EduWonderLab Student Notebook

Represent 3-D Figures in 2-D

Learn how a flat pattern called a net can fold into a solid shape. You will look at faces, edges, and vertices—and explain your ideas in clear, careful sentences.

Then you will use structure (how faces connect and fold) to decide which flat patterns can become real 3-D solids.

Content ObjectiveI can use a 3-D figure to create a 2-D net and use structure to decide which solid the net makes.In simpler words: I can match a net to the correct solid and show how the faces connect when the net folds.
Language ObjectiveI can describe how the faces of a 2-D net connect and explain which 3-D solid the net forms.In simpler words: I can use words like face, edge, vertex, fold, and net in complete sentences.

Start Here

Start Here: What are we figuring out?

A net is a flat pattern. When you fold it the right way, it becomes a 3-D solid.

Today you will study structure: how faces meet, where folds happen, and how pieces connect. You will test ideas and explain your reasoning with precise math language.

Big Question: How can a flat pattern become a solid?
netfaceedgevertexfoldsolid
Different flat patterns made of connected squares

Notice & Wonder

Be Curious: Notice & Wonder

Nine square patterns that might fold into nets

Focus: shapes made of squares, matching edges, rotations, and possible folds.

Student Move: Choose one pattern. Use a kernel sentence, then add your own math details.
NOTICEWhat do you see?
WONDERWhat questions do you have?

Check My Notice & Wonder

A strong response uses observation words, question words, or math vocabulary such as square, fold, edge, face, pattern, rotate, or net.

Vocabulary

Vocabulary: Use precise math words

Net
a flat pattern that folds into a 3-D solid
This net folds into a ___.
flat pattern
Face
a flat surface of a 3-D figure
This solid has ___ faces.
Labeled face image
Edge
where two faces meet
The two faces meet at an edge.
Labeled edge image
Vertex
a corner point where edges meet
The solid has ___ vertices.
Labeled vertex image

Quick Match: Use the labeled images

Choose the word that matches each image. These are the exact labeled image types from the notebook source.

Image labeled FACE
Image labeled edge
Image labeled Vertex

3-D Figures & Nets Reference

Count the faces.
Match the face shapes.
Picture the folds.
How to use this tab: Keep it open when you build or check a net. First name the solid, then compare the faces in your net to the reference example.

Mini-Lesson

Mini-Lesson: From Solid to Net

Key Idea: A net shows every face of a solid laid flat. When the faces are connected in the right places, the net folds into the solid.
3-D solid unfold 123456 Rectangular prism net
Check for Structure
Count the faces. Then ask: Which faces touch when the net folds?

Try It

Try It: Guided Problem

Read: The solid shown is a cube. Use its faces, edges, and vertices to build a flat net that could fold back into this cube.

Your job: create a possible cube net on the grid, then explain why the 6 square faces are connected in places that can fold without overlapping.

Interactive 3-D model
faceedgevertex

Drag to orbit · Scroll or pinch to zoom — explore faces, edges, and vertices in three dimensions

Target solid: cube

Create the Net

Click squares to build a flat pattern. A cube needs 6 connected square faces.

Practice: Which Net Works?

Practice: Match the 3-D Cube to the Correct Net

Explore
faceedgevertex

Drag to rotate · Scroll to zoom

Target solid: cube

Look at the 3-D cube first. Then choose the flat net that could fold to make that cube. A cube has 6 square faces. The correct net must have exactly 6 connected squares and fold without overlapping.

face = one flat square surface
edge = where faces meet
vertex = corner point

I think A works.

I think B works.

I think C works.

Partner Practice: Paper Cubes

Partner Practice: Build a Paper Cube

Yuzuki is making a paper cube model. What can help her cut, fold, and tape a flat pattern into a cube?

Unit cube

Drag · Zoom — pairs with the diagram below

Cube → net unfold cube net 1 2 3 4 5 6 Cube check: A cube net has 6 square faces connected along full edges.
Partner Talk:
Partner A: Point to two faces that will touch when folded.
Partner B: Ask, “Which edge connects them?” Then switch.

Net Builder

Net Builder: Rectangular Prism

Build Steps: Choose the solid. Count the faces. Draw each face flat. Connect faces along shared edges. Imagine folding the net.

Need help?

  • Start with a strip of 4 side faces.
  • Add 2 matching end faces to the strip.
  • Keep all faces connected by edges.
  • Before checking, picture which faces touch when it folds.
Partner Talk:
Partner A: Explain how it folds.
Partner B: Ask, “Which faces touch?” Then switch roles.

Find the Error

Find the Error

A student said, “This net will fold into a cube.” Find it, fix it, and explain.

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Discuss: From 2-D Back to 3-D

Discuss: From 2-D Back to 3-D

123456
Reasoning Moves: Count faces. Name face shapes. Decide which faces touch. Picture the folds. Name the solid.

Independent Practice: Create a Net

Independent Practice: Create a Net

Click the grid to build your net. For a square pyramid, use one square as the base and describe where the triangular faces attach.

Hints / Help

  • Choose a solid first.
  • Count how many faces your solid needs.
  • Keep every face attached by a full edge.

Planning Checklist

Exit Ticket + Reflection

Exit Ticket + Reflection

Exit Ticket: A net has 6 faces: 2 long rectangles, 2 short rectangles, and 2 matching rectangles for the ends. What 3-D figure could it make? Explain.

Self-Check

Rate your confidence from 1 to 4.

I can identify faces in a net.

I can match a net to a solid.

I can explain why a net works.