Exponential Growth & Decay PBL | Real-World Algebra 1 Project | ELL Scaffolded

★ **A 5-DAY, REAL-WORLD PROJECT-BASED LEARNING UNIT ON EXPONENTIAL GROWTH & DECAY — WITH EMBEDDED ELL SCAFFOLDS** ★

Turn “when will I ever use this?” into “wait, that’s how interest works?!” This comprehensive **50-page PBL unit** takes Algebra 1 students through four authentic real-world datasets—compound interest on a 30-year savings account, U.S. census data from 1790–2020, E. coli bacterial growth, and an SIR epidemic simulation—to make exponential functions genuinely matter.

📋 **WHAT'S INSIDE (50+ PAGES)**

**Day 1 — Patterns That Multiply** The chessboard-and-wheat launch hook, introduction to **A(t) = A₀ · bᵗ**, guided practice, partner discourse stems, and an exit ticket.

**Day 2 — Compound Interest (Real Federal Reserve Rates)** Students model **$1,000** growing at the actual Fed funds rate over 30 years. Includes a real Fed rate data table (2000–2024), the compound interest formula **A = P(1 + r/n)^(nt)**, worked examples, and practice problems.

**Day 3 — U.S. Population Growth (1790–2020 Census)** Students fit an exponential model to real census data, then explore when and why the model breaks down. Includes the complete 230-year census dataset and a labeled scatter plot with linear-vs-exponential comparison.

**Day 4 — Bacterial Growth + Viral Spread (SIR Model)** **Part A:** E. coli doubling every 20 minutes (lab-derived data). **Part B:** A simplified SIR epidemic model using historical R₀ values: seasonal flu = 1.3, 1918 Spanish flu = 2–3, measles = 12–18.

**Day 5 — Student Choice Board + Data Story Presentation** Students choose one scenario, build a model, graph it, and present a 3-sentence “data story” using structured sentence starters.

✨ **WHAT MAKES THIS UNIT DIFFERENT**

✅ **Real Data, Not Made-Up Numbers:** Federal Reserve rates, U.S. Census Bureau counts, lab-derived bacterial doubling times, and published epidemiological R₀ values. ✅ **ELL Scaffolds Embedded Throughout:** Vocabulary cards with formulas and “common error” tips, sentence frames for describing, comparing, predicting, and justifying, structured partner-talk stems, and a data-story presentation template. ✅ **Detailed Worked Solutions:** Every practice problem and exit ticket comes with a step-by-step answer key using the **Given → Formula → Substitution → Interpretation** structure. ✅ **Labeled Diagrams:** Eight custom figures covering growth/decay curves, doubling-time visualization, compound interest comparison, U.S. population scatter with fit lines, E. coli growth curve, SIR epidemic simulation, half-life decay, and a student choice board. ✅ **Two Complete Rubrics:** A 4-criterion project rubric covering model, graph, data story, and presentation, plus a daily participation rubric with ELL-specific language criteria. ✅ **30-Term Glossary:** Student reference glossary with embedded formulas.

📏 **STANDARDS ALIGNMENT**

**CCSS-Math:** HSF-LE.A.1 — Distinguish linear vs exponential situations HSF-LE.A.2 — Construct exponential functions from tables/graphs HSF-LE.A.3 — Observe exponential eventually exceeds linear HSF-LE.B.5 — Interpret parameters in context HSF-IF.C.7e — Graph exponential functions HSF-BF.A.1a — Write explicit function from context HSA-CED.A.1 — Create equations to solve problems HSN-Q.A.2 — Define appropriate quantities for modeling

**WIDA ELD Standards (2020):** ELD-LS.1-3, ELD-R.1-3, ELD-W.1-3, ELD-LC, ELD-DC.C1 (Math)

👥 **WHO THIS IS FOR**

Algebra 1 teachers (Grades 9–10) teaching exponential functions Math teachers with multilingual learners / ELLs at WIDA levels 1–4 Schools implementing project-based learning in math Teachers who want rigorous, real-data modeling rather than formula drills Long-term sub plans—the unit is self-contained and fully scripted

📦 **FILE FORMAT**

**1 PDF, 50 pages** — print-and-teach, no prep required All fonts embedded; high-resolution vector diagrams UM Printables branding on every page

⭐ **TEACHERS ARE SAYING**

*(Leave space for reviews—they will appear here once buyers leave feedback.)*