Can your students solve a mathematical mystery?
In this 50-minute lesson, students become Continuity Detectives and investigate whether a function is continuous at a given point. Instead of starting with formulas, they begin with a graph, make predictions, collect evidence, and justify their final verdict.
The lesson follows the 5E Instructional Model with a detective theme:
- Engage – Crime Scene : Students observe a graph and make their first prediction: Continuous or Not Continuous?
- Explore – Find the Evidence : Working in small groups, students investigate the graph and record their mathematical evidence using Freeform.
- Explain – Crack the Continuity Code : Students discover the three conditions of continuity and connect them with left-hand and right-hand limits.
- Elaborate – Forensic Data : Using Numbers, students calculate function values as x approaches a point from both sides. They use the data to decide whether the function passes the continuity test.
- Evaluate – Final Case : Students solve a piecewise-function challenge individually or in pairs and justify their conclusion using the continuity conditions.
Why I designed this lesson
I wanted students to see continuity beyond simply applying three conditions and experience it as investigating mathematical evidence to reach a conclusion.
Closing Reflection
This lesson reminded me that mathematics becomes more meaningful when students are given the opportunity to explore, discuss, and justify their thinking. By turning continuity into a detective investigation, students were not just finding answers. They were using mathematical evidence to explain why.
Sometimes, a simple change in how we present a concept can make learning more engaging and meaningful.
Learn. Investigate. Explain. Case closed! 🔍
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