By the end of this module, Pre-K students will be able to:
- Identify relative positions of objects in space using appropriate language
- Recognize and name basic two-dimensional shapes (circles, squares, triangles, rectangles)
- Identify various two-dimensional shapes using appropriate language
- Create and represent three-dimensional shapes (sphere/ball, cube/box, cylinder/tube)
- Use various materials to build and compose shapes
- Describe shapes using informal language
- Recognize shapes in the environment
- Understand positional vocabulary (beside, inside, next to, above, below, apart)

Spatial Relationships

Young children learn to describe where objects are in space:
- Position words: beside, next to, near, close to, far from
- Directional words: above, below, over, under, on, in
- Relative position: between, in front of, behind, apart, together

These concepts help children navigate their environment and communicate about location.

Two-Dimensional (Flat) Shapes

Pre-K children learn to recognize and name common 2D shapes:
- Circle: round, no corners, rolls
- Square: four equal sides, four corners
- Triangle: three sides, three corners
- Rectangle: four sides (two long, two short), four corners

Note: Focus on recognition and informal properties, not formal definitions.

Three-Dimensional (Solid) Shapes

Children learn 3D shapes through exploration:
- Sphere (ball): rolls, round all around
- Cube (box): square faces, can stack
- Cylinder (tube, can): round, rolls, has two flat circles

Children use everyday names (ball, box, can) alongside math names (sphere, cube, cylinder).

Shapes in the Environment

Geometry connects to the real world:
- Doors and windows are rectangles
- Wheels are circles
- Roofs are sometimes triangles
- Boxes are cubes or rectangular prisms
- Balls are spheres

Composing and Decomposing Shapes

Children build larger shapes from smaller ones:
- Two triangles make a square
- Two squares make a rectangle
- Shapes can be combined in many ways

This builds understanding of part-whole relationships in geometry.

• Basic language skills
• Ability to follow simple directions
• Fine motor skills to manipulate objects and materials
• Visual discrimination skills
• Counting skills helpful but not required for this module

Topics build from simple to complex:

1. Positional Language - Understanding and using location words
2. Recognizing Circles - Identifying circles in various sizes and contexts
3. Recognizing Squares - Identifying squares
4. Recognizing Triangles - Identifying triangles
5. Recognizing Rectangles - Identifying rectangles
6. Exploring 3D Shapes - Balls/spheres, boxes/cubes, tubes/cylinders
7. Shapes in Our World - Finding shapes in the environment
8. Creating with Shapes - Building and composing
9. Describing Shapes - Using informal language about attributes
10. Shape Patterns - Simple repeating patterns with shapes

Geometry appears everywhere in children's lives:

At Home:
- "The clock is a circle."
- "Your sandwich is cut into triangles."
- "The TV is a rectangle."
- "Your ball is a sphere."
- "The tissue box is a cube."

At School:
- Blocks of different shapes
- Books (rectangles)
- Tables (often rectangular or circular)
- Pattern blocks for creating designs

Outdoors:
- Shapes in architecture
- Nature: sun (circle), mountains (triangles), tree trunks (cylinders)
- Playground equipment
- Signs (various shapes)

Art and Design:
- Drawing shapes
- Collage with shape cutouts
- Building with blocks
- Painting shapes

Public-domain connections:
- NASA: Planets are spheres, spacecraft have various shapes
- Architecture: Public-domain images of buildings with geometric shapes
- Nature: Leaves, flowers, crystals with geometric patterns
- Maps: Understanding spatial relationships of places

Mastery at Pre-K level looks like:
- Correctly identifying circles, squares, triangles, rectangles when shown
- Using position words appropriately: "The toy is under the table"
- Recognizing shapes in different orientations and sizes
- Naming at least 2-3 three-dimensional shapes
- Building simple structures with blocks
- Finding shapes in the environment
- Using shape names in play and conversation

