Problem: A jacket costs $80 and is discounted by 25%. What is the sale price?
Solution:
25% of $80 = $20
$80 − $20 = $60
You can read those lines in a few seconds. Learning from them requires explaining why they work and recognizing when the same method applies.
Worked examples show a task, its intermediate steps, and a completed solution. They are useful when you are learning a process that would otherwise require too much unguided searching.
The challenge is to study the reasoning rather than reproduce the page.
MIT Open Learning’s guide to worked and faded examples emphasizes self-explanation, varied examples, and gradually removing support as learners become more proficient.
The annotated lesson below uses fictional prices. Its purpose is to demonstrate a study method, not to give shopping advice.
Example A: Add the Missing Explanation
Return to the jacket problem.
25% of $80 = $20
The important question is what $20 represents. It is the amount removed from the original price.
$80 − $20 = $60
This subtraction produces the price remaining after the discount.
Now write the explanation beside the calculation:
“I first calculate the discount amount, then subtract it from the original price because the question asks what the customer pays.”
That sentence connects the operations to the task.
Without it, a student might remember that 25% of $80 is $20 and give $20 as the sale price. The arithmetic would be correct for a different question.
Explain the Choice Before Repeating the Calculation
For each step, ask:
- What quantity am I finding?
- Why is this operation appropriate?
- What does the result represent?
- Does the answer address the original question?
These are suggested study prompts. You do not need to write a paragraph beside every routine calculation once the reasoning is secure.
While learning, however, a short explanation can expose confusion that neat working conceals.
The Australian Education Research Organisation’s explicit-instruction guide recommends using worked examples to demonstrate learning and reducing support as students develop expertise.
The timing of that reduction should reflect understanding, not simply the number of examples copied.
Example B: Complete the Missing Step
A bag costs $120 and is discounted by 15%.
The partially completed solution reads:
15% of $120 = $18
________________
Complete the missing line and explain it.
The final step is:
$120 − $18 = $102
This task requires you to supply part of the method rather than follow a fully visible answer.
If you write $18 as the final answer, return to the meaning of the intermediate result. You have found the discount amount, while the task asks for the price after the discount.
A missing step should be chosen carefully. Removing too much support before you understand the process can turn the exercise into guessing.
For a teacher or tutor, the student’s explanation helps determine what to show next. For an independent learner, an answer key or knowledgeable person can provide feedback.
An Alternative Route
You can also recognize that a 15% discount leaves 85% of the original price:
85% of $120 = $102
Compare the two methods.
Both address the same relationship, but one calculates what is removed and the other calculates what remains.
Understanding that connection is more flexible than memorizing a single sequence of symbols.
Example C: Decide Whether the Method Fits
A different question asks:
“A jacket now costs $60 after a 25% discount. What was the original price?”
The numbers resemble the first example. The unknown quantity has changed.
Subtracting another 25% from $60 would not reconstruct the original price. The $60 represents 75% of that original amount.
The calculation is:
$60 ÷ 0.75 = $80
Explain the difference before practicing.
In the first problem, the original price was known. In this problem, the reduced price is known.
Comparing related problems helps reveal which information determines the method. It also discourages choosing an operation because familiar numbers appear.
Use questions appropriate to your course and current level. If the underlying percentage relationship is unclear, seek an explanation before extending the exercise further.
Now Solve Without the Model
Close the example and attempt a new problem:
“An item costs $150 and is discounted by 20%. What is the sale price?”
Write the working independently.
The discount is $30, leaving a sale price of $120.
Then explain how you checked the result. For example, you might calculate that 80% remains and confirm that 0.8 × $150 gives the same answer.
A correct response provides evidence about this attempt. It does not establish that you will recognize every related problem or remember the method indefinitely.
The Institute of Education Sciences’ guide to organizing instruction and study recommends combining worked solutions with problems learners solve themselves.
That combination gives examples a clear role: support the reasoning that independent work will later require.
Carry the Method Into Other Subjects
The same approach can be adapted beyond arithmetic.
For a sample paragraph, identify how evidence supports the main claim. A science calculation, explain the selected relationship and units. For a short program, trace how each step changes the data.
The example should match the skill being learned. A polished final product alone may conceal the decisions a beginner needs to see.
When studying a video demonstration, pause at a meaningful decision and predict the next step. Then compare your reasoning with the explanation provided.
Keep a record of the point where your prediction differed. That tells you where further instruction may help.
Finish a study session with a fresh task rather than another copy of the same solution. Your notes should show an explanation, a completed gap, and an independent attempt.
The next time you open a worked example, cover the final line for a moment. Explain what the preceding steps establish and predict what the task still requires. Then uncover the answer and examine the reasoning behind any difference.
