Grade 6 Math WebQuest · Unit 10 · 6.G.A.2 & 6.G.A.4

The Aquarium Build-Out

Harbor City is opening the Blue Current Aquarium, and the build team has hired your engineering crew to design the acrylic display tanks. Every tank must hold the right amount of water, and every panel of clear acrylic must be cut to the exact size. Find the volume each tank holds, unfold each tank into a net, and use the net to order the surface area of acrylic — then submit your build packet before opening day.

⏱ 2–3 class periods 🧊 Volume of prisms 📦 Nets 📐 Surface area

Your Crew Gets the Contract

A display tank is a sealed box of glass and acrylic. Engineers think about it two completely different ways. The inside is hollow space that holds water — that is volume, measured in cubic units. The outside is flat panels that must be cut and glued — that is surface area, measured in square units. The tool that connects them is the net: the tank unfolded flat, like a cardboard box opened up.

The Driving Question

How do engineers use volume, nets, and surface area to build a container that holds exactly the right amount and uses exactly the right materials?

Level 1 · Support Volume = how much space fills the inside (cubic units, like ft³). Surface area = how much material covers the outside (square units, like ft²). Picture filling a tank with sugar cubes (volume) versus wrapping it in paper (surface area). En español: El volumen es cuánto espacio llena el interior (unidades cúbicas, pie³). El área de superficie es cuánto material cubre el exterior (unidades cuadradas, pie²). Imagina llenar el tanque con cubitos (volumen) o envolverlo en papel (área de superficie).

Level 2 · Enrichment Two tanks can hold the same volume but need very different amounts of acrylic. A tall, skinny tank has more surface area than a cube of the same volume. As you design, watch how shape — not just size — changes your material cost.

The Task

By the end of this WebQuest, your crew will submit a Tank Build Packet for the Blue Current Aquarium. A complete packet must:

Find the volume of the Reef Tank (a rectangular prism with fractional edge lengths).
Find the volume of the small Feeding-Prep Box by counting unit cubes.
Unfold the Reef Tank into a net and label all six faces.
Use the net to find the surface area of acrylic to order.
Find the surface area of the pyramid-topped Touch-Tank Sign using its net.
Pass the Check Your Understanding self-check at the bottom.

The Process

Work through the steps in order. Each step finishes one page of your Build Packet.

Step 1 — Stock your formula toolbox

Keep these ideas open as you build. Volume fills the inside; surface area covers the outside; a net is the tank unfolded flat.

Volume of a prism

V = l × w × h

Net of a prism

6 faces unfolded flat

Net of a pyramid

1 base + triangle faces

Surface area

add the area of every face

Step 2 — Fill the Reef Tank (volume with fractions)

The Reef Tank is a rectangular prism. Use these tank dimensions (in feet) and the volume formula. Record the volume on your Build Packet.

Length: 4½ ft (4.5 ft)
Width: 2 ft
Height: 3 ft

Worked example — Volume of the Reef Tank:

V = l × w × h = 4½ × 2 × 3 = 4.5 × 2 × 3 = 9 × 3 = 27 ft³

That means the tank holds 27 cubic feet of water. (1 ft³ ≈ 7.48 gallons, so that is a lot of fish!)

Level 1 · Support A fraction edge does not change the steps — multiply the three numbers. Turn 4½ into 4.5 first if that is easier, then multiply across. En español: Una arista con fracción no cambia los pasos — multiplica los tres números. Convierte 4½ a 4.5 si es más fácil, y luego multiplica.

Step 3 — Count cubes in the Feeding-Prep Box

The small Feeding-Prep Box is packed with 1-ft unit cubes so staff can measure scoops of food. Count the cubes to confirm the volume, then check that it matches l × w × h. The box is 3 ft long, 2 ft wide, 2 ft high.

Counting cubes layer by layer should give the same answer as the formula. This proves why the formula works.

Level 2 · Enrichment One bottom layer holds 3 × 2 = 6 cubes, and there are 2 layers tall. Notice that "area of the base × height" gives the same result as "l × w × h." Use that base-area idea to find the volume of any prism, even one with a triangle base.

Step 4 — Unfold the Reef Tank into a net

To order acrylic, the build team unfolds the tank flat into a net. A rectangular prism has 6 faces in 3 matching pairs: top & bottom, front & back, and two sides. Find the area of each face, then add them all to get the surface area.

The Reef Tank unfolded: 6 faces, 3 matching pairs.

Tank dimensions: l = 4½ ft, w = 2 ft, h = 3 ft. The three pairs of faces are:

Front & back: 4½ × 3 each
Two sides: 2 × 3 each
Top & bottom: 4½ × 2 each

Worked example — Surface area of the Reef Tank:

Front + back = 2 × (4.5 × 3) = 2 × 13.5 = 27
Two sides = 2 × (2 × 3) = 2 × 6 = 12
Top + bottom = 2 × (4.5 × 2) = 2 × 9 = 18
Surface area = 27 + 12 + 18 = 57 ft² of acrylic.

Step 5 — Order the Touch-Tank Sign (pyramid net)

The entrance Touch-Tank Sign is topped with a square pyramid. Its net is one square base plus four identical triangles. Find the area of the base, find the area of one triangle, then add them to get the surface area of the sign topper.

Square base: side = 4 ft.
Each triangle face: base = 4 ft, slant height = 5 ft.

