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 |