Geometric Solids
The geometric solids are ten blue wooden shapes, from the sphere and the cube to the egg-shaped ovoid. A child of about 3.5 who knows the flat shapes from the geometric cabinet feels each solid with closed eyes, rolls it to see how it moves, and learns its name.
Sourced from the texts, not yet presented at home
| Typical age | 3.5 to 6 years |
|---|---|
| Area | Sensorial |
| Before this | |
| Materials | |
| Direct aim | To know the solid forms by touch and by sight, and to learn their names. |
| Control of error | Nothing in the solids corrects the child; the hand and the eye check each other. A solid named with the eyes closed is then looked at. For the names, the adult's second and third periods are the check, and a wrong name is left for another day. |
| Leads to | Later lessons in this line are in preparation. |
| Time | About 10 minutes (our estimate). |
| Grouping | One child at a table or on a rug |
| Parent prep | Low. Pick three very different solids before the child sits down. |
| Cost | Buy about $177 to $202. Make: hard to make accurately. |
| Other names | Blue geometric solids, Geometric solids basket, Solid figures, 3D shapes |
What the work teaches
Direct aim. To know the solid forms by touch and by sight, and to learn their names.
Indirect aims, the ones you will not see at once
- The stereognostic sense: knowing a shape through the hand's movement over it
- Words for shapes met every day: a ball, a can, an egg, a box
- Noticing which shapes roll and which stand still
- Later geometry: faces, edges, and the flat shapes hidden inside a solid
Set it out before you invite the child
Ten solids painted pale blue, in a basket or on a tray: sphere, cube, cylinder, cone, triangular prism, rectangular prism, square-based pyramid, triangular-based pyramid, ovoid and ellipsoid.
Stands for the rounded ones. Nienhuis includes three clear stands for the curved solids, and Alison's set adds five flat base shapes and a box.
Montessori's 1914 handbook lists pale blue solids: a sphere, a prism, a pyramid, a cone and a cylinder. The modern ten add the cube, a second prism and pyramid, and two egg shapes.
A blindfold or a soft scarf, for the guessing game that comes later.
A rug or a table. A dropped solid dents a wooden floor, and a rug keeps it quiet.
Presentation, step by step
- 1Carry the basket to the table. Take out the sphere and the cube, and set the cone beside them.
- 2Pick up the sphere in both hands. Turn it slowly, letting your palms pass over the whole surface.
- 3Hand it to the child to feel the same way, then set it down.
- 4Do the same with the cube. Flat palms on each face, then a fingertip along each edge and into each corner.
- 5Do the same with the cone: the round base, the curved side, the point.
- 6Roll each one gently across the table. The sphere goes anywhere, the cone circles round its point, and the cube stays where it is.
- 7Give the three names: "This is a sphere. This is a cube. This is a cone."
- 8On later days, bring in two or three more solids at a time until all ten are known. Then offer the blindfold.
Details that hold the child's attention
The cone rolling in a circle round its own point.
The cylinder, which rolls on its side and stands still on its end.
A pyramid that won't tip over, beside a prism that does.
The ovoid, an egg shape that rolls in a curve.
How the child sees a mistake
Nothing in the solids corrects the child; the hand and the eye check each other. A solid named with the eyes closed is then looked at. For the names, the adult's second and third periods are the check, and a wrong name is left for another day.
The words come after the hands
| Words | Shown with |
|---|---|
| sphere, cube, cylinder, cone | The first names, given three at a time. |
| prism | Triangular and rectangular, told apart by the shape of the ends. |
| pyramid | Square-based and triangular-based, told apart by the base. |
| ovoid, ellipsoid | The egg shape and the evenly rounded one. Give them last. |
| roll, stand | What each solid does when pushed gently. |
The three-period lesson, scripted
You need three very different solids: the sphere, the cube and the cone.
| Period | What you do and say |
|---|---|
| 1. Naming | Hold each in turn: "This is a sphere." "This is a cube." "This is a cone." |
| 2. Recognition | "Give me the cone." "Roll the sphere to me." "Put the cube in the basket." |
| 3. Recall | Point to one and ask "What is this?" |
Montessori's handbook says that names of forms, unlike gradations of size, can be given several at once. Three solids that differ this much follow the same rule.
Extensions and variations
- The blindfold game: feel one solid with eyes closed, name it, then look
- Standing each solid on the flat base shape it matches, such as the cylinder on a circle
- Finding solids in the kitchen: a can, a ball, a cereal box, an egg
- Putting the solids in the mystery bag and finding a named one by touch
- Modelling them in clay, as Montessori's children learned to do
Variations
- Sorting the solids into two groups: those that roll and those that don't
- A basket of three solids only, for a child who has just turned 3
Make it or buy it
| Material | Make it | Buy, approx. |
|---|---|---|
| Geometric Solids | Hard to make accurately | $177 to $202 |
Prices noted . Approximate US street prices for home-use versions; they vary by maker and change often, so recheck before buying.
Making it at home
Household solids make a fair start if they are all wrapped in one color. A ball stands in for the sphere and a can for the cylinder. A matched blue set of ten is hard to make well.
What to check when buying a set
Look for clean points on the cone and pyramids and an even coat of paint. A set with stands keeps the egg shapes from rolling off the shelf.
Printables for this age
This work needs only the material, so it has no printable of its own. The shelf plan below places it among the other works for the same age.
