Chapter VI
Geometry and Playing with Shapes
Why is it worth teaching geometry through play?
Geometry is not only recognizing shapes, but also developing the skill of spatial thinking, analyzing the properties of objects, and noticing regularities in the world around us. For children aged 7–9, getting to know geometric figures and solids is an opportunity to practice classifying, comparing, describing, and constructing. It is also an excellent moment to learn orientation in space and to understand ideas such as: symmetry, angle, side, face, edge, or vertex.
In early-school education it is essential that learning geometry takes place in action — through handling objects, joining them, transforming them, and observing. Thanks to this the child not only memorizes the names of figures, but begins to understand their structure and use.
Blocks support this process very well. Children can:
- build plane figures and spatial solids from real, three-dimensional pieces,
- create patterns, symmetries, and geometric arrangements,
- experiment with movement (e.g. gears as figures turning around an axis),
- discover the properties of figures on their own in the course of play and constructing.
Thanks to this, learning geometry becomes an adventure that engages imagination, thinking, and action.
After completing the tasks in this chapter, the pupil:
- Recognizes and names basic plane geometric figures, such as: triangle, square, rectangle, circle.
- Builds models of plane figures and spatial solids using blocks.
- Determines the number of sides, vertices, and faces in the figures and solids they have learned.
- Compares geometric figures by shape, number of sides, length of sides, and angle.
- Distinguishes symmetrical figures and creates symmetrical arrangements relative to an axis (vertical or horizontal).
- Creates rhythmic geometric patterns (e.g. sequences of colors, shapes, or arrangements).
- Uses spatial terms such as: above, below, next to, in the middle, behind, in front of, between — while building arrangements.
- Builds and describes simple geometric solids (cube, cuboid).
- Understands the difference between a plane figure and a spatial solid.
- Uses mathematical language to describe constructions: number of sides, vertices, shape of the base, symmetry, and so on; building in 3D, patterns on the sides, comparing sides, and so on.
Figures from Blocks
Learning goal
Recognizing and creating basic geometric figures.
Needed elements
- Gears
- Cylinders
- Connectors
How it goes
Children build plane figures (triangle, square, rectangle) from cylinders or gears arranged next to one another. Then they determine how many sides and vertices each figure has.
Variants
Creating figures from only one color and type of piece — checking, e.g., what the largest rectangle that can be built may be (attention should be paid to making the number of blocks in the two longer sides the same, and the same in the two shorter ones).
Block Symmetries
Learning goal
Recognizing and creating symmetrical arrangements.
Needed elements
- Blocks
- Paper and a pencil for each group
How it goes
Children arrange a pattern on one side of a platform (e.g. they place a red cylinder somewhere, a blue gear), and then pass it to another child, who arranges a symmetrical pattern on the other side.
Variants
Building horizontal and vertical symmetry.
Enlarging the platform, e.g. 4×4, and creating a pattern as a group (e.g. a turning construction, also “upward”).
Map of Figures
Learning goal
Consolidating spatial and geometric ideas.
Needed elements
- Platforms
- Cylinders
- Cross connectors and straight connectors
How it goes
Children create a “city map” on which buildings have the shapes of geometric figures (e.g. in the form of a parallelogram, a cube, a plaza in the form of a rectangle or a square, and so on). Then they describe the position of objects relative to one another.
Variants
Adding a scale — e.g. “each cylinder = 4 meters and a cross connector is 2 m”. What is the height and width of the building?
How Many Sides? How Many Faces?
Learning goal
Distinguishing plane figures and spatial solids.
Needed elements
- Cylinders
- Platforms
- Gears
- Connectors
How it goes
Children build simple solids (e.g. a cube, a cuboid, a square, a rectangle) and determine: how many faces, vertices, and edges they have.
Variants
While building solids, children arrange the same color patterns on sides of the same length (e.g. cylinder blue-green-blue).
Geometric Patterns
Learning goal
Creating and continuing rhythmic sequences of figures.
Needed elements
Blocks
How it goes
One child arranges a pattern on a platform: cylinder — gear — cylinder — gear... The child's task is to continue the pattern and create their own design.
Variants
Two-element patterns, three-element patterns, varying in color.
Encoded Figures
Learning goal
Developing logical thinking and geometric coding.
Needed elements
- Cards with a “code” for a figure (e.g. 4 sides, 4 right angles)
- Blocks
How it goes
Children receive a card with a description of a figure and build it from blocks — without a given name. Then they check whether it matches the given features.
Variants
Swapping roles: pupils prepare riddles.
Figures on a Geoboard
Learning goal
Creating geometric figures on a coordinate grid.
Needed elements
- A large platform (built from four platforms) as a plane
- Rubber bands
How it goes
The teacher asks the pupils, using rubber bands, to build geometric figures on the platform, e.g. build a square with a side length of two pegs.
Variants
Pupils work in pairs and propose challenges to one another.
Adding extra figures overlapping the previous ones to the task.
Setting an extra parameter when arranging, e.g. the top-right vertex is in the first row in the second space.
We Build Solids
Learning goal
Building and analyzing simple solids from blocks.
Needed elements
- Cylinders
- Platforms
- Gears
- Connectors
How it goes
Pupils try to build spatial shapes (e.g. a cube, a prism), using platforms, cylinders, and connectors as sides.
Variants
Build the largest solid possible.