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Learn how to put shapes together to build brand-new shapes!
People have been putting shapes together for a very long time! Long ago, builders used shapes like rectangles and triangles to make houses, castles, and bridges. Artists used circles and squares to make beautiful pictures called mosaics (pictures made from small shape pieces). Even today, we put shapes together every time we build with blocks or play with puzzles!
So here is the big question: How can we put small shapes together to make bigger, new shapes? That is what we will learn in this lesson!
When we compose shapes, we put two or more shapes together to make a new shape. The new shape we make is called a composite shape. Think of it like snapping puzzle pieces together!
Let's look at how flat (2D) shapes can be put together. In the picture below, you will see small shapes on the left side. On the right side, you will see the new composite shape they make when joined together!
Look at the diagram above. On the left you see the smaller shapes by themselves. The arrow shows them being composed (put together). On the right you see the new composite shape. The dashed lines inside the composite shape help you see the smaller shapes that are hiding inside!
When you compose shapes, you follow simple steps. You pick your shapes, you slide them together so their edges touch, and then you look at the new shape you made! Let's think about counting the shapes inside, too.
When you look at a composite shape, you can count how many smaller shapes are inside. If you put 2 squares side by side, you get a rectangle. That rectangle is made of 2 squares. If you put 4 squares together in a grid (2 on top, 2 on bottom), you get a bigger square!
We can also compose 3D shapes! Think about stacking blocks. When you put a cone on top of a cylinder, you get a shape that looks like a rocket or a pencil. When you put two cubes side by side, you get a rectangular prism (a long box shape). Let's look at some examples!
Look around your room! A pencil looks like a cone on top of a cylinder. A house looks like a rectangular prism with a triangle shape on top for the roof. You already see composite shapes every day!
Let's work through an example together. We will build a house shape using flat (2D) shapes!
You can compose both flat shapes and solid shapes, but they work a little differently. Let's compare!
| Feature | 2D (Flat) Shapes | 3D (Solid) Shapes |
|---|---|---|
| What are they? | Flat shapes you can draw on paper | Solid shapes you can hold |
| Examples | Squares, rectangles, triangles, circles | Cubes, cones, cylinders, prisms |
| How to compose | Slide edges together on a flat surface | Stack or place faces together |
| Real-world example | Two right triangles make a paper square | A cone and cylinder make a rocket toy |
| Fun activity | Cut paper shapes and glue them together | Stack building blocks and cans |
Now that you can compose shapes, you are getting ready for some exciting math ideas that come next! In second grade and beyond, you will learn to partition shapes (break them apart into equal pieces). You will also learn about area (how much space a shape covers) and fractions (parts of a whole). Composing shapes is the first step!
| What You Learn Now | What Comes Next |
|---|---|
| Put shapes together (compose) | Break shapes apart (partition/decompose) |
| Name composite shapes | Find halves, thirds, and fourths |
| Use squares, triangles, circles | Measure area using square units |
| Build with 3D blocks | Count faces, edges, and vertices on 3D shapes |
Every time you compose shapes, you are training your brain to think like a builder and a problem solver. These skills will help you in math for many years to come!
Try these problems! Start with the easy ones and work your way up. Take your time and think about the shapes.
In this lesson, you learned that to compose shapes means to put smaller shapes together to make a new, bigger shape called a composite shape. You can compose 2D (flat) shapes like rectangles, squares, triangles, trapezoids, half-circles, and quarter-circles. You can also compose 3D (solid) shapes like cubes, rectangular prisms, cones, and cylinders.
You can always look at a composite shape and find the smaller shapes hiding inside. Two right triangles placed together can make a rectangle or a square. A square and a triangle (with a matching base) can make a house shape. A cone and a cylinder can make a rocket. The same composite shape can sometimes be made in more than one way. Keep composing and building — you are becoming a shape expert!