50 min a b c a b c 50n mi Consulting Author Dr Dicky Susanto MATHS MINDS-ON Workbook Workbook 2nd Edition Singapore Maths Method Maths Exploration Active-learning Approach 21st Century Learning Skills ©Praxis Publishing Singapore Pte. Ltd.
IV Chapter 1 Whole Numbers...........................1 Exercises.....................................4 Chapter 2 Addition and Subtraction ...........14 Exercises...................................16 Chapter 3 Multiplication and Division .........27 Exercises...................................35 Chapter 4 Factors and Multiples ................51 Exercises...................................54 Chapter 5 Fractions....................................65 Exercises ..................................69 Chapter 6 Perimeter...................................85 Exercises...................................86 Chapter 7 Area...........................................98 Exercises...................................99 Chapter 8 Angles...................................... 119 Exercises.................................121 Chapter 9 Triangles and Quadrilaterals ...130 Exercises.................................131 Chapter 10 Data Analysis and Presentation ............................148 Exercises.................................148 Chapter 11 Whole Numbers Greater Than 100 000 ..........................166 Exercises.................................168 Contents SCAN ME For General Revision ©Praxis Publishing Singapore Pte. Ltd.
1 Minds-on Maths Workbook Grade 5 Place value Ten thousands Thousands Hundreds Tens Ones Digit 7 4 2 5 1 Digit value 70 000 4000 200 50 1 Expanded form 70 000 + 4000 + 200 + 50 + 1 In numerals 74 251 In words Seventy-four thousand two hundred and fifty-one • 95 386 (5-digit number) is greater than 5386 (4-digit number) because 95 386 has more digits than 5386. Which number is greater, 95 386 or 5386? Which number is smaller, 95 386 or 95 836? Smaller Greater { { 95 836 > 95 386 95 386 < 95 836 95 386 > 5386 5386 < 95 386 Ten Thousands Thousands Hundreds Tens Ones Reading and writing numbers Place value and expanded form Comparing numbers • 95 386 is smaller than 95 836. Same Whole Numbers Chapter 1 ©Praxis Publishing Singapore Pte. Ltd.
2 Chapter 1 Whole Numbers Round to 110 113 120 113 is between 110 and 120. It is nearer to 110 than to 120. 113 is 110 when rounded off to the nearest ten. 113 110 H T O 1 1 3 The nearest tens are 10 and 20. It shows that 113 is before the halfway point. We should round it to the nearest ten before which is 10. Round to 110 118 120 118 is between 110 and 120. It is nearer to 120 than to 110. 118 is 120 when rounded off to the nearest ten. 118 120 H T O 1 1 8 The nearest tens are 10 and 20. It shows that 118 is after the halfway point. We should round it to the nearest ten after which is 20. Round to 110 115 120 115 is exactly halfway between 110 and 120. 115 is 120 when rounded off to the nearest ten. 115 120 H T O 1 1 5 The nearest tens are 10 and 20. It shows that 115 is exactly on halfway point. We should round it to the nearest ten after which is 20. Rounding off numbers to the nearest ten ©Praxis Publishing Singapore Pte. Ltd.
10 Chapter 1 Whole Numbers J Tick (✓) the greater number. K Cross (✘) the smaller number. L Fill in each blank with ">", "<" or "=". 1. 17 208 17 280 2. 34 550 3455 3. 40 694 46 094 4. 56 178 65 178 5. 62 347 62 343 6. 70 001 7100 7. 79 526 79 526 8. 83 625 83 925 9. 21 489 20 000 + 1000 + 400 + 80 + 9 10. 98 760 9000 + 800 + 70 + 6 1. 3. 1020 1002 29 863 59 863 48 237 48 732 1. 2. 3. 4392 65 964 14 392 64 964 4. 86 711 87 711 2. 31 424 31 444 ©Praxis Publishing Singapore Pte. Ltd.
