Mathematics
Grade 10
15 min
Nets and drawings of three-dimensional figures
Nets and drawings of three-dimensional figures
What you'll learn
- Identify the missing fractional factor in a multiplication equation by using visual models like area models or fraction bars with at least 80% accuracy.
- Solve multiplication problems involving two fractions using visual models to represent the product, correctly shading the appropriate area to arrive at the solution in at least 3 out of 4 attempts.
- Explain how a visual model represents the multiplication of two fractions, connecting the shaded areas to the numerator and denominator of the resulting fraction, in a written explanation that demonstrates understanding.
- Apply the understanding of visual models to create their own model that demonstrates the multiplication of two given fractions, and correctly identify the product of the fractions with 100% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the three-dimensional figure that can be formed from a given net.
Draw at least two different valid nets for a given cube, rectangular prism, and triangular prism.
Create isometric drawings of simple three-dimensional figures on dot paper.
Create orthographic projections (top, front, and side views) of a three-dimensional figure.
Interpret a set of orthographic projections to sketch the corresponding three-dimensional figure.
Relate the surface area of a 3D figure to the total area of its net.
How does a flat piece of cardboard become a shipping box? 📦 This lesson explores how we can represent 3D objects in a 2D world!
We will learn how to 'unfold' three-dimensional figures into two-dimensional patterns called nets, and how to draw th...
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Key Concepts & Vocabulary
TermDefinitionExample
Three-Dimensional Figure (Solid)A geometric figure that has three dimensions: length, width, and height. It occupies space.A cube, a sphere, a pyramid, or a cylinder.
NetA two-dimensional pattern that can be folded along its edges to form a three-dimensional figure. It is like the 'unfolded' version of a solid.A cross shape made of six squares is a net for a cube.
Isometric DrawingA method for visually representing three-dimensional objects in two dimensions, where the object is viewed from an angle to reveal multiple sides. All vertical lines are drawn vertically, and all horizontal lines are drawn at a 30° angle to the horizontal.A drawing of a cube on isometric dot paper where all faces are visible and edges appear to be of equal length.
Orthographic Pro...
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Core Formulas
Euler's Formula for Polyhedra
V - E + F = 2
For any convex polyhedron, the number of Vertices (V) minus the number of Edges (E) plus the number of Faces (F) will always equal 2. Use this formula to check if you have correctly counted the parts of a solid or to find a missing value.
Surface Area from a Net
SA = \sum_{i=1}^{n} A_i
The total Surface Area (SA) of a 3D figure is the sum of the areas of all the individual shapes (faces) in its net. To find the surface area, calculate the area of each 2D shape in the net and add them all together.
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Challenging
An isometric drawing shows a structure made of 1x1x1 cubes. The structure has a 3x3 base, a 2x2 layer on top of that, and a single cube on the very top, all centered. How many total cubes are used to build this structure?
A.6
B.9
C.14
D.36
Challenging
The top view of a structure made of cubes is a 3x3 square. The front view is also a 3x3 square. What is the minimum number of cubes required to build a structure that satisfies these two views?
A.9
B.11
C.18
D.27
Challenging
A net of a right pyramid with a square base has a total area of 100 cm². The area of the square base is 36 cm². What is the slant height of the pyramid's triangular faces?
A.5 cm
B.8 cm
C.10 cm
D.12.5 cm
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What grade level is "Nets and drawings of three-dimensional figures"?
Nets and drawings of three-dimensional figures is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Nets and drawings of three-dimensional figures?
You'll be able to: Identify the missing fractional factor in a multiplication equation by using visual models like area models or fraction bars with at least 80% accuracy; Solve multiplication problems involving two fractions using visual models….
Is "Nets and drawings of three-dimensional figures" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Nets and drawings of three-dimensional figures?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.