A word problem asks your child to turn a situation into mathematics. Accurate arithmetic matters, but so does choosing a calculation that answers the actual question. Before working with the numbers, ask: “What do I need to find, and how are the quantities related?”
These original teaching examples cover averages, percentages and travel time. They are independent practice exercises, not official QASMT or BSHS questions.
A method to practise before adding a timer
- Read the whole question. Identify the quantity to find and its unit.
- Represent the relationship. Use a short equation, labelled diagram or sentence.
- Check that representation. Does it match the wording, including any exclusions or conditions?
- Calculate. Keep track of units and intermediate results.
- Check the answer. Estimate whether it is reasonable and reread what the question asked.
During practice, keep the working visible so you can distinguish a misunderstanding from an arithmetic error. On test day, use only the working materials and equipment permitted for that sitting.
Example 1: An average after removing a value
Question: What is the average of 12, 18, 25, 30, 42 and 50 after the second-highest number is removed?
- A. 23
- B. 26.75
- C. 32
- D. 27
Answer: D, 27. The highest number is 50, so the second-highest is 42. Remove 42 before finding the mean.
The remaining total is 12 + 18 + 25 + 30 + 50 = 135. There are now five numbers, so the average is 135 ÷ 5 = 27.
Two details matter: which number is removed, and how many numbers remain. Dividing by six would use the original count, not the count requested by the question.
Check: 27 is between the smallest and largest remaining values. That does not prove the calculation correct, but it is a useful reasonableness check. To verify, multiply 27 by five and confirm that it returns 135.
Example 2: Find the part that is left
Question: A crate contains only apples and oranges. The fruit has a total mass of 12 kg, excluding the crate. Oranges account for 40% of that mass. What is the mass of the apples?
- A. 3.2 kg
- B. 4.8 kg
- C. 6 kg
- D. 7.2 kg
Answer: D, 7.2 kg. Apples account for 100% − 40% = 60% of the fruit's mass. Therefore, 0.6 × 12 = 7.2 kg.
Another valid method is to calculate the oranges first: 0.4 × 12 = 4.8 kg. Then subtract: 12 − 4.8 = 7.2 kg.
B is a plausible distractor because it is a correctly calculated quantity—the oranges—but not the one requested. Encourage your child to label the intermediate result “oranges” before subtracting it.
Check: Apples make up more than half of the mass, so their mass should exceed 6 kg. Also, 7.2 + 4.8 = 12 kg.
Example 3: Keep the units consistent
Question: A vehicle travels 240 km at a constant speed of 60 km/h without stopping. How long does the journey take?
- A. 2 hours
- B. 3 hours
- C. 4 hours
- D. 5 hours
Answer: C, 4 hours. Time = distance ÷ speed, so 240 ÷ 60 = 4 hours. The speed is in kilometres per hour and the distance is in kilometres, so the time is in hours.
Check: In four hours at 60 km/h, the vehicle travels 4 × 60 = 240 km.
Now change one condition: the vehicle also stops for 30 minutes. The driving time remains four hours, but the total elapsed journey time becomes four hours and 30 minutes. A small wording change can alter the quantity being requested.
Do not choose an operation from one keyword
Words such as “more”, “left” and “altogether” can help describe a situation, but they do not replace reading the relationship.
For example: “Mia has 8 marbles, which is 3 more than Ben. How many does Ben have?” The word “more” appears, but finding Ben's amount requires 8 − 3 = 5. Sketching Mia's amount as Ben's amount plus three makes the relationship clearer.
What to do when no option matches
Check both your interpretation and your arithmetic. Did you use the wrong value, forget a condition, mix units or make a calculation error? There is no rule that a mismatch must come from one particular step.
Avoid changing a sound method merely to force an answer to match. Return to the question, check the work and follow the test's instructions about moving on if you remain unsure.
Turn a mistake into useful practice
Ask your child to say what each number in their calculation represents. Then change one feature of a worked example and have them explain what must change in the solution. This helps reveal whether they understand the relationship rather than remember an answer.
For pattern questions, continue with number series and number grids. For a sample section, choose your pathway through QASMT or BSHS. You can also compare available practice tests.