Rates of change from graphs – Year 10 maths lesson
Lesson 37 of 37 in the Year 10 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 10 (ages 14–15) 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 10 (ages 14–15)
- 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: “What would a distance-time graph look like if someone walked, stopped, then ran?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Reading the scale wrongly when finding the gradient. Use the axis values, not the number of squares.
- Thinking a steeper line means slower. Steeper means faster change.
Tip for home: Look at graphs of prices or temperatures and talk about how fast they change.
What your child will learn
We are learning to find and interpret rates of change from graphs.
Success looks like
- I can find a gradient from a graph.
- I can explain what the gradient means.
- I can estimate a rate of change on a curve.
Key words
- gradient
- steepness: change up ÷ change across
- rate of change
- how fast one quantity changes compared with another
- tangent
- a line that just touches a curve
- chord
- a line joining two points on a curve
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Fill a jar with water at a steady rate and sketch how the height changes over time.
The big ideas (for the adult)
The gradient of a straight-line graph is the rate of change: change up ÷ change across.
On a distance-time graph the gradient is the speed. A flat line means stopped.
For a curve, the rate of change at a point is the gradient of the tangent there; the average rate is the gradient of a chord.
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 10 maths lessons
- Systematic listing and counting
- Standard form
- Laws of indices
- Surds
- Fractions, decimals and recurring decimals
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Pythagoras' theorem
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Vectors
- Circle theorems
- Bearings
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Histograms
- Pie charts and time series graphs
- Scatter graphs and correlation
- Sampling
- Combined events and tree diagrams
- Simplifying expressions
- Expanding brackets
- Factorising
- Solving linear equations
- Inequalities
- Sequences and the nth term
- Straight-line graphs
- Simultaneous equations
- Quadratic equations
- Functions
- Graphs of functions
- Algebraic proof and identities
- Growth and decay
- Direct and inverse proportion
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 10: “interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion”
National Curriculum for England, Year 10: “{interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of instantaneous and average rate of change (gradients of tangents and chords) in numerical, algebraic and graphical contexts}”
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Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.