Florida B.E.S.T. MA.7.GR.1.2
The Standard
Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students draw lines to split an irregular shape into familiar triangles and quadrilaterals. They find each smaller area, then add or subtract those areas to get the total.
What Mastery Looks Like
- Given labeled dimensions, a student chooses a valid decomposition, finds missing lengths, and applies the correct area formulas. The final answer includes square units and is reasonable for the diagram.
Common Misconceptions
