A Resource for Free-standing Mathematics Qualifications
Points of View
Part 1
The following photographs show some everyday objects.
Some photographs have been taken from above and some from the front or side.
Identify each object.
Object B
Object A
Object D
Object C
Object E
Object G
Object H
Object F
Object I
Object J

Object K
Object L
Photo-copiable
The Nuffield Foundation
1
A Resource for Free-standing Mathematics Qualifications
Points of View
Part 2
The diagrams below represent three-dimensional objects.
The plan shows a view of the object from above and the elevations show views from the front and side.
In each case draw a three-dimensional sketch of the object.
Object A
Object C
Object B
Plan
Plan
Plan
Front
Side
Front
Side
Front
Object D
Object E
Side
Object F
Plan
Plan
Plan
Side
Side
Front
Side
Front
Front
Sometimes edges cannot be seen when the object is viewed from a particular direction.
Such edges are shown as dotted lines.
Object G
Object I
Object H
Plan
Plan
Plan
Side
Front
Side
Front
Side
Front
Object L
Object K
Object J
Plan
Plan
Plan
Front
Front
Front

Side
Side
Side
Photo-copiable
The Nuffield Foundation
2
A Resource for Free-standing Mathematics Qualifications
Points of View
Part 3
Sketch the plan, front elevation and side elevation of each of these objects, from the directions given.
For objects A to F use dotted lines to show any hidden edges.
Object C
Object A
Object B
Plan
Plan
Plan
Side
Side
Side
Front
(open-ended)
Front
Front
Object F
Object E
Plan
Object D
Plan
Plan
Side
Side
Front
Side
Front
Front
For objects G, H, I and J show only the observed external surfaces.
For objects K and L also show the hidden edges (using dotted lines).
Object H
Object G
Plan
Object I
Plan
Plan
Side
Front
Front
Side
Side
Front
Object J
Object K
Plan
Plan
Object L
Plan
Front
(solid handle)
Front

The Nuffield Foundation
Side
Side
Side
Front
Photo-copiable
3
A Resource for Free-standing Mathematics Qualifications
Points of View TN
Teacher Notes
Unit
Intermediate Level, Solving problems in shape and space
Skills used in this activity:
• identifying objects from plans and elevations (using photographs and sketches)
• drawing three dimensional sketches (showing external surfaces only)
• drawing plans and elevations of objects, using dotted lines for hidden edges.
Preparation
Students will need to know how to draw 3D sketches of objects.
(Note that in this activity only external surfaces are shown in the 3D sketches.)
Notes
This activity can be used at the beginning of the course to introduce the idea of representing objects using
plans and elevations. Students could attempt Part 1 immediately. Discussion of plans and elevations,
including the use of dotted lines for unseen edges, is advisable before students try Part 2. Part 3 can be
done immediately after Part 2 or left until a later date if you wish.
Note that only rough sketches are requested in this activity rather than accurate scale drawings and the
answers given below are not exact. Although the plans and elevations given in Part 2 and the answers are
presented as third angle orthogonal projections, it is not intended that this should be done formally.
Answers
Part 1
A Teapot
F Toast Rack
K Wine Glass
B Fork
G Kettle
L Lamp
C Can Opener
H Plant Pot
D Hole Punch
I Crash Helmet
E Nail Brush
J Shoe
Part 2
Object A
Object B
Object C
Object G
Object E
Object D
Object H
Object F
Object K
Object L
Object J
Object I

Photo-copiable
The Nuffield Foundation
1
A Resource for Free-standing Mathematics Qualifications
Points of View TN
Part 3
Object B
Object A
Object C
Plan
Plan
Plan
Side
Front
Side
Front
Side
Front
Object E
Object D
Object F
Object E
Plan
Plan
Plan
Front
Front
Side
Object G
Object I
Plan
Object H
Plan
Plan
Front
Side
Front
Side
Side
Front
Front
Side
Side
Object J
Object K
Object L
Plan
Plan
Plan
Front
Side
Front
Side
Front

Side
Photo-copiable
The Nuffield Foundation
2