Learning Targets

Standard: CCSS 6.RP.A.3 (a–d) Time: ~40 min Materials: This activity (device or printed), scratch paper Grade 6
Teacher Notes (not printed)

Pacing

  • Launch (5 min): Read "The Engineering Brief." Preview the three tools students must move between fluidly: unit rates (per 1), percents (of a quantity and percent change), and measurement conversions via ratio reasoning.
  • Design work (25–30 min): Students work the ramp, tank, conversion, and budget questions in order, then make a stamped recommendation that integrates all three skills.
  • Debrief (5–10 min): Compare flow-rate reasoning in Q4.1 and the percent-over result in the budget — both are unit-rate comparisons in disguise.

Answer Key

  • Q1.1 — Ramp grade: 1.5 ÷ 12 × 100 = 12.5%. This FAILS the 8.33% (1:12) ADA limit.
  • Q1.2 — Required run: 30 in ÷ 12 = 2.5 ft of rise; at 1:12, run = 12 × 2.5 = 30 ft.
  • Q2.1 — Drain time: 2,400 L ÷ 15 L/min = 160 minutes.
  • Q2.2 — Net fill rate: 20 in − 15 out = 5 L/min net filling.
  • Q3.1 — Tank in gallons: 2,400 ÷ 3.785 ≈ 634 gallons.
  • Q3.2 — Footing in gallons: 40 ft³ × 7.48 gal/ft³ = 299.2 gallons.
  • Q4.1 — Faster pump: A = 360 ÷ 24 = 15 L/min; B = 200 ÷ 16 = 12.5 L/min, so Pump A is faster.
  • Q5.1 — Percent of budget: 0.45 × 8,000 = $3,600.
  • Q5.2 — Percent over budget: overage = 4,320 − 3,600 = 720; 720 ÷ 3,600 × 100 = 20% over.

Common Misconceptions

  • Forgetting to ×100 when turning a ratio (1.5 ÷ 12) into a percent.
  • Dividing by the wrong conversion factor — keep units in the ratio (L ÷ L/gal → gal) to self-check.
  • Computing percent change off the new value instead of the original (use the original budget as the base in Q5.2).

Standard

CCSS 6.RP.A.3 (a–d) — Use ratio and rate reasoning to solve real-world problems, including unit rates, percents, and measurement-unit conversions.

Unit 4 · Math Architect · Rates, Percents & Conversions (6.RP.A.3)

Design Challenge: The Greenway Park Commission

The city hired your engineering firm to design Greenway Park: an accessible entry ramp, a rainwater tank with an irrigation pump, and a native-plant budget. Every decision runs on the same three tools — unit rates, percents, and measurement conversions. Get the math right and the park gets built. Get it wrong and it fails inspection.

Standard 6.RP.A.3 Unit Rates Percent of a Quantity Measurement Conversion STEM Design Cycle
1 · DefineRead the brief, codes & budget.
2 · MeasureRead rates & dimensions off each drawing.
3 · CalculateApply rate, percent & conversion math.
4 · EstimateTurn the math into a build decision.
5 · DecideAdjust to pass inspection & budget.
Stations approved: 0 / 9

The Engineering Brief

A civil engineer turns goals into measured, code-compliant plans. Work through four design stations. Each gives you a tool, a drawing, and a decision. Then write your stamped recommendation and submit.

Deliverable 1 · Rate
Size the ramp and pump using unit rates.
Deliverable 2 · Percent
Check grade compliance and budget allocation.
Deliverable 3 · Convert
Switch between metric and customary units.
Three tools every engineer uses:  Unit rate (amount ÷ 1 unit)  ·  Percent (part ÷ whole × 100)  ·  Conversion (× a ratio equal to 1)
Level 1 · Support

A grade (steepness) is a percent. A flow rate is a unit rate. Reading a gauge in liters, gallons, or cubic feet is a conversion. Engineers use these three ideas every day.

Español: Una pendiente es un porcentaje. Un caudal es una tasa por unidad. Leer un medidor en litros, galones o pies cúbicos es una conversión.

Station 1 · The Accessible Ramp Percent · grade

The entrance sits on a rise. To be wheelchair-accessible (ADA code), a ramp's grade — its steepness as a percent — must be no steeper than 8.33% (a 1 ft rise for every 12 ft of run). Drag the slider; the grade and verdict update live.

run = 12 ft rise 8.3%
Section view · entry ramprun fixed at 12 ft
1.0 ft

grade = (rise ÷ run) × 100 = (1.0 ÷ 12) × 100 = 8.3%

✓ Compliant — within the 8.33% ADA limit.
Level 1 · Support

"Per cent" means "per 100." A 8% grade rises 8 ft for every 100 ft you travel forward. Grade = rise ÷ run, written as a percent.

