Use these examples after reviewing an answer. The methods support our original practice; they do not replace your school’s current familiarisation materials.
Keep place values aligned. Estimate before calculating, and use an inverse operation to check your result. Multiplication and division come before addition and subtraction unless brackets change the order.
For 608 − 279, subtract 200, then 70, then 9: 408, 338, 329. Check that 329 + 279 = 608.
Division asks how many equal groups there are, or how much is in each equal group. Use a known multiplication fact and check the units.
To share 84 stickers equally among 7 people, calculate 84 ÷ 7 = 12. Check: 7 × 12 = 84.
The denominator tells you the number of equal parts; the numerator tells you how many parts to take. To add or compare fractions, first express them with the same denominator.
To find 3/5 of 35, divide by 5 to get 7, then multiply by 3 to get 21. For 1/3 + 1/6, use sixths: 2/6 + 1/6 = 3/6 = 1/2.
Percent means out of 100. Build unfamiliar percentages from 10%, 5% or 1%. For a discount, subtract the reduction from the original price.
15% of 60 is 10% + 5%: 6 + 3 = 9. A 15% discount on £60 therefore leaves £51.
Identify the shape and the measurement requested. Perimeter measures the distance around a shape; area measures its surface and volume measures the space inside it.
A rectangle 7 cm long and 4 cm wide has perimeter 2 × (7 + 4) = 22 cm. Its area is 7 × 4 = 28 cm².
For the mean, add all the values and divide by how many values there are. If a value is missing, work backwards from the total implied by the mean.
Three values have mean 9, so their total is 27. If two are 6 and 10, the missing value is 27 − 16 = 11.
Use the angle total that fits the diagram: 180° on a straight line, 180° inside a triangle, or 360° around a point. Subtract the known angles.
A triangle with angles 35° and 80° has third angle 180 − 35 − 80 = 65°.
Keep pounds and pence consistent. Find the total cost before calculating change, and write money answers with the appropriate units.
Three items at £2.40 cost £7.20. Change from £10 is £10 − £7.20 = £2.80.
Treat the unknown as a number in a balanced equation. Undo operations in reverse order and check by substituting your answer.
For 4x + 6 = 30, subtract 6 to get 4x = 24, then divide by 4 to get x = 6. Check: 4 × 6 + 6 = 30.
A clock hour contains 60 minutes, not 100. Add hours and minutes separately, carrying minutes past 60 into the next hour.
09:45 plus 50 minutes is 10:35: 15 minutes reaches 10:00, then another 35 reaches 10:35.
For equally likely outcomes, probability is favourable outcomes divided by all possible outcomes. Count the whole set carefully and simplify the fraction if needed.
A bag has 3 yellow and 5 purple counters. The probability of yellow on one random draw is 3/8.
Find the amount per one unit first, then scale to the requested amount. Constant speed or a constant filling rate is necessary for this method.
A pump delivers 18 litres in 6 minutes at a constant rate: 3 litres per minute. In 4 minutes it delivers 12 litres.
Add the ratio parts, divide the total into that many equal parts, then multiply by the parts needed. A ratio part is not automatically one object.
For a 2:3 ratio with 35 objects, there are 5 parts of 7. The groups contain 14 and 21 objects.
Compare consecutive terms. Look for a repeated difference, a multiplier, alternating rules or steadily changing differences. Check the rule against every given term.
In 3, 7, 13, 21, the gaps are 4, 6 and 8. The next gap is 10, so the next term is 31.
Align decimal points when calculating. Compare numbers using place value, adding trailing zeroes if helpful. Trailing zeroes after a decimal do not change its value.
Compare 0.6, 0.58 and 0.605 as 0.600, 0.580 and 0.605. The largest is 0.605.
Area counts square units covering a surface. Multiply length by width for a rectangle; use half of base × perpendicular height for a triangle.
A triangle with base 12 cm and perpendicular height 5 cm has area 12 × 5 ÷ 2 = 30 cm².
Write the conversion fact first. Multiply when converting to smaller units and divide when converting to larger units. Include the unit in the answer.
1 km = 1,000 m. So 2.3 km = 2,300 m, while 450 cm = 4.5 m because 100 cm = 1 m.
List what you need to find in order. Carry the result of each step into the next and estimate whether the final answer is reasonable.
Six packs contain 5 cards each: 30 cards. If 8 are given away, 30 − 8 = 22 remain.
