Continuing Tessellations Activity Sheet (teacher made) - Free Printable

The image shows two printable worksheets titled "Continuing Tessellations", designed to help students practice extending geometric patterns using tessellation principles. A tessellation is a repeating pattern of shapes that covers a plane with no gaps or overlaps.

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🔍 What’s in the Image?

There are two pages:

1. Left Page (Printable):
- Contains two separate tiling patterns:
- Top: A pattern made of hexagons.
- Bottom: A pattern made of diamonds (rhombuses).
- Each shape is placed on a dotted grid, and the goal is to continue the pattern.

2. Right Page (Ink-Saving Eco Version):
- Shows two more patterns:
- Top: A sequence of triangles forming a zigzag line.
- Bottom: A combination of triangles and rhombuses forming a more complex pattern.
- The question asks: *"Can you continue these tiling patterns?"*

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🧩 How to Solve These Problems

To complete the tessellation, follow these steps:

#### ✔ Step 1: Understand the Pattern
Look at how the shapes are arranged:
- Are they repeated in a straight line?
- Are they rotated or reflected?
- Is there a consistent direction or symmetry?

#### ✔ Step 2: Identify the Unit Cell
Find the smallest group of shapes that repeats. This is called the unit cell.

#### ✔ Step 3: Extend the Pattern
Copy the unit cell repeatedly in the same orientation or transformation (translation, rotation, reflection) to fill the space.

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🔎 Let's Analyze Each Pattern

#### 🔹 Top Left: Hexagon Pattern
- Three hexagons form a cluster.
- They are arranged so that each shares sides.
- To continue: Place another set of three hexagons adjacent to the existing ones, maintaining the same arrangement.

👉 Solution: Add more hexagons in a honeycomb-like structure — each new hexagon must touch the previous one along an edge.

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#### 🔹 Bottom Left: Diamond (Rhombus) Pattern
- Two diamonds share a side, forming a parallelogram.
- The next diamond is added to extend the pattern horizontally.
- This appears to be a repeating horizontal row.

👉 Solution: Continue placing pairs of diamonds side by side in a row, ensuring no gaps or overlaps.

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#### 🔹 Top Right: Triangle Zigzag
- Triangles are arranged in a zigzag line (like a sawtooth).
- Each triangle points alternately up and down.
- The pattern continues horizontally.

👉 Solution: Keep adding triangles alternating up/down, forming a continuous zigzag line across the page.

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#### 🔹 Bottom Right: Mixed Triangle & Rhombus Pattern
- One rhombus is flanked by two triangles.
- The shapes appear to form a symmetrical tile that can be repeated.
- The pattern suggests a vertical or diagonal extension.

👉 Solution: Copy the entire group (rhombus + two triangles) and place it next to the existing one, aligning edges perfectly.

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✔ Final Answer: How to Complete the Worksheet

For each pattern, students should:
1. Observe the current arrangement.
2. Identify the repeating unit.
3. Draw the next units in the same style, ensuring:
- Shapes fit together perfectly.
- No gaps or overlaps.
- Consistent orientation or symmetry.

> 💡 Tip: Use the dotted grid as a guide to align shapes accurately.

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🌱 Why This Matters

Tessellations teach:
- Geometry concepts (shapes, angles, symmetry)
- Spatial reasoning
- Problem-solving through pattern recognition

These worksheets are great for hands-on learning in math classrooms.

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Let me know if you'd like a visual solution or printable answer key!