Español: "Por ciento" significa "por cada 100." Una pendiente de 8% sube 8 ft por cada 100 ft de avance.

Q1.1 — The crew measured a rise of 1.5 ft over the 12 ft run. What is the grade, as a percent? (Round to the nearest tenth.)

%

Level 2 · Enrichment

ADA requires a flat landing after 30 in of rise. The entry rise is 30 in. At the maximum 8.33% grade (a 1:12 ratio), what is the minimum run, in feet?

Q1.2 — Minimum run for a 30 in rise at 8.33% (1:12) grade?

ft

Station 2 · Rainwater Tank & Flow Rate Unit rate

The roof channels rain into a 2,400 L storage tank. The irrigation pump has a flow rate — a unit rate in liters per minute (L/min). Size the system so the tank drains on schedule.

roof catchment 1,800 L capacity 2,400 L full ½ empty PUMP 15 L/min
Schematic · tank & pumppump = 15 L/min
Time pumping Liters moved
2 min 30 L
5 min 75 L
10 min 150 L
1 min (unit rate) 15 L

Q2.1 — At 15 L/min, how many minutes to empty the full 2,400 L tank?

min

Q2.2 — A storm adds water at 20 L/min while the pump removes 15 L/min. What is the net fill rate (L/min)?

L/min

Level 1 · Support

A unit rate is the amount for 1 unit. Time to empty = total ÷ rate. Net rate = in − out.

Español: Una tasa por unidad es la cantidad por 1. Tiempo = total ÷ tasa. Tasa neta = entra − sale.
Level 2 · Enrichment

Two pumps are for sale. Pump A: 360 L in 24 min. Pump B: 200 L in 16 min. Which has the faster unit rate? Type A or B.

Q2.3 — Which pump is faster — A (360 L in 24 min) or B (200 L in 16 min)? Type A or B.

Station 3 · Conversion Lab Measurement conversion

The pump is rated in liters, the city bill is in gallons, and the contractor pours concrete in cubic feet. Convert cleanly between systems.

LITERS metric GALLONS customary CUBIC FT concrete 3.785 L = 1 gal 7.48 gal = 1 ft³
Conversion ladder× a ratio equal to 1
Level 1 · Support

A conversion ratio equals 1, so multiplying never changes the amount — only the unit label. Keep the unit you want on top.

Español: Una razón de conversión es igual a 1. Multiplicar no cambia la cantidad, solo la unidad.

Q3.1 — The tank holds 2,400 L. Using 3.785 L = 1 gal, about how many gallons is that? (Nearest whole gallon.)

gal

Q3.2 — The concrete footing needs 40 ft³. Using 7.48 gal = 1 ft³, how many gallons of volume is that?

gal

Level 2 · Enrichment

The pump moves water at 15 L/min. Write the conversion chain that tells you how many gallons per minute that is, using 3.785 L = 1 gal. (Show your ratio multiplication step by step.)

Station 4 · Native-Planting Budget Percent of a whole

The park has an $8,000 landscaping budget allocated by percent. Read the blueprint pie, verify a dollar amount, then choose a headline tree species and watch the live cost.

Trees 45% Shrubs 25% Ground 20% Mulch 10% Budget $8,000
Budget allocationtotal $8,000

Q4.1 — Trees get 45% of $8,000. How many dollars is that?

$

Choose a headline tree species

Species
—
Tree budget
$3,600
Trees you can buy
—

Trees you can buy = $3,600 ÷ price per tree (a unit-rate use). Cheaper trees → more trees.

Level 2 · Enrichment

After bids, trees actually cost $4,320. By what percent did the tree budget go over its $3,600 plan? (Nearest whole percent.)

Q4.2 — Percent over budget: $4,320 actual vs. $3,600 planned.

% over

Deliverable · Your Stamped Recommendation

Engineers don't just compute — they recommend. Use your numbers to make the final call.

Deliverable: Complete all four stations, write your recommendation above, enter your name in the field below, then press Submit plan & grade to save your score as a PDF or DOC.

Performance Rubric — Greenway Park Commission (6.RP.A.3)

Level Score Descriptor
4 — Exceeds 9 / 9 Computes grade, flow rates, conversions, and percents correctly, including both enrichment items. Writes a clear, number-supported recommendation.
3 — Meets 7–8 / 9 Most rate, percent, and conversion items correct with at most one slip. Reaches a valid build recommendation.
2 — Approaching 4–6 / 9 Some items correct but errors show partial understanding (e.g., inverts a conversion ratio or forgets ×100 for percent).
1 — Beginning 0–3 / 9 Few correct. Needs reteaching on unit rate, percent of a quantity, and converting with ratios.