MathIsimple
Unit 4: Lesson 2

Composing & Decomposing Shapes

Become a shape architect! Learn to build bigger shapes from smaller ones, break shapes apart, and create amazing designs. Build your spatial reasoning superpowers!

40-50 min
Medium
Combining Shapes
Breaking Shapes
Pattern Blocks
Tangrams

πŸ—οΈ Shape Builder Studio!

Combine and create with interactive shape activities!

Compose Shapes

What shapes make this bigger shape?

Medium
6 minutes
🧩

⬜ What shape can you make with 2 triangles?

Click to interact β†’

How Many Triangles?

Count the pieces!

Easy
5 minutes
πŸ”Ί

⬑ How many small triangles fill a hexagon?

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Click Composite Shapes

Which shapes are made of smaller shapes?

Easy
5 minutes
🧱

Click the composite shapes (made of multiple small shapes)

Click all correct options

Selected: 0
Click to interact β†’

Master These 8 Composition Skills

Build your spatial reasoning! Learn to combine and decompose shapes like an architect!

1

What is Composing Shapes?

Composing means PUTTING TOGETHER smaller shapes to make a BIGGER shape! Like building with blocks - you combine pieces to create something new. Two triangles can make a square! Three triangles can make a bigger triangle!

πŸ’‘ Think of composing like building with LEGO - combining small pieces to create bigger structures!

🌟Examples:

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Triangles Make a Square

Put two identical triangles together = one square! The shapes fit perfectly!

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Squares Make a Rectangle

Place two squares side by side = one rectangle! Wider than it is tall!

🏠

Building a House

Square for the house + triangle for the roof = house shape!

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Pattern Block Fun

6 triangles arranged in a circle make a hexagon! Perfect fit!

Common Mistake Alert! ⚠️

Leaving gaps between shapes! Shapes must touch edge-to-edge with no spaces!

2

What is Decomposing Shapes?

Decomposing means BREAKING APART a big shape into smaller shapes! It's the opposite of composing. A square can be split into 2 triangles. A hexagon can be split into 6 triangles. Like cutting a sandwich!

πŸ’‘ Think of decomposing like cutting a pizza - one whole becomes many slices!

🌟Examples:

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Square into Triangles

Cut a square diagonally = 2 triangles! The line splits it perfectly!

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Rectangle into Squares

Cut a rectangle in half = 2 squares! (If it's twice as long as it is wide)

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Circle into Half Circles

Cut a circle through the center = 2 half circles (semi-circles)!

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Hexagon Split

A hexagon can be split into 2 trapezoids, 3 diamonds, or 6 triangles!

Common Mistake Alert! ⚠️

Not counting all the pieces! Make sure you see every shape the big shape splits into!

3

Building New Shapes

You can create BRAND NEW shapes by combining different shapes! A square + triangle = a house. Circle + rectangle = a lollipop. Let your imagination guide you! Architects do this to design buildings!

πŸ’‘ Think like an architect - use basic shapes as building blocks to create anything!

🌟Examples:

🏠

House Design

Rectangle (walls) + triangle (roof) + square (window) + rectangle (door) = house!

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Robot Builder

Rectangles for body and legs, square for head, circles for eyes = robot!

🌳

Tree Shape

Rectangle (trunk) + triangle or circle (leaves) = tree!

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Car Design

Rectangle (body) + 2 circles (wheels) + rectangles (windows) = car!

Common Mistake Alert! ⚠️

Thinking shapes must be used the 'right' way. Be creative - there's no wrong way to build!

4

Pattern Blocks Magic

Pattern blocks are special shapes that fit together perfectly! Green triangles, orange squares, blue diamonds, red trapezoids, yellow hexagons, and tan diamonds. They're designed to combine in amazing ways!

πŸ’‘ Think of pattern blocks like a shape puzzle where pieces fit together in multiple ways!

🌟Examples:

⬑

Hexagon Patterns

6 triangles = 1 hexagon. Or 3 diamonds = 1 hexagon. Or 2 trapezoids = 1 hexagon!

