Graphs of functions – Year 11 maths lesson
Lesson 15 of 17 in the Year 11 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 11 (ages 15–16) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 11 (ages 15–16)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “How can a graph help you solve an equation you cannot solve by hand?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Joining plotted points of a curve with straight lines. Draw a smooth curve through the points.
- Mixing up the shapes of x² and x³ graphs. Try x = −2: is y positive or negative?
Tip for home: Sketch a graph of a journey to school and tell its story.
What your child will learn
We are learning to recognise, sketch and interpret graphs of linear, quadratic, cubic and reciprocal functions.
Success looks like
- I can recognise graph shapes.
- I can read solutions from a graph.
- I can interpret real-life graphs.
Key words
- linear
- a straight-line graph
- quadratic
- a U-shaped curve
- cubic
- an S-shaped curve with x³
- reciprocal
- y = k/x, two curves that never touch the axes
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Plot y = x² and y = x³ from tables of values and compare the shapes.
The big ideas (for the adult)
Each type of function has a typical shape: straight line (linear), U or ∩ shape (quadratic), S shape (cubic) and two separate curves (reciprocal).
Read graphs to solve equations: the solutions of f(x) = k are where the graph meets the line y = k.
Real-life graphs tell a story: on a distance-time graph, steeper means faster and flat means stopped.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 11 maths lessons
- Volume and surface area
- Trigonometry: SOH CAH TOA
- Sine rule, cosine rule and area of a triangle
- Transformations
- Similarity and congruence
- Vectors
- Circle theorems
- Factorising
- Inequalities
- Sequences and the nth term
- Quadratic equations
- Iteration
- Functions
- Algebraic fractions
- Algebraic proof and identities
- Growth and decay
Curriculum
National Curriculum for England, Year 11: “recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = [Fraction:1/x] with x ≠ 0, {the exponential function y = k^{x} for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size}”
National Curriculum for England, Year 11: “{calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts}”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.