Mathematics, Classes I-V (Paper I): key facts and practice questions

Revise Mathematics, Classes I-V (Paper I) for CTET and state TETs: the facts and distinctions that keep coming up, a one-glance revision list, and 10 practice questions with answers and explanations.

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Key concepts and facts

• Numbers: Place value is the value a digit gets from its position; face value is the digit itself. In 4,73,256 the 7 has place value 70,000 and face value 7. In the Indian system the first comma comes after the hundreds and then after every two digits: 1 lakh = 1,00,000 = 100 thousands. Zeros hold empty places, so four lakh five thousand thirty is 4,05,030. To round to the nearest hundred, look at the tens digit: 6,449 becomes 6,400 but 6,451 becomes 6,500. Even numbers end in 0, 2, 4, 6 or 8; odd + odd and even + even are even, while odd + even is odd. Ordinals: a child 14th from the front and 9th from the back stands in a queue of 14 + 9 - 1 = 22.
• Addition and Subtraction: Write place under place and regroup: ten ones make one ten. 7,003 - 2,486 needs regrouping across zeros and gives 4,517; check: 2,486 + 4,517 = 7,003. Addition and subtraction undo each other, which is how missing numbers are found.
• Multiplication and Division: Multiplication is repeated addition, or an array of rows and columns. Order does not change the product, and a number can be split: 23 × 15 = 23 × 10 + 23 × 5 = 345. In 47 × 36 the second partial product is 47 × 30 = 1,410, not 141. Division is equal sharing or repeated subtraction. Dividend = divisor × quotient + remainder, and the remainder is always less than the divisor: 1,000 ÷ 7 gives quotient 142 and remainder 6. In word problems decide what the remainder means: 460 children in buses of 45 need 11 buses, not 10. Factors divide a number exactly (36 has 9), multiples never end, and common multiples tell when two bells next ring together.
• Fractions and decimals: A fraction names equal parts of a whole or of a collection: 3/4 of 56 mangoes is 42. Multiplying or dividing numerator and denominator by the same number gives equivalent fractions: 2/8 = 1/4. Among like fractions, the one with the larger numerator is larger. Tenths and hundredths extend place value to the right: 0.37 is 3 tenths and 7 hundredths, ₹ 25 and 5 paise is ₹ 25.05, and 6.08 m is 6 m 8 cm.
• Geometry, shapes and solids: Children meet solids (cube, cuboid, cylinder, cone, sphere) before flat shapes. A cube has 6 faces, 12 edges and 8 vertices; a cuboid has the same numbers but rectangular faces; a cylinder has 2 flat circular faces and 1 curved surface; a cone has 1 flat face and 1 vertex; a sphere has only a curved surface. A square has 4 lines of symmetry, a non-square rectangle 2 and an equilateral triangle 3. Nets, tangrams, angles (right, acute, obtuse), simple maps and top views build spatial understanding.
• Measurement, weight, time and volume: 1 m = 100 cm, 1 km = 1,000 m and 1 cm = 10 mm; 1 kg = 1,000 g; 1 litre = 1,000 mL. 1 hour = 60 minutes and 1 day = 24 hours; 4:30 p.m. is 16:30 on the 24-hour clock. Perimeter is the distance around a shape, 2 × (length + breadth) for a rectangle; area is the number of unit squares that cover it, length × breadth. A 5 cm by 3 cm rectangle has perimeter 16 cm and area 15 square cm. At this level volume is found by counting unit cubes.
• Data handling, patterns and money: Tally marks record data; pictographs and bar graphs show it. Read the key: if one symbol stands for 5 children, 4 symbols mean 20. Patterns include repeating patterns, growing number patterns (2, 5, 10, 17, 26 has differences 3, 5, 7, 9), sums of odd numbers (the first n odd numbers add up to n × n) and magic squares: with 1 to 9, every line adds up to 15 and 5 sits in the centre. Money: ₹ 1 = 100 paise; add and subtract amounts by lining up the decimal points, and make simple bills as rate × quantity.
• Common errors: dropping a zero in the quotient, subtracting the smaller digit from the larger in every column, adding numerators and denominators (1/2 + 1/4 is 3/4, not 2/6), thinking 0.65 is greater than 0.7, leaving a remainder that is not less than the divisor, and mixing up area and perimeter. Check every answer a second way: estimate, use the inverse operation or substitute back.

One-glance revision list

• Place value: in 4,73,256 the 7 is worth 70,000, while its face value is 7.
• Indian system: 1 lakh = 1,00,000 = 100 thousands, so four lakh five thousand thirty = 4,05,030.
• Rounding: 4,67,549 to the nearest thousand is 4,68,000, because 549 is at least 500.
• Subtraction across zeros: 7,003 - 2,486 = 4,517; check with 2,486 + 4,517 = 7,003.
• Division check: 1,000 = 7 × 142 + 6, so 1,000 ÷ 7 gives quotient 142 and remainder 6 (6 < 7).
• Zero in the quotient: 8,424 ÷ 8 = 1,053, not 153, because 4 hundreds ÷ 8 gives 0 whole hundreds, so the quotient has 0 in its hundreds place.
• Equivalent fractions: 3/5 = 21/35 (multiply both by 7) and 2/8 = 1/4 (divide both by 2).
• Decimals: ₹ 25 and 5 paise = ₹ 25.05, 6.08 m = 6 m 8 cm, and 0.7 = 0.70 is greater than 0.65.
• Solids: a cube has 6 faces, 12 edges and 8 vertices; a cone has 1 flat face, 1 curved surface and 1 vertex.
• Area and perimeter: a 5 cm by 3 cm rectangle has area 15 square cm and perimeter 16 cm.
• Magic square 1 to 9: rows 4, 9, 2 / 3, 5, 7 / 8, 1, 6; every row, column and diagonal adds up to 15.

Practice questions

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