Courseversity

Surface area using nets

Primary EducationGrade 6MathematicsCV-PRI-G06-MATH-MEA-U01-L0745–60 min

You will learn

  • Unfold a prism into a net.
  • Add face areas.
  • Use the cube formula.
  • Solve problems.

Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.

Student lesson

The lesson in 60 seconds

  1. Surface area is the total area of all faces.
  2. A net shows every face laid flat.
  3. A cube has 6 equal faces.
  4. A box has 3 pairs of equal faces.

Words to know

surface area
Total area of all faces.
net
Flat pattern.
face
Flat surface.
cube
Six equal square faces.

1. Discover: wrapping a gift

How much paper wraps a cube of side 3 cm?

2. Understand: surface area

  • A cube has 6 square faces: 6 × 3 × 3 = 54 cm².
  • A box 4 by 3 by 2: faces 12, 12, 8, 8, 6, 6 add to 52 cm².
  • A cube of side 5: 6 × 25 = 150.
  • A 5 by 2 by 1 box: 10 + 10 + 5 + 5 + 2 + 2 = 34.

Idea 1: Cube

Cube of side 3: 6 × 9 = 54 cm². Side 5: 6 × 25 = 150 cm².

Idea 2: Box

Box 4 by 3 by 2: faces 12, 8 and 6, each twice: 2 × 26 = 52 cm². Box 5 by 2 by 1: 34 cm².

Idea 3: Faces

A box has 6 faces. Gift paper for a 3 cm cube needs 54 cm².

Why a net? It lets you see every face once.

Remember: Find every face and add.

3. Worked examples

Example 1 (I show you): Cube

Side 3

  1. 9 per face.
  2. 6 × 9.

Answer: 54 cm²

Example 2 (We do it together): Box

4 by 3 by 2

  1. 12, 8, 6.
  2. 2 × 26.

Answer: 52 cm²

Example 3 (You try): Box

5 by 2 by 1

Show the steps and answer
  1. 10, 5, 2.
  2. 2 × 17.

Answer: 34 cm²

Did you know?

A cube has 11 different nets.

Why this matters

Surface area tells how much material wraps a box.

4. Explore: net

You need paper.

  1. Draw the net.
  2. Find each face area.
  3. Add all faces.
  4. Write cm².
Think about it: what did you notice?

54 cm².

5. Practise

Say it in a sentence

Use these starters when you talk about the lesson. Say them out loud.

  • One face has area ___.
  • The pairs of faces are ___, ___ and ___.
  • Total = 2 × ( ___ + ___ + ___ ).
  • The surface area is ___ cm².

Guided practice

Question 1. Faces of a cube?

6.

Question 2. 6 × 9?

54.

Question 3. 4 by 3 by 2 total?

52.

Independent practice

Level 1: Start

  1. Cube of side 3
  2. Cube of side 5
  3. Box 4 by 3 by 2
  4. Box 5 by 2 by 1
  5. Faces on a box

Level 2: Grow

  1. Cube of side 2
  2. Cube of side 4
  3. Cube of side 10

Level 3: Stretch

  1. Box 3 by 2 by 1
  2. Box 6 by 4 by 2
  3. Ben says the box 4 by 3 by 2 has surface area 24. What is wrong?

Answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

Wrapping paper for a 3 cm cube needs how much?

Show a sample answer

54 cm².

Another one. A cube has surface area 150 cm². Find its side.

Show a sample answer

5 cm

7. Common mistakes

Mistake: Counting only 3 faces.
Fix: A box has 6 faces.
Another mistake: Mixing volume and surface area.
Fix: Surface area adds face areas.
Another mistake: Missing the hidden faces.
Fix: Count all 6 faces.

8. Lesson summary and revision card

I can…

  • I can unfold a prism into a net.
  • I can add face areas.
  • I can use the cube formula.
  • I can solve problems.

9. Check and master

Answer all 14 questions. You will see feedback after each one.

1. Cube of side 3:

2. Cube of side 5:

3. Box 4 by 3 by 2:

4. Box 5 by 2 by 1:

5. Faces of a box:

6. Cube of side 2

7. Cube of side 4

8. Cube of side 10

9. Box 3 by 2 by 1

10. Box 6 by 4 by 2

11. Box 5 by 3 by 2

12. The surface area of a solid is…

Challenge 1. Gift paper for a 3 cm cube:

Challenge 2. A cube has surface area 150 cm². Its side is

Your result appears here after you answer every question.

10. Key takeaways

  • Draw the net.
  • Add all faces.
  • Square units.