Worked example — Surface area of the pyramid:

Base = 4 × 4 = 16 ft²
One triangle = ½ × 4 × 5 = 10 ft²; four triangles = 4 × 10 = 40 ft²
Surface area = 16 + 40 = 56 ft²

Level 1 · Support A pyramid net = 1 base + 4 triangle "flaps." Find each shape's area on the flat net, then add. The net lets you see every face at once so none is forgotten. En español: La red de una pirámide = 1 base + 4 triángulos. Halla el área de cada figura en la red plana y súmalas. La red te deja ver todas las caras a la vez.

Resources

Use these Neft Teacher tools as you build. They open in the same window — use your back button to return.

Unit 10 · 3D Volume & Nets LabBuild prisms, fold and unfold nets, and watch volume fill in 3D. Volume Architect ActivityPractice volume and surface area step by step. Reveal Evidence StudioWrite your Claim–Evidence–Reasoning for the build packet. Math Writing Help · EN/ESSentence frames and bilingual vocabulary support.

Key vocabulary · Vocabulario clave

Volume / Volumen — the space inside a solid, in cubic units (ft³).
Surface area / Área de superficie — the total area of all faces, in square units (ft²).
Net / Red (plantilla) — a 3D solid unfolded flat into all of its faces.
Prism / Prisma — a solid with two matching ends and flat faces (a box is a rectangular prism).
Pyramid / Pirámide — a solid with one base and triangle faces that meet at a point.

Evaluation

Your Tank Build Packet will be scored on this rubric.

Criteria	4 · Lead Engineer	3 · Builder	2 · Apprentice	1 · Getting started
Volume accuracy	Both volumes correct, including the fractional edge.	One volume fully correct.	Right formula, arithmetic error.	Volume missing or incorrect.
Nets	Both nets drawn with all faces labeled correctly.	One net drawn and labeled.	Net attempted with missing faces.	No net shown.
Surface area	Prism and pyramid surface areas both correct.	One surface area correct.	Faces added with an error.	Surface area missing.
Units & labels	ft³ for volume, ft² for surface area, every time.	Most answers labeled correctly.	Units mixed up in places.	No units shown.
Reasoning	Clear claim–evidence–reasoning explanation.	Explains most choices.	Brief or partial reasoning.	No explanation.

Teacher Notes & Answer Key (not printed)

Aquarium Build-Out · Tank Build Packet — pairs with the Evaluation rubric above.

Sample Answers — Tank Build Packet

Reef Tank volume: V = l × w × h = 4½ × 2 × 3 = 4.5 × 2 × 3 = 27 ft³.
Feeding-Prep Box (unit cubes): bottom layer 3 × 2 = 6 cubes × 2 layers = 12 cubes (12 ft³) — matches l × w × h.
Net: a rectangular prism unfolds into 6 faces in 3 matching pairs (top/bottom, front/back, two sides).
Surface area: add all six face areas (2lw + 2lh + 2wh); for the 4.5 × 2 × 3 tank that is 2(9) + 2(13.5) + 2(6) = 18 + 27 + 12 = 57 ft².

Facilitation

Volume fills the inside (ft³); surface area covers the outside (ft²) — keep units distinct.
Use the net so no face is missed; opposite faces come in equal pairs.

Standard

CCSS 6.G.A.2 & A.4.

Check Your Understanding

Answer all six. Click Check My Answers when you are done. These match the builds in your packet.

1.Reef Tank: length = 4½ ft, width = 2 ft, height = 3 ft. What is the volume?

Hint / Pista: V = l × w × h. 4½ = 4.5.

2.Feeding-Prep Box: 3 ft long, 2 ft wide, 2 ft high. What is its volume?

Hint / Pista: V = l × w × h, or count 6 cubes per layer × 2 layers.

3.Which statement about the net of the Reef Tank (a rectangular prism) is true?

A rectangular prism's net always has exactly 4 faces. The net has 6 rectangles that form 3 matching pairs. The net is made of 4 triangles and a square. A prism cannot be unfolded into a net.

4.Using the Reef Tank net (l = 4½ ft, w = 2 ft, h = 3 ft), what is the total surface area of acrylic?

Hint / Pista: add all 6 faces: 2(13.5) + 2(6) + 2(9).

5.Touch-Tank Sign pyramid: square base side = 4 ft; each triangle face has base 4 ft and slant height 5 ft. What is the surface area?

Hint / Pista: base (4×4) + four triangles (each ½×4×5).

6.The team has two tank plans that each hold the same 24 ft³ of water. Which statement is true?

They must use the exact same amount of acrylic. The taller, thinner tank always uses less acrylic. Same volume can need different surface areas, so the shape matters for material cost. Volume and surface area are always equal.

Conclusion

You did exactly what aquarium engineers, package designers, and architects do every day: you measured the inside of a container as volume, unfolded it into a net, and added every face to find the surface area of material to order. Your Reef Tank holds 27 ft³ of water and needs 57 ft² of acrylic — the Blue Current Aquarium is ready for opening day!

Take it further · Level 2

Redesign the Reef Tank to hold the same 27 ft³ of water but use less acrylic. What dimensions get you closest to a cube? Compare the surface areas.

Reflect · Reflexiona

How did drawing the net make the surface area easier to find? Explain in 2–3 sentences. ¿Cómo te ayudó dibujar la red a hallar el área de superficie?

Real careers · Carreras reales

Aquarium engineers, shipping-box designers, and architects all use volume, nets, and surface area to build containers that hold the right amount and use the right materials — exactly what you just did.

iYour Crew Gets the Contract