14 Chapter 2 Addition and Subtraction Step 1 Add the ones. 6 ones + 3 ones = 9 ones Step 2 Add the tens. 5 tens + 4 tens = 9 tens Step 3 Add the hundreds. 4 hundreds + 0 hundreds = 4 hundreds Step 4 Add the thousands. 3 thousands + 5 thousands = 8 thousands Step 1 Add the ones. 2 ones + 3 ones = 5 ones Step 2 Add the tens. 5 tens + 8 tens = 13 tens Regroup the tens. 13 tens = 1 hundred 3 tens Step 3 Add the hundreds. 1 hundred + 4 hundreds + 6 hundreds = 11 hundreds Regroup the hundreds. 11 hundreds = 1 thousand 1 hundred Step 4 Add the thousands. 1 thousand + 4 thousands + 2 thousands = 7 thousands Th H T O 3 4 5 6 + 5 0 4 3 8 4 9 9 Th H T O 1 1 4 4 5 2 + 2 6 8 3 7 1 3 5 The sum of 3456 and 5043 is 8499. The sum of 4452 and 2683 is 7135. Find the sum of 3456 and 5043. Find the sum of 4452 and 2683. Addition and Subtraction Chapter 2 Addition without regrouping Addition with regrouping ©Praxis Publishing Singapore Pte. Ltd.
27 Minds-on Maths Workbook Grade 5 × 1 2 3 4 5 6 7 8 9 10 1 1 2 3 4 5 6 7 8 9 10 2 2 4 6 8 10 12 14 16 18 20 3 3 6 9 12 15 18 21 24 27 30 4 4 8 12 16 20 24 28 32 36 40 5 5 10 15 20 25 30 35 40 45 50 6 6 12 18 24 30 36 42 48 54 60 7 7 14 21 28 35 42 49 56 63 70 8 8 16 24 32 40 48 56 64 72 80 9 9 18 27 36 45 54 63 72 81 90 Find the product of 234 and 2. The product of 234 and 2 is 468. Step 1 Multiply the ones by 2. 4 ones × 2 = 8 ones Step 2 Multiply the tens by 2. 3 tens × 2 = 6 tens Step 3 Multiply the hundreds by 2. 2 hundreds × 2 = 4 hundreds H T O 2 3 4 × 2 8 H T O 2 3 4 × 2 6 8 H T O 2 3 4 × 2 4 6 8 Multiplication and Division Chapter 3 Multiplication table 1 to 10 Multiplication without regrouping ©Praxis Publishing Singapore Pte. Ltd.
31 Minds-on Maths Workbook Grade 5 Quotient and remainder Division without remainder and regrouping Dividend No remainder Divisor Remainder Quotient 54 ÷ 8 = 6 R 6 When we divide a number by another number, the answer we get is called the quotient. The amount left over is called the remainder. Find the quotient of 468 and 2. Therefore, 468 ÷ 2 = 234. The quotient of 468 and 2 is 234. 123 2 4 6 8 4 2 3 2 4 6 8 4 6 6 2 3 4 2 4 6 8 4 6 6 8 8 0 Step 1 Divide the hundreds by 2. 4 hundreds ÷ 2 = 2 hundreds Step 2 Divide the tens by 2. 6 tens ÷ 2 = 3 tens Step 3 Divide the ones by 2. 8 ones ÷ 2 = 4 ones 2 ©Praxis Publishing Singapore Pte. Ltd.
39 Minds-on Maths Workbook Grade 5 H Multiply. I Multiply. 1. 2 × 20 = 2. 300 × 4 = 3. 6 × 500 = 4. 800 × 7 = 5. 2 × 101 = 6. 122 × 2 = 7. 3 × 213 = 8. 220 × 4 = 2 0 6 × 2 3 4 0 × 4 4 6 4 × 7 4 2 7 × 6 3 7 5 × 5 2 3 1 × 3 1. 4. 2. 5. 3. 6. ©Praxis Publishing Singapore Pte. Ltd.
46 Chapter 3 Multiplication and Division S Find the quotients of the numbers below. 1. 2 2 4 8 2. 3 2 7 9 3. 4 4 5 2 4. 5 6 5 5 5. 6 8 8 6 6. 7 9 1 7 7. 4 4 9 8 8. 6 9 5 6 9. 7 7 9 1 ©Praxis Publishing Singapore Pte. Ltd.