Note: Pre-K students are NOT expected to:
- Define shapes formally
- Count sides and corners precisely
- Distinguish complex shapes (hexagons, pentagons, trapezoids)
- Draw shapes with accuracy
- Understand terms like "parallel" or "perpendicular"

Multi-Sensory Exploration

Children learn shapes through multiple senses:
- Visual: Looking at shapes
- Tactile: Touching and tracing shapes
- Kinesthetic: Making shapes with bodies, walking shape outlines
- Manipulative: Playing with shape toys and blocks

Varied Examples

Show shapes in many forms:
- Different sizes (big circle, tiny circle)
- Different orientations (triangle pointing up, sideways, down)
- Different colors and textures
- Solid shapes and outlines
- Perfect and imperfect examples

Shape Hunts

Regular shape searches build recognition:
- "Find all the circles in our classroom."
- "Look for rectangles on our walk."
- "What shapes do you see in this picture?"

Building and Creating

Provide many opportunities to work with shapes:
- Pattern blocks
- Tangrams (simple versions)
- Building blocks (wooden, foam, cardboard)
- Playdough for creating 3D shapes
- Paper shapes for collage
- Drawing tools

Integrate with Literature

Use books about shapes:
- Shape concept books
- Stories featuring shapes
- Illustrations with clear geometric forms
- Make your own shape books

Spatial Language in Routine

Use position words constantly:
- "Put your coat on the hook."
- "The blocks are in the bin."
- "Sit beside your friend."
- "The bird is above the tree."
- "Put the puzzle under the shelf."

1. Attend to precision: Noticing shape attributes ("It has corners" vs. "It's round")
2. Use tools: Manipulating shapes, tracing, building
3. See structure: Recognizing shapes are made of parts
4. Model: Representing real objects with shapes
5. Explain: "This is a square because..." (informal reasoning)
6. Look for patterns: Shapes in repeating patterns

Shape Names:

• circle, square, triangle, rectangle
• sphere, ball, cube, box, cylinder, tube, can

Shape Attributes:

• round, straight, curved
• side, edge, corner, point
• flat, solid
• same, different

Position Words:

• Basic: in, on, under, over, up, down
• Near/Far: beside, next to, near, far, close to, away from
• Directional: above, below, on top of, underneath
• Between: between, in the middle, in front of, behind
• Together/Apart: together, apart, separate

Action Words:

• build, make, create, stack, combine
• find, look for, search, hunt
• trace, draw, color
• name, identify, point to

For students who need support:
- Start with one shape at a time (focus on circles first)
- Use very clear, distinct examples
- Provide hand-over-hand guidance for tracing
- Use larger shapes and manipulatives
- Focus on recognition before naming
- Use fewer position words (in, on, under only)
- Accept pointing if naming is difficult

For students ready for more:
- Introduce additional shapes (oval, hexagon, pentagon)
- Explore more complex 3D shapes (cone, pyramid)
- Use precise vocabulary (sides, corners, vertices, faces)
- Create complex structures with multiple shapes
- Sort shapes by attributes
- Compose pictures using many shapes
- Use more sophisticated position language (between, in front of, behind)
- Recognize shapes in any orientation

Families can support geometry learning:
- Point out shapes at home and in the community
- Use position words in everyday conversation
- Provide building toys (blocks, LEGOs, magnetic tiles)
- Read books about shapes
- Play "I Spy" with shapes: "I spy a circle!"
- Draw shapes together
- Make shape collages
- Cook together: "These cookies are circles"
- Look for shapes in nature on walks

• Use age-appropriate materials (no sharp edges)
• Supervise when using small manipulatives
• Ensure building materials are stable (won't tip onto children)
• Use non-toxic materials for art projects
• Be aware of choking hazards with very small blocks or shapes

Activity 1: Shape Sort

Provide mixed collection of shape manipulatives:
"Put all the circles in this basket."
"Find all the triangles."
"Which pile has more?"

