Chapter X
Spatial Relationships in Mathematics
Spatial relationships in mathematics
Understanding spatial relationships is a foundation of many mathematical, language, and logical skills. It is thanks to them that a child can recognize where something is, in which direction it is moving, how to arrange objects relative to one another, and also describe the world around them.
In this chapter children learn through action and play how to recognize and describe the position of objects relative to one another, using ideas such as: above, below, beside, between, in front, behind, on the left, on the right, inside, outside, closer, farther. All of this happens in a friendly, active way - with Korbo blocks, which can be arranged, moved, and used to build bridges, towers, mazes, and whole spatial worlds.
During the games children handle pieces such as gears, cylinders, platforms, and connectors, learning not only spatial orientation, but also developing speech, eye-hand coordination, concentration, and spatial imagination. They create miniature scenes, recreate arrangements, and give each other instructions - and in this way they learn precise thinking and communicating.
The games in this chapter prepare children for learning geometry and coding, and also for understanding maps, diagrams, directions, and logical structures. This is mathematics immersed in movement, language, and building - the kind that engages the child's whole body and mind.
After completing the tasks in this chapter, the child:
- recognizes and correctly uses words describing the position of objects, such as: above, below, beside, in front, behind, on the left, on the right, between, inside, outside,
- recreates spatial arrangements, placing blocks according to a spoken instruction or a visual model,
- creates their own constructions taking into account spatial relations between the particular pieces (e.g. "a bridge over a river", "a block behind a tower"),
- moves according to given directions, e.g. "go two steps to the right, then forward",
- talks about the position of objects, using correct spatial vocabulary,
- plans and describes a route or an arrangement of pieces in space (e.g. a robot route, an obstacle-course layout),
- makes comparisons of the position of objects, e.g. "This block is farther than that one", "This gear is closer to the platform than the cylinder",
- carries out instructions containing complex spatial relations, e.g. "Place a blue cylinder behind the red gear, under the yellow gear",
- builds spatial constructions from Korbo pieces that show knowledge of directions, relations, and positions (e.g. gear machines, towers, tunnels, houses),
- cooperates with a classmate when solving spatial tasks, e.g. giving spoken instructions, recreating a partner's arrangement.
What Is on Top, and What Is at the Bottom?
Learning goal
Recognizing the position of pieces vertically (top/bottom).
Needed elements
Blocks.
How it goes
The child builds constructions from different pieces. The teacher asks: "What is on top?", "What is underneath?", "What color is the block that is above, for example, the yellow gear?"
Variants
Swapping places: the child moves pieces from the bottom to the top.
Above, Below, Beside - a Block Maze
Learning goal
Developing spatial vocabulary (above, below, beside).
Needed elements
- Two platforms joined together horizontally
- gears
- cylinders
How it goes
The teacher says: "Place a blue gear at the top, in the first space on the left, next to it place a green cylinder... etc." Children carry out the tasks according to the instructions.
Variants
The child invents an instruction for a classmate.
A puzzle with eyes closed (a spoken instruction, without looking; the child feels the pieces - we do not talk about colors, and instead: place a cylinder, a gear...).
Who Is Closer, Who Is Farther?
Learning goal
Developing the skill of describing distance.
Needed elements
- Gears
- platforms
- connectors
How it goes
On the platform children place blocks at different distances from a "little house" (e.g. this may be a tower of several blocks). Then they describe the positions of the blocks, e.g.: "This block is closer", "This one is farther".
Variants
Measuring length with connectors ("This block is 2 connectors away").
In Front and Behind - the Block Train
Learning goal
Understanding the ideas "in front", "behind", "in the middle".
Needed elements
- Gears as cars
- platforms as the track
How it goes
Children arrange a train according to our instructions. Then they answer questions: "Which block is in front of the red one?", "Which is behind the yellow one?", "Which block is in the second place behind the third yellow one?"
Variants
Changing the order of the cars according to the teacher's instructions.
Inside - a Block Fence
Learning goal
Understanding the ideas "inside" and "outside".
Needed elements
- Cylinders as fence posts
- platforms
- gears as "little animals"
How it goes
The child builds a fence from cylinders and places "little animals" inside. They describe: "The blue gear is inside", "The red gear is outside".
Variants
Moving pieces into/out of the inside.
A fence with a gate - opening and closing that moves (using gears, "cross" connectors, and cylinders).
A Path across the Platforms
Learning goal
Moving along a set route - spatial directions.
Needed elements
- Platforms as a map (e.g. 8 joined platforms per pair of children)
- gears as markers
- figures made from blocks
- animal figures
How it goes
The child arranges a path from platforms and moves along it with a finger/figure. The teacher gives instructions: "Go left, place a red gear in this space, then three steps forward (pegs), place a blue cylinder in this space, turn right...".
Variants
The child designs the path themselves and gives a classmate the instruction.
Variant: a route with bans (e.g. "do not go right").
Where Is the Gear? - a Game with a Figure
Learning goal
Establishing position relative to objects.
Needed elements
- A figure or a small block as a character
- gears
- cylinders
- platforms
How it goes
We arrange a large board of platforms with the children, and on it gears, cylinders, arrangements, constructions. Then the child places the figure in different places: "on the platform", "between two cylinders", "behind the gear" according to our instructions, e.g. "Find the yellow gear that has a green cylinder above it - place the figure on the green cylinder".
Position and Movement - We Program a Robot
Learning goal
Developing the skill of tracking position and direction.
Needed elements
- Platforms as a board
- gears as markers
- cylinders as obstacles
How it goes
The child "programs a robot" (e.g. with a finger or a figure), e.g.: "Start from the top-left space. Move two spaces left and one space down, place a green gear in this space".
Variants
The child arranges a "movement code" for a classmate themselves.
Introducing symbols: arrows as directions. E.g. two arrows pointing down, then one arrow pointing left. After it a green gear as information (place a green gear in this space).
A Block Obstacle Course
Learning goal
Moving relative to objects in space (over, under, between, around).
Needed elements
- Cylinders as obstacles
- platforms as "ground"
- gears as route markers
How it goes
The child leads a figure through the course: "Go between the cylinders, go under the bridge made from a platform, step onto the red gear".
Variants
Changing the order of the route.
Where Is the Block? - a Guessing Game
Learning goal
Describing spatial relations in words.
Needed elements
Various blocks.
How it goes
One child describes a block without showing it: "It is to the left of the red gear, next to the green cylinder". The rest of the group guesses which block it is.
Right - Left - Middle
Learning goal
Developing directional orientation (left/right).
Needed elements
- Four platforms as a base for each child
- gears
- cylinders
How it goes
The teacher gives an instruction; the child arranges only after listening to the whole instruction, e.g.: "Place a red gear in the second row, in the second space from the left. To the left of this gear place a green cylinder, and to the right a yellow gear".
Position and Shape - Are They the Same?
Learning goal
Distinguishing position and identifying differences.
Needed elements
Two arrangements of blocks.
How it goes
The teacher builds two similar arrangements of blocks with small changes. The child compares the two arrangements and says what is different: "This gear is on the left, and in the other one it is on the right".
Variants
A "find three differences" task.
Variant: one child changes the arrangement - the other has to find it.
