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