Percent HQ
Percent is just a ratio with 100 in the second seat. At fundraiser headquarters, students find parts from percents, recover wholes from parts, and convert units with ratio reasoning — all on the same double number line.
Common Core standards covered
- 6.RP.A.3Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
- 6.RP.A.3.cFind a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
- 6.RP.A.3.dUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Teacher-facing overview
Big idea: Find a percent of a quantity as a rate per 100, solve problems finding the whole given a part and the percent, and use ratio reasoning to convert measurement units.
Student target: “I can compute a percent of a quantity as a per-100 rate, find the whole when given a part and its percent, and convert units by ratio reasoning.”
Success criteria: I can place a percent problem on a double number line. · I can find a part: r% of Q as (r/100) × Q. · I can find the whole: part ÷ percent-as-fraction. · I can convert units by multiplying by a for-every ratio.
Essential question
Thirty percent means 30 out of every 100. How does that one sentence find parts, recover wholes, and even convert feet to inches?
Learning target: I can compute a percent of a quantity as a per-100 rate, find the whole when given a part and its percent, and convert units by ratio reasoning.
Success criteria
- I can place a percent problem on a double number line.
- I can find a part: r% of Q as (r/100) × Q.
- I can find the whole: part ÷ percent-as-fraction.
- I can convert units by multiplying by a for-every ratio.
Why this matters
6.RP.A.3.c-d turns ratio reasoning into two of life's most-used skills. Percent-of and whole-from-part are the same double number line read in opposite directions — a symmetry that prevents the divide-or-multiply guessing that plagues percent work for years. And unit conversion as multiply-by-a-ratio is the habit every science class assumes. Grade 7 builds tax, tip, and discount directly on this per-100 foundation.
Students should already be able to
- Ratio tables and unit rates — Smoothie Bar Ratios.
- Fraction and decimal equivalents.
- Multiplication and division of decimals.
Vocabulary to define explicitly
- Percent (per 100)
A ratio whose second quantity is always 100.
Example: 30% means 30 for every 100 — of dollars, students, anything.
Not an example: '30%' with no whole named — 30 per 100 OF WHAT?
🔒 3 more terms with examples and non-examples — Part from percent, Whole from part, Conversion ratio — 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 line reads.
- Board setups during floor work.
- Supply-run direction checks.
Summative — the graded evidence: The exit ticket (both directions plus a conversion), scored with the four-criterion rubric.
The task students work on
Fundraiser HQ tracks everything in percents. THE THERMOMETER: 30% of the $40 mini-goal — how many dollars? THE BIG BOARD: 45% of the 260 raffle tickets are sold — how many? THE MYSTERY JAR: $15 in the jar is 25% of its goal — what's the goal? THE RECOUNT: 18 volunteers is 30% of sign-ups — how many signed up? THE SUPPLY RUN: 3 feet of banner per table (in inches?), 4.5 kg of popcorn (in grams?), and a 90-minute shift (in hours?). Every answer rides a double number line or a for-every ratio.
HQ board — line or table shown for every job.
| Job | Setup | Work | Answer |
|---|---|---|---|
| 30% of $40 | |||
| 45% of 260 tickets | |||
| $15 is 25% of the goal | |||
| 18 is 30% of sign-ups | |||
| 3 ft → in; 4.5 kg → g; 90 min → h |
Anticipated student strategies
The line gives both directions one home, ten-percent steps make it mental, decimals compress it — picture, strategy, shorthand.
- Double number line. The student marks percent below, quantity above, and rides landmarks (10%, 25%, 50%) to the answer.
The unifying picture — both directions live on one line. Share first.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
Line drawn: 100% ↔ 40, so 10% ↔ 4, and 30% ↔ 12. The per-100 sentence stated: 30 of every 100 goal-dollars are in. Decimal shorthand ties on: 0.30 × 40 = 12.
Listen for: 100% split into ten equal steps — each is a tenth of the whole. The line makes the rule.
Recount modeled by ten-stepping: 30% ↔ 18 → 10% ↔ 6 → 100% ↔ 60.
- Part = r% of whole; whole = part ÷ (r/100).
- Under-100 percent → whole > part. Check every answer against it.
Listen for: $15 is only a quarter of the goal; recovering the whole scales UP. If the 'whole' comes out smaller, the direction was wrong.
🔒 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
- “30% of 40 is 30 × 40.” Percent is per-HUNDRED: 30/100 × 40 = 12. Losing the 100 invents money — the line never loses it.
- “To find the whole from $15 at 25%, take 25% of 15.” — the teacher response is in the full lesson.
- “Converting always multiplies.” — the teacher response is in the full lesson.
- “Percents can't pass 100.” — 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 4 independent.
- I doFind 45% of 260 raffle tickets by ten-percent stepping, then confirm with decimals.
🔒 5 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
- 40% of 35 raffle bags — how many?
🔒 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: Read percent as per-100 on a double number line. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Find parts from percents. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Recover the whole from a part and its percent. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Convert units with the same ratio reasoning. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: The double number line carries every problem; extend with over-100% and chained conversions.
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 part-from-percent, one whole-from-part, and one unit conversion, each on a double number line or ratio table.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.