Sum of two integers is –112. If one of the integers is 582, then find the other. 11. Find the value of 28 + (–77) + (31) + (–18). Is the answer greater than –41? 12. Using number line find the value of i) 10 – 12 ii) – 4 – (–8) 13. Find the value of – 78 – (– 27) 14. Fill in the blank with >., <, = sign. –12 + 18 _____ –12 – 18 PRACTICE SHEET - 2 (PS-2) I. Choose the correct option. 1. The sign of the integer less than 0 is ______. (A) - (B) + (C) × (D) ÷ 2. The predecessor of integer – 4 is ____. (A) – 3 (B) – 5 (C) 0 (D) 3 3. Which of the following shows the maximum rise in temperature? (A) – 5ºC to 9ºC (B) – 6ºC to 1ºC (C) 0ºC to 11ºC (D) – 12ºC to – 9ºC 4. The greatest integer lying between – 8 and – 2 is ____. (A) – 2 (B) – 1 (C) – 7 (D) – 8 5. The additive inverse of a negative integer is (A) always positive (B) always negative (C) 0 (D) the same integer 6. The numerical representation of the addition shown by the number line is _______. (A) (-4) + 3 + 4 (B) (-4) + 7 + 4 (C) 4 + (-7) + (-4) (D) 4 + 7 + 4 7. Solve and choose the correct sum of (- 6) + (- 4) + (- 5) = _____. (D) – 5 (A) 15 (B) 5 (C) – 15 (D) 12 – (-6) 8. The pairs(s) of integers that have 6 as a difference is/ are: (A) 12, -12 (B) – 12, - 12 (C) 12 – 6 46

PRACTICE SHEET - 2 (PS-2) 9. In which of the following pairs of integers, the first integer is NOT on the left of the other integer on the number line? (A) (-6, -4) (B) (-1, 0) (C) (-8, 8) (D) (-4, -6) Ans: D 10. The statement “When an integer is added to itself, the sum is greater than the integer” is (A) never true (B) true only when the integer is positive (C) always true (D) true for negative integers Ans: B II. Short Answer Questions. 1. Mark the integers on the number line. - 5, 4, -8, 9. 2. Draw a number line and add the following integers using it. (i) (–3) + (–5) + 4 (ii) (+2) + (–7) + (-1) 3. Identify the integers of column A and match with that of column B. Column A Column B (i) The greatest negative integer A) -2 (ii) The greatest integer greater than every negative integer B) -5 (iii) The additive inverse of +5 C) -1 (iv) The greatest negative even integer D) 0 III. Long Answer Questions. 1. Place appropriate symbol > or < or = in the blanks given between the two integers. (i) 18 _____ –21 (ii) –7 _____ –7 (iii) 13 ______ – 13 (iv) –26 _____ –19 2. Arrange the given integers in ascending order and descending order. (i) -3, -6, 4, -1, 5, 0 (ii) 8, -8, 12, 3, -4, 2 47

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Fill in the blanks. (1 Mark) ----------- is a non-negative and non-positive integer. (2 Marks) 2. Define additive inverse. What is the additive inverse of–25? 3. Subtract the following i) –0012 from –0238 ii) –259 from 0  (1 Mark) 4. Arrange the numbers in ascending order. 25, –18, 78, –32, –98, 12.  (1 Mark) 5. State whether true or false. (3 Marks) i) –1 is the largest negative integer. ii) When two positive integers are added, we move in rightward on the number line. iii) When two negative integers are added, we get a positive integer. 6. Describe the way of adding one positive integer and one negative integer. Show with an example on a number line. (2 Marks) 7. A taxi travels 55 km to north and 215 km to south. Find the distance travelled by taxi from origin. (2 Marks) 8. Ramesh works in a company and his monthly salary is Rs. 31,200. Out of his salary, he spends Rs. 6000 for room rent, Rs. 4000 for travelling and Rs. 12000 for miscellaneous purposes. Calculate savings of Ramesh per month. (3 Marks)   48

7. Fractions Learning Outcome By the end of this lesson, a student will be able to: • Reduce fractions to their simplest form. • Represent fractions on number line. • Compare like and unlike fractions. • Solve for improper, mixed and equivalent fractions. • Add and subtract fractions Concept Map Key points simplest form is to find the HCF of the numerator and denominator and then divide both of them by • Fraction is a number representing a part of a the HCF. whole. The whole may be a single object or a group • Like fractions:- Fractions with same denominator of objects. • Unlike fractions:- Fractions with different denominator. • In x , x is the numerator, y is the denominator • While comparing 2 fractions with same y denominator, the fraction with greater numerator is greater. • When expressing a condition of counting points to • While comparing 2 fractions, having same write fractions, it must be ensured that all parts are numerator, the fraction with the smaller equal. denominator is greater of the two. • While comparing 2 fractions, whose numerator • Fractions can be represented on a number line. and denominator are different, Using equivalent Every fraction has a point associated with it on the fractions method, convert the denominators of number line. the given fractions such that they are equal. Then proceed with comparison. • Proper fraction:- Numerator is less than • To add 2 or more like fractions. denominator a. Add the numerators. b. Retain the (common) denominator. • Improper fraction:- Numerator is greater than c. Write the fraction as: Result of step 1 / Result of denominator step 2. • Difference of 2 like fractions can be obtained as • Mixed fraction:- combination of whole and a part follows • Improper fractions can be written as mixed fractions a. Subtract the smaller numerator from the bigger by dividing the numerator by the denominator to numerator. obtain quotient and remainders. b. Retain the (common) denominator. • Each proper or improper fraction has many c. Write the fraction as: Result of step 1/ Result of equivalent fractions • To find an equivalent fraction of a given fraction step 2 multiply or divide both the numerator and the • To add or subtract unlike fractions, we first denominator of the given fraction by the same number. have to find equivalent fractions with the same • Simplest form of a fraction: - Fraction is said to be 49 in the simplest (or lowest) form if its numerator and denominator have no common factor except 1. • Shortest way to find the equivalent fraction in the

