Exponential Growth & Decay PBL | Real-World Algebra 1 Project | ELL Scaffolded
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Quick overview
About This Resource
The **Exponential Growth & Decay Project-Based Learning Unit** is a ready-to-teach **5-day Algebra 1 PBL unit for Grades 9–10** that connects exponential functions to authentic real-world data and applications.
Students investigate **compound interest, U.S. population growth, bacterial growth, and epidemic spread** while learning to distinguish exponential from linear change, build and interpret exponential models, analyze graphs and data, and communicate mathematical conclusions. The progression moves from foundational patterns to modeling, data analysis, and a culminating student presentation.
Product description
★ 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 legendary 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 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 discover exactly 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 pick 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 — not bolted on. Vocabulary cards with formulas and "common error" tips, sentence frames for every language function (describe, compare, predict, justify), structured partner-talk stems, and a data-story presentation template. ✅ Detailed worked solutions for every problem. Every practice problem and exit ticket comes with a step-by-step answer key showing the Given → Formula → Substitution → Interpretation structure. ✅ Labeled diagrams. Eight custom matplotlib figures: 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 (model, graph, data story, presentation) and a daily participation rubric with ELL-specific language criteria. ✅ 30-term glossary with embedded formulas — print and distribute as a student reference. 📏 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 — not 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
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❓ FREQUENTLY ASKED QUESTIONS
Q: Is this a full unit or just activities? A: It's a complete 5-day instructional unit with lesson plans, direct instruction, guided practice, independent practice, exit tickets, answer keys, rubrics, and a culminating project. Print and teach.
Q: How long does each lesson take? A: Each day is designed for a 55-minute period. The unit can be compressed to 3 days (combine Days 1+2 and 4+5) or extended to 7 days (add a build day and a presentation day for Day 5).
Q: Are the answer keys included? A: Yes — every practice problem and exit ticket has a detailed step-by-step solution showing the Given → Formula → Substitution → Interpretation structure. The answer key section is 9 pages long.
Q: Do my students need graphing calculators? A: Scientific calculators with an exponent key are sufficient. Desmos, GeoGebra, or TI-84s work great for the graphing activities but are not required.
Q: Is this resource really ELL-appropriate, or is that just marketing? A: Genuinely ELL-appropriate. The vocabulary cards, sentence frames, structured discourse stems, and data-story template are embedded into every lesson — not optional add-ons. The unit follows SIOP Model and WIDA ELD (2020) frameworks.
Q: Can I use this for a long-term sub plan? A: Yes. The unit is fully self-contained and scripted. A substitute with basic Algebra 1 knowledge can deliver it.
Q: Are the datasets real? A: Yes. Federal Reserve funds rates come from the FRED database. U.S. population counts come from the Census Bureau. Bacterial doubling times are published microbiology values. R₀ values are from Anderson & May (1991) and recent epidemiological literature.
Q: Is this resource editable? A: The PDF is not editable, but the included Python scripts (for regenerating diagrams and the full document) are available upon request — contact UM Printables through TPT Q&A.
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Frequently Asked Questions
What's included in this resource?
This resource contains 50 pages of ready-to-print materials. It is no-prep, answer keys, visual supports.
Is this a no-prep resource?
Yes, this resource is completely no-prep. Simply print the pages and they're ready to use in your classroom immediately. Answer keys are included for easy grading.
What format is this resource in?
This resource is a printable PDF. After downloading from TPT, you can print the pages directly or use them digitally with a document camera or interactive whiteboard.
