A Four-Step Method for Multi-Step Word Problems in Mathematical Reasoning
Learn a simple four-step method for solving multi-step word problems in NSW OC and Selective Mathematical Reasoning: understand, plan, solve and check.
A Four-Step Method for Multi-Step Word Problems in OC and Selective Mathematical Reasoning
Multi-step word problems can be challenging because students need to do more than calculate correctly.
They have to understand the situation, decide what information matters, choose the right operations, complete the calculations accurately, and check whether the answer makes sense.
This kind of reasoning appears regularly in both NSW Opportunity Class and Selective Mathematical Reasoning. Questions may combine familiar ideas such as money, fractions, time, measurement, ratios or number operations in an unfamiliar situation.
A simple way to approach these questions is:
Understand → Plan → Solve → Check
The method is easy to remember and can be applied to many different types of Mathematical Reasoning questions.
Step 1: Understand
Before calculating, make sure you understand what the question is asking.
Students should ask:
What information have I been given?
What am I trying to find?
Which details are important?
Are the quantities using the same units?
A common temptation is to see two numbers and immediately start adding, subtracting, multiplying or dividing.
Instead, first identify the structure of the problem.
Example
A school buys 9 boxes of pencils. Each box contains 24 pencils.
It gives 75 pencils to Year 4 students and 68 pencils to Year 5 students.
How many pencils are left?
We know:
9 boxes
24 pencils in each box
75 and 68 pencils are given away
We need to find the number remaining.
Before subtracting anything, we first need to know how many pencils there were altogether.
That leads to the next step.
Step 2: Plan
Decide what calculations are needed before starting them.
For the pencil problem:
Find the total number of pencils.
Find the total number given away.
Subtract the amount given away from the starting total.
A quick plan could be:
9 × 24
75 + 68
total − given away
This takes only a few seconds, but it can stop students from losing track halfway through the question.
Work backwards from the question
Another useful strategy is to ask:
“What do I need to know immediately before I can answer this?”
To find how many pencils are left, we need:
Starting amount − amount used
If either of those values is still unknown, calculate it first.
This is especially useful when the problem contains three or four steps.
Step 3: Solve
Once the plan is clear, carry out the calculations carefully.
For the example:
9 × 24 = 216
75 + 68 = 143
216 − 143 = 73
So there are 73 pencils left.
The important point is that the student did not simply use the numbers in the order they appeared. They followed the structure of the problem.
Clear working also helps:
Total pencils = 216
Given away = 143
Left = 73
This is useful in both OC and Selective Mathematical Reasoning because calculators are not allowed.
Step 4: Check
Students should not stop immediately after finding an answer.
Checking does not always mean doing the full calculation again.
A quick check can ask:
Does the answer make sense?
In the pencil example, there were 216 pencils initially and 143 were given away.
An answer of 73 is reasonable.
An answer greater than 216 would clearly be impossible.
Use estimation
Estimation is also useful.
9 × 24 is about 225.
75 + 68 is about 140.
225 − 140 is about 85.
So an exact answer of 73 is within a sensible range.
A result such as 173 or 7 should make the student check their working.
Some problems are easier backwards
The four-step method does not mean every question should be solved in the same way.
Sometimes working backwards is more efficient.
Example
Lena has some money.
She spends $18 on a book.
She then spends half of the money she has left on a game.
After that, she has $21 remaining.
How much money did she have at the start?
Understand
We know the final amount, but not the starting amount.
Plan
Work backwards:
$21
→ undo the halving
→ add back $18
Solve
Before buying the game:
21 × 2 = 42
Before buying the book:
42 + 18 = 60
So Lena started with $60.
Check
$60 − $18 = $42
Half of $42 is $21, leaving $21.
The answer works.
This shows why the planning step matters. Sometimes the best strategy is not the most obvious one.
When should students draw a diagram?
Not every word problem needs one, but diagrams can be useful for:
fractions
sharing problems
ratios
distance
perimeter and area
time sequences
repeated patterns
For example, if a problem says that half of an amount is used and then one third of what remains is used, a quick bar model may be easier to understand than trying to hold everything mentally.
The diagram does not need to look neat. Its purpose is simply to make the relationships clearer.
Use the answer choices strategically
Because OC and Selective Mathematical Reasoning questions are multiple choice, the options can also help with checking.
After solving, students can ask:
Is my answer listed?
Are some options obviously too large or too small?
Does one option represent a likely intermediate result rather than the final answer?
Would testing the options be quicker than solving from scratch?
The answer choices should not replace understanding, but they can sometimes save time.
Speed comes after understanding
Under time pressure, students may feel they need to calculate immediately.
But spending a few seconds understanding and planning can actually make the whole solution faster.
A student who starts with the wrong operation may waste much more time correcting it later.
For multi-step problems, efficiency means choosing the right path before calculating.
A quick version students can remember
Students can reduce the whole method to four questions:
Understand
What do I know, and what do I need?
Plan
What steps will get me there?
Solve
Do the calculations clearly.
Check
Does my answer make sense?
They do not need to write these four headings for every question. The goal is for the process to become automatic through practice.
At Selective Journey, students can practise Mathematical Reasoning questions with detailed explanations and review their answers after each test.
For Selective High School preparation, explore the NSW Selective practice tests.
For Opportunity Class preparation, explore the NSW OC practice tests.
You can also register for a free trial.