7. Fractions denominator and then proceed. • To add or subtract mixed fractions, one way is to do the operation separately for the whole parts and the other way is to write the mixed fraction as improper fractions and then directly add (or subtract) them. Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET PS – 1 Fraction • Introduction • Write fraction of shaded portion PS - 2 Worksheet for “Fractions” • Shade fractions Evaluation with Self Check • Proper fractions PS – 3 or Peer Check* • Improper fractions PS – 4 • Mixed fractions PS - 5 • Equivalent fractions Self Evaluation Sheet • Represent fraction on number line • Reduce fraction to simplest form • Compare fractions • Like and unlike fractions • Addition and subtraction of fraction ---- 50

PRACTICE SHEET - 1 (PS-1) 8. Find the fraction of composite numbers from 98 to 111. 1. Write the fraction representing the shaded portion. 9. What fraction of an hour is 23 minutes? 10. What fraction of numbers from 1 to 10 is a. divisible by 2? b. c. 2. Colour the part according to the given fraction. a. a−3 8 b. 8 c. 15 1 4 3. What fraction of month is 15 days? 4. Ramu had to iron 10 shirts, 10 pants and 10 sarees. He has so far finished 3 shirts, 4 pants and 3 sarees. Find a. What fraction of dresses he has finished? b. What fraction of shirts he has finished? 5. What fraction of prime numbers lies between natural numbers 1 to 20? 6. Anuj bought 6 chocolate bars. How would be divide them between 4 friends? How much would each of them get out of each chocolates bar? 7. Seema has 28 books. She has given 17 books to Meera. What fraction of books does Seema have? 51

PRACTICE SHEET - 2 (PS-2) 1. Express the following as mixed fractions. a. 30   b. 19   c. 51   d. 37   e. 89 3 7 9 5 4 2. Express the following as improper fractions: a. 7 3   b. 5 4 c. 10 4   d. 8 3   e. 9 2 4 5    9 7 9 3. Draw number lines and locate the points on them. a. 1,2,4,5 b. 8,9,6,7 6666 7777 4. Find the correct number. a. 3 = 21 b. 2 = 7 9 18 c. 60 = 2 d. 36 = 90 42 7 5. Reduce the following fractions to simplest form. a. 180 b. 81 c. 13 d. 72 50 135 52 90 6. Find the equivalent fraction of 4 having 7 a. Denominator 35 b. Numerator 44 c. Denominator 91 d. Numerator 60 7. Abdul has 30 chocolates, Rahul has 15 chocolates. After sometime, Abdul has eaten 10 chocolates, and Rahul has eaten 5 chocolates. What fraction did each use up? Are they equivalent? 8. Find four equivalent fractions of the following. a. 3 b. 4 c. 5 d. 1 5 78 7 9. Write the fractions. Are all these fraction equivalent? a. b. 10. Find equivalent fraction of 110 with 220 a. Numerator 10 b. Denominator 110 52

PRACTICE SHEET - 3 (PS-3) 1. Compare the fraction and put an appropriate c. 1 1 , 5 , 7 d. 1 1 , 3 1 , 5 1 sign. 3 3 3 4 4 4 a. 3 2    b. 8 5    c. 1 7    d. 1 3 10. In an exam results, Raju get 5 of the total and 5 of the total. Total 6 420. 55 55 77 33 Ram gets 7 marks is 2. Compare the fraction and put an appropriate Who gets more marks? sign. a. 8 and 3     b. 9 and 1 1    3 8 2 3 c. 2 1 and 1 1 d. 8 1 and 8 1 3 2 5 6 3. Look at the following figures and write ‘<’ or ‘>’, ’=’ between the given pair of fraction 0 12345 5 55555 0123456 7 7777777 7 012 345678 888 888888 a. 3 a nd 1 b. 15 a nd 6 c.  72 an d 3 d. 7 and 4 5 7 5 8 7 5 4. Ramu cuts an apple into 4 pieces and eats 8 of 3 them , Shamu eats 5 of an apple. Who ate more? 5. Arrange the following in ascending order. a. 5 , 5 , 5 , 5 , 5   b. 2 , 2 , 2 , 2 , 2 6 13 12 16 19 17 19 21 51 81 6. Write shaded portion as fraction and compare. 3 8 7. Rana studied 2 of a day, Rohit studied of a 3 day. Who studied more? 1 8. Sonu watched 5 of 8 hours of T.V. Rema watched 2 of 8 hours of T.V. Ramesh watched 6 3 7 of 10 hours of T.V. Who watched T.V. for more time? 9. Arrange the following in descending order a. 1 , 4 , 7 b. 1 , 1 , 1 9 9 9 10 50 9 53

PRACTICE SHEET - 4 (PS-4) 1. Solve the following: 9. Shalu bought 2 metre rope to pack her box. After 5 a. 2 + 7   b. 7 + 7   c. 9 − 7 19 19 13 17 11 11 1 her use, she gave 3 metre of rope to Seema. How d. 7 − 2   e. 1 + 3   f. 5 − 5 much did Shalu use? 11 13 9 11 g. 7 − 1   h. 1 − 3   i. 6 + 3 10. Athpeloret cotwanngeur lpaurrpclhoats. eHse53wams of wire for fence 7 2 4 7 7 able to cover only 2. Find the missing fractions: 3 of the plot. Additionally, he purchased m72 umch wire to cover the remaining area. How a. 9 − =121    b. 9 − =119   o4f 11 19 wire was purchased? c. − 3 =261 d. + 2 =85   21 5 e. − 1 =12    f. + 3 =53 4 7 3. Subract the following: a. 1 from 5 b. 7 from 2 21 5 4 6 c. 2 from 11 d. 1 from 3 5 5 7 15 4. A rectangle park of are 600 mm2 has 1 area of 5 empty space. The rest is planted with roses. What is the area of roses planted? 5. In a school of 1000, one-fourth are Science, two- fifth are Arts and rest are English students. Find the number of English students. 6. Solve the following. a. 2 1 + 2 1    b. 7 1 − 5 3   c. 22 + 7 − 1 3 5 19 7 7 9 5 d. 2 1 + 4    e. 3 1 + 2 1 − 317 5 7 6 5 7. Ramesh takes 3 1 minutes to run across the park. 6 Ragav takes 9 minutes to do the same. Who takes 5 less time and what fraction? 8. Akash’s gym is 6 km from office. He takes auto and travels 2 7 he walks the remaining 3 km. Later distance. How for did he walk? 54

