The Geometry Cabinet
A wooden cabinet, typically about 40cm × 40cm × 30cm deep, with six drawers. Each drawer contains a tray of shape insets: wooden shapes that fit precisely into matching holes.
Drawer 1: the demonstration tray. A triangle, a square and a circle. Used for initial presentation; the three most basic shapes.
Drawer 2: circles. Graduated circles from small to large. Visual size work with a single shape type.
Drawer 3: triangles. The classification of triangles: equilateral, isosceles, scalene, right-angled, obtuse, acute. Six or more triangles, each distinct.
Drawer 4: quadrilaterals. Square, rectangle, rhombus, parallelogram, trapezium, trapezoid, kite. The major named four-sided figures.
Drawer 5: regular polygons. Pentagon, hexagon, heptagon, octagon, nonagon, decagon. Regular polygons with five to ten sides.
Drawer 6: curved figures. Oval, ellipse, curvilinear triangle, quatrefoil. Miscellaneous curved shapes that appear in art and geometry.
The work. The child takes each drawer out in turn, removes the insets, places them on a mat, returns them to their matching holes. The control of error is the fit: an inset placed in the wrong hole will not sit flat. The child learns shapes by handling them.
Nomenclature. Three-period lessons introduce the names: "This is an equilateral triangle. This is an isosceles triangle. This is a scalene triangle." Matched with three-part cards showing real-world examples of each shape. Over time the child can name all the shapes and identify them by sight.
A full Geometry Cabinet costs £150-300 new. Second-hand sets £80-180. Individual drawers can be bought separately from some suppliers if the full cabinet is unaffordable.
The Constructive Triangles
Five boxes, each containing a specific set of precisely-cut triangles. The triangles in each box combine (by sliding them together) to form larger shapes.
Box 1: the rectangular box. Right-angled triangles that combine to form rectangles and a square. Introduces the idea that a rectangle is two right-angled triangles.
Box 2: the triangular box. Scalene, isosceles and equilateral triangles that combine to form a large equilateral triangle. Introduces triangle congruence and the structure of large triangles.
Box 3: the large hexagonal box. Triangles that combine to form a regular hexagon.
Box 4: the small hexagonal box. A smaller version of Box 3 with additional classifications.
Box 5: the blue triangles box. A set of triangles of different classes, for free exploration and creative combination.
The work. The child takes one box to a mat, takes the triangles out, combines them to form the parent shape (rectangle, equilateral triangle, hexagon). Then variations: same triangles, different combinations. The child discovers geometric relationships by manipulating pieces.
A full set of all five boxes costs £80-160 new. Second-hand often £50-100. Some UK families buy Boxes 1 and 2 first and add the others later.
What they are actually teaching
Geometry Cabinet work is discrimination and naming. The child learns, sensorially, the difference between an equilateral and a scalene triangle; between a rhombus and a parallelogram; between a regular hexagon and an irregular one. This is the vocabulary and categorisation of plane geometry, done with the hands.
Constructive Triangles work is relation and composition. The child learns that a rectangle is two right-angled triangles; that a hexagon is six equilateral triangles; that an equilateral triangle is four smaller equilateral triangles. This is the structural geometry of shapes: how larger shapes are built from smaller ones.
Together the two materials prepare for formal Plane 2 geometry in the way the Binomial Cube prepares for algebra. A nine-year-old doing angle work, congruence proofs, parallelogram-area formulas or tessellations has already handled the relationships physically. The formal geometry is a re-naming of what the child knows.
Plane 2 extensions
In Plane 2 (six to twelve) both materials continue with extensions.
Geometry Cabinet extensions. Three-part cards for shape definitions (not just names). "A rectangle is a quadrilateral with four right angles and two pairs of equal parallel sides." Vocabulary work builds from nomenclature to formal definition.
Constructive Triangles extensions. Congruence, similarity and equivalence. The child discovers that two triangles can have different positions but be congruent, or similar but not congruent, or have the same area but different shapes. These discoveries become the basis for Plane 2 area-and-angle work.
Geometry sticks and angle measure. A related Plane 2 material: wooden sticks with protractor marks that the child uses to measure and create angles. Builds on the shape-recognition from Plane 1 into numerical geometry.
Nomenclature cards for the Plane 2 geometry canon. Types of angle (acute, right, obtuse, reflex). Parallel lines and transversals. Types of triangle by angle. Types of triangle by side. Quadrilateral classifications. Circle parts (radius, diameter, chord, arc, sector).
Most home families continue Plane 2 geometry through a combination of the Constructive Triangles, Nomenclature cards and a textbook supplement (the Singapore Maths Primary Mathematics series covers plenty of geometry with accessible UK vocabulary).
Common home mistakes
Buying a cabinet too small. Some "travel" Geometry Cabinets have only three drawers or are too small to hold full-sized insets. The full six-drawer cabinet is the standard; smaller versions miss content.
Skipping the Constructive Triangles. Geometric Cabinet is the better-known material but the Constructive Triangles do the generative work. Skipping them leaves the child with shape-recognition but not shape-relationships.
Introducing formal definitions too early. "A rhombus is a parallelogram with all four sides equal." The child can hold a rhombus, name it, even classify it, at five; the definition works from around seven or eight upwards.
Treating the shapes as decoration. Both materials end up as shelf display in some homes. The handling is the work; a displayed shape is not.
Not connecting to Plane 2 when it comes. A nine-year-old meeting angle definitions for the first time should have the Constructive Triangles pulled off the shelf. The physical referent is key to the formal vocabulary landing.
A real family's geometry progression
A mum we will call Rhianwen bought the Geometry Cabinet second-hand for £120 when her daughter was three and a half. She bought the Constructive Triangles Boxes 1 and 2 new for £38 each around the same time.
Year one: Geometry Cabinet work mostly in the demonstration drawer and Drawers 2 and 3 (circles, triangles). Constructive Triangles Box 1 (rectangles from right-angled triangles) became a favourite.
Year two: Quadrilaterals and regular polygons drawers of the cabinet. Constructive Triangles Boxes 3 and 5 added. Her daughter began creating elaborate compositions with the triangles, building repeated hexagons across the floor.
Year three to six (age six and a half to nine): nomenclature work, angle introductions, area discussions using the Constructive Triangles. A Plane 2 geometry notebook with drawings of triangles, quadrilaterals, polygons; formal definitions added slowly.
By age nine, her daughter could classify any triangle by angle and side, identify any regular polygon up to a decagon, compute the area of a rectangle, triangle or parallelogram using the formula, and recognise tessellation patterns in Islamic art and floor tiles.
Total spent across six years on geometry materials: £196 (cabinet £120, Constructive Triangles £76). Daughter arrived at formal Plane 2 geometry with a solid concrete foundation.