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Symmetry Designs

Arrange pattern blocks in mirror patterns - same on both sides! Beautiful designs!

🌸

Growing Patterns

Make a flower: hexagon center + 6 triangles around = flower with petals!

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Tessellations

Repeat the same pattern over and over to cover a surface - no gaps!

Common Mistake Alert! ⚠️

Forcing blocks that don't fit! Pattern blocks have specific angles that work together!

5

Tangram Puzzles

A tangram is a Chinese puzzle with 7 pieces: 5 triangles (2 big, 1 medium, 2 small), 1 square, 1 parallelogram. You can rearrange these 7 pieces to make THOUSANDS of different shapes! Ancient brain teaser!

πŸ’‘ Think of tangrams like a magic shape transformer - 7 pieces, endless possibilities!

🌟Examples:

🐱

Making Animals

Arrange tangram pieces to make cats, dogs, birds, fish - all from the same 7 pieces!

πŸƒ

Making People

Create running, sitting, jumping people figures using the 7 tangram pieces!

β›΅

Making Objects

Form boats, houses, candles, trees - your imagination is the limit!

⬜

Square Challenge

Can you arrange all 7 pieces back into the original square? Tricky puzzle!

Common Mistake Alert! ⚠️

Overlapping pieces or leaving gaps. Tangram pieces must touch edge-to-edge perfectly!

6

Spatial Reasoning Skills

Spatial reasoning means thinking about how shapes FIT together in SPACE! Can you rotate this triangle to fit here? Which way should I turn this rectangle? This skill helps with puzzles, building, and even parking cars when you grow up!

πŸ’‘ Think of spatial reasoning like playing Tetris - figuring out how pieces fit as they fall!

🌟Examples:

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Rotation Practice

Turn a triangle 90 degrees (quarter turn) and it fits in a different spot!

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Flip and Fit

Sometimes you need to FLIP a shape (like flipping a pancake) to make it fit!

🧩

Puzzle Solving

Look at empty space in a puzzle - what shape would fit? Visualize it!

πŸ’­

Mental Math

Imagine combining shapes in your mind before physically moving them!

Common Mistake Alert! ⚠️

Giving up too quickly! Spatial skills take practice - keep trying different orientations!

7

Shape Puzzles & Challenges

Shape puzzles challenge you to think creatively! Can you make a square using only triangles? Can you build a bigger hexagon from smaller shapes? These challenges strengthen your geometry muscles!

πŸ’‘ Think of shape challenges like workout exercises for your brain - they make you stronger!

🌟Examples:

πŸ”Ί

Triangle Challenge

Using 4 small triangles, make one big triangle! Arrange them point-to-point!

⬜

Square from Rectangles

Can you make a square using 2 identical rectangles? Yes - place them side by side!

⬑

Hexagon Builder

Make a large hexagon using 6 small triangles arranged around a center point!

🎨

Shape Art Challenge

Use exactly 10 shapes to create a picture. What can you make?

Common Mistake Alert! ⚠️

Thinking there's only one solution! Many shape puzzles have multiple correct answers!

8

Creative Composition

Creative composition means using shapes to EXPRESS yourself! Make art, tell stories, design buildings - all with geometric shapes! Famous artists like Kandinsky and Mondrian used geometric shapes to create masterpieces!

πŸ’‘ Think of shapes as your art supplies - like crayons, but with geometry!

🌟Examples:

😊

Shape Portraits

Make a face using circles (eyes), triangle (nose), rectangle (mouth). Shape people!

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City Skyline

Build a city with rectangles (buildings), triangles (roofs), squares (windows)!

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Nature Scenes

Create trees, flowers, sun, clouds - all from basic shapes! Geometric nature!

🎭

Abstract Art

Arrange shapes in interesting patterns - no rules, just creativity!

Common Mistake Alert! ⚠️

Being afraid to experiment! There are no mistakes in creative composition - only discoveries!

Ready to Build with Shapes?

Test your shape composition skills!

Start Practice Quiz
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