PRACTICE SHEET - 5 (PS-5) I. Choose the correct option. 1. Find the greatest fraction among the given fractions? (A) 3 (B) 3 (C) 3 (D) 3 5 7 4 8 2. The fraction represented by the given figure is: (C) 3 (A) 1 (B) 2 (D) 5 8 8 8 8 3. Which of the following is th(Be)lik85e fracti on of 56 ? (C) (A) 3 5 (D) 6 6 7 9 4. Which of the following is the difference of the shaded parts of ? (A) 1 (B) 1 (C) 1 (D) 3 4 12 3 4 5. Sum of 4 and 10 is 11 11 (A) 14 (B) 6 (C) 14 (D) 7 22 11 11 11 6. On subtracting 3 from 7 we get 8 8 (A) 4 (B) 10 (C) 4 (D) 4 0 16 16 8 7. Solve and find the value of x in 5 = 15 9 x (A) 27 (B) 18 (C) 36 (D) 9 8. Rita solved 30 sums out of 90 sums. What fraction of sums did she solve? (A) 1 (B) 1 (C) 1 (D) 2 2 3 4 5 9. Which of the following fractions is NOT equal to 4 ? 5 12 20 6 24 (A) 15 (B) 25 (C) 10 (D) 30 10. Which of the following is NOT in the lowest form? (A) 13 (B) 21 (C) 6 (D) 11 17 25 7 33 55

PRACTICE SHEET - 5 (PS-5) II. Short Answer Questions. 1. Represent the following fractions on number line. (i) 3 (ii) 2 8 5 2. Solve: (i) 3 + 2 (ii) 4 4 −1 2 7 7 99 3. Write shaded portion as fraction. Arrange them in ascending and descending order. III. Long Answer Questions. 1. Convert the given fractions into standard form. (i) 16 (ii) 9 (iii) 14 (iv) 18 64 54 35 36 2. Arrange the following fractions in descending order: 3,4,5,2 5793 56

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Express 99 as mixed fraction (1 Mark) 7 2. Compare 9 and 7 (1 Mark) 7 9 3. Solve 2 + 3 + 5 − 7 (1 Mark) 3 5 7 9 (2 Marks) 8 + ? = 11 4. Find missing fraction 11 8 5. In a company of 10000 employees, 1 are Germans, 1 are French and rest of them are Indians. What 5 4 fractions of Indians are working here? (3 Mark) 6. Arrange the following in ascending and descending order (3 Mark) 1 1 1 1 6 4 5 7 a. 6 , 6 , 6 , 6   b. 5 , 3 , 2 , 7 c. 13 , 13 , 19 , 19 7 11 13 17 7. Rajesh has to cover a distance of 9 Km. He runs 7 Km and rest of the distance, he walks. Find the 4 5 fraction of kilometers he walked.       (4 Marks) 57

8. Decimals Learning Outcome By the end of this lesson, a student will be able to: • Conversion of units. • Represent decimals on number line. • Compare the decimals. • Convert decimals to fractions and fractions to • Add and subtract the decimals. decimals Concept Map Key points • To understand parts of one whole we represent the whole by a block. One block divided into 10 equal parts means each part is 1/10 ( one-tenth) of the whole. If can be written as 0.1 in the decimal notation. • Every fraction with denominator 10 can be written in decimal form and vice versa. • 1/10 in decimal form is 0.1; where 0 is in the units place and 1 is in the tenth place. • One block divided into 100 equal parts means each part is 1/100 i.e, one-hundredth of a whole. It is written as 0.01. • Every fraction with denominator 100 can be written in decimal notation and vice-versa. 58

8. Decimals • In the place value table, as we go from left to right. The multiplying factor becomes 1/10 of the previous factor. Thousand Hundred Ten Ones Tenths Hundredths Thousandths (1/10) (1000) (100) (10) (1) (1/100) (1/1000) • 1/1000 in decimal form is 0.001 • All decimals can also be represented on a number line. • While comparing 2 decimal numbers, start with the whole parts. If the whole numbers ae equal then the hundredths and so on. 59

8. Decimals Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET • Representing on number line Decimals • Decimals to fraction PS – 1 • Fractions to decimal Worksheet for “Decimals” • Place value table(1/10)th PS - 2 Evaluation with Self Check or • Place value table(1/100) PS – 3 Peer Check* • Comparing decimals PS - 4 • Using decimals Self Evaluation Sheet • Addition and subtraction of decimals ---- 60

PRACTICE SHEET - 1 (PS-1) 1. Write numbers given in the following place value park in cm. table in decimal form: Hundreds Tens Ones Tenths (100) (10) (1) (1/10) a. 19 4 b. 3 9 9 9 c. 6 0 1 1 d. 90 9 e. 1 0 0 1 2. Write the following decimals in place value table. a. 30.5 b.400.7 c. 1.5 d. 666.6 e. 06.7 3. Write each of the following decimals a. Nine-tenths b. Three hundred and one tenth c. six tens and six tenths d. Seven hundred and six ones 4. Write decimals for the following. 3 a. 7 b. 3 + 2 c. 20 + 3 + 10 10 10 d. 500 + 40 + 3 + 5 e. 3 3 f. 13 10 4 5 g. 3 h. 7 i. 9 1 5 5 3 j. 19 5 5. Write the following as fractions, simplest form. a. 0.6 b. 0.8 c. 0.5 d. 1.2 e. 7.5 f. 13.8 g. 70.2 h. 90.5 6. Express the following as centimetre in decimals. a.5 mm b.9 mm c. 3 cm 5 mm d. 90 mm e. 90 cm 9 mm f. 750 mm 7. Write the following decimals in words. a. 0.5 b. 1.2 c. 10.5 d. 110.2 8. Show the following on the number line. a. 0.7 b. 3.9 c. 2.2 d. 1.5 9. The length of rectangular park is 5 cm 9 mm. The breadth of the park is 2 cm 8 mm. Find the side of 61

