Composing Shapes
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) to create composite shapes, and compose new shapes from the composite shape
What a learner can do afterwards
- Combine two triangles to form a rectangle or larger triangle
- Put together half-circles and quarter-circles to form circles or new shapes
- Decompose a composite shape and describe which simpler shapes make it up
- Names triangles, circles, rectangles, squares and trapezoids by their straight side counts.
1 · Read
You already know how to put two shapes together to make a new one. Now you will go further. You can put together shapes like triangles, half-circles, and quarter-circles to build new shapes. You can even use the new shape you just built to build something even bigger. Four same-size quarter-circles fit together to make one whole circle, just as two half-circles do.
Leo has two same-size triangles, each with one square corner like the corner of a book. He flips one over so their long slanted sides touch with no gaps. Now the two triangles together make one rectangle.
A shape you build, like Leo's rectangle, is called a composite shape. You can use a composite shape like any other piece. Put a triangle on top of the rectangle, and you have built a house. That rectangle uses 2 triangles. Triangles have 3 straight sides. Trapezoids and rectangles have 4. Circles have none.
When you see a shape, look for the smaller shapes inside it: which flat shapes made this one?
Put simple shapes together to build new shapes, then use those new shapes to build something even bigger.
The rewritten reading was written for this dataset.
More to read
Measure a shape made from smaller shapes
A house shape or rocket shape can be made from smaller shapes. Look for a rectangle below a triangle, or two or three squares side by side.
The space inside a flat shape is its area. Equal-sized square tiles can help us measure it.
For a rectangle, count the tiles in one row. Add that number for each row. This is multiplying length by width. A square has matching length and width, so multiply one side by itself.
A triangle covers half the area of a rectangle with the same bottom width and height. Find that rectangle's area, then take half.
Add the areas of the pieces to find the whole area. The pieces must fill the shape with no gaps or overlaps.
Draw a fish on squared paper with a rectangle body and a triangle tail. Find the two areas, then add them.
Composing and decomposing shapes
You can build them up or break them down.
To build up means to put small shapes together to make a bigger one. Two triangles can become a rectangle. Two half-circles can become a whole circle. Lots of small squares can become a big quilt pattern.
To break down means to split a big shape into small ones. A house shape can be split into a square and a triangle. A funny-looking garden can be split into rectangles and triangles.
Why do this? Because small shapes are easy to measure, and big strange shapes are hard. If you know the rectangles and triangles inside a big shape, you can find the size of the whole thing by adding up the small parts.
Builders and artists use this trick all the time. When you see a shape that looks too hard, just ask: what small shapes is it made of?
Explore more
2 · Watch
En anglaisTake it off screen
Where it sits
Learn first
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.