Chapter VIII
Creating Symmetry
Creating symmetry
Symmetry is one of the key ideas that develop logical thinking, visual perception, and spatial orientation in children. A child who can notice and recreate a symmetrical arrangement of pieces better understands the ideas of order, balance, and pattern - that is, the foundations of mathematical and engineering thinking.
In this chapter children learn what reflection symmetry is - by handling real objects: gears, cylinders, platforms, and connectors from the sets. The activities are based on play, constructing, and experimenting - children build mirror reflections, symmetrical towers, arrangements around an axis, and patterns.
The tasks have been planned so that children can: recognize and create symmetrical arrangements, develop hand-eye coordination, improve visual analysis and spatial memory, and try planning constructions on their own.
Symmetry appears in the natural world (e.g. leaves, insects, faces), in art (patterns, decorations), and in technology (gears, machines). Through work with blocks, children not only understand this phenomenon better, but above all experience it in practice - by building, comparing, and correcting their constructions. This is learning by doing, which supports the development of mathematical thinking from the earliest years.
After completing the tasks and games from this chapter, the child:
- Recognizes symmetry in simple spatial and flat arrangements (e.g. buildings, patterns).
- Notices an axis of symmetry and can point out where it runs (e.g. through the middle of a building, between two wings).
- Creates constructions that are symmetrical about a vertical or horizontal axis, using blocks.
- Recreates a mirror reflection of simple arrangements built from blocks (e.g. gears and cylinders in a set layout).
- Chooses pieces in pairs (e.g. two identical gears on both sides of the axis) and places them symmetrically.
- Experiments with different forms of symmetry - flat (on a platform) and spatial (building towers, bridges, figures).
- Keeps symmetry while building with color, size, and number of pieces.
- Develops visual analysis and spatial orientation by handling pieces on both sides of an axis.
- Tries designing symmetrical arrangements independently, using the materials available.
- Understands that symmetry is "balance" between the sides, and can check whether an arrangement has been built correctly.
A Mirror of Blocks
Learning goal
Developing the skill of recreating an arrangement of blocks as a mirror reflection.
Needed elements
Platforms (4 per child, two yellow and two green arranged in a 2x2 square), gears (different colors).
The teacher may divide the platforms among the pairs, e.g. for one pair 8 green platforms (two squares of 4 platforms), for the next 8 yellow platforms (in the same arrangement).
How it goes
The children place their platforms against each other along one edge - they do not join them. This space is our axis of symmetry. Then, taking turns - one child takes a gear and places it on one of the platform pegs. The other takes a gear of the same color and places it symmetrically relative to the axis on their platform. Next, the child who arranged second takes a gear and places it on the platform, and the first child places a gear of the same color symmetrically.
Variants
The first child arranges three gears and then covers their part (e.g. with a sweater). The second tries to recreate the pattern symmetrically from memory.
The teacher arranges a layout on their set of platforms, saying that this is, for example, the left side of the axis. Each child is to arrange the right side. The teacher places their part against the children's arrangement and checks whether it is correct.
A Symmetrical Butterfly
Learning goal
Building a symmetrical arrangement in the shape of "wings".
Needed elements
Platforms as the body, gears, cylinders.
How it goes
Children build "wings" from gears or cylinders on both sides of the platform (the body) (we place cylinders or gears next to each other). The wings are to be a mirror reflection.
Variants
A butterfly in different colors - the reflection must take color and shape into account (e.g. a simple construction - a cross connector and four cylinders arranged in a cross or an x).
A Block Reflection of a Face
Learning goal
Consolidating the idea of an axis of symmetry by creating a face.
Needed elements
Gears (eyes), cylinders (nose, ears); platforms may serve as a base; you can also build on the carpet.
How it goes
Children build a "face" - one eye, ear, and cheek is built by the teacher for one part of the group. The other part of the children recreates the other side of the face.
Variants
Change the position of the axis: a face with a closed eye, a sad face, a different eye color.
A Bridge of Symmetry
Learning goal
Building a spatial construction while keeping symmetry.
Needed elements
Cylinders, platforms, gears.
How it goes
Children in groups arrange a line of platforms on the carpet. This line will be a road / a river / a chasm. Over this line and in front of it the children are to build a symmetry bridge - the number of cylinders, the color, the arrangement - everything must be symmetrical.
Variants
Introduce extra decorative pieces on both sides.
Build the bridge so that it will hold a vehicle from one team and from the other.
Axis of Symmetry - a Puzzle
Learning goal
Recognizing and creating symmetrical arrangements.
Needed elements
Four platforms of the same color per child (green or yellow), gears and cylinders of different colors.
How it goes
The child arranges blocks (gears and cylinders) on one side of the platforms - e.g. on two platforms on the left / two on the right / the two top ones / the two bottom ones. Then they recreate the arrangement on the other side, creating symmetry.
Variants
Instead of single blocks, the child arranges a construction which they then have to recreate on the other side.
A Symmetrical Tower
Learning goal
Creating a vertical construction while keeping reflection symmetry.
Needed elements
Cylinders, gears, platforms, straight connectors - one cross connector.
How it goes
Children build a tower where the middle - a cross connector - is the axis of symmetry. Above and below the platform they build an identical number of cylinders joined with straight connectors.
Variants
The tower may have different colors - the child must keep them in symmetry.
Cylinders may also be joined with cross connectors, with extra branches to the side (these must also be symmetrical).
Even and Symmetrical
Learning goal
Linking the idea of symmetry with even numbers.
Needed elements
Gears and cylinders in an even number, four platforms of one color for each child.
How it goes
The teacher agrees an axis of symmetry with the children (vertical, horizontal). Then the child receives two of each piece. The task is to arrange them symmetrically relative to the axis on their platform.
A Flower of Symmetry
Learning goal
Creating symmetrical patterns around a central point.
Needed elements
A central platform, gears and cylinders as petals.
How it goes
Children arrange a "flower" - the petals must be placed evenly and symmetrically. Change the colors of the petals - children analyze whether symmetry has been kept.
Variants
Multi-layered flowers.
Symmetrical Domino
Learning goal
Recognizing a pattern and recreating it on the other side of an axis of symmetry.
Needed elements
Four platforms per child (in one color - they may be 4 yellow or 4 green), gears and cylinders.
How it goes
The teacher joins four platforms into one square (2x2) - and also agrees with the children that everyone should build in the same way (e.g. all pegs pointing up and to the right). Then the teacher arranges any layout of gears and cylinders on the platform. The children's task, one after another, is to attach their platform (4x4) and recreate the arrangement along the axis of symmetry (the join between the previous platform and the next one). Platforms may be attached on any side - to any arrangement already attached.
Variants
- We compare which arrangements are the same.
- Instead of single gears and cylinders, the teacher may build a simple construction.
- The constructions may join with one another on the particular platforms.