Public Practice Guide
Use this guide to see the type of reasoning MathRoutine expects for grade 7 discount and markup word problems with answers. The goal is not worksheet volume; it is helping students read the situation, choose a model, and explain why the answer fits.
What Students Practice
Reasoning Patterns
Sample Problems
These grade-specific examples show the kind of student-visible reasoning MathRoutine is designed to support: identifying the important quantities, choosing the right structure, and checking the final answer against the story.
A backpack costs $56 before a 25% discount. What is the sale price?
Answer
$42
Reasoning Strategy
Find 25% of the original price, then subtract it.
AI Support Preview
Separate discount amount from final sale price.
A jacket is marked down 20%, then the sale price is taxed 6%. The original price is $75. What is the final cost?
Reasoning Strategy
Apply the discount first, then apply tax to the discounted price.
AI Support Preview
Make the changing base explicit so the percent is not applied to the wrong amount.
A student answered 36 questions correctly on a 45-question quiz. On a retake, the student answered 42 correctly. By how many percentage points did the score improve?
Reasoning Strategy
Find each percent score, then compare the percentages.
AI Support Preview
Distinguish percentage points from percent increase.
A club had 80 members. Membership increased by 25% in September and then decreased by 10% in October. How many members were in the club after October?
Reasoning Strategy
Use the new September total as the base for the October decrease.
AI Support Preview
Show why the second percent does not use the original 80 as its base.
A backpack costs $64 before a 15% discount. What is the sale price?
Reasoning Strategy
Find the discount amount and subtract it from the original price.
AI Support Preview
Distinguish discount percent from final percent paid.
A class answered 42 out of 50 review questions correctly. What percent were correct?
Reasoning Strategy
Use part divided by whole, then convert to percent.
AI Support Preview
Label 42 as the part and 50 as the whole.
A game score increased from 80 to 92 points. What was the percent increase?
Reasoning Strategy
Find the increase, then compare it to the original score.
AI Support Preview
Warn that percent change uses the starting value as the base.
A $80 backpack is discounted by 15%. What is the sale price?
Answer
$68
Reasoning Strategy
Find 15% of 80 and subtract the discount.
AI Support Preview
Distinguish discount amount from price paid.
Keep Practicing
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Practice Ladder
Modeled after middle-school workbook expectations: combine fluency with ratio, percent, equation, and geometry reasoning rather than only isolated computation.
Begin with unit rate or percent-part-whole identification.
Add a missing value, comparison, discount, markup, or scale factor.
Finish with a context where the base quantity is hidden or changes during the problem.
Assessment Signals
A guide is useful only if it clarifies what teachers and parents should look for in student work. MathRoutine tracks these signals during practice instead of treating every miss as the same mistake.
Common Mistakes
Learning Loop
A strong word problem platform should not only say right or wrong. It should notice the pattern: missed unit rate, ignored leftover, reversed comparison, wrong base percent, or equation setup error.
1
Attempt
2
Diagnosis
3
Next practice
Diagnosis Examples
Each word problem should create evidence about setup, calculation, vocabulary, hidden quantities, or final-question confusion. These examples show what MathRoutine is designed to separate after an attempt.
If the attempt shows
The student uses the final amount as the percent-change base.
Likely diagnosis
Original amount is not being protected as the reference whole.
Next practice
Use percent-change stories that explicitly mark original, change, and final.
If the attempt shows
The student subtracts the percent from 100 but forgets to apply it to the amount.
Likely diagnosis
Percent language is understood, but the part-whole calculation is incomplete.
Next practice
Practice percent-of-a-number problems inside shopping and survey contexts.
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