Learning Targets

Standard: CCSS 6.RP.A.1–3 Time: ~40 min Materials: This activity (device or printed), scratch paper Grade 6
Teacher Notes (not printed)

Pacing

  • Launch (5 min): Read "The Brief" together. Anchor the mixing ratio idea using the beaker figure: "for every 1 part concentrate we add 4 parts water." Stress that a ratio compares two amounts.
  • Design work (25–30 min): Students complete Task 1 → 4 in order. Task 1 is a hands-on mixer; Task 4 (Pump Selection) uses unit rates students built in Task 3.
  • Debrief (5–10 min): Compare the two unit-rate strategies in Task 4, and discuss the Level 2 scaling/inequality extensions.

Differentiation

  • Level 1 (support): Use the green callouts and bilingual (EN/ES) prompts. Let students use the interactive mixer to see equivalent ratios before computing. Provide a printed ratio-table scaffold.
  • Level 2 (enrichment): Have students justify why equivalent ratios share the same unit rate, and solve the scaling problem for an arbitrary number of bottles.

STEM Connection

  • This is an authentic process-engineering task: process and fluids engineers design beverage and water-treatment systems by holding a mixing ratio constant while scaling volume, and by comparing flow rates (a unit rate, liters per minute) to size pumps. Students do the exact reasoning a real systems engineer uses.
Unit 1 · Math Architect · Ratios & Unit Rates (6.RP)

Design Challenge: The Stadium Hydration Station

You are a systems engineer for AquaWorks. Brookside Stadium needs a hydration station that mixes electrolyte concentrate with water and refills bottles fast on a hot game day. Use ratios, ratio tables, and unit rates to mix the formula correctly, scale it for the crowd, and select the right pump.

Standard 6.RP.A.1–3 Mixing Ratios Ratio Tables Unit Rates Process Engineering
1 · DefineRead the brief, the formula ratio & constraints.
2 · MixHold the 1 : 4 ratio while scaling volume.
3 · ScaleBuild a ratio table for the whole crowd.
4 · RateFind the flow rate (L/min) for each pump.
5 · DecideCompare unit rates & pick the pump.
Specs approved: 0 / 8

The Brief

The stadium operations team handed you the official AquaWorks formula and the day's targets. Your station has a concentrate tank, a water line, a mixing tank, and a fill nozzle. The schematic below shows how they connect.

FORMULA  1 part concentrate : 4 parts water  ·  serve ice-cold & refill fast

Concentrate 1 part Water 4 parts Mixing Tank electrolyte mix fill nozzle → bottle
System schematic · 1 : 4 formulanot to scale
Deliverable 1
Mix the formula so the ratio is exactly 1 part concentrate to 4 parts water.
Deliverable 2
Scale the recipe to fill enough mix for the whole crowd with a ratio table.
Deliverable 3
Compare pump flow rates (L/min) and pick the best pump for the line.
Level 1 · Support

A ratio compares two amounts. "1 : 4" means for every 1 cup of concentrate you add 4 cups of water — so 5 cups total. A unit rate tells you "how much for 1" — like liters per 1 minute.

Español: Una razón compara dos cantidades. "1 : 4" significa que por cada 1 de concentrado agregas 4 de agua. Una tasa unitaria dice "cuánto por 1", como litros por 1 minuto.

Task 1 · Mix the Formula Equivalent ratios

Use the mixer to batch the formula. Add scoops of concentrate and cups of water. The batch is correct only when the ratio is equivalent to 1 : 4. Watch the tank fill as you adjust it.

Mixing beaker 1 : 4
Live mix preview5 cups total
1
4
Current ratio
1 : 4
Simplest form
1 : 4
Status
—

Q1.1 — Set the mixer to a batch that is equivalent to 1 : 4 but uses 3 parts concentrate. How many parts of water do you need?

parts water

Level 1 · Support

Equivalent ratios are made by multiplying both numbers by the same amount. 1 : 4, then ×3 on each part, gives 3 : 12.

