Shape and Space Problems Year 7
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Examples
Page Ref 
Problem
Title 
Objectives
Ref 
Description 
Key Words 
178, 184 
A
Cute Triangle 
Angle
properties in a Triangle 
Cutting
a triangle into smaller, acuteangled triangles 
Acute,
Dissect, Angles at a point etc 
182 
Isosceles
Triangle 
Angle
properties in a Triangle 
A
first, though nontrivial, 'proof' involving angles 
Angle
sum, Base angles, Proof 
184, 185 
When
The Boat Comes In 
Triangles,
Proof 
The
sum of any 2 sides of a triangle is greater than the third, so... 
Geometric
property, Proof 
184, 189, 213 
Rectangle
Cut 
2D Shape,
Symmetry 
A nice trick to
cut any rectangle in quarters 
Scale
factor, Stretch, Map 
184, 185 
Card
Folding 
2D Shape,
Symmetry 
Deduce
the original shape of paper from the twice folded final shape. 
Reflect,
Congruent, Symmetry 
184, 202 
Two
Triangles 
Transformations,
Deductions 
An
example of very simple geometric reasoning 
Proof,
Rotate, Identical, Congruent 
185, 188, 209 
Overlapping
Figures 
Angles, Symmetry,
Similar triangles 
How much overlap
between 2 congruent regular polygons ? 
Corresponding,
Symmetry, Isometric 
186, 187 
Cut
A Rectangle 
Triangles,
Quadrilaterals 
Make
a triangle from a rectangle, using a single cut... 
Geometric
property, Symmetry 
186, 189 
How
Many Triangles 
Triangles 
How
many different triangles can you make with a choice of 6 rods ? 
Geometric
property, Proof, Sequence, General term 
198 
Parcel
wrap 
3D
Shape, Nets 
What's
the least wastage when wrapping a parcel? 
Nets,
Face 
198, 199 
Pyramid
Scorpion 
3D
Shape, Nets 
The
shortest route across a Pyramid ? 
Nets,
Face, Vertex, Perpendicular 
198, 199 
Polyball 
3D
Shape, Symmetry 
How many balls
can you get to touch one in the middle? 
Plan
view, Plane, Symmetry 
200, 207 
TetraCubes 
3D Shape 
Identify shapes,
then use to build mini
Soma Cubes 
Plan,
View, Symmetry 
100, 206, 260 
Mean
Square 
Puzzles,
Symmetry, Transformations 
A
Magic Square, using means 
Symmetry,
Transform, etc 
133, 227, 234 
Overlapping
Squares 1 
Area,
Loci,
Trial + Improvement 
This problem offers an
element of surprise in that there are an infinite number of possible solutions
 more than pupils may well expect ! 
Region,
Proof, Sketch 
100, 228 
Smart
Weights 
Mental methods,
Mass 
The most
efficient choice of weights is based on binary, but tertiary is even
smarter ! 
Power,
Mass, Expression 
144,
229 
Britain
Rules The Weights? 
Binary,
Imperial weights 
Metric weights aren't quite as
efficient as you would hope... 
Power,
Gram, Ounce 
234 
Stained
Glass Windows 
Area
in 2D shapes 
Diagonal
tilings and a formula for their areas 
Area,
Formulae 















