Not sure why some maths teachers dislike graphics calculators. With a Casio, students see why sin(30°) = sin(150°) — it's where the line crosses the sine curve. Suddenly, it clicks. Visual learning matters.

Embracing the Calculator: Why A-Level Maths Needs Graphical Technology

Introduction: Time to Rethink the Calculator

Somewhere in the corridors of mathematical nostalgia, a few teachers still champion the humble "basic" calculator as the only tool a student should need. But times—and specifications—have changed. A-Level Mathematics and Further Mathematics now expect students to be fluent with technology, including graphical calculators.

This isn't just about pushing buttons faster. It's about understanding concepts deeply, checking solutions efficiently, and bridging algebra with geometry. Used well, a calculator is not a crutch—it’s a microscope.

Why Calculators Are Essential in A-Level Maths

1. They Reflect the Exam Requirements

The current OCR, Edexcel, and AQA A-level maths specifications require:

Knowledge of numerical methods
Understanding the graphical behaviour of functions
Solving equations that cannot be done algebraically

Without a graphical calculator, students are at a disadvantage.

2. They Enhance Conceptual Understanding

Take the example of the sine function. When students input sin(30) and sin(150) and get the same result, they might memorise this fact without knowing why. But plot y = sin(x) on a Casio fx-CG50 or fx-CG100, add a horizontal line at y = 0.5, and they can see the two points of intersection. Suddenly, it makes sense.

3. They Aid in Visualising Transformations

When teaching topics like transformations of graphs, modulus functions, or asymptotic behaviour, nothing beats being able to overlay graphs and trace changes live:

Show how y = f(x) becomes y = f(x) + a
Illustrate the modulus graph and its sharp corners
Zoom in on points of interest for gradient analysis

4. They Support Exploratory Learning

Students can experiment and ask:

What happens if I change this coefficient?
Where does this function cross the x-axis?
What’s the area under this curve?

With a graphical calculator, they can ask and answer their own questions—a vital step towards mathematical independence.

Lesson Plan: Introducing the Graphical Calculator (Casio fx-CG50)

Year Group: Year 12 or Year 13 (A-Level Maths or Further Maths)
Topic: Graphs of Trigonometric and Polynomial Functions
Duration: 60 minutes
Objective: To use the graphical calculator to explore and understand properties of functions.

Starter (10 min): Graphs on Paper

Begin by sketching y = sin(x) on the board or on paper. Ask students:

What’s the value of sin(30)? Of sin(150)?
Why do they think these are the same?

Many will respond with “because of symmetry” or “because I remember it”. This sets up the lesson.

Main Activity (30 min): Discovering with Casio

Part A: Sine Graph Intersections

Plot y = sin(x) on the calculator.
Add the line y = 0.5.
Use the G-Solv → Intersect function to find the two x-values where this occurs.
Discuss how this shows sin(30) = sin(150).

Part B: Roots of Quadratic/Quartic Equations

Input y = x^4 - 3x^2 + 2.
Use the graph trace and roots functions to find where it crosses the x-axis.
Show how you can check algebraic factorisation or verify numerical methods.

Part C: Exploring Transformations

Input y = f(x) (any function: e.g., x^2 or sin(x)).
Ask students to input variants: y = f(x) + a, y = f(x + a), y = af(x), and observe changes.
Overlay graphs to visually compare.

Plenary (10 min): Reflection and Connection

Ask:

How did the calculator help you understand the function more deeply?
Did you spot anything unexpected?
How might this help in the exam?

Homework/Extension Ideas

Use the calculator to explore y = tan(x) and why it has vertical asymptotes.
Investigate a polynomial function with complex roots and explain why some roots don't appear on the graph.
Plot a parametric curve (like a circle) and explain how the values change as the parameter increases.

Final Thoughts: From Technician to Mathematician

We should be training students not just to "do maths" but to think like mathematicians. That includes:

Asking questions
Testing ideas
Understanding the why as well as the how

A graphical calculator like the Casio fx-CG50/100 transforms the learning environment from routine calculation into dynamic exploration. If students only ever use it to check answers, we're missing its full potential.

Let’s stop fearing the calculator—and start using it to build better mathematicians.

09 July 2025