51 Minds-on Maths Workbook Grade 5 Factors of whole numbers A factor of a whole number is a number that can divide the whole number exactly, without leaving any remainder. For example, the factors of 20 are 1, 2, 4, 5, 10 and 20. Prime factors A prime number is a whole number that has only two factors, that is 1 and itself. For example, 2, 3, 5, 7, 11 and 13 are all prime numbers. A prime factor is a prime number that is a factor of a whole number. For example, the prime factors of 20 are 2 and 5. Prime factorisation of a whole number Example: Prime factorise 36. By division So, the prime factorisation of 36 is 2 × 2 × 3 × 3 or 22 × 32 . 2 2 3 3 Divide until a quotient of 1 is obtained. 36 18 9 3 1 Begin dividing by the smallest prime number, 2. When the quotient is indivisible by 2, divide it by the next prime number, 3. By using factor tree 36 6 × 6 2 × 3 2 × 3 Factors and Multiples Chapter 4 ©Praxis Publishing Singapore Pte. Ltd.
59 Minds-on Maths Workbook Grade 5 K Find the HCF of each of the following sets of numbers by using prime factorisation. Example: 10 and 52 Answer: 10 = 2 × 5 52 = 2 × 2 × 13 Therefore, the HCF of 10 and 52 is 2. 1. 12 and 24 2. 21, 49 and 63 3. 26, 78 and 208 4. 18, 34, 46 and 54 ©Praxis Publishing Singapore Pte. Ltd.
65 Minds-on Maths Workbook Grade 5 Fractions equivalent to whole numbers A fraction that has the same numerator and denominator is equivalent to 1. 2 —2 = 3 —3 = —– 12 12 = —– 15 15 = 1 Fractions with numerators that are divisible by their denominators are equivalent to whole numbers. 4 —2 = 2, 9 —3 = 3, —– 16 4 = 4, —– 10 5 = 2, —– 30 10 = 3 Proper fractions and improper fractions Proper fractions have numerators that are smaller than their denominators. 1 —2 , 4 —5 , 7 —9 , and — 10 13 are examples of proper fractions. Improper fractions have numerators that are equal to or greater than their denominators. 4 —2 , 3 —3 , 7 —5 , and —– 11 6 are examples of improper fractions. Fractions Chapter 5 ©Praxis Publishing Singapore Pte. Ltd.
67 Minds-on Maths Workbook Grade 5 Adding and subtracting fractions (a) 3 4 + 7 8 = 3 4 × 2 × 2 + 7 8 (b) 2 – 5 9 = 2 1 × 9 × 9 – 5 9 = 6 8 + 7 8 = 18 9 – 5 9 = 13 8 = 13 9 = 8 8 + 5 8 = 9 9 + 4 9 = 1 + 5 8 = 1 4 9 Conversion of fractions Mixed number 3 2 5 = 3 1 × 5 × 5 + 2 5 = 15 5 + 2 5 = 17 5 Improper fraction 17 5 = 17 ÷ 5 = 3 R 2 = 3 2 5 3 5 ) 17 15 2 Remainder Quotient Always write mixed numbers and fraction answers in the simplest form. Simplest form ©Praxis Publishing Singapore Pte. Ltd.
69 Minds-on Maths Workbook Grade 5 A Write each answer as a mixed number. 1. 2 + 3 4 = 2. 7 + 8 9 = 3. 5 + 1 2 = 4. 1 + 2 3 = 5. 9 + 3 8 = 6. 4 7 + 3= 7. 5 6 + 4 = 8. 1 12 + 1= 9. 3 11 + 6 = 10. 2 5 + 8= B Fill in the blanks to show the wholes and parts shaded. Then write the mixed number it represents. 1. wholes and eighths = 2. wholes and sixths = Exercises ©Praxis Publishing Singapore Pte. Ltd.
71 Minds-on Maths Workbook Grade 5 E Write an improper fraction for each of the following. 1. There are halves in 2 1 2 . 2 1 2 = + + + + = 2. There are fifths in 3 3 5 . 3 3 5 = fifths = 3. There are sixths in 3 5 6 . 3 5 6 = sixths = ©Praxis Publishing Singapore Pte. Ltd.
