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, acute-angled triangles |
Acute,
Dissect, Angles at a point etc |
182 |
Isosceles
Triangle |
Angle
properties in a Triangle |
A
first, though non-trivial, '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 2-D shapes |
Diagonal
tilings and a formula for their areas |
Area,
Formulae |
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