Compose New Shapes from Smaller Shapes

Students combine triangles, rectangles, squares, and other shapes to create composite shapes and describe how the parts form a whole.

Review Basic Shapes

A shape has features that help us name it. A triangle has 3 straight sides and 3 corners. A rectangle has 4 straight sides and 4 corners. Its opposite sides are the same length. A square also has 4 straight sides and 4 corners, but all 4 sides are the same length. A circle is round and has no straight sides or corners. Look at each shape and trace its sides with your finger. Then point to each corner. For example, compare a triangle and a square. The triangle has fewer sides and corners than the square. Knowing these shapes and their features will help you fit them together to make larger shapes.

Model Combining Shapes

We can join smaller shapes to make one larger shape. The shapes should touch along a full side without overlapping. Start with two matching right triangles. Turn one triangle so its long side faces the long side of the other triangle. Slide them together until the long sides meet. The outside edge now forms a square. The line where the triangles meet is still visible, so we can see the two parts. We made one whole square from two triangle parts. We can also separate the square along that line to find the triangles again. Turn and slide shapes in different ways to see which sides fit together.

Build Composite Shapes

A composite shape is a whole shape made from two or more smaller shapes. You can build one by placing shapes side by side. Try making a simple house shape. Put one rectangle upright for the walls. Place one triangle above it so the bottom side of the triangle touches the entire top side of the rectangle. Together, the rectangle and triangle form one composite shape. There should be no gap between the roof and the walls, and the pieces should not overlap. Next, try a different composite shape by joining two squares along matching sides to make a larger rectangle. Count the pieces in each whole and name every shape you used.

Describe the Parts and Whole

When you describe a composite shape, tell about both the parts and the whole. First, name and count the smaller shapes. Then explain how they are joined. Finally, name or describe the whole shape. For example, two equal squares can be placed side by side with one full side touching. The parts are 2 squares, and the whole is a rectangle. You can say, “I used 2 squares to make 1 rectangle.” Look closely at the seam to find where one part ends and the next part begins. Remember that turning a shape does not change its name. A square is still a square even when it looks like a diamond.

Create a New Shape

A composite shape can become a part of an even larger shape. Begin with the house-shaped composite made from 1 rectangle and 1 triangle. Make a second matching house. Slide the two houses together so their rectangular sides touch. Now the two composite shapes form a new, larger composite shape. Count all the original pieces: 2 triangles and 2 rectangles. You may also rearrange the pieces to invent another design, such as a rocket, boat, or tall tower. Turn, flip, and slide the pieces, but do not bend or cut them. Make sure the pieces touch without overlapping. Your new shape can look like a familiar object or be your own design.

Share and Check

Show your composite shape to a partner. Explain which smaller shapes you used and how they touch. You might say, “I joined 2 triangles and 1 square to make my rocket.” Ask your partner to check the shape. Do all pieces lie flat? Do the pieces touch without gaps where they are meant to join? Are any pieces overlapping? Can your partner point to each part and count the same number you counted? If something does not fit, turn or slide a piece and check again. Then trace the outside edge of the whole shape with your finger. The outside edge shows the new shape, while the inside seams show how the smaller parts form the whole.