Grade by Grade
E. Spatial Sense · Spatial Sense: 3D Objects, Transformations, Circles, Surface Area and Volume

Views, Perspective Drawings and Scale

E1.2 A1About 50 minutes
Learning goals
  • I can choose a scale that fits my drawing on the page.
  • I can draw the top, front and side views of an object or a space using a scale.
  • I can draw a perspective view of an object on isometric dot paper.
  • I can use scale drawings to find real measurements and to build scale models.

Words to know

view
A drawing of an object as seen straight on from one side: top, front or side.
perspective view
A drawing that shows an object in 3D, with more than one face showing at once.
isometric dot paper
Paper with dots arranged in triangles. It helps you draw 3D objects with vertical lines and two sets of slanted lines.
scale
A ratio that compares lengths on a drawing or model with real lengths, such as 1 cm : 50 cm.
scale drawing
A drawing in which every length is the real length multiplied or divided by the same number.
scale model
A 3D model whose lengths are all in the same ratio to the real object's lengths.

Remember from earlier grades

In Grade 5 you drew the top, front and side views of objects and cube structures. In Grade 6 you built cube structures from their views. In Grade 7 you will draw views of real objects and spaces to scale, draw perspective views, and build scale models.

Let's start with a shed

A family wants to build a garden shed: 3 m wide, 2 m deep and 2.5 m tall, with a flat roof. A 3 m drawing won't fit on paper! So they make a scale drawing. Each real length is divided by the same number, so the drawing has the same shape as the shed, only smaller.

A small wooden garden shed with a flat roof, one door and one window, in a backyard garden.
A real shed is too big to draw full size. A scale drawing shrinks every length by the same factor so the shape stays the same. AI-generated image

What a scale means

A scale of 1 cm : 50 cm means every 1 cm on the drawing stands for 50 cm in real life.

  • Real → drawing: divide the real length by 50. 3 m = 300 cm, and 300 ÷ 50 = 6 cm.
  • Drawing → real: multiply the drawing length by 50. 4 cm × 50 = 200 cm = 2 m.

Always change real lengths to the same unit as the scale first. Use the same scale for every view, so the views match each other.

3 m2.5 mfront view3 m2 mtop view2 m2.5 mside view
The three views of the shed, drawn to the same scale. In each view, every metre is the same length, so the 3 m sides match and the 2.5 m heights match.
Worked example

Example 1: Draw the views to scale

Draw the front, top and side views of the shed (3 m wide, 2 m deep, 2.5 m tall) at a scale of 1 cm : 50 cm.

  1. Change to centimetres: 300 cm wide, 200 cm deep, 250 cm tall.
  2. Divide each by 50: width 6 cm, depth 4 cm, height 5 cm.
  3. Front view shows width and height: a rectangle 6 cm by 5 cm.
  4. Top view shows width and depth: a rectangle 6 cm by 4 cm.
  5. Side view shows depth and height: a rectangle 4 cm by 5 cm.

Front 6 cm × 5 cm, top 6 cm × 4 cm, side 4 cm × 5 cm. Write the scale 1 cm : 50 cm on the drawing.

Worked example

Example 2: Choose a scale

Draw a floor plan (top view) of a bedroom that is 4 m by 3.5 m on paper about 21 cm by 27 cm. Which scale is best: 1 cm : 10 cm, 1 cm : 20 cm or 1 cm : 50 cm?

  1. 4 m = 400 cm and 3.5 m = 350 cm.
  2. 1 cm : 10 cm → 40 cm by 35 cm. Too big for the paper.
  3. 1 cm : 20 cm → 20 cm by 17.5 cm. Fits, and fills the page.
  4. 1 cm : 50 cm → 8 cm by 7 cm. Fits, but small, so the furniture would be tiny.

1 cm : 20 cm is best: it fits and is as big as possible, so details are easy to see.

Worked example

Example 3: From a drawing to real life

On a park plan with scale 1 cm : 2 m, an outdoor skating rink is 15 cm long and 7.5 cm wide. How big is the real rink?

  1. Each 1 cm stands for 2 m.
  2. Length: 15 × 2 = 30 m. Width: 7.5 × 2 = 15 m.

The rink is 30 m by 15 m.

Perspective views on isometric dot paper

A perspective view shows three faces at once: the top, the front and a side. On isometric dot paper:

  1. Draw vertical edges straight up and down along the dots.
  2. Draw edges that go left-right and front-back along the two slanted directions of the dots.
  3. Count the same number of dot spaces for equal lengths. Edges that are parallel on the object stay parallel in the drawing.
  4. Draw the front corner first, then build out from it. Shade the top, front and side in three different shades so the 3D shape pops out.

To draw a box that is 3 units wide, 2 units deep and 1 unit tall, start with a vertical edge 1 space long, go 3 spaces along one slant and 2 spaces along the other slant, then finish the top.

