“turn this into worksheets: Here is a simplified, highly engaging **40-minute lesson** designed around setting up proportions to solve for missing sides using these released test questions. --- ## 40-Minute Lesson Plan: "Architects & Blueprints" | Component | Focus & Connections | | --- | --- | | **TEKS** | **7.5(A)** Solve problems involving similar figures by setting up proportions. | | **Real-World Connection** | **Architecture & Blueprint Scaling** (Designing billboards and buildings from smaller scale models). | | **Cross-Curricular Link** | **Social Studies / Texas History** (Scaling historical landmarks like the Alamo or Texas State Capitol) & **Art** (Proportional sketching and scaling). | --- ## T-TESS Alignment Summary * **Domain 1 (Planning):** Uses clear step-by-step scaffolds (Match $\rightarrow$ Set Up $\rightarrow$ Solve) to directly align with STAAR-formatted items. * **Domain 2 (Instruction):** Visual color-coding strategy simplifies side-matching and eliminates confusion when shapes are flipped or turned. * **Domain 3 (Learning Environment):** Partner-based "Architect & Inspector" roles build accountability and self-correction. --- ## Lesson Timeline ``` [00:00 - 00:05] Hook: The Blueprint Mystery │ ▼ [00:05 - 00:15] Mini-Lesson: "Color-Match & Cross-Multiply" │ ▼ [00:15 - 00:32] Partner Activity: "Blueprint Expansion Project" │ ▼ [00:32 - 00:40] Exit Ticket & Wrap-Up ``` --- ### Phase 1: Hook & Context (5 Minutes) **The Blueprint Mystery (Architecture & Art)** * **Real-World Hook:** Show a miniature 3D model or picture of a skyscraper/monument. Ask: *"Why can't an architect just draw a building the exact size they want to build it? How do they make sure the real building doesn't look stretched or squished compared to the paper draft?"* * **Core Concept:** Real builders use **proportions** to keep side lengths matching so the large version is identical in shape to the small blueprint. --- ### Phase 2: Mini-Lesson — Color-Match Strategy (10 Minutes) Introduce the 3-Step Strategy using Image 1 (Parallelogram Problem): $$\frac{\text{Small Figure Side}}{\text{Large Figure Side}} = \frac{\text{Small Figure Side}}{\text{Large Figure Side}}$$ ``` Step 1: COLOR-MATCH corresponding sides • Left slant side (Small: 12) <---> Left slant side (Large: 30) • Bottom side (Small: 16) <---> Bottom side (Large: PQ) Step 2: SET UP the matching proportion 12 16 ──── = ──── 30 PQ Step 3: CROSS-MULTIPLY and divide to solve 12 • PQ = 16 • 30 12 • PQ = 480 PQ = 40 inches (Answer choice A)[cite: 1] ``` --- ### Phase 3: Partner Activity — "The Blueprint Expansion" (17 Minutes) Students work in pairs as an **Architect** (sets up proportion) and an **Inspector** (solves and checks work). #### Station Tasks (Using Test Questions) * **Station 1 (Pentagons - Image 2):** * **Real-World Task:** Scaling a pentagonal park sign. * **Proportion Setup:** Match corresponding side $KF$ ($6\text{ cm}$) to side $TM$ ($9\text{ cm}$), and side $JH$ ($9\text{ cm}$) to side $SQ$ ($x\text{ cm}$). * $$\frac{6}{9} = \frac{9}{x} \implies 6x = 81 \implies x = 13.5\text{ cm} \quad (\text{Choice A})$$ * **Station 2 (Quadrilaterals - Image 3):** * **Real-World Task:** Enlarging a historic blueprint outline. * **Proportion Setup:** Match side $KN$ ($36\text{ cm}$) to $PT$ ($4\text{ cm}$), and side $LM$ ($x$) to $QR$ ($7\text{ cm}$). * $$\frac{36}{4} = \frac{x}{7} \implies 4x = 252 \implies x = 63\text{ cm} \quad (\text{Choice D})$$ --- ### Phase 4: Debrief & Exit Ticket (8 Minutes) Have students complete a 1-question check to verify mastery: > **Exit Ticket:** > A small rectangular blueprint frame has a height of $5\text{ in}$ and a width of $8\text{ in}$. A matching billboard display has a height of $15\text{ ft}$. > 1. Set up a proportion matching corresponding sides to find the width ($x$) of the billboard display. > 2. Solve for $x$. > > $$\frac{5}{15} = \frac{8}{x} \implies 5x = 120 \implies x = 24\text{ ft}$$”