Chapter 47: Three-Dimensional Objects, Nets, and Structures
Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Three-Dimensional Objects, Nets, and Structures in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
Key Technical Terms
- Three-dimensional objects (Three-dimensional objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Faces (Faces is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Edges (Edges is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Vertices (Vertices is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Prisms (Prisms is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Pyramids (Pyramids is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
How to Learn This Chapter
Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
47.1 Three-dimensional objects
Three-dimensional objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Three-dimensional objects. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.2 Faces
Faces is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Faces. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.3 Edges
Edges is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Edges. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.4 Vertices
Vertices is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Vertices. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.5 Prisms
Prisms is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Prisms. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.6 Pyramids
Pyramids is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Pyramids. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.7 Cylinders
Cylinders is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Cylinders. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.8 Nets
Nets is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Nets. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.9 Matching nets to objects
Matching nets to objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Matching nets to objects. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.10 Building structures
Building structures is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Building structures. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.11 Views of 3D structures
Views of 3D structures is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Views of 3D structures. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.12 Comparing 3D objects
Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Use Comparing 3D objects to analyze the values 26 and 16. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 2
Problem: Use Comparing 3D objects to analyze the values 8 and 3. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 3
Problem: Use Comparing 3D objects to analyze the values 23 and 10. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 4
Problem: Use Comparing 3D objects to analyze the values 7 and 9. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 5
Problem: Use Comparing 3D objects to analyze the values 11 and 10. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 6
Problem: Use Comparing 3D objects to analyze the values 5 and 2. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 7
Problem: Use Comparing 3D objects to analyze the values 29 and 9. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 8
Problem: Use Comparing 3D objects to analyze the values 29 and 20. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 9
Problem: Use Comparing 3D objects to analyze the values 29 and 20. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 10
Problem: Use Comparing 3D objects to analyze the values 14 and 8. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Practice Exercise
Create one new Grade 6 problem about Comparing 3D objects. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
47.13 Real-life structures
Real-life structures is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Describe a cube.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 2
Problem: Describe a rectangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 faces, 12 edges, 8 vertices
Worked Example 3
Problem: Describe a triangular prism.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 9 edges, 6 vertices
Worked Example 4
Problem: Describe a square pyramid.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 5 faces, 8 edges, 5 vertices
Worked Example 5
Problem: Describe a cylinder.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 circular bases and 1 curved surface
Worked Example 6
Problem: Describe a cube net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 connected squares
Worked Example 7
Problem: Describe a rectangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 6 rectangles, with some faces possibly squares
Worked Example 8
Problem: Describe a triangular prism net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 2 triangles and 3 rectangles
Worked Example 9
Problem: Describe a square pyramid net.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: 1 square and 4 triangles
Worked Example 10
Problem: Describe a 3D structure.
- Identify its flat faces or bases.
- Count edges and vertices when those features apply.
Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.
Answer: can be described using faces, edges, vertices, and views
Practice Exercise
Create one new Grade 6 problem about Real-life structures. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
30 Review Questions and Answers
Q1. What is important to understand about Three-dimensional objects?
Answer: Three-dimensional objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q2. What is important to understand about Faces?
Answer: Faces is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q3. What is important to understand about Edges?
Answer: Edges is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q4. What is important to understand about Vertices?
Answer: Vertices is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q5. What is important to understand about Prisms?
Answer: Prisms is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q6. What is important to understand about Pyramids?
Answer: Pyramids is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q7. What is important to understand about Cylinders?
Answer: Cylinders is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q8. What is important to understand about Nets?
Answer: Nets is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q9. What is important to understand about Matching nets to objects?
Answer: Matching nets to objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q10. What is important to understand about Building structures?
Answer: Building structures is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q11. What is important to understand about Views of 3D structures?
Answer: Views of 3D structures is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q12. What is important to understand about Comparing 3D objects?
Answer: Comparing 3D objects is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q13. What is important to understand about Real-life structures?
Answer: Real-life structures is a Grade 6 mathematics idea in Three-Dimensional Objects, Nets, and Structures. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships that are harder to see in words alone.
Q23. Why are tables useful?
Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.
Q24. Why are graphs useful?
Answer: Graphs make relationships, changes, trends, and comparisons visible.
Q25. Why should you explain your reasoning?
Answer: An explanation shows why a method works instead of only giving a final number.
Q26. Why can more than one strategy be correct?
Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.
Q27. What should you do before using a formula or rule?
Answer: Check what each quantity means and whether the rule matches the situation.
Q28. How does practice help in mathematics?
Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.
Q29. What is a good way to learn from a mistake?
Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.
Q30. Why should you compare an exact answer with an estimate?
Answer: The estimate gives a quick reasonableness check for the exact calculation.