PRACTICE SHEET - 2 (PS-2) 1. Write the numbers given in the following place value table in decimal form: Hundreds Tens Ones Tenths Hun- Thou- (100) (10) (1) (1/10) dredth sandth 1/100 `1/1000 a. 3 01 1 b. 0 30 0 2 3 c. 5 67 8 0 1 d. 1 23 3 9 0 e. 0 00 7 2 1 f. 1 11 1 8 9 1 1 2. Write the following decimals in the place value table. a. 0.753 b. 2.078 c. 123.98 d.23.998 e. 700.712 f.128.009 3. Write the following in decimals. 3 2 4 a. 40 + 9 + 10 + 100 + 1000 b. 300 + 20 + 5 1000 c. 600 + 50 + 4 + 3 + 2 + 1 10 100 1000 4. Write the following decimals in words. a. 0.051 b. 1.004 c. 21.124 d. 0.001 5. Write as fractions in the lowest form. a. 0.004 b. 23.128 c. 0.255 d. 0.755 e. 0.077 f. 0.005 6. Which is greater? a. 0.03 or 0.04 b. 3.567 or 3.067 c. 4.56 or 4.65 d. 3.251 or 3.25 e. 0.001 or 0.015 f. 1.115 or 1.100 g. 1.1 or 1.100 h. 1.750 or 2.75 5 i. 0.010 or 0.01 j. 2.5 or 2 7. Express the following as rupees using decimals. a. 10 paise b. 750 paise c. 1005 paise d. 5 rupees 70 paise e. 50 paise 8. Express following as metres using decimals a. 150 cm b. 5 cm c. 2m 90 cm d. 575 cm e. 8 m 80 cm 9. Express following as cm a. 10 mm b.570 mm c. 420 mm d. 5cm 40 mm e. 100 mm 10. Express the following as Kg a. 10g b. 5650g c. 10Kg 10g d. 550g e. 750 g 11. Express the following as Km a. 10000m b. 979m c. 70 Km 70 m d. 5Km 500m e. 666m 12. A man purchased a pen for 150 paise, a pencil of 20 paise, a book for 1050 paise and an ink bottle for 2050 paise. How much did the man spend in rupees? 62

PRACTICE SHEET - 3 (PS-3) 1. Find the sum of the following. a. 0.05 + 1.12 + 8 b. 25 + 75.25 + 0.025 c. 0.75 + 2 + 0.975 d. 3.75 + 2.75 + 4.75 e. 280.123 + 3350.456 + 450.789 2. Rohit spent Rs. 75.45 to buy pizza and Rs. 40.25 to buy juice. What is the total money Rohit spent. 3. Naveen ran 3025m in the morning. Later during the day, he walked 1000cm. Again in the evening he ran 4040m. What is the total distance covered by him throughout the day( in km). 4. Ramu purchased 15 Kg 500g wheat, 30 kg 350g rice, 750g flour and 3Kg 350g rice,750g flour and 3Kg sugar. Find the total weight of his purchases in Kg. 5. Subtract a. 7.75 from 9.75 b. 30.54 from 50.45 c. 300.875 from 970.89 d. 40.789 from60.9 e. 0.005 from 0.015 6. Solve the following. a. 0.055 + 3.2 – 1.555 b. 1.25 + 1.75 – 0.0055 c. 3.5 + 4.5 – 0.5 – 3 d. 100. 123 + 150.456 – 50.789 e. 0.153 + 10.1 – 8.999 7. Anjali bought 5 Kg 750g tomatoes, 3Kg 250g Onions, 7Kg mangoes, out of these, 475g of tomatoes was rotten and 333g of mangoes was rotten. Find the total weight of all her purchases after all rotten ones are thrown. 8. Anand buys 6 m 30 cm of cloth. He use 3m 20cm for stitching his shirt. How much was used to make him a pair of pant? 9. Anu has Rs.300 with her. She buys icecream for 2000 paise, buys burger for Rs.100, pays for her bike parking 575 paise. After all these, how much is Anu left with? 10. Priya travels 5 Km 20m by car, than she takes bus for 3km 330m. Rest of the distance to office she walks. Total distance to her office is 12Km 525m. Find the distance she walks? 63

PRACTICE SHEET - 4 (PS-4) I. Choose the correct option. 1. The digit in one tenths place of 19.256 is_______. (A) 1 (B) 9 (C) 2 (D) 5 2. 12 m 6 cm is _______ m. (A) 1.26 (B) 12.6 (C) 12.06 (D) 126 3. 7 hundred forty-five point five tenths seven thousandths is _____. (A) 745.507 (B) 745.57 (C) 74557 4. 0.146 as fraction in lowest terms is _____. (A) 73 (B) 73 (C) 146 73 50 500 100 (D) 25 5. Expanded form of 92.706 is: (A) 9+ 2 +7 +0 +6 (B) 900 + 20 + 7 + 0 +6 10 100 1000 10000 10 100 1000 (C) 90 + 2 + 7 +0 +6 (D) 90 + 2 + 7 +0 +6 10 100 1000 1 10 100 6. Short form of 400 + 20 + 8 + 1 + 3 is: 10 1000 (A) 428.13 (B) 428.103 (C) 42.813 (D) 428.31 7. In which of the following situations we use decimals? (A) While buying vegetables in kg and g (B) Using rupees and paise (C) While converting cm into m (D) All of these 8. Solve 0.06 + 0.007 and choose the correct answer. (A) 0.13 (B) 0.013 (C) 0.067 (D) 0.67 9. Identify the largest decimal among the following: (A) 0.194 (B) 0.32 (C) 0.086 (D) 0.058 10. Identify the smallest decimal among the following: (A) 0.099 (B) 1.99 (C) 0.99 (D) 9.99 II. Short Answer Questions. 1. Write the following decimals in the place value table. (a) 11.6 (b) 2.1 (c) 0.65 (d) 224.93 2. The cost of one book is Rs. 54. 75 and a chart is Rs. 6. 45. What is the total cost of a book and a chart? 3. Arrange the given decimals in ascending order. 2.16, 14.57, 0.39, 1.18, 63.904 III. Long Answer Questions. 1. Simplify: (i) 37.004 + 21.19 +17.83 – 33.6 (ii) 145.07 + 39.61 + 42.009 – 103.5 2. Arrange the given decimals in ascending order and descending order: (i) 5.237; 54.732; 52.237; 58.372 (ii) 888. 134; 863.934; 824.943; 857.264 64

