Represent Three-Dimensional Figures in Two Dimensions
I can find the surface area of a solid by using its net.
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🎯 Content Objective / Objetivo de contenido
I can find the surface area of a solid by using its net.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
To find how much wrapping paper a time capsule box needs, why is unfolding it into a net more helpful than looking at the 3D box?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Time Capsule Project
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!
Concept Launch
💡 How do we find the surface area of a box?
Surface area is the total area of all the flat faces of a solid. A net unfolds the box flat so you can see and add all 6 faces. The answer uses square units.
Representing 3D Solids with Nets. 1. A net is a 2D flat pattern that folds into a 3D solid without overlapping. 2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs. 3. Surface Area is the total sum of the areas of all flat faces on the net
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Surface Area Using Nets Área de superficie usando redes |
The total area of all the faces of a solid. A net unfolds the solid flat so you can see every face and add their areas. El área total de todas las caras de un cuerpo. Una plantilla lo despliega para ver cada cara y sumar sus áreas. |
A box with 6 faces: 2(8×5) + 2(8×3) + 2(5×3) = 158 square units | |
| Surface area Área de superficie |
The total area of all the flat sides of a solid. El área total de todos los lados planos de un sólido. |
A box 6 × 4 × 2: SA = 2(24) + 2(12) + 2(8) = 88 in² — like wrapping paper needed | |
| Net Plantilla (desarrollo plano) |
A flat shape that folds up into a solid. Una figura plana que se dobla y forma un sólido. |
Cut along the edges of a cereal box and unfold it flat — you see all 6 faces | |
| Face Cara |
One flat side of a solid shape. Un lado plano de una figura sólida. |
A rectangular prism has 6 faces: top, bottom, front, back, left, right | |
| Two-dimensional Bidimensional |
A flat shape with length and width, but no thickness. Una figura plana con largo y ancho, pero sin grosor. |
A rectangle drawn on paper is 2D — it has length and width but no depth | |
| Edge Arista |
The line where two flat sides of a solid meet. La línea donde se unen dos lados planos de un sólido. |
A cube has 12 edges — the lines where two flat faces connect |
Which Word Fits?
The total area of every face, found by adding the faces in a net, is the ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
To find how much wrapping paper a time capsule box needs, why is unfolding it into a net more helpful than looking at the 3D box?
👂 Listen For
Students explain a rectangular prism has 6 faces, and the net unfolds the solid into a flat (two-dimensional) pattern so every face is visible to measure.
Extend: Is there more than one correct net for the same box? Justify your thinking.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
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.
✍️ Explore Discourse
The total surface area is 158 in². Which face pair contributes the most area? Why does that make sense when you look at the dimensions?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
For the box l = 8, w = 5, h = 3, you found three face pairs. How did you use the net to organize the faces into pairs, and which pair had the largest area?
👂 Listen For
Students explain opposite faces are congruent (3 pairs), identify the top/bottom 8×5 = 40 as largest (80 in² for the pair), and total to 158 in².
Extend: How can you tell which face pair will be largest just by looking at the dimensions, before doing any multiplication?
Practice Check A
A cube has edges of 5 cm. What is its surface area?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
A rectangular prism has l = 6 in, w = 4 in, h = 2 in. What is its surface area?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Area Grid Shading
Click cells to shade area. Count shaded squares.
✍️ Justify Your Thinking
Sort each label into the correct box.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Representing 3D Solids with Nets. 1. A net is a 2D flat pattern that folds into a 3D solid without overlapping. 2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs. 3. Surface Area is the total sum of the areas of all flat faces on the net" — and it works because ___.
Because Surface Area Using Nets means ___, but a tricky part is ___, so I have to ___.
