Study Guide
Learning Objectives
- Identify periodic relationships from verbal contexts (3.1.A.1).
- Construct a multi-cycle graph from a single cycle (3.1.A.2).
- Define and find the period $k$ (3.1.B.1–B.2).
- Describe repeating key characteristics across periods (3.1.B.3).
Suggested Practice Sequence
1. Sort contexts: periodic vs not. 2. From a story, sketch one cycle with labeled axes. 3. Extend to 2–3 periods. 4. State $f(x+k)=f(x)$ and find smallest $k$. 5. From a table, estimate where the pattern repeats. 6. List increase/decrease (or max/min) and note they recur each period.
Classroom / Check-In Moves
- "One cycle card → extend the mural."
- Period hunt on tables (smallest $k$).
- Feature transfer: "If it peaks at $t=2$ in the first cycle, where next?"
Misconception Watch-List
- Using $2k$ or $3k$ as "the period."
- Graphs that drift (not true repeats).
- Confusing period with amplitude (amplitude comes more fully in later topics).
- Assuming trig formulas are required for 3.1 (verbal/graphical is enough here).
Vocabulary to Own
- periodic relationship / periodic function
- cycle
- period $k$
- repeating pattern
- equal-length intervals
- key characteristics (increase, decrease, concavity, rates)
Materials Map
- Practice: identify, graph, find period
- Word: real repeating contexts
- Mixed / multi-*: verbal $\leftrightarrow$ graph $\leftrightarrow$ table
- Review & practice test: period + cycle fluency
- Interactive: period and cycle checks