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins (1 Mark) 1. Write the following decimals in place value table. a. 50.45 b. 123.456 2. Write each of the following in decimals (1 Mark) a. 300 + 34 b. 20 + 4 100 100 3. Solve the following . (1 Mark) 30 a. 100 + 0.25 +123.75 b. 75.005 + 80.25 −13.999 4. Anuj spent 3250 paise on books. Later he spent Rupees 70 on food and 150 paise on chocolate. Find the total money spent. (2 Marks) 5. Ram walks 3Km 500m from home. Later he comes back 1Km 25m and takes an auto to the bus stop which is 5Km 333m. He travels by bus for 15000m and reaches office. Find the distance from his home to office in Km. (3 Marks) 65

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 6. Rani buys 7Kg 250g mangoes, 3Kg 300g of apples. She gives 3350g of mangoes and 1550g of apples to her friend. Find how much Rani is left with of her total purchase. (3 Marks) 7. Vivek buys 10m 30cm cloth. He uses 3cm 50cm to stitch a shirt and 3m 25cm to stitch a pair of pants. How much cloth is left over? (4 Marks) 66

9. Data Handling Learning Outcome By the end of this lesson, a student will be able to: • Interpret a bar graph • Organise a given set of data using tally marks • Draw a bar graph C•HAInPteTrpErRet:aQpuicatodgrraapthic Equations Concept Map Key points • Bars of uniform width are drawn horizontally or vertically with equal spacing between them. The • Data is a collection of numbers gathered to give length of each bar gives the required information. some information • If the numbers in the data are large, appropriate • Tally marks ae used to get particular information scales are to be used in a bar biagram from the given data • To represent a given data by a bar diagram, • Pictograph represents data in the form of pictures, a. Draw 2 perpendicular lines, one vertical and objects or part of objects. one horizontal b. Along the horizontal line, mark the 1st • While drawing pictorgraphs simpler symbols may set of data along vertical line, mark the be used to represent multiple units. Eg:- represents corresponding data. 5 students -> to represent 1 students-etc • Data can be represented by using bar diagrams or bar graphs also 67

9. Data Handling Work Plan: CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET PS – 1 Data handling Organise and interpret data using tally marks PS - 2 Interpret pictographs PS – 3 Draw pictographs PS - 4 Self Evaluation Sheet Interpret bar graphs Draw bargraph Worksheet for “Data Handling” Evaluation with Self Check ---- or Peer Check* 68

PRACTICE SHEET - 1 (PS-1) 1. Using the tally marks, represent the numbers a. 8 b.4 c.11 2. The marks (out of 10) obtained by 28 students in a mathematics test are given below: 8 1 2 6 5 5 5 0 1 9 7 8 0 5 8 3 0 8 10 10 3 4 8 7 8 9 2 0 Determine the number of students who obtained marks more than or equal to 5 3. The choices of the fruits of 42 students in a class is as follows, where A,B,G,M and O stand for the fruits Apple, Banana, Grape, Mango and Orange respectively which 2 fruits ae liked by an equal number of students? Which fruit is liked by most of the students? A OBMA G B G A G BMAGMA BGMB AOMOGBOMG A A BMOMGB AMOMO 4. The length in centimetres of 30 carrots are given as follow. 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 Arrange the data given above in a table using tally marks and answer the following questions a. What is the number of carrots which have length more than 20cm? b. What length of carrots occur maximum number of times? c. What length of carrots occur minimum number of times? 5. Thirty students were interviewed to find out what they want to pursue as a career. Their response are listed 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 engineer doctor pilot officer doctor pilot doctor engineer. Arrange the data in a table using tally marks. 6. Following are the choices of games of 10 students of class VI. football cricket football hockey football football cricket football cricket hockey a. Arrange the data in a table using tally marks b. Which game is liked most by the students. 69

PRACTICE SHEET - 2 (PS-2) 1. Following pictograph represents some 3. The following pictograph depicts the surnames of people listed in the telephone information about the areas in sq km of some directory of a city Karnantaka state. a. what is the area of Kodagu district? Surname No.of People =100 people b. Which 2 districts have same area? c. How many districts have area more than 5000 Khan sq.km2 Patel Rao District Area(in Km2) = 1000 km2 Roy Kadam Raichur Singh Ballari Kodagu a. How many people have the surname Roy? Mysore b. Which surname appear maximum number of Udupi Karwar times and how many times? c. Which surname appear least number of times 4. The number of bottles of cold drinks sold by a shopkeeper on 6 consecutive days is as follows: and how many times? d. Which 2 surnames appear equal number of Day Sunday Monday Tuesday Wednesday Thursday Friday times? No. of 350 200 300 250 100 150 2. The number of scouts in a school is depicted by bottles the following pictograph. Answer the following Prepare a pictograph of the data using one a. Which class has the maximum number of symbol to represent 50 bottles scouts 5. Table below gives information about the b. which class has the maximum number of circulation of newspapers in a town in 5 different languages. Prepare a pictograph scouts using one symbol to represent 100 c. How many scouts are there in class VI newspapers. d. What is the total number of scouts in classes Languauge English Hindi Tamil Malayalam Telugu VI to X? e. Which class has exactly 4 times scouts as that No. of Papers 5000 8500 500 2500 1000 of class X? 6. Annual expenditure of a company in the year 2017-2018 is given below. Class No. of scouts # = 10 scouts Items Expenditure(in lakhs) VI #### Salaries of employers 65 VII ## Advertisement 10 VIII ###### Purchase of machinery 85 IX ### Electricity and water 15 X # Transportation 25 Other exprenses 30 Prepare a pictograph of the above data using an appropriate symbol to represent 10 lakhs 70