A common mistake with Surface Area Using Nets is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Surface area to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Representing 3D Solids with Nets. 1. A net is a 2D flat pattern that folds into a 3D solid without overlapping. 2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs. 3. Surface Area is the total sum of the areas of all flat faces on the net because ___
Representing 3D Solids with Nets. 1. A net is a 2D flat pattern that folds into a 3D solid without overlapping. 2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs. 3. Surface Area is the total sum of the areas of all flat faces on the net but ___
Representing 3D Solids with Nets. 1. A net is a 2D flat pattern that folds into a 3D solid without overlapping. 2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs. 3. Surface Area is the total sum of the areas of all flat faces on the net so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
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.
| Face Pair | Dimensions | Area of One Face (in²) | Number of Faces | Total for Pair (in²) |
|---|---|---|---|---|
| Top & Bottom | 8 × 5 | 2 | ||
| Front & Back | 8 × 3 | 2 | ||
| Left & Right | 5 × 3 | 2 | ||
| Total SA: |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
A rectangular prism has l = 6 in, w = 4 in, h = 2 in. What is its surface area?
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A gift shop wraps boxes with decorative paper. A box is 14 inches long, 10 inches wide, and 6 inches tall. One sheet of wrapping paper covers 400 square inches.
✍️ Connection Reasoning
How many sheets of wrapping paper are needed to cover the entire box?
The box's surface area is ___ in² because SA = 2(___×___) + 2(___×___) + 2(___×___) = ___ + ___ + ___ = ___. You need ___ sheets because ___ ÷ 400 ≈ ___.
Turn & Talk — Connect
A gift box is 14 × 10 × 6 in and one sheet of paper covers 400 in². Talk through how to find how many sheets are needed to cover the whole box.
👂 Listen For
Students compute SA = 280 + 168 + 120 = 568 in², then 568 ÷ 400 = 1.42, and round up to 2 sheets to cover the whole box.
Extend: Why must you round the number of sheets up instead of down, and what does the leftover paper represent?
Summarize: Represent Three-Dimensional Figures in Two Dimensions
Representing 3D Solids with Nets. 1. A net is a 2D flat pattern that folds into a 3D solid without overlapping. 2. Rectangular prism net has 6 rectangular faces in 3 congruent opposite pairs. 3. Surface Area is the total sum of the areas of all flat faces on the net
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
A rectangular prism has l = 9 in, w = 5 in, h = 3 in. What is the surface area?
Bonus Exit Check
How many faces does a rectangular prism have?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students explain a rectangular prism has 6 faces, and the net unfolds the solid into a flat (two-dimensional) pattern so every face is visible to measure.
• Students explain opposite faces are congruent (3 pairs), identify the top/bottom 8×5 = 40 as largest (80 in² for the pair), and total to 158 in².
• Students compute SA = 280 + 168 + 120 = 568 in², then 568 ÷ 400 = 1.42, and round up to 2 sheets to cover the whole box.
• Students explain a prism has opposite congruent faces (three pairs), so SA = 2lw + 2lh + 2wh, and missing a '2' undercounts one whole face.
Common mistake: A common mistake in Surface Area Using Nets is finding the area of only one face from each of the 3 matching pairs and forgetting to double it, instead of counting all 6 faces. For a box that is 9 in × 4 in × 5 in, a student might add just one face from each pair: (9×4) + (9×5) + (4×5) = 36 + 45 + 20 = 101 in², but the net actually has two of each face, so the correct total is 2(36) + 2(45) + 2(20) = 72 + 90 + 40 = 202 in² — exactly double. Before you submit, ask: 'Did I count both matching faces in each pair, or only one from each pair?'
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 150 cm² — A cube has 6 identical faces. Each face: 5 × 5 = 25 cm². Total SA = 6 × 25 = 150 cm².
✓ Practice 2: 88 in² — SA = 2(6×4) + 2(6×2) + 2(4×2) = 48 + 24 + 16 = 88 in².
✓ Practice 3: 6 — A rectangular prism has 6 faces: top, bottom, front, back, left, and right.
✓ Practice 4: Square units (in², cm², ft²) — Surface area measures flat surfaces, so it uses square units. Volume uses cubic units.
✓ Exit ticket: 174 in² — SA = 2(9×5) + 2(9×3) + 2(5×3) = 90 + 54 + 30 = 174 in². Surface area uses square units (in²).