Shape and Space Problems Year 8
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Examples
Page Ref |
Problem
Title |
Objectives
Ref |
Description |
Key Words |
181, 185 |
Inner
Rectangle |
2-D
Shape, Angle Properties of Quadrilaterals |
A cute
result about angles around a quadrilateral - suitable for investigation
with Dynamic Geometry |
Congruent,
Corresponding, Complementary |
183 |
Isosceles
Triangle |
Angle
properties in a Triangle |
A
first, though non-trivial, 'proof' involving angles |
Angle
sum, Base angles, Proof |
183,
221 |
No
Rights |
Angle
properties in a Triangle |
A very
simple first proof 'by contradiction' involving angles in a triangle |
Angle
sum, Proof, Bisector, Dynamic Geometry |
184 |
Two
Triangles |
Transformations,
Deductions |
An
example of very simple geometric reasoning |
Proof,
Rotate, Identical, Congruent |
184, 189, 213 |
Rectangle
Cut |
2-D Shape, Symmetry, |
A nice trick to
cut any rectangle in quarters |
Scale
factor, Stretch, Map |
184, 185 |
Card
Folding |
2-D Shape, Symmetry, |
Deduce
the original shape of paper from the twice folded final shape. |
Reflect,
Congruent, Symmetry |
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 |
184,235 |
Ratio
Cut |
Area,
Transformation |
A
simple transformation makes easy work of a rectangle division. |
Area,
Ratio, Height
|
187 |
Triangle
Sections |
Triangles,
Proof |
Prove
a simple relation within a triangle, using areas |
Geometric
property, Proof |
185, 187 |
L-Shape |
Area, Proof |
How to divide any
2-rectangle 'composite' in half? |
Symmetry,
Proof, Bisect |
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 |
191 |
The
Radius |
Congruence,
Similarity |
A
simple application of Similar triangles |
Congruent,
Similar |
191, 193, 217 |
Triangle
Dissections |
Congruence,
Similarity, Enlargement |
A
series of puzzles concerned with dissecting equilateral triangles into
smaller parts |
Congruent,
Similar |
61, 81, 193, 215 |
Pendants |
Similarity,
Enlargement |
'Area Factors'
under enlargement give quick answers to this problem |
Similar,
Enlargement, Scale factor |
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 |
203 |
Move
That Flag |
Transformations |
Use 2
reflections to effect a translation |
Image,
Translate, Reflect |
213 |
Square
in a Triangle |
Transformations,
Symmetries |
How to
squeeze the largest possible square inside any triangle? |
Enlargement |
215, 221 |
Forensic
Triangles |
Constructions, Dynamic Geometry |
Reconstruct the
original triangle from the sides' mid-points |
Medians,
Similar, Parallel |
221 |
Eggs |
Constructions,
Compasses |
Take
an egg... |
Compasses, Perpendicular, Arc, Tangent |
221,
223 |
Triangle
in a Square |
Constructions,
Dynamic Geometry |
How
to squeeze the largest possible equilateral triangle inside a square? |
Compasses, Rotation |
223, 245 |
Height
of the Tower |
Similar Triangles,
Scale Drawing |
There's a tower,
see, across this river, and what you've got to do is... |
Similarity,
Elevation |
133, 227, 234 |
Overlapping
Squares 1 |
Loci,
Graphs, 2-D shape |
This problem offers an
element of surprise in that the locus of possible solutions isn�t the
straight line that pupils may well expect |
Region,
Proof, Locus |
144,
229 |
Britain
Rules The Weights? |
Binary, Imperial weights |
Metric weights aren't quite as
efficient as you would hope... |
Power,
Gram, Ounce |
233 |
Anglesey |
Bearings |
Which is which
village? - using points of the compass. |
Points
of the compass |
235 |
Trapezium
Cuts |
2-D
Shape, Quadrilaterals, Area |
Dividing a
trapezium in several different ways - excellent for area calculations |
Area,
Base, Intersection |
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