Compose New Shapes from Smaller Shapes

Students combine two-dimensional shapes to create composite shapes and identify the smaller shapes used.

Review Basic Shapes

Before we build new shapes, let us review some shapes we know. A triangle has three straight sides and three corners. A square has four equal sides and four corners. A rectangle also has four sides and four corners. A circle is round and has no straight sides or corners. Look at each shape and trace its outside edge with your finger. Then count the sides and corners. For example, imagine a square cracker beside a round plate. The cracker has four straight sides, but the plate has a curved edge. Knowing the parts of each shape will help you recognize it when it becomes part of a larger shape.

Model Combining Shapes

We can put smaller shapes together to make a larger composite shape. A composite shape is one shape made from two or more shapes. Start with two matching right triangles. Turn them so their longest sides face each other. Slide the triangles together until the longest sides touch exactly. Do not leave a gap, and do not place one triangle on top of the other. The outside edge now forms a square. The line inside the square shows where the two triangles meet. We used two triangles to compose, or build, one square. Even though we can see the two smaller triangles, we can also look at the whole outside edge and name the new shape.

Build Composite Shapes

Now use a square and a triangle to build a composite shape. Place the triangle above the square. Match the bottom side of the triangle with the top side of the square. The sides should touch with no gap and no overlap. The whole shape may look like the front of a house. The square is the main part, and the triangle is the roof. Look only at the outside edge. It has five straight sections, but the new figure does not need a special name. We can call it a composite shape. Try moving the triangle to a different side of the square. The same two smaller shapes can make different composite shapes when their positions change.

Name the Smaller Shapes

A composite shape can be taken apart in our minds. Look for lines inside the large shape. Each inside line may show where two smaller shapes meet. For example, a long rectangle can be made from two equal squares placed side by side. The line down the middle separates the squares. Point to the left part and name it: square. Point to the right part and name it: square. Then describe the whole figure: two squares make one rectangle. Be careful to name the pieces you can actually see. Count them one at a time so you do not miss a shape or count one twice. You can also cover each piece with your hand after you name it.

Create a New Shape

We can use a composite shape as a building piece for another new shape. First, join two equal squares side by side. Together, they make a rectangle. Keep this composite rectangle in place. Next, attach a triangle to each short end of the rectangle. Make sure one full side of each triangle touches one short side of the rectangle. Now the figure has four smaller parts: two squares and two triangles. It also has the rectangle we made first inside it. This shows two steps of composing shapes. First, squares made a rectangle. Then the rectangle and two triangles made a new composite shape. Try turning the entire figure. Turning it changes its direction, but it does not change its parts.

Share and Check

Show your composite shape to a partner and explain how you built it. Use shape names and position words such as above, below, beside, and between. For example, you might say, “I put two squares side by side to make a rectangle. Then I placed one triangle above the left square.” Your partner can check the shape by pointing to each smaller piece and naming it. Together, check that touching sides meet without gaps or overlaps. Count how many of each shape were used. Then look at the whole outside edge and describe the new shape. If your partner cannot find a piece, trace the line where that piece meets another shape. Careful sharing and checking help everyone explain their mathematical thinking.