74 Chapter 5 Fractions J Change each improper fraction to a mixed number in its simplest form. 1. 7 3 = 2. 25 6 = 3. 23 5 = 4. 19 2 = 5. 43 8 = 6. 34 4 = 7. 27 7 = 8. 59 9 = 9. 38 12 = 10. 95 10 = K Circle the greater fraction. 1. 2. 3. 4. 5. 6. L Circle the smaller fraction. 1. 2. 3. 4. 5. 6. 2 5 20 28 3 14 17 24 13 4 1 5 2 8 13 18 23 12 13 8 11 8 9 2 10 30 3 4 10 7 20 6 21 8 1 15 1 2 20 9 50 24 70 56 7 40 10 16 3 2 5 1 3 4 7 1 5 ©Praxis Publishing Singapore Pte. Ltd.
85 Minds-on Maths Workbook Grade 5 Perimeter of quadrilaterals Square Perimeter = 4 × Length of side Rectangle Perimeter = Length + Breadth + Length + Breadth = 2 × (Length + Breadth) Breadth Length Length Perimeter Chapter 6 Perimeter of triangles Perimeter of triangle = Sum of the lengths of all sides = a + b + c a c b Height Base ©Praxis Publishing Singapore Pte. Ltd.
87 Minds-on Maths Workbook Grade 5 B Find the length of the unknown side of each triangle with the given perimeter. 1. XYZ is a triangle. Its perimeter is 21 cm. Find the length of XZ. 2. EFG is a triangle. Its perimeter is 14.5 cm. Find the length of EG. 3. ABC is an equilateral triangle. Find the length of BC if the perimeter is 24 cm. 4. PQR is an isosceles triangle. Find the length of PR if the perimeter is 30 cm. 7 cm Y X Z 6 cm 3 cm F 4.5 cm E G B A C 9 cm P Q R ©Praxis Publishing Singapore Pte. Ltd.
98 Chapter 7 Area Area of quadrilaterals Square Area = Length of side × Length of side Rectangle Area = Length × Breadth Base and height of a triangle The base and height of a triangle is always perpendicular to each other. Height Base Height Base Height Base Area of triangle = 1 2 × Base × Height Breadth Length Length Area Chapter 7 ©Praxis Publishing Singapore Pte. Ltd.
111 Minds-on Maths Workbook Grade 5 1. The area of parallelogram ABCD is 38.5 cm2 . Find BC. 5.5 cm A D C P Q B 2. The area of parallelogram MNOP is 504 cm2 . Find MN. N 28 cm O P M 3. The area of rhombus EFGH is 750 cm2 . Find GI. 30 cm E I F G H 4. The area of parallelogram STUV is 15.6 cm2 . Find TW. 3 cm S T U V W N Find the length of the unknown base or height of each quadrilateral with the given area. ©Praxis Publishing Singapore Pte. Ltd.
119 Minds-on Maths Workbook Grade 5 Types of angles Type of angle Size Example Remarks Right angle 90° A B C ∠ABC is a right angle. ∠ABC = 90° Acute angle Less than 90° D E F ∠DEF is an acute angle. ∠DEF , 90° Obtuse angle More than 90° but less than 180° J K L ∠JKL is an obtuse angle. 90° , ∠JKL , 180° Straight angle 180° P Q R ∠PQR is a straight angle. ∠PQR = 180° Reflex angle More than 180° but less than 360° Y X Z ∠XYZ is a reflex angle. 180° , ∠XYZ , 360° Angles Chapter 8 ©Praxis Publishing Singapore Pte. Ltd.
124 Chapter 8 Angles E Use a protractor to measure each of the angles below. a b c d e f g h i ∠a = 90° ∠b = 90° ∠c = 90° ∠d = 90° ∠e = 90° ∠f = 90° ∠g = 90° ∠h = 90° ∠i = 90° F Use a protractor to measure and state the sizes of the interior angles of the following diagrams. 1. 2. 3. 4. ©Praxis Publishing Singapore Pte. Ltd.
128 Chapter 8 Angles L Look at the places around the park. Write down the direction of each place from the park. Supermarket Swimming pool School Playground Library Clinic Restaurant Market Library Supermarket Market Swimming pool Restaurant Clinic Park N 1. The school is of the park. 2. The playground is of the park. 3. The library is of the park. 4. The clinic is of the park. 5. The restaurant is of the park. 6. The market is of the park. 7. The swimming pool is of the park. 8. The supermarket is of the park. ©Praxis Publishing Singapore Pte. Ltd.
