Graphing functions – Grade 9 math lesson
Lesson 16 of 17 in the Grade 9 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 9 (ages 14–15) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 9 (ages 14–15)
- You need
- Paper, a pencil and this page
- Graded
- 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 graded straight away with a worked explanation, so you never have to grade 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
Learning goal: recognize, sketch and interpret graphs of linear, quadratic, cubic and reciprocal functions.
Success looks like
- I can recognize 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 | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded 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 graded instantly.
More practice
More Grade 9 math lessons
- Rates and unit rates
- Converting units
- Upper and lower bounds
- Simplifying expressions
- Expanding expressions
- Factoring
- Solving equations
- Inequalities
- Rearranging formulas
- Systems of equations
- Quadratic equations
- Identities and proof
- Arithmetic and geometric sequences
- Linear functions and slope
- Functions
- Exponential functions
Curriculum
Common Core State Standards HSA.REI.D.11: “Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*”
Common Core State Standards HSF.IF.B.6: “Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.