Shadow Sleuths Poster GuideShadow Sleuths Project Guide: Indirect Measurement Poster Name: Date: Mission Objective Your mission is to determine the height of an "unreachable" object (like a flagpole, tree, or building) using only a meter stick, the sun, and your knowledge of Similar Triangles. You will present your findings on a professional-grade poster. Step 1: Field Data Collection Head outside and record the following measurements carefully. Precision is key! Object Description: Length of Object's Shadow \( (s_1) \): Length of Meter Stick Shadow \( (s_2) \): Field Sketch Label height (h) and shadow (s) for both objects. Step 2: Shadow Trigonometry The Similarity Ratio Object Height (x) Object Shadow = Stick Height Stick Shadow Show your step-by-step calculation work below: Step 3: Poster layout Essentials Visual Evidence Photos or detailed diagrams showing you measuring the shadows in the field. Mathematical Proof The proportion equation and the clear solution for the unknown variable \( x \). Similarity Logic Explanation of why the triangles are similar (the "Angle-Angle" relationship).
Artful Proportions Art GuideArtful Proportions Project Guide: Similarity & Tessellation Art Artist Name: The Creative Constraint Similarity is the backbone of art and architecture. Create a fractal-inspired tessellation where every piece is a similar figure to your base shape. The Master Shape Draw your polygon Master Shape below. Label all side lengths. The Scale Ratios Define three different scale factors used in your piece: Ratio A Ratio B Ratio C Requirements Pattern covers 75% of canvas. All figures are geometrically similar. Use color to show corresponding parts. Include a scale factor key. Draft Canvas Space Use this area for a rough draft of your pattern layout.
Similarity Showdown Presentation GuideSimilarity Showdown Defending Geometrical Relationships with Logic The Presentation Challenge In this project phase, you will identify real-world pairs of similar objects and prove their relationship using similarity criteria. Required Proofs: AAA Similarity SAS Similarity SSS Similarity Indirect Measurement (Shadows) 6 - 8 Slides Total Professional design required Layout: Similarity Pair 1 The Objects High-quality photos of the two objects. Explain why you chose them. 2 The Data Tables showing lengths of sides and measures of angles. 3 The Logic Formal proof (AAA, SSS, or SAS) and scale factor calculation. Layout: Indirect Measurement Dedicated slide for your shadow project results: Clear diagram of the two right triangles. The proportion equation: \(\frac{h_1}{s_1} = \frac{h_2}{s_2}\). Final height of the object in proper units. Insert Field Work Photo Here Presentation Standards Visuals • NO text smaller than 24px. • High contrast colors (no light on light). • One concept per slide. Content • Geometric vocabulary used correctly. • Proofs are step-by-step. • Units included for all measurements.
Project Master Rubric Teacher GuideProject Master Rubric Similarity Superstars Project Sequence Total: 100 PTS Phase 1: Shadow Sleuths Poster (30 pts) CriteriaExceptional (10)Proficient (7-9)Developing (0-6)Data PrecisionAll field measurements are accurate and labeled with units.Most measurements are accurate; units are present.Inaccurate measurements or missing units.Math AccuracyProportions are set up correctly and solved with zero errors.Minor calculation error but logic is sound.Major errors in proportion setup or solving.Similarity ProofClear justification of why triangles are similar (AAA).Mention of similarity but lacks formal detail.No similarity justification provided. Phase 2: Artful Proportions (30 pts) CriteriaExceptional (10)Proficient (7-9)Developing (0-6)Geometric SimilarityAll art elements are perfect dilations of the base shape.Most elements are similar; minor distortions present.Figures are not geometrically similar.Scale ApplicationThree distinct, accurate scale factors used and documented.Two scale factors used correctly.One or no scale factors used; inaccurate scale.Artistic EffortHigh level of polish, color, and complexity.Completed work with moderate effort and color.Incomplete or low-effort artistic output. Phase 3: Similarity Showdown (40 pts) CriteriaExceptional (13-14)Proficient (9-12)Developing (0-8)Similarity Logic (14 pts)Flawless application of AAA, SAS, and SSS proofs.Logical proofs for most criteria.Flawed or missing similarity proofs.Real-World Links (13 pts)Innovative choice of objects; clear photos/data.Standard objects used; clear photos.Unclear photos or poor choice of objects.Professionalism (13 pts)Slide design is exceptional; text size is compliant.
Similarity Blueprint Reference SheetSimilarity Blueprint Essential Formulas & Relationships Ratios & Proportionality The Scale Factor (k) \( k = \frac{\text{New Length}}{\text{Original Length}} \) Triangle Proportionality Theorem: If a line is parallel to one side of a triangle, it divides the other sides proportionally. a b c d \( \frac{a}{b} = \frac{c}{d} \) Similarity Criteria AA (Angle-Angle) Two pairs of congruent angles. SSS (Side-Side-Side) All corresponding sides are proportional. SAS (Side-Angle-Side) Two pairs of proportional sides + included angle is congruent. Shadow Math (Indirect Measurement) Sun rays are parallel, forming similar right triangles for objects and their shadows at the same time. \( \frac{\text{Height 1}}{\text{Shadow 1}} = \frac{\text{Height 2}}{\text{Shadow 2}} \) Object Stick PRO TIP: Consistency is key! If you put the Height on top for the first object, you MUST put the Height on top for the second object in your proportion equation.
