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Cross sections of 3-D figures – Grade 10 math lesson

Lesson 15 of 16 in the Grade 10 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 10 (ages 15–16) 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 10 (ages 15–16)
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.

  1. Read what your child will learn and the big ideas together.
  2. Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
  3. 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.
  4. Finish with the exit ticket and the talk question: “What shapes can you get by slicing a cube?”
  5. 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

45 minutes in 5 parts
PartTimeHow it is checked
Starter: quick recall5 minGraded by Classfern
Teaching input10 minNot assessed, self-checked
Worked examples and guided practice9 minNot assessed, graded by Classfern
Independent practice15 minGraded by Classfern
Closure and exit ticket6 minGraded 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

All Grade 10 math lessons and tests · Math Department

More Grade 10 math lessons

Curriculum

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.