Shape and Space Problems Year 7                                       

To view the problem statement, double click on the problem title. This will open up the problem in a new window. From there, you can download the full problem-and-solution Word document.

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


Send site mail to [email protected]  or personal comments direct to with questions or comments about this web site.
Last modified: June 18, 2007