Español: Las razones equivalentes se hacen multiplicando los dos números por la misma cantidad. 1 : 4, por 3, da 3 : 12.

Task 2 · One Bottle, One Rate Unit rate

Each sports bottle holds 500 mL (0.5 L). The station mixed a 15 L batch that filled 30 bottles. Engineers always reduce to a unit rate — the amount for exactly one — so the system is easy to scale.

Batch 15 L … 30 bottles 0.5 L each
Batch → bottles0.5 L per bottle

Q2.1 — Unit rate: how many liters of mix per 1 bottle?

L / bottle

Q2.2 — Using that unit rate, how many liters of mix are needed to fill 120 bottles?

L

Level 1 · Support

Unit rate = total ÷ number of items. To go back up, multiply the unit rate by how many you want.

Español: Tasa unitaria = total ÷ número de objetos. Para volver a subir, multiplica la tasa unitaria por la cantidad que quieres.
Level 2 · Enrichment

Write a rule that gives the liters of mix L for any number of bottles b. (Hint: it uses your unit rate.) Then explain why that rule is the same as the ratio 15 L : 30 bottles.

Task 3 · Scale the Batch Ratio table

The crowd needs a big batch. Keep the formula at 1 : 4 and fill in the ratio table so every row is an equivalent ratio. Each row must keep concentrate : water = 1 : 4 (and total = concentrate + water).

Concentrate (L) Water (L) Total mix (L)
1 4 5
3 15
20 25
12 48

Double number line · stays 1 : 4 Concentrate (L) 1 3 5 12 Water (L) 4 12 20 48
Each pair multiplies 1 : 4×3, ×5, ×12
Level 2 · Enrichment

Every row of this table has the same unit rate of water per concentrate. What is that unit rate, and why does it never change even though the totals grow?

Task 4 · Choose the Pump Compare unit rates

Three pumps can move the mix to the fill nozzle. The faster the flow rate (liters per minute), the quicker the lines move. Flow rate is a unit rate: liters per 1 minute. Find each rate, then pick the fastest pump.

Liters Minutes 2 4 6 A B C
Steeper = faster flowL vs. min

Q4.1 — Pump A moves 18 L in 3 min. Flow rate?

L / min

Q4.2 — Pump B moves 20 L in 5 min. Flow rate?

L / min

Select the pump for the line

Selected
—
Flow rate
—
Decision
—

Q4.3 — With the fastest pump, how many minutes to move your 60 L crowd batch?

min

Level 1 · Support

Flow rate = liters ÷ minutes. The bigger the L/min number, the faster. Time = liters ÷ flow rate.

Español: Tasa de flujo = litros ÷ minutos. Número mayor = más rápido. Tiempo = litros ÷ tasa de flujo.
Level 2 · Enrichment

Pump C moves 9 L in 3 min. Show its unit rate and explain, using the graph, why a steeper line always means a faster pump.

Engineer's Sign-off

When the formula mixes 1 : 4, the table scales correctly, and you have chosen the fastest pump, submit your design report. Enter your name in the field below, then press Submit design & grade to save your score as a PDF or DOC.

Performance Rubric — Hydration Station (6.RP.A.1–3)

Level Score Descriptor
4 — Exceeds 8 / 8 Builds equivalent ratios accurately, completes the ratio table, computes every unit rate correctly, and selects the fastest pump. Can explain why equivalent ratios share one unit rate.
3 — Meets 6–7 / 8 Computes most ratios and unit rates correctly with at most one slip. Completes the table and reaches a valid pump choice.
2 — Approaching 4–5 / 8 Finds simple unit rates but struggles to keep the ratio constant while scaling, or compares rates inconsistently. Partial table.
1 — Beginning 0–3 / 8 Few correct rates. Confuses ratio with unit rate or misreads the formula. Needs reteaching on equivalent ratios and unit rates.