PRACTICE SHEET - 3 (PS-3) 1. The following bar graph shows the number of 3. The bar graph given below represents houses (out of 100) in a town using different approximate length in kms of some national types of fuels for cooking. Read the graph and highways in India. Study the bar graph answer the following questions. &answer the following questions. Scale 1 Unit length = 200km Scale:- 1 unit length= 5 houses a. Which fuel is used in maximum number of a. Which national highway is the longest among houses? the above? b. How many houses are using coal as fuel? b. Which national highway is the shortest among c. Suppose the total no. of houses in the town the above? is 1 lakh from the above graph estimate the c. National highway 9 is 1000kms number of houses using electricity. d. NH10 is 500 kms 2. The following bar graph represents the data for different sizes of shoes worn by the students 4. The bar graph below represents the circu- in a school. Read the graph and answer the lation of newspapers in different languages in following questions. Scale:- 1 Unit length = 50 a tours. Study the bar graph and answer the students following question. Scale:- 1 Unit length = 200 Newpapers. a. What is the circulation of English newspa- pers? b. What is the circulation of English newspaper? c. By how much is the circulation in Hindi more than in Bengali? a. Find the number of students whose shoe sizes are collected? b. What is the number of students wearing size 6? c. What are the different sizes of shoes worn by the students? d. Which shoe size is worn by maximum number of students? e. Which shoe size is worn by minimum number of students? 71

PRACTICE SHEET - 3 (PS-3) 5. Length of some major rivers (in Km) in India is given below:- River Length( in Km) Narmada 1500 Mahanadi 1000 Brahmaputra 3000 Ganga 2500 Kaveri 500 Krishna 1500 Draw a bar graph to represent the above informa- tion 6. The number of ATM’s of different banks in a city is shown below. Draw a bar graph to represent the information. Bank No. of ATM’s Syndicate Bank 5 SBI 15 Indian Bank 20 ICICI Bank 25 Vijaya Bank 10 7. Number of mobile phone users in various age groups in a city is listed below. Draw a graph to represent this information. Age-group(in years) No.of mobile users 1-20 25000 21-40 40000 41-50 35000 61-80 10000 Scale 1 unit = 5000 No. of users 72

PRACTICE SHEET - 4 (PS-4) I. Choose the correct option. 1. Which of the following is the collection of information? (A) Group (B) Frequency (C) Data (D) Tally marks 2. When the data is represented in the form of pictures or symbols, then it is called ______. (A) Pictograph (B) Bar graph (C) Tally marks (D) Table 3. The tally mark is equal to ______. (C) 5 (A) 8 (B) 7 (D) 9 4. If represents 90 balls then represents ___ balls. (A) 10 (B) 15 (C) 20 (D) 25 5. The widths of the bars in a bar graph will _______ for all the bars. (A) be different (B) be same (C) decreases from left to right (D) increases from left to right 6. Which of the following is the tally mark of the numeral 12? (A) (B) (C) (D) 7. If represents 5 flowers then, how do you represent 3 flowers? (A) (B) (C) (D) 8. If represents 6 flowers, the group of symbols that represents 30 flowers is: (A) (B) (C) (D) The favourite sport of class 6 students is shown in the given bar graph. Understand the graph and answer the questions that follow: (9 and 10) 9. Which sport is the favourite sport of equal number of students? (A) Football and Baseball (B) Hockey and Volleyball (C) Basketball and Volleyball (D) Football and Hockey 10. How many students’ favourite sport is track and field? (A) 5 (B) 20 (C) 25 (D) 50 73

PRACTICE SHEET - 4 (PS-4) II. Short answer questions. 1. The marks obtained out of 25 by 20 students of a class in an examination are given below. 21, 7, 12, 20, 8, 11, 11, 7, 20, 20, 21, 21, 20, 8, 21, 8, 7, 21, 21, 12 Represent the data in a table using tally marks. 2. The table shows the number of novels sold by Srinivasa store in a week. Make a pictograph using pic- tures. Monday Tuesday Wednesday Thursday Friday Saturday 12 8 24 20 16 4 3. The following pictograph shows the number of students of class 6, having different talent. Talent Number of students Singing Dancing Painting Mimicry Sports Answer the following questions based on the pictograph given above- (i) Which talent do most of the students have? (ii) How many students have the talent of singing? III. Long answer questions. 1. Define: (i) Pictograph (ii) Bar graph 2. The students of class 6 come to school by different means of transport as given in the pictograph. Inter- pret the graph and answer the questions. Scale: 1 = 2 students On Foot (i) How many students come by ? (ii) How many more students come by than by ? (iii) What means of transport is used by maximum number of students? (iv) What is the strength of the class? 74

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Using tally marks represent the (1 Marks) 4. A survey was conducted to find favourite subject numbers. of students in a school. The data is given below. (2 Marks) a. 18 b.06 a. Which subject is most popular? b. How many students like mathematics ? Subject No. of students = 50 students Hindi English Mathematics Science 2. Marks obtained by 5 students are given below. Arrange the data using tally marks. 02 03 03 02 03 (1 Mark) 5. The number of 2 wheelers owned individually by each of 30 families are listed below make a table using tally marks. 11211121203212231102232131031 2 Find the number of families having 2 or more two wheelers (3 Marks) 3. Following table gives number of vehicles passing through a toll gate. Draw a bar graph representing the data. (2 Marks) Time Interval(in hrs) 8:00-9:00 9:00-10:00 10:00-11:00 No. of Vehicles 250 450 300 75

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 6. The graph below gives information about the 7. Following table represents data of number of number of railway tickets sold for different schools (stage-wise) in the year 2002. Draw a cities on a railway ticket counter. Read the pictograph to represent the data: graph and answer the following. (3 Marks) a. How many tickets were sold in all? b. To which city was the maximum no. of tick- Stage No. of schools ets sold. (in thousands) c. Name the cities for which the no. of tickets sold is more than 50? Primary 80 (3 Marks) Scale:- 1 unit length = 20 tickets Upper primary 55 Secondary 30 Higher secondary 20 76

