Unit 10 · Standard 6.G.4
Surface Area Using Nets
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
A box 6 × 4 × 2: SA = 2(24) + 2(12) + 2(8) = 88 in² — like wrapping paper needed
Surface area
The total area of all the flat sides of a solid.
Cut along the edges of a cereal box and unfold it flat — you see all 6 faces
Net
A flat shape that folds up into a solid.
A rectangular prism has 6 faces: top, bottom, front, back, left, right
Face
One flat side of a solid shape.
A rectangle drawn on paper is 2D — it has length and width but no depth
Two-dimensional
A flat shape with length and width, but no thickness.
A cube has 12 edges — the lines where two flat faces connect
Edge
The line where two flat sides of a solid meet.
Key Ideas & Notes
- Your class is designing custom wrapping paper for time capsule boxes.
- To figure out how much paper you need, you have to find the total surface area of each box.
- The trick?
- Unfold the box into a net so you can see every face laid flat!
- Identify each face of the rectangular time capsule box (l = 8 in, w = 5 in, h = 3 in). Find the area of each face pair, then calculate the total surface area.
Think About It
- How many faces does a rectangular prism have?
- What shapes do you see when the box is unfolded?
- Are all the faces the same size?
My Notes
Guided Examples
Example 1
A rectangular prism has l = 6 in, w = 4 in, h = 2 in. What is its surface area?
Solution: SA = 2(6×4) + 2(6×2) + 2(4×2) = 48 + 24 + 16 = 88 in².
Answer: A. 88 in²
Example 2
How many faces does a rectangular prism have?
Solution: A rectangular prism has 6 faces: top, bottom, front, back, left, and right.
Answer: A. 6
Example 3
Surface area is measured in which type of unit?
Solution: Surface area measures flat surfaces, so it uses square units. Volume uses cubic units.
Answer: A. Square units (in², cm², ft²)
Write About the Math The Writing Revolution
I can explain my work using the words surface area, net, face, and two-dimensional.
1. Kernel Sentence subject + verb
Model: Surface area is the total area of all the flat sides of a solid.Área de superficie es el área total de todos los lados planos de un sólido.
Write a kernel sentence about surface area. Use a subject and a verb.Escribe una oración base sobre área de superficie. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Surface area matters in mathÁrea de superficie importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Surface area matters in math because ___.Área de superficie importa en matemáticas porque ___.
Surface area matters in math, but ___.Área de superficie importa en matemáticas, pero ___.
Surface area matters in math, so ___.Área de superficie importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about surface area.Di un hecho verdadero sobre surface area.
Surface area ___.
Ask a question about surface area.Haz una pregunta sobre surface area.
How does ___ ?¿Cómo ___ ?
Show excitement about surface area.Muestra entusiasmo sobre surface area.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with surface area.Dile a un compañero qué hacer con surface area.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The net shows ___ faces.La red muestra ___ caras.
I added the areas to get ___.Sumé las áreas para obtener ___.
This helps with ___.Esto ayuda con ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Surface area is measured in which type of unit?
- Square units (in², cm², ft²)
- Cubic units (in³, cm³, ft³)
- Linear units (in, cm, ft)
- No units needed
2. A cube has edges of 5 cm. What is its surface area?
- 150 cm²
- 125 cm²
- 150 cm³
- 30 cm²
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Two boxes have the same volume of 60 in³. Box A is 5 × 4 × 3. Box B is 10 × 6 × 1. Which box uses less wrapping paper (has less surface area)? Show your calculations and explain why a more cube-like shape might use less material.
Sentence starter: Box A: SA = 2(___) + 2(___) + 2(___) = ___ in². Box B: SA = 2(___) + 2(___) + 2(___) = ___ in². Box ___ uses less wrapping paper because ___.
Reflect — Exit Ticket
A rectangular prism has l = 9 in, w = 5 in, h = 3 in. What is the surface area?
- 174 in²
- 135 in²
- 174 in³
- 87 in²
Answer Key & Teacher Guide
- Try It 1: A. Square units (in², cm², ft²) — Surface area measures flat surfaces, so it uses square units. Volume uses cubic units.
- Try It 2: A. 150 cm² — A cube has 6 identical faces. Each face: 5 × 5 = 25 cm². Total SA = 6 × 25 = 150 cm².
- Exit Ticket: A. 174 in² — SA = 2(9×5) + 2(9×3) + 2(5×3) = 90 + 54 + 30 = 174 in². Surface area uses square units (in²).
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Surface area is the total area of all the flat sides of a solid.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).