- Shelf plan for age 3PDF, 1 page, 250 KBEvery work for this age on one page, in order, with a column to date each presentation.
Every printable for one age, by email
The shelf plan and the lesson printables for your child's age in one email, then three short emails on the first lesson, what to make or buy, and what comes next.
Signs the child is ready, and signs it is done
Ready for the first presentation
- Places the shapes from a geometric cabinet drawer with no trial fits.
- Carries an object in two hands across the room.
- Names the shapes from the cabinet's first tray.
- Watches a slow presentation to its end.
Ready for the next lesson
- Names all ten solids by sight.
- Names them with the eyes closed.
- Spots a cylinder or a sphere around the house and names it.
- Stands each solid on its matching base shape without help.
Fitting it into a home, not a classroom
| If you have | Do this |
|---|---|
| A tight budget | Gather household solids, such as a ball and a can, with a funnel for the cone. Wrap or paint them one color so that shape is the only difference. |
| A toddler sibling | The solids are heavy for their size and hurt a bare foot. Keep the basket at the back of a low shelf and work on a rug. |
| A child who knows the names already | Go to the blindfold game and to matching bases. The feeling is the real work. |
| No geometric cabinet yet | Card circles, squares and triangles cut for the cabinet's first lessons work as base shapes. |
When it does not go to plan
| When | Try this |
|---|---|
| The solids get rolled across the room. | Show the roll again on the table, with a hand ready to stop it. Rolling belongs on the table or the rug. |
| Prism and pyramid get mixed up. | Set them side by side and run a finger up to the pyramid's point. Name one of the pair for a few days. |
| The child names solids by size. | Hold up two of similar size, so that shape is the only difference. |
| Interest fades once the names are known. | Bring out the blindfold. Montessori found the guessing game made children look at the solids with fresh interest afterwards. |
Hazards to check before each session
Solid wood is heavy for its size. Store the solids low and work on a rug or at a table.
Check the paint now and then. A chipped point can splinter.
Where other sequences and standards place it
We have not bought the paid homeschool curricula, so they are not listed here.
| Framework | Where it sits |
|---|---|
| This site's Sensorial sequence | Lesson 11 of 12 published, after Geometric Cabinet (Plane Geometric Insets). Checked in: the scope and sequence |
| Montessori, Dr. Montessori's Own Handbook (1914) | Pale blue solids: sphere, prism, pyramid, cone and cylinder. Felt with closed eyes, named, and rolled to compare how each moves. Checked in: Sensory Education |
| Montessori, The Montessori Method (1912) | Montessori argued that plane insets should come before solids, since a solid is harder to recognize by sight and rarely appears pure in everyday objects. Checked in: Chapter XV, Intellectual Education |
| Common Core, Kindergarten math | K.G.A.3: identify shapes as two-dimensional (flat) or three-dimensional (solid). K.G.B.4: compare two- and three-dimensional shapes using informal language. Checked in: tasks.illustrativemathematics.org |
| Head Start Early Learning Outcomes Framework, preschool | P-MATH 9: the child identifies, describes, compares and composes shapes. Checked in: www.in.gov |
Geometric solids: questions parents ask
What are the Montessori geometric solids?
Ten wooden shapes painted pale blue. Some have flat faces, like the cube and the pyramids; others are curved, like the sphere and the egg-shaped ovoid. Children feel them, name them, and roll them to see how each one moves.
What age are the geometric solids for?
From about 3.5, after the geometric cabinet, and on this site they run to 6. Montessori's handbook ties recognizing forms by touch to the child from three to six.
Why are all the solids the same color?
One color leaves shape as the only difference, so that's what the child attends to. Montessori's 1914 handbook already describes them as pale blue.
Should solids come before flat shapes?
Montessori thought not. She wrote in 1912 that flat shapes are easier to see and far more common around us: doors, windows, tabletops, plates. This site follows her and puts the geometric cabinet first.
Sources cited by book and chapter
- Maria Montessori, Dr. Montessori's Own Handbook (1914)
Sensory Education
In the didactic material there are geometrical solids, pale blue in color: a sphere, a prism, a pyramid, a cone and a cylinder.
The most attractive way to teach a child to recognize these forms is to let him touch them with closed eyes and guess their names, after which he observes them with livelier interest.
The sphere rolls in every direction, the cylinder rolls in one direction only, the cone rolls round itself, and the prism and pyramid stand still, though the prism falls over more easily.
The Method
The material for the education of the senses includes various geometric solids: prism, pyramid, sphere, cylinder and cone.
A Children's House
On the sitting-room tables are placed games of patience and various geometric solids, with which the children can play at pleasure, constructing figures.
Language and Knowledge of the World
When the names to be taught are those of colors or of forms, the teacher can give more than two names at the same time, such as square, triangle and circle.
- Maria Montessori, The Montessori Method (1912)
Chapter XV, Intellectual Education
Presenting geometric forms in the solid rather than the plane is a prejudice, since the visual recognition of a solid figure is more complex than that of a plane one.
As their clay modelling becomes recognisable, the children learn to reproduce the geometric solids.
Reviewed by
What to offer next
Once the child chooses this work unprompted and finishes it without help, the next lesson to prepare is Trinomial Cube.
- Geometric cabinet3 to 5 years
- Mystery bag3 to 5.5 years
- Binomial Cube3.5 to 6 years
- Geometric solids3.5 to 6 years
- Trinomial Cube4 to 6 years