Ring 2: Assembling

Problem: Block Game: Budget is $\text{20}$ points. Wooden blocks ($\text{W}$) cost $\text{1}$, Stone blocks ($\text{S}$) cost $\text{2}$. Show every possible combination that fits the budget.

Numerical Proof: Budget Rule: $\text{W + 2S} \le \text{20}$. The solution is the Feasible Region on a graph where the axes are W and S.

The Discovery: You discover algebra is a tool to visualize all possibilities (the feasible region) when facing limits (constraints).

Certification Problems

Visual Theme: Teens planning a block-building project within a budget.

Action: Two students ("Logic Builders") look at a screen displaying a 2D coordinate graph that looks like a blueprint.

The Scene: The equation $W + 2S \le 20$ (Budget) is prominent. A single diagonal line (the budget limit) crosses the graph.

Key Highlights: The entire triangular area bounded by the axes and the budget line is brightly shaded and labeled "My Possible Builds!"

Symbols: Small wooden block and stone block icons, plus a gear icon.

Final Prompt: "Concept Illustration, Educational Cartoon, Clean Vector Style, Landscape Aspect Ratio. Two teens ('Logic Builders') over a screen displaying a 2D coordinate graph (Blueprint Style). Equation 'W + 2S <= 20 (Budget)' is prominent. The triangular area bounded by the budget line is brightly shaded and labeled 'My Possible Builds!'. Include block icons and a gear icon. Bright, imaginative colors."

The Polya Studio

The Polya Studio

Ring 2: Assembling

Certification Problems

The Polya Studio

Ring 2: Assembling

Certification Problems

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