130 Chapter 9 Triangles and Quadrilaterals Equilateral triangle Isosceles triangle Scalene triangle • All the three sides are equal. • All the three angles are equal, always 60o . • Two sides are equal. • Two angles are equal. • All the sides are of different lengths. • There are no equal angles. Acute-angled triangle Obtused-angled triangle Right-angled triangle • All angles are acute angles (less than 90°). • One of the angles is an obtuse angle (more than 90°). • One of the angles is a right angle (90°). Triangles and Quadrilaterals Chapter 9 Properties of triangles Classification of triangles based on their sides: Classification of triangles based on their angles: ©Praxis Publishing Singapore Pte. Ltd.
145 Minds-on Maths Workbook Grade 5 N Match correctly. All sides are equal. The diagonals are equal. All sides are equal. The diagonals are not equal. The opposite sides are equal. The opposite sides are parallel. Only 1 pair of opposite sides is parallel. The sum of adjacent angles on the non-parallel sides is 180º. The opposite sides are equal. All the angles are 90º. A pair of opposite angles is equal. The diagonals are not equal. 1. 2. 3. 4. 5. 6. ©Praxis Publishing Singapore Pte. Ltd.
149 Minds-on Maths Workbook Grade 5 A Stanley uses tallies to record the number of different types of vegetables he saw in a garden. Study the table below and answer the following questions. IIII IIII IIII IIII IIII IIII IIII III IIII IIII IIII IIII IIII IIII I IIII IIII IIII IIII II IIII IIII IIII II Count the tallies and complete the table below. Types of vegetables Chilli Tomato Courgette Aubergine Number of vegetables Use the table to answer the following questions. 1. Which type of vegetable did Stanley see most in the garden? 2. There are 9 more than . 3. Stanley forgot to record the number of carrots. If there are twice as many carrots as aubergines, how many carrots are there? 4. How many vegetables are there altogether in the garden? Exercises Data Analysis and Presentation Chapter 10 ©Praxis Publishing Singapore Pte. Ltd.
155 Minds-on Maths Workbook Grade 5 G The information below shows a survey on the sizes of uniforms worn by pupils in Class 5A of a school. M M M M M M M M XL XL XL XL XL XL XL L L L L L L L L L L S S S S S Complete the following table. Sizes S M L XL Number of pupils Use the information provided above to complete the bar graph below. Uniform Sizes of Class 5A Pupils S M L XL Number of pupils 0 4 8 2 6 10 Uniform size 1. The most number of pupils wear size . 2. The least number of pupils wear size . 3. There are more pupils who wear size M than size S. 4. There are fewer pupils who wear size XL than size L. 5. There are pupils participated in this survey. ©Praxis Publishing Singapore Pte. Ltd.
167 Minds-on Maths Workbook Grade 5 Reading and writing numbers up to 100 000 A number that is greater than 100 000 has more than 5 digits. When writing a number that has more than four digits, we leave a space between the thousands place and the hundreds place to guide us to read the numbers easily. In numerals In words 1000 10 000 100 000 1 000 000 10 000 000 One thousand Ten thousand One hundred thousand One million Ten million In numerals 3 684 725 In words Three million six hundred and eighty-four thousand seven hundred and twenty-five + + + + + + Whole Numbers Greater Than 100 000 Chapter 11 Millions 3 3 000 000 600 000 80 000 4000 700 20 5 6 8 4 7 2 5 Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones ©Praxis Publishing Singapore Pte. Ltd.
168 Chapter 11 Whole Numbers Greater Than 100 000 Comparing numbers Start by comparing the digits in the highest place value of both numbers. For example, 456 789 and 456 879 can be compared using a place value table as shown below. Therefore, 456 879 is greater than 456 789 (456 879 > 456 789) or 456 789 is smaller than 456 879 (456 789 < 456 879). 41 000 41 500 42 000 42 500 43 000 + 500 + 500 + 500 + 500 6000 5000 4000 3000 2000 – 1000 – 1000 – 1000 – 1000 Same 8 is greater than 7 Number pattern First, determine if the series is in ascending or descending order. Then, determine the difference between adjacent numbers. For example, Number Hundred thousands Ten thousands Thousands Hundreds Tens Ones 456 789 4 5 6 7 8 9 456 879 4 5 6 8 7 9 Ascending order: Descending order: ©Praxis Publishing Singapore Pte. Ltd.