Combine Pieces Without Gaps or Overlap

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: A rectangle is cut straight down the middle into two smaller rectangles.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A larger shape can be made from smaller pieces. The pieces must fit with their edges touching and their inside regions separate. A gap leaves some of the whole missing; an overlap counts part of the space twice. Matching pieces can be moved or turned to fit.

Use the supplied description of a shape split into pieces. Imagine or draw the pieces in their original positions. Decide which completed whole they rebuild when matching edges meet.

Trace the target outline before joining pieces. A correct flat composition has no inside gaps or overlaps. Draw the original whole and indicate each separate piece with a different pattern.

1. Draw the original whole and indicate each separate piece with a different pattern.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Use the supplied description of a shape split into pieces.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Take it further

Sketch a rectangle split into two triangles. Expected: matching diagonal edges can rebuild the rectangle.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.