Composing New Shapes from 2D Figures (Pattern Blocks) - First Grade Mathematics

In mathematics, "compose" means to put smaller things together to build something completely new! Think about playing with colorful pattern blocks: when you take two identical green triangles and push their flat sides together, they suddenly transform into a blue rhombus! If you push two red trapezoids together, they form a giant yellow hexagon! Composing shapes is like being an architect of geometry. In this chapter, you will discover how smaller 2D shapes combine to create larger, composite shapes, and explore the relationships between pattern blocks.

The Magic of Combining Triangles

The green triangle is the basic building brick of many pattern blocks.

Building New Shapes from Green Triangles:

1. Two Triangles Make a Rhombus:
         ^       +       v       =       /\
        / \             / \             /  \
       +---+           +---+             \  /
                                          \/
   (2 Green Triangles = 1 Blue Rhombus!)

2. Three Triangles Make a Trapezoid:
         ^       v       ^       =       +-------+
        / \     / \     / \             /         \
       +---+---+---+---+---+           +-----------+
   (3 Green Triangles = 1 Red Trapezoid!)

3. Six Triangles Make a Hexagon:
   (6 Green Triangles = 1 Yellow Hexagon!)

The Triangle Power

Notice how fractions and geometry connect: one triangle is one-half of a rhombus, one-third of a trapezoid, and one-sixth of a hexagon!

Composing Shapes with Squares and Rectangles

You can also compose new shapes using squares and rectangles.

Combining Squares:

Two Equal Squares:       [===] + [===] = [=======]  -> A Rectangle!

Four Small Squares:      [=][=]
                         [=][=] = [====]           -> A Giant Square!

From Squares to Rectangles

When you push two equal squares together side by side, you create a rectangle whose length is twice its height. When you put four equal squares together in a 2x2 grid, you create a larger square!

Tangrams: The Ancient Shape Puzzle

A tangram is an ancient Chinese puzzle made of seven geometric pieces (called tans) cut from a single large square: 5 triangles, 1 square, and 1 parallelogram.

The 7 Tangram Pieces:
- 2 Large Triangles
- 1 Medium Triangle
- 2 Small Triangles
- 1 Square
- 1 Parallelogram

Infinite Compositions

Using just these seven pieces, mathematicians can compose hundreds of creative figures: birds, houses, cats, boats, and geometric polygons! When composing with tangrams, pieces must touch edge-to-edge without overlapping.

Practice Exercises

Exercise 1: How many green triangle pattern blocks does it take to make one red trapezoid?

Exercise 2: How many red trapezoid pattern blocks does it take to make one yellow hexagon?

Exercise 3: You have 2 identical squares. What new shape can you compose by putting them together side by side?

Exercise 4: Explain what the mathematical word "compose" means in geometry.

Solutions and Explanations

Solution to Exercise 1: It takes exactly 3 green triangle pattern blocks to compose one red trapezoid.

Solution to Exercise 2: It takes exactly 2 red trapezoid pattern blocks to compose one yellow hexagon.

Solution to Exercise 3: By placing 2 identical squares side by side along their edges, you compose a rectangle.

Solution to Exercise 4: In geometry, "compose" means joining two or more smaller shapes together to build a new, larger composite shape.