A method to follow on paper.
- 01
Write down what you need to find
Read the whole question before choosing an operation. Restate the task in a sentence: “I need to find the price of one notebook”. Identify the unit. This helps distinguish the required answer from an intermediate calculation.
- 02
Organise the data and relationships
Note quantities, units and what each number means. You do not need to combine all numbers immediately. Look for relationships: a total, a difference or equal groups. Use a small table or simple diagram if helpful.
- 03
Build a model before calculating
Choose an unknown where useful and describe the relationship in words or symbols. Each term must have a meaning in the question. Check compatible units: adding euros to a number of objects does not describe a cost.
- 04
Work through one step at a time
Write calculations in order and retain units in your answers. In an equation, apply the same operation to both sides. If the result changes unexpectedly, return to the last clear step rather than erasing everything.
- 05
Put your answer back into the problem
Substitute your result and reconstruct the original total or relationship. Check whether the value is plausible and answers the question. Checking is not simply repeating the same calculation: it should verify the relationship described in the text.
Three notebooks and a pen
Three notebooks at the same price and a €1.50 pen cost €9 altogether. How much does each notebook cost?
- Let x be the price of one notebook in euros. The three notebooks cost 3x.
- The relationship is 3x + 1.50 = 9. The pen adds a separate cost.
- Subtract the pen’s cost: 3x = 9 − 1.50 = 7.50. Divide by 3: x = 2.50.
- Check: 3 × 2.50 + 1.50 = 7.50 + 1.50 = €9. Each notebook therefore costs €2.50.
Calculating 9 ÷ 3 = 3 immediately and forgetting the pen. Checking gives 3 × 3 + 1.50 = €10.50, which does not match the total.
Now try it yourself.
Four notebooks at the same price and a €2 pen cost €14 altogether. How much does each notebook cost? Write a relationship first and then a check.
Open the check after your attempt
4x + 2 = 14, so 4x = 12 and x = €3. Check: 4 × 3 + 2 = €14. If you obtained €3.50, you divided the total without subtracting the pen’s cost.
What can you do already?
After your attempt, mark each item on paper: independently, with a prompt or still unclear. Use the comparison to choose your next goal.
- I have stated what the answer represents.
- Each number has a meaning and a unit.
- The relationship includes every required cost or quantity.
- My steps are readable and consistent.
- My check reconstructs the original data.
How to fit it into a week.
- Days 1–2: identify the question, data and units in short problems.
- Days 3–4: write relationships and compare correct and incorrect examples.
- Days 5–6: solve similar problems with different numbers and wording.
- Day 7: try a new problem and explain your check independently.
Fit this framework around real assignments and deadlines. The WISE routine totals 45 minutes: 20 working, 5 resting and another 20 working, with the final 5 minutes of the second block for checking and reflection.
For the person supporting the student
Before suggesting an operation, ask “what are you looking for?” and “what does this number represent?”. If calculation is secure but modelling is not, focus the next goal on interpreting the problem rather than adding more calculations.
Common questions
Does one keyword always tell me the operation?
No. Words such as “altogether” or “more” need to be interpreted within the whole relationship. Check what is known and what you need to find.
Do I always need an equation?
No. Arithmetic reasoning, a diagram or a table may fit the level and teacher’s instructions. The meaning of each step should remain clear.
Is the right answer enough?
You also need a method consistent with the question. Explaining and checking steps helps distinguish sound reasoning from a chance answer.
Start with your own schoolwork.
These examples are general. A personalised WeekBook starts from a test, assignment or subject syllabus and is checked by a tutor before delivery.
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