The Percent Report
The school news data desk measures everything in percents — enrollment growth, attendance drops, how wrong the predictions were, and what the club's savings earn. One skill under it all: divide the change by the RIGHT baseline.
Common Core standards covered
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Teacher-facing overview
Big idea: Solve multistep percent problems involving percent increase and decrease, percent error, and simple interest, attending to the correct base in each.
Student target: “I can compute percent increase and decrease (change over ORIGINAL), percent error (miss over ACTUAL), and simple interest (I = prt), naming the baseline in each.”
Success criteria: I can compute percent change with the original as the base. · I can compute percent error with the actual value as the base. · I can run I = prt with time in years, including fractional years. · I can explain why up r% then down r% does not return to the start.
Essential question
Thirty more students, twelve fewer attendees, a $15 miss, $24 of interest — every headline needs a percent. Percent OF WHAT? The denominator decides everything.
Learning target: I can compute percent increase and decrease (change over ORIGINAL), percent error (miss over ACTUAL), and simple interest (I = prt), naming the baseline in each.
Success criteria
- I can compute percent change with the original as the base.
- I can compute percent error with the actual value as the base.
- I can run I = prt with time in years, including fractional years.
- I can explain why up r% then down r% does not return to the start.
Why this matters
7.RP.A.3's list ends with percent increase and decrease and percent error, and this lesson gives them the one idea that organizes all of it: every percent is a ratio to a CHOSEN baseline, and the three formulas differ only in which baseline they choose. That's also why up-25-then-down-25 loses money — the two 25s use different baselines. Simple interest brings the year's k machine to banking (I/t = pr is proportionality in time), and the news-desk framing builds the data literacy every citizen needs when headlines shout percents.
Students should already be able to
- Multiplier machine and chains — The Sneaker Exchange.
- Fraction-to-percent conversion.
- One-variable equations — The Goal Line.
Vocabulary to define explicitly
- Percent change
The change divided by the ORIGINAL amount: (new − original)/original.
Example: 250 → 280: 30/250 = 12% increase.
Not an example: 30/280 ≈ 10.7% divides by the new value — a different (and wrong) question.
🔒 3 more terms with examples and non-examples — Percent error, Simple interest (I = prt), Baseline (the base) — are defined in the full lesson. See plans →
Where this shows up outside the classroom
Assessment plan
Formative — for feedback during the lesson
- Warm-up fact-check of the 30% headline.
- Fact-check sheet baselines during desk work.
- The columnist correction in headline form.
Summative — the graded evidence: The exit ticket (change, error, interest — all with baselines), scored with the four-criterion rubric.
The task students work on
The school paper's data desk fact-checks four stories before Friday's edition. GROWTH: enrollment rose from 250 to 280 — the draft headline says 'up 30%.' SLUMP: game attendance fell from 80 to 68 — how bad, in percent? THE FORECAST: the events team predicted 60 people at the fair; 75 came — score the prediction with percent error. THE TREASURY: the club's $400 sits at 3% simple interest for 2 years — how much does it earn, and what's the balance? And the columnist's claim to test: 'the stock went up 25% then down 25%, so it's back where it started.' Every fact-check names its baseline.
Fact-check sheet — baseline first, then the percent.
| Story | Numbers | Baseline | Computation | Verdict |
|---|---|---|---|---|
| Growth | 250 → 280 | |||
| Slump | 80 → 68 | |||
| The forecast | predicted 60, actual 75 | |||
| The treasury | $400, 3%, 2 years | |||
| The columnist | up 25%, down 25% |
Anticipated student strategies
Baseline-first prevents the classic errors, the multiplier translation connects to the chain machine, and benchmarks keep both honest at a glance.
- Baseline-first protocol. The student answers 'percent of WHAT?' before dividing — original for change, actual for error, principal for interest.
The organizing habit. Share first; every error in this domain is a baseline error wearing arithmetic clothes.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
The writer counted 30 STUDENTS and stapled a percent sign on. The percent question divides: 30/250 = 12%. Benchmark check: 10% of 250 is 25, and 30 is a bit more — 12% is credible. Board the desk's first law: percent of WHAT — name the baseline before you divide.
Listen for: The growth is measured against where we STARTED — 'up from 250.' Dividing by 280 answers a different question (what fraction of the new total is new).
Board the baseline table: change→original, error→actual, interest→principal. Interest side note: t is in YEARS, so 18 months enters as 1.5.
- Same skeleton every time: (relevant amount)/(chosen baseline).
- I = prt is the k machine with time attached — p·r is dollars per year, a unit rate.
Listen for: Dividing by the guess grades us on our own curve. Reality is the standard — the error's ruler must be the actual value.
🔒 The remaining 4 steps — fully scripted with teacher-says lines, discourse questions, look-fors, and interventions — are in the full lesson. See plans →
Misconceptions and how to respond
- “250 to 280 is a 30% increase — the change is 30.” Thirty STUDENTS, not thirty percent. The percent divides by the original: 30/250 = 12%. A change only becomes a percent after meeting its baseline.
- “Percent error divides by the prediction.” — the teacher response is in the full lesson.
- “Up 25% then down 25% cancels out.” — the teacher response is in the full lesson.
- “18 months at 4% means t = 18.” — the teacher response is in the full lesson.
🔒 Every misconception ships with a tested classroom response. See plans →
Scaffolded practice
The workbook follows gradual release rather than a page of blank prompts: 1 fully worked, 1 partially completed, then 5 independent.
- I doFact-check the growth story: enrollment 250 → 280, drafted as 'up 30%.'
🔒 6 more prompts across all three release tiers are in the full lesson. See plans →
Worked solutions and scaffolds for every prompt are in the downloadable kit, included with membership. See plans and pricing.
Exit ticket
- Club membership grew from 40 to 46. Percent change, with the baseline named.
🔒 2 more exit-ticket questions are in the full lesson. See plans →
Worked answers, the completed answer tables, and the scoring rubric are in the downloadable kit, included with membership. See plans and pricing.
Printable handouts in the kit
All handouts are in Printable_Handouts.pdf inside the kit download.
Materials and classroom resources
Student experience
Students enter through a low-floor prompt, build or sketch a model, test a strategy, revise their thinking, collaborate, and present a final solution. The task remains accessible while allowing for sophisticated reasoning.
Detailed facilitation notes
- Step 1: Measure percent increase and decrease against the original. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Score predictions with percent error against the actual. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Compute simple interest with I = prt. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Bust the up-then-down 'it evens out' myth. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: The baseline question — 'percent OF WHAT?' — is the built-in scaffold; every card asks it first. Extend with the round-trip asymmetry and the two-account interest race.
Language support: “I started by…”, “My model shows…”, and “I know my answer is reasonable because…”.
Extension: Require a second solution, alter a condition, or have students write a challenge for another group.
Accessibility: Manipulatives, enlarged visuals, oral response choices, partner reading, and reduced-copy student pages.
Assessment plan
Formative checks: Strategy choice, accuracy, representation, collaboration, and explanation.
End evidence: One percent change, one percent error, and one interest computation — each with its baseline named.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.