Recognising functions through mappings
What is the smallest change to the arrows that makes this relation a function?
Open lessonSENIOR 1 · THINK TOGETHER
Chapter 3 · Functions
From mappings and graphs to justified choices
PAPER · PROJECTION · DISCUSSION
Make a prediction. Change a condition. Explain why.
Keep your paper worksheet beside you. Take turns at the model, record evidence, compare designs and return to the definition.
Inputs, rules and representations
Reading function notation and the three elements
Do equal formulas always define the same function?
Open lessonWriting allowed inputs with intervals
What changes when an endpoint is included, and can infinity be included?
Open lessonCombining domain restrictions and finding ranges
How many gates must an input pass, and can simplifying the formula reopen a closed gate?
Open lessonMoving between tables, graphs and formulas
Why can the same formula give separate dots in one situation and a line in another?
Open lessonPiecewise functions and boundary points
Can changing one endpoint create a gap or two different outputs?
Open lessonComposition as two successive steps
Does swapping two function machines keep the answer the same?
Open lessonProperties and powers
Reading increase, decrease and extrema from graphs
If outputs get closer and closer to a bound, must a maximum or minimum exist?
Open lessonExplaining monotonicity with its definition
Do several rising samples prove a function is increasing everywhere on the interval?
Open lessonUnderstanding odd and even functions through symmetry
Can restricting the domain change the parity of an unchanged formula?
Open lessonRecognising five basic power functions
What does the exponent tell us, and what must we still check about the domain?
Open lessonUsing power-function properties to compare values
Does a larger positive exponent always produce a larger value?
Open lessonComposition and decisions
Composition rules and simple substitution
Does “10% off, then subtract 20” cost the same as “subtract 20, then 10% off”?
Open lessonUsing functions to make justified choices
Can the cheaper plan change more than once?
Open lessonA lesson with room to think
A suggested 40-minute lesson: 5 minutes for prediction, 12 for exploration, 8 for reasoning, 12 for paper practice and 3 for an exit task. Each lesson includes teacher questions and a printable observation sheet.
All fourteen lesson boards work without a sign-in. Classroom notes and backups use the existing learning workspace. Paper responses remain each student’s own evidence.