Cross sections of 3-D figures – Grade 7 math lesson
Lesson 16 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: “What shapes can you get by slicing a cube?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Drawing hidden edges in a plan. Draw only what you can see from that direction.
- Counting the same edge twice. Use the base: a prism with an n-sided base has 3n edges.
Tip for home: Slice fruit or cheese in different directions and look at the cross-sections.
What your child will learn
Learning goal: describe 3-D figures, their cross sections and the solids made by rotating shapes.
Success looks like
- I can count faces, edges and vertices.
- I can draw plans and elevations.
- I can describe cross-sections.
Key words
- top view
- the view from above
- front or side view
- the view from the front or side
- cross-section
- the face made by a slice
- vertex
- a corner (vertices)
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Build a shape from cubes and draw it from the top, the front and the side.
The big ideas (for the adult)
A 3-D shape has faces, edges and vertices. For a prism or pyramid, count them from its base shape.
Views from the top, front and side show a solid in two dimensions.
A cross-section is the shape you see when you slice a solid. Rotating a flat shape around a line makes a solid, such as a cylinder from a rectangle.
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
- Volume and surface area
- Probability
- Experimental probability
- Compound events
- Box plots and interquartile range
- Sampling and making inferences
Curriculum
Common Core State Standards 7.G.A.3: “Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.”
Common Core State Standards HSG.GMD.B.4: “Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.