Study guide: Analyze Shapes and Equal-Area Partitions
Identify polygons, count rectangle tiles, and distinguish equal shares from equal-looking shapes.
Ideas to explain in your own words
- A polygon is a closed flat figure built from straight sides.
- A rectangle can be partitioned into equal squares with no gaps or overlap.
- Three equal-area shares of one whole are thirds.
- Equal shares need equal area, but their outlines do not always need the same shape.
Useful vocabulary
- quadrilateral
- A closed polygon with four straight sides.
- third
- One of three equal shares of a whole.
Watch your reasoning
- Equal side lengths are not required for the broad polygon names.
- Count tiles, not grid intersections or the outside outline.
- Three pieces are not automatically three equal shares.
- Different outlines do not automatically mean different amounts of a whole.
A worked review example
A closed figure with five straight sides is a pentagon. It does not need all sides equal to have that name. A circle has no straight polygon sides, so it is not a pentagon or another polygon just because it is closed. Count all sides along one complete trip around the boundary. Equal side lengths are not required for the broad polygon names. Mark each straight side once and count the marks.
Make a practice plan
- Identify Polygons by Sides and Corners: Draw a five-sided polygon with unequal sides. Expected: it is still a pentagon.
- Count Equal Squares in Rows and Columns: Four rows of five equal squares contain 20 squares.
- Name Three Equal Shares as Thirds: Shade two of three equal strips. Expected: two thirds shaded; one third unshaded.
- Recognize Equal Area in Differently Shaped Shares: A 12-tile whole has pieces of 4,4,4 tiles with different outlines. Expected: three equal-area thirds.