Activity 2: Body Shapes

Children make shapes with their bodies:
"Can you make a circle with your arms?"
"Stand in a line - we made a straight line!"
"Three friends hold hands - you made a triangle!"

Activity 3: Shape Building

Pattern blocks or tangrams:
"Can you make a house using these shapes?"
"What shapes did you use?"
"Can you make a different design?"

Activity 4: Position Game

"Put the bear on the chair."
"Put the block under the table."
"Stand beside your friend."
"Put your hands above your head."

Activity 5: Shape Hunt Walk

Take a walk looking for shapes:
"I see a round manhole cover - a circle!"
"That window is a rectangle."
"The yield sign is a triangle."

Activity 6: 3D Shape Exploration

Provide balls, boxes, cans:
"Which ones can roll?"
"Which ones can we stack?"
"What shapes are the faces (ends)?"

Geometry naturally integrates with art:
- Create shape collages
- Paint shapes
- Stamp with shape sponges
- Make shape prints
- Explore artists who used geometric forms (Mondrian, Kandinsky - public domain works)
- Create patterns with shapes

Shapes are fundamental to building:
- Blocks and building toys
- Houses, buildings use geometric shapes
- Bridges often have triangular supports
- Domes are curved shapes
- Public-domain photos of famous buildings

• Geometric patterns in textiles worldwide
• Traditional designs using shapes (quilts, mosaics, pottery)
• Architecture varies by culture but uses geometric forms
• Games and toys featuring shapes exist globally

Pre-K geometry builds foundations for:
- Spatial reasoning: Crucial for math, science, engineering
- Geometric thinking: Recognizing, naming, comparing shapes
- Composing/decomposing: Understanding part-whole relationships
- Transformation: (Later) rotating, flipping, sliding shapes
- Measurement: Shapes have measurable attributes
- Symmetry: (Later) recognizing balanced designs

This Pre-K module prepares students for Kindergarten standards:
- K.G.1: Describe objects in environment using shape names
- K.G.2: Correctly name shapes regardless of orientation or size
- K.G.3: Identify shapes as 2D or 3D
- K.G.4: Analyze and compare shapes
- K.G.5: Model shapes in the world
- K.G.6: Compose simple shapes to form larger shapes

Even without formal definitions, children notice:

Circles:
- Round
- No corners
- All the same distance from center (informal)
- Roll

Triangles:
- Three sides
- Three corners/points
- Can be different types (wide, narrow, pointing different directions)

Squares:
- Four sides that are the same length
- Four corners
- All corners are the same (square corners)

Rectangles:
- Four sides
- Four corners
- Two long sides, two short sides
- Squares are special rectangles (but don't need to teach this formally)

3D Shapes:
- Spheres: roll all directions, smooth, round
- Cubes: flat faces, square faces, corners, stack well
- Cylinders: two circle ends, roll one direction, curved side

• "Triangles must point up" - Show triangles in all orientations
• "Shapes must be perfect" - Show imperfect but recognizable shapes
• "All rectangles are long and thin" - Show various rectangles including squares
• "Shapes are always the same color" - Use varied colors

Correct gently through many examples, not through direct instruction.

Shape understanding typically develops:
1. Matching identical shapes
2. Recognizing shapes in standard form
3. Recognizing shapes in various sizes
4. Recognizing shapes in various orientations
5. Recognizing shapes with variations (all triangles, even different types)
6. Naming shapes
7. Describing shape attributes
8. Creating shapes
9. Composing shapes from other shapes

Pre-K students work across these levels, with most in stages 2-7.

In Pre-K geometry:
- Exploration matters more than mastery
- Play with shapes should be fun
- Accept approximations cheerfully
- Celebrate discoveries: "You found a circle!"
- Follow children's interests
- Integrate shapes naturally into play and routine

Geometry at this age should build confidence, curiosity, and positive feelings about mathematics!