Grade 7 · Surface area
Packaging studio: Account for every box face
Packaging studio investigation: account for every box face. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.
Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
Understand what you are seeing
The idea behind the motion.
Surface area adds the areas of the outside faces rather than measuring the space inside a box. A rectangular prism has three different face products, each appearing twice. A net exposes all six rectangles so hidden faces are not forgotten. This investigation begins with length = 3.5; width = 2.5; height = 3.5. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.
A relationship to keep
S = 2(ab + ac + bc)
Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.
- STEP 1
Represent the given quantities
Identify the three kinds of faces: ab, ac, and bc, each with an opposite partner.
- STEP 2
Follow the changing model
Playback highlights the six rectangles one at a time. The net is arranged schematically to keep every face visible.
- STEP 3
Check and explain the relationship
Add two copies of each face area and compare with volume, which uses the product abc and different units.
Your turn to explain
Make a prediction. Test your reasoning.
Packaging studio: Find the outside area of a closed box with dimensions 3.5, 2.5, and 3.5.
Use the values specified in the question. Reset restores the initial values for this investigation.
Compare your explanation
59.5 square units, from 2(8.75 + 12.25 + 8.75).
Work through a full lesson
Connect the animation to a worked example and practice questions.