11. Next lesson

Next lesson: Measurement applications. Keep going with the next idea in this course.

Exam practice

These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.

  1. Find the surface area of a cube with side 3 cm. [2 marks]
  2. Find the surface area of a cube with side 5 cm. [2 marks]
  3. Find the surface area of a box 4 cm by 3 cm by 2 cm. [3 marks]
  4. Find the surface area of a box 5 cm by 2 cm by 1 cm. [3 marks]
  5. Ali says the box 4 by 3 by 2 has surface area 24 cm². Is he right? Explain. [3 marks]

Total: 13 marks.

Marking guide and model answers
  1. 6 faces, each 3 × 3 = 9 [1]; 6 × 9 = 54 cm² [1]
  2. 6 × 25 [1]; 150 cm² [1]
  3. Face areas 12, 8 and 6, each twice [1]; 2 × (12 + 8 + 6) [1]; 52 cm² [1]
  4. Face areas 10, 5 and 2 [1]; 2 × 17 [1]; 34 cm² [1]
  5. No [1]. 24 is the volume [1]. Surface area adds all faces: 52 cm² [1].

Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.

Printable worksheet

  1. Cube of side 3
  2. Cube of side 5
  3. Box 4 by 3 by 2
  4. Box 5 by 2 by 1
  5. Faces on a box
  6. Cube of side 3
  7. Cube of side 5
  8. Box 4 by 3 by 2
  9. Box 5 by 2 by 1
  10. Faces on a box

Homework

Make a net of a box and find its area.

Answer key and marking scheme

Question Expected response Marks
Cube of side 3 54 2
Cube of side 5 150 2
Box 4 by 3 by 2 52 2
Box 5 by 2 by 1 34 2
Faces on a box 6 2
Total 10

Practice answers: Worksheet: 1 54; 2 150; 3 52; 4 34; 5 6.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.

Extra worksheet answers (items 6 onward): 6 54 cm²; 7 150 cm²; 8 52 cm²; 9 34 cm²; 10 6.

Independent practice answers. Level 1: 1 54 cm²; 2 150 cm²; 3 52 cm²; 4 34 cm²; 5 6. Level 2: 1 24 cm²; 2 96 cm²; 3 600 cm². Level 3: 1 22 cm²; 2 88 cm²; 3 24 is the volume. Surface area is 52 cm²..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Unfold a prism into a net Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O2 Add face areas Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O3 Use the cube formula Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O4 Solve problems Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation

Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.

If a learner struggles

  1. Find the misconception: Counting only 3 faces. A box has 6 faces.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Area of rectangles.
  4. Guided practice: work through one example together and let the learner try the next one.
  5. Reassess: use the quiz again or the worksheet.
  6. Move on when the learner shows Silver-level evidence independently.

For parents and guardians

In this lesson your child finds surface area using nets. You do not need to be good at mathematics to help.

  • Wrap a small box with paper.
  • Ask: have I counted all 6 faces?
  • Unfold a box to see the net.
  • Ask “how do you know?” after each answer, and listen.
  • Praise effort, not only right answers. Mistakes are how we learn.
  • Ten to fifteen minutes a day is better than one long session.

Teacher package

1–5. Objectives, prerequisites, materials, preparation, duration

Lesson objectives. Learners will: unfold a prism into a net; add face areas; use the cube formula; solve problems.

Prerequisite knowledge. Lesson 6.

Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.

Preparation. Gather the counters and draw the example pictures on the board before the lesson.

Suggested duration. 45–60 minutes. It can be split into two shorter sessions.

6–9. Teaching procedure, explanation notes, guided and independent activities

Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.

Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.

Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.

Independent activity (10 min). Learners complete the independent practice and the worksheet.

Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.

Key questions. How many faces? Which are equal?

Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.

10–12. Differentiation, formative assessment, common misconceptions

Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.

Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.

Misconceptions. Counting only 3 faces. A box has 6 faces.

13–15. Assessment questions, answer keys, marking scheme

Use the quiz and worksheet on this page. The 13-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.

16–19. Remediation, enrichment, homework, teacher reflection

Remediation. Area of rectangles. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.

Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.

Sources and standards

This lesson is based on the sources below, and no official endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Where a standard code is named, it points to the official framework.

Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 6 » Ratios & Proportional Relationships; Grade 6 » Geometry. These pages list the standards that cover this topic area; read them alongside the lesson.

Research used to shape this lesson. Common Core 6.G.A.4; Cambridge Primary Mathematics Stage 6 (surface area). These sources informed the lesson.

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