10. Mensuration Learning Outcome By the end of this lesson, a student will be able to: • Define area C•• HACDaePlfciTnuEelaRptee:rpQimeureimatedertrear toifcvaErqiouusasthiaopness • Calculate area of various shapes Concept Map Key points:- a. Formulas for standard shapes b. Using squared paper method • Perimeter is the distance covered along the • Area of square = side × side boundary forming a closed figure when you go • Area of rectangle = length × breath round the figure once. • Conversions to be adopted while using squared • Perimeter of a square= 4 X length of its side paper method to determine area are as followed. Perimeter of a rectangle = 2X (Length + breadth) a. The area of one full square is taken as 1 square Perimeter of a triangle = 3 X ( length of a side) • Shapes in which all sides and angles are equal are unit. b. Ignore portions portions of the area that are less called regular closed shapes. • Amount of surface enclosed by a closed figure is than half of square. c. If more than half a square is in a region, It should called its area. • Area of a figure can be calculated by using be counted as one square d. It exactly half the square is in a region then count that as ½ square units. 77

10. Mensuration Work Plan CONCEPT COVERAGE COVERAGE DETAILS PRACTICE SHEET Mensuration Perimeter of Shapes PS – 1 Area of Shapes PS - 2 Worksheet for “Mensuration” PS - 3 Evaluation with Self Check or ---- PS - 4 Peer Check* Self Evaluation Sheet 78

PRACTICE SHEET - 1 (PS-1) 1. Following figures are formed by joining 6 unit squares. Determine the perimeter of each of them. 2. Following figures are formed by joining 8, ½ square units. Which of them has a smaller perimeter? 3. Three squares are joined together as shown in the figure. Their sides are 4 cm, 10 cm and 3 cm. Find the perimeter of the figure. 4. Each of the following figures measure 2 cm. Determine their perimeters. 5. Determine the perimeter of the following figures. 6. Two regular hexagons of perimeter 30 cm each are joined as shown in the figure. Calculate the perimeter of the new figure. 79

PRACTICE SHEET - 2 (PS-2) Find the cost of of fencing the flower bed at the rate of Rs. 10/m? 1. The side of a square is 10 cm. What will the new perimeter become if the sie of the square is doubled? 2. A square shaped part ABCD of side 100 m has 2 equal rectangular flower beds each of size 100 m × 5 m as shown in the figure. Find the perimeter of the remaining park. 3. Four regular hexagons are combined to form a figure as shown below. If the perimeter of the figure is 28 cm, find the length of each side of the hexagon. 4. Perimeter of an isosceles triangle is 50 cm. If one of the two equal sides is 18 cm, find the length of the third side. 5. Length of a rectangle is 3 times its breadth. Perimeter of the rectangle is 40 cm. Find its length and breadth. 6. Length of a rectangular field is 250 m and width is 150 m. Anuradha runs around this field 3 times. How far did she run? How many times should she run around the field to cover a distance of 4 km? 7. Bajinder runs ten times around a square track and covers 4 km. Find the length of the track. 8. Perimeter of a regular pentagon is 1540 cm. How long is each of its side? 9. In the figure, calculate the length of the outer boundary of the park. What will be the total cost of fencing it, at the rate of Rs. 20/m? There is a rectangular flower bed in the center of the part. 80

PRACTICE SHEET - 3 (PS-3) 1. Find the areas of rectangles whose sides are i) 3 cm and 6 cm ii) 10 m and 15 m iii) 1 km and 0.5 km iv) 3 m and 80 cm 2. Find area of squares whose sides are i) 5 cm ii) 20 m iii) 2.5 km 3. Area of a rectangular garden 30 m long is 600 sq m. Find the width of the garden. 4. Determine the cost of manuring a rectangular flower bed 60 m in length and 30 m in breadth at the rate of Rs. 30 per sq meter. 5. How many square slabs each with side of 90 cm are needed to cover a floor area of 81m2? 6. The length of a rectangular field is 8 m and breadth is 2 m. If a square field has the same perimeter as the rectangular field, find field has greater area. 7. A floor is 6 m long and 3 m wide. A square carpet of sides 2 m is laid on the floor. Find the area of the floor that is not carpeted. 8. 6 square pits each of sides 1 m are dug on a piece of lang 6 m long and 5 m wide. What is the area of the remaining part of the land? 9. Find the area of the following figures: 10. By counting square, estimate the area of the figure 11. Amit runs around a square park of side 75 m. Raghav runs around a rectangular park of length 60m and breadth 45m who covers less distance? 81

PRACTICE SHEET - 4 (PS-4) I. Choose the correct option. 1. The perimeter of a rectangle whose length is x and breadth is y: (A) 2(x + y) (B) 2xy (C) xy (D) x + y 2. What is the side of a square whose perimeter is P: (A) 2P (B) P (C) P + 4 (D) 4P 3. A square has 4 (A) two equal opposite sides (B) two equal adjacent sides (C) three equal sides (D) four equal sides 4. The area of the given figure if = 1 cm2 is ____. (A) 14 cm2 (B) 12 cm2 (C) 10 cm2 (D) 8 cm2 5. Perimeter of the given figure is ____ m. (A) 48 (B) 52 (C) 56 (D) 60 6. The perimeter of the given figure is ____ cm. (A) 34 (B) 36 (C) 38 (D) 40 7. What is the length of a rectangle whose area and breadth are 180cm2 and 10 cm respectively? (A) 16 cm (B) 18 cm (C) 20 cm (D) 21 cm 8. What is the area of a square with perimeter 32 cm? (A) 8 cm2 (B) 64 cm2 (C) 16 cm2 (D) 24cm2 9. The perimeter of the given figure is ____. (A) x + y + z + w (B) x + y + z + w + (z – x) + (y – w) (C) x + y – z + w (D) x + y + z – w 10. The perimeter of a regular pentagon of side 6 cm is _____. (A) 30 cm (B) 36 cm (C) 48 cm (D) 42 cm 82

PRACTICE SHEET - 4 (PS-4) II. Short answer questions. 1. What is the area and perimeter of the given figure? 2. Find the cost of painting four walls of a room at the rate of Rs. 20 per sq. m, if each wall is square shaped of side 8 m. 3. The length of a rectangular field is twice its breadth. Atul jogged 10 times and covered 5 km. What is the length of the field? III. Long answer questions. 1. Find the area and perimeter of the given figures if each is a square of side 1 cm. (i) (ii) 2. The perimeters of a rectangle and a square are same. If the length and breadth of the rectangle are 16 cm and 14 cm respectively, then find which figure has greater area and by how much? 83

