Common Mistakes
Geometry · Honors Math · Similarity
Real mistakes students make on dilations and scale factor—and how to catch and fix them.
Focus for this topic: Perform dilations; relate scale factor to corresponding lengths.
Frequent mistakes
### 1. Combining unlike terms
What it looks/sounds like: Adding 3x² and 3x as if they were like terms.
Why it happens: Same coefficient feels “alike” even when degrees differ.
How to fix: Group by identical variable powers before adding.
### 2. Forgetting the GCF first
What it looks/sounds like: Jumping to trinomial factoring while a common factor remains.
Why it happens: Students hunt for number pairs and skip the greatest common factor.
How to fix: Always factor out the GCF, then factor what remains.
### 3. FOIL / distribution errors
What it looks/sounds like: Missing one of the four products when multiplying binomials.
Why it happens: Mental FOIL drops a term under speed pressure.
How to fix: Write a 2×2 area model or check by expanding again.
### 4. Sign errors in factoring
What it looks/sounds like: Factors that multiply to the right product but add to the wrong sum.
Why it happens: Students match the constant and ignore the middle sign.
How to fix: Check by expanding the candidate factors before moving on.
### 5. Assuming every trinomial factors nicely
What it looks/sounds like: Forcing integer factors when none exist.
Why it happens: Classroom practice over-represents “nice” factorizations.
How to fix: If pairs fail, say so and switch method (complete square / formula) when allowed.
How to avoid them
1. Restate what 3.1 asks in one sentence before computing. 2. Name the method or representation you will use. 3. Define variables with units before writing symbols. 4. Check one easy special case, diagram estimate, or unit/domain check after a long solution. 5. Ask: does this answer match the required form and the prompt?
Quick self-check
- [ ] I can name two mistakes for 3.1
- [ ] I can explain why one of those mistakes happens
- [ ] I can fix one wrong solution by naming the broken step
- [ ] I can check that my final form matches what the prompt asked
Related materials
- Parent Guide, Exam Strategy, and Study Guide for 3.1 (same folder)
- Review and practice-test tiers under this topic when present