Daily SHSAT mistake lab
SHSAT Daily Mistake #6: The Percent-Change Base Trap
Percent-change questions are often missed because students use the wrong base. A decrease after an increase is taken from the new amount, not the starting amount.
Free printable mini-lesson
Daily Mistake #6: The Percent-Change Base Trap
Print one SHSAT-style percent-change question, let your child label each base, then review why the tempting shortcut fails.
- One focused percent-change word-problem question
- Answer key with a parent-friendly explanation
- Next-step links to the free tracker and diagnostic
Download printable PDF
Why This Mistake Matters
A common SHSAT-style math mistake is treating two percent changes as if they happen from the same base.
If a price increases by 20% and then decreases by 25%, the 25% decrease is not taken from the original price. It is taken from the increased price.
The Student Move
Before calculating, write the starting amount as x. Then apply each percent change in order as a multiplier.
For example, a 20% increase means multiply by 1.20. A 25% decrease from the new amount means multiply by 0.75.
One-Question Practice
Question: A price increases by 20%, then decreases by 25% from the new price. The final price is $90. What was the original price?
Correct answer: $100.
Why: after the 20% increase, the price is 1.20x. After the 25% decrease, the price is 0.75 x 1.20x = 0.90x. If 0.90x = 90, then x = 100.
What to Watch For Next
If your child misses this kind of item, do not only review percent formulas. Ask them to state the base for every percent before computing.
If percent-change errors appear with ratio-base or word-problem translation misses, use the free weak-spot tracker after the next practice set. If the weak spot is unclear, use the $1.99 diagnostic to map both ELA and math before choosing the next practice block.
Recommended next step
Use the Diagnostic First, Then Build a 4-Week Plan
For most families, the cleanest summer path is one printable diagnostic, followed by short daily ELA and math practice where the child actually needs it.
Questions Parents Ask
What is the percent-change base trap?
It is the mistake of applying multiple percent changes to the same starting amount when later changes are actually based on the new amount.
How should a rising Grade 8 student check this?
Use x for the starting amount and apply each percent change in order with a multiplier, such as 1.20 for a 20% increase or 0.75 for a 25% decrease.
What should parents do after this mini-lesson?
Use a few focused percent-change and ratio word problems. If the student keeps choosing the wrong base, use the free tracker or the $1.99 diagnostic to see whether word-problem translation is the main weak spot.
Is this affiliated with SHSAT, NYC schools, or any test publisher?
No. Original Practice Lab creates independent practice materials with original questions. The materials are not affiliated with, endorsed by, or sponsored by any test publisher, school district, or testing organization.
