Continuity Detective: Case Closed?

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:

1. Engage – Crime Scene : Students observe a graph and make their first prediction: Continuous or Not Continuous?
2. Explore – Find the Evidence : Working in small groups, students investigate the graph and record their mathematical evidence using Freeform.
3. Explain – Crack the Continuity Code : Students discover the three conditions of continuity and connect them with left-hand and right-hand limits.
4. 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.
5. 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! 🔍