Add Areas of Non-Overlapping Parts

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: An L-region is split into a 3×5 rectangle and an adjoining 2×4 rectangle with no overlap.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A composite region can be split into rectangles whose interiors do not overlap. Find each area and add them to count the whole. Shared boundary segments have no area, but an actual overlapped patch would be counted twice. The partition should cover all of the target region.

Use the supplied non-overlapping rectangular parts. Calculate each product, add their areas, and label the combined result in square units. Explain why the non-overlap statement makes direct addition valid.

Check that the stated parts cover the region completely. Do not add overlapped areas without correcting the double count. Draw the two rectangular parts with distinct patterns and their shared boundary marked.

1. Draw the two rectangular parts with distinct patterns and their shared boundary marked.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Use the supplied non-overlapping rectangular parts.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

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Take it further

Parts 4×6 and 3×2 with no overlap have total area 30 square units.

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