Support-polygon model
Classify a centre-of-gravity projection as inside, on or outside a support region.
Adult planning suggestion: about9–12 · Shape & spatial thinking
- Players
- 2–3 per group
- Time
- 15–20 minutes
- Materials
- Coordinate grid, triangle support points(0,0),(6,0),(0,6) and centre-point cards.
Prepare
Use a paper model of a rigid object on a level surface under vertical gravity. Its three point supports are(0,0),(6,0),(0,6). Draw their triangular convex support region. The supplied cards state where the centre-of-gravity projection lies; you are not estimating an unknown object’s real mass distribution.
Play
Classify each point using x≥0, y≥0 and x+y≤6. Strictly positive x,y with x+y<6 is inside. Equality on one boundary is on the edge; a violated inequality is outside. A projection outside cannot be balanced by these supports in this ideal model. Edge cases are marginal, not a robust-stability guarantee.
Worked example
P(2,2) is inside because 2+2=4<6. Q(4,4) is outside because 8>6. R(3,3) lies on the diagonal boundary because 3+3=6. A point(-1,2) is outside even though its coordinate sum is below 6: every condition must hold.
Finish and check
Swap four new point cards and explain each verdict with the diagram and inequalities. Do not call every point inside the rectangle 0–6 stable: the actual support region is a triangle. Finish after every verdict has a stated reason and a partner has checked one boundary case.
Adaptation and limits
For thirty learners use ten trios with plotter, condition reader and checker. This is a seated paper model, not a balancing exercise for bodies or heavy objects. The physics source explains centre of gravity and base of support; real flexible objects, motion, friction and load distribution require more than this simplified classification.
Purpose, observation and provenance
Within this activity: Classify a centre-of-gravity projection as inside, on or outside a support region.
Check all three inequalities and distinguish a modelling assumption from a physical experiment.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
OpenStax College Physics2e — Stability — Centre-of-gravity/base-of-support physics background, not a study of our classroom activity or age choice.
Age bands are planning suggestions. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player materials · Support-polygon model
Support triangle(0,0),(6,0),(0,6). Points P2,2 / Q4,4 / R3,3 / S−1,2.
Point / x≥0 / y≥0 / x+y≤6 / inside,edge,outside.
Player record · keep host key separate
| Point | x≥0 | y≥0 | x+y≤6 | Class |
|---|---|---|---|---|
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ |
Host key · separate from players
P inside, Q outside, R boundary, S outside. Boundary is marginal in this model, not robust stability.
Run the round
Use a paper model of a rigid object on a level surface under vertical gravity. Its three point supports are(0,0),(6,0),(0,6). Draw their triangular convex support region. The supplied cards state where the centre-of-gravity projection lies; you are not estimating an unknown object’s real mass distribution.
Classify each point using x≥0, y≥0 and x+y≤6. Strictly positive x,y with x+y<6 is inside. Equality on one boundary is on the edge; a violated inequality is outside. A projection outside cannot be balanced by these supports in this ideal model. Edge cases are marginal, not a robust-stability guarantee.
P(2,2) is inside because 2+2=4<6. Q(4,4) is outside because 8>6. R(3,3) lies on the diagonal boundary because 3+3=6. A point(-1,2) is outside even though its coordinate sum is below 6: every condition must hold.
Swap four new point cards and explain each verdict with the diagram and inequalities. Do not call every point inside the rectangle 0–6 stable: the actual support region is a triangle. Finish after every verdict has a stated reason and a partner has checked one boundary case.
For thirty learners use ten trios with plotter, condition reader and checker. This is a seated paper model, not a balancing exercise for bodies or heavy objects. The physics source explains centre of gravity and base of support; real flexible objects, motion, friction and load distribution require more than this simplified classification.