3 units2 units1 unit
A box 3 units wide, 2 units deep and 1 unit tall on isometric dot paper. Vertical edges go straight up and down; the other edges follow the two slanted rows of dots.

Scale models

A scale model uses the same idea in 3D. For a model of the shed at 1 cm : 20 cm, every length is divided by 20: 15 cm wide, 10 cm deep, 12.5 cm tall. Read the measurements from your views, cut out the faces and tape them together.

Hands-on activity

Measure it, draw it, build it

You need: a tape measure or ruler, a small piece of furniture (a stool, a nightstand) or a cereal box, paper (grid or isometric dot paper if you have it, or print free isometric dot paper), scissors and tape.

  1. Measure the length, width and height of the object.
  2. Choose a scale so all three views fit on one page (for a nightstand, try 1 cm : 5 cm; for a cereal box, 1 cm : 2 cm).
  3. Draw the front, top and side views to scale and label each with the real measurements and the scale.
  4. Draw a perspective view on isometric dot paper.
  5. Bonus: build a small scale model out of paper or thin cardboard from your views. Ask a grown-up to help with scissors.

What to look for: matching lengths in the views (the width in the front view equals the width in the top view) and the scale written on the page.

Just for fun

A map drawn at a scale of 1 cm : 1 cm would be exactly as big as the place it shows. Very accurate... but good luck folding it into your backpack.

Your turn

1

The scale is 1 cm : 50 cm. A real wall is 3 m long. How long is it on the drawing?

2

The scale is 1 cm : 50 cm. A line on the drawing is 4.5 cm. How long is the real object?

3

A box is 30 cm long, 20 cm wide and 10 cm tall. Draw its front view (length and height) at 1 cm : 5 cm. What are the measurements of the drawing?

4

Same box. What are the measurements of its top view at 1 cm : 5 cm?

5

A can stands upright. Which view is a circle?

6

A can is 8 cm across and 12 cm tall. Draw its front view at a scale of 1 cm : 2 cm. What are the measurements?

More practice: warm-up

1

Scale 1 cm : 10 cm. A real table leg is 80 cm. How long is it on the drawing?

2

Scale 1 cm : 100 cm. A drawing line is 7 cm. How long is the real object?

3

Which view shows the width and the depth of an object?

4

On isometric dot paper, how do you draw vertical edges?

5

What shape is the front view of a cube?

More practice: on your own

1

A classroom is 9 m by 7 m. Your paper is 20 cm by 25 cm. Which scale is best: 1 cm : 20 cm, 1 cm : 50 cm or 1 cm : 200 cm? Explain.

2

A garage floor plan is 12 cm by 8 cm at a scale of 1 cm : 50 cm. What is the real size?

3

A right square pyramid sits on its base. Describe its front view and its top view.

4

A model car is built at a scale of 1 cm : 20 cm. The real car is 4.6 m long. How long is the model?

5

A picnic table top is 180 cm by 75 cm. What are the measurements of its top view at 1 cm : 15 cm?

Challenge

1

Ella draws the front view of a shed at 1 cm : 50 cm and the side view at 1 cm : 25 cm. What problem will this cause?

2

A communication tower is 120 m tall. You want a model that fits on a table and is less than 50 cm tall. Would 1 cm : 1 m or 1 cm : 5 m work? Explain.

3

A cylinder-shaped log lies on its side on the ground, with its round ends facing left and right. Describe its top, front and side views.

Check your understanding

Quiz

1.

The scale is 1 cm : 20 cm. A real object is 1 m long. How long is it on the drawing?

2.

The scale is 1 cm : 2 m. A line on the drawing is 3 cm. How long is the real object?

3.

Why should all the views of an object use the same scale?

4.

What does the top view of an upright cylinder look like?

5.

What does a perspective view on isometric dot paper show?

6.

Which scale is best for drawing a 30 m long mini soccer field on paper 25 cm wide?

For parents and teachers

Big idea: E1.2 asks Grade 7 students to work with top, front, side and perspective views of objects and physical spaces using appropriate scales, and to make objects and models from them. This builds on Grade 5 (drawing views) and Grade 6 (building from views).

How to help at home: Draw a floor plan of a room together. Let your child choose the scale and check that the plan fits the page. Ask "How long is the real couch if it's 9 cm on the plan?" Free isometric dot paper can be printed from many websites.

Common difficulties:

  • Forgetting to convert units (metres to centimetres) before dividing by the scale.
  • Using different scales for different views.
  • Perspective drawings that slope the wrong way. Remind them: vertical stays vertical, and parallel edges stay parallel.

Choosing a scale is a great A1 skill: there is more than one workable answer, and students should explain why their choice is the best fit.