The counterexample quilt

Your mission path0/4 checkpoints ready

Before you begin, make a prediction.

Does the same amount of fabric always need the same length of edging? What do you expect, and why?

A prediction is a starting idea. You can revise it after exploring.

Change something. Notice what happens.

Preparing your interactive workspace…

Test the idea.

A new square patch shares two full edges with a connected design. How does exposed-edge perimeter change?

It always increases by 4 cm because a square has four sides.It increases by 2 cm because only the new square matters.It stays unchanged: +4 candidate edges − 2 for each of the two shared edges = 0 cm.

Explain your discovery.

Which exact pair of designs disproved a claim about area and perimeter? Explain a shared-edge observation and one limit of the patch model.

A researcher’s debrief

Make a claim that answers the mission question.
Use a result from your investigation as evidence.
Explain why that evidence supports the claim.
Name a limitation or an observation that could change your mind.

Use at least 40 characters and include an observation. Your writing is saved as evidence; it is not automatically judged for accuracy.

What counts as completing this lab?

A prediction of at least 8 characters.
At least one interaction with the workspace.
A correct knowledge-check answer, with retries allowed.
Save two connected equal-area designs with different perimeters and interpret the counterexample.
Predict and test the area and perimeter change when a patch shares three edges.
A reflection of at least 40 characters.

This records completion of this demonstration. It is not an official grade or a claim of mastery.

Start with a short prediction.

Curriculum context & source notes

This is an original Bodhi learning activity. Official references establish its curriculum context, rather than endorsement of the simulation or complete syllabus coverage.

Maths Mela · Grade 5 · Grandmother’s Quilt
Printed pp.147–154. Current official chapter body inspected before authoring; exact SHA and decomposition in BATCH3-PRIMARY-MATH-SOURCES.md. Selected bounded objective only; original tasks and diagrams. Educator review and complete chapter coverage remain pending.
Source checked · 2026-10-21
Bodhi original learning design
Original activities, questions, reading passages and fictional archives. A curricular connection does not make a Bodhi activity an official NCERT exercise. Broader grade adaptation awaits educator review.
Mapping under review · 2026-10-21

Opening your next discovery…

Before you begin, make a prediction.

Change something. Notice what happens.

Test the idea.

Explain your discovery.

The counterexample quilt

Before you begin, make a prediction.

Change something. Notice what happens.

Build a counterexample, not just a drawing

Saved design A

Saved design B

Transfer: can more fabric need less edging?

Test the idea.

Explain your discovery.

Build a counterexample, not just a drawing

Saved design A

Saved design B

Transfer: can more fabric need less edging?