Volume and surface area – Grade 7 math lesson
Lesson 15 of 21 in the Grade 7 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 7 (ages 12–13) 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 7 (ages 12–13)
- 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: “Can two shapes have the same volume but different surface areas?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Mixing up volume and surface area units. Volume: cm³. Area: cm².
- Missing hidden faces in surface area. Draw the net and label every face.
Tip for home: Work out how much a tin or a fish tank holds.
What your child will learn
Learning goal: find the volume and surface area of prisms, cylinders, cones and spheres.
Success looks like
- I can find the volume of prisms and cylinders.
- I can find surface areas.
- I can use the formulas for cones and spheres.
Key words
- volume
- space inside a solid (cubic units)
- surface area
- total area of all the faces (square units)
- prism
- a solid with the same cross-section all along
- cross-section
- the shape you see when you slice across
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Find the volume of a tin or a cereal box by measuring, then check with water or rice.
The big ideas (for the adult)
The volume of a prism is the area of its cross-section × its length. A cylinder is a prism with a circle cross-section: πr²h.
Surface area is the total area of all the faces. Sketch the net to make sure no face is missed.
Cones and spheres have their own formulas: cone volume = ⅓πr²h; sphere volume = ⁴⁄₃πr³. Density = mass ÷ volume links volume to mass.
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 7 math lessons
- Ratios
- Percent
- Proportional relationships
- Operations with integers
- Repeating decimals
- Evaluating expressions
- Simplifying expressions
- Expanding expressions
- Solving equations
- Inequalities
- Scale drawings and maps
- Angle relationships
- Area of triangles, parallelograms and trapezoids
- Circles: circumference and area
- Cross sections of 3-D figures
- Probability
- Experimental probability
- Compound events
- Box plots and interquartile range
- Sampling and making inferences
Curriculum
Common Core State Standards 7.G.B.6: “Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.