SELF-EVALUATION SHEET Marks: 15 Time: 30 Mins 1. Find the area of the figure. (2 Marks) 5. The area of a rectangular garden 30 m long is 300 sq m. Find the width of the garden. (1 Mark) 6. Find the area and perimeter of the figure, if area of each small square is 1 cm2. (3 Marks) 2. Determine the perimeter of the given figure: (1 Mark) 3. Total cost of fencing the park shown is 7. Pasminder walks around a square park once Rs. 20,000. Find the cost of fencing per meter. and covers 800 m. What will be the area of this park? (3 Marks) (2 Marks) 4. Length of a rectangular field is 6 times its breadth. If the length of the field is 120 cm, then find the breadth and perimeter of the field. (3 Marks) 84

11. Algebra Learning Outcome • Create and read algebraic expressions • Form algebraic equations and find solution By the end of this lesson, a student will be able to: • Understand the idea of variables • Solve mathematical problems by using variables Concept Map Algebra Features of Idea of a variable Use of Variables in Expression with Equation Algebra Common Rules Variables Example of Solution to Variables an Equation Key Points Now let us write letter n for the number of ‘L’ patterns • Introduction: Algebra is one of the important branches of n = 1, for one ‘L’ formed n = 2, for two ‘L’ formed mathematics. ie., n can be any natural number, n = 1, 2, 3, …. It is a branch of mathematics in which symbols Number of matchstick required = 2 × Number of (letters) are used to represent variables. ‘L’ • Main features of algebra are              = 2 × n = 2n o  Letters are used to write rules and formulae. i.e., 2 × n can be written as 2n. o  Letters may stand for unknown quantities. i.e., for n = 1, Number of matchsticks required = 2 ×   Methods of determining unknown quantities 1=2 for n = 2, Number of matchsticks required = 2 × help to solve puzzles and problems from daily 2=4 life. for n = 5, Number of matchsticks required = 2 × 5 o As letters stand for numbers, operations can = 10 be performed on letters as on numbers, which So by using this rule, i.e., (2n) one can easily find leads to the study of algebraic expression and the number of matchsticks required for to make their properties. any number of ‘L’ patterns and there is no need to • Matchstick Patterns draw pattern each and every time. • Idea of a Variable n is an example of variable. The value of variable is not fixed and it can take any A single ‘L’ pattern can be formed using two match natural number, i.e., 1, 2, 3, 4,…. and we write the number of matchsticks required using variable n. sticks. So the word variable means something that can To make 2 ‘L’ patterns we need 4 matchsticks. vary or change. The value of a variable is not fixed and can take any different values. Likewise • Other matchstick patterns Number of matchsticks required = 2 × number of ‘L’ patterns required i.e., Number of matchsticks required is twice the number of ‘L’ patterns formed. 85

11. Algebra Pattern of Letter ‘C’ If Vijay wants to buy wants to buy 8 notebooks, then To make one ‘C’, 3 matchsticks are required. m=8 Total cost in rupees = 25m By observing the figures, we can relate the number = 25 × 8 = Rs. 200 of ‘C’ with the number of matchsticks required. The rule will be number of matchsticks required = 3n, iii) For a Republic Day celebration in a school, where n stands for the number of ‘C’. Here n is a children stand 12 in a row to perform a drill. How variable and can take on values of natural numbers, many children can be there in the drill? i.e., 1,2, 3, 4, …. Answer: Number of children in the drill depends on the For Pattern ‘F’, what could be the rule? For one ‘F’ we need 4 matchsticks. number of rows. Rule for making patterns of ‘F’ will be: If there are r rows, then the number of children in Number of match required to form pattern ‘F’ = 4n the drill = 12r Variables can be represented by any of the letters Here r is a variable and can take on values 1, 2, 3, 4, like m, n, p, x, y, z, q, etc. Always remember that the variable is a number which does not have a fixed … value or a single value. • All the examples discussed so far involved Example: multiplication of a variable by a number. – Number 11 or Number 25 or any other given Situations in which numbers are added or number is not a variable. They have fixed subtracted from variables can also be encountered. values. Example: – Number of Angles of a triangle will have fixed i) Rajesh has 15 more chocolates than Shamanth, value, i.e., 3 – Number of corners in a pentagon will have fixed ie., value.  If Shamanth has 20 chocolates then Rajesh will But in matchstick example, ‘n’ was a variable which can take values 1, 2, 3, 4, …. have 35 chocolates.  If Shamanth has 30 chocolates then Rajesh has • Examples of Variables i) If price of 1 notebook is Rs. 25, and Vijay wants 3 45 and so on. We can say that notebooks, what will be the price of 3 notebooks?  Number of chocolates with Rajesh = Number of Answer: Price 1 notebook is Rs. 25 chocolates with Shamanth + 15 Total cost in rupees = Price of 1 notebook ×  Let us denote, number of chocolates with Sha- number of notebooks manth by letter x, where x is a variable and can required take any value 1, 2, 3, 4, …10, 20,….. = 25 × m Using x, we can write, = 25 m  Number of chocolates with Rajesh = x + 15. Here m is the number of notebooks required and  (x + 15) is read as ‘x plus fifteen’, which means can take any value 1, 2, 3, 4, .. fifteen is added to x. Note that 15x is different from (x + 15) Number of notebooks 12345 Example: If x = 5, then 15x = 15 × 5 = 75 required x + 15 = 5 + 15 = 20 Total cost in rupees 25 50 75 100 125 ii) Ramesh and Reshma are children in a family. Vijay wants to buy 3 notebooks, so total cost = 25 × Ramesh is 5 year younger than Reshma, i.e., 3 = Rs. 75   when Reshma is 10 years old Ramesh is 5 years old;  when Reshma is 20 years old Ramesh is 15 years old and so on. If we denote Reshma’s age by a letter p, then Ramesh’s age = p – 5 Expression (p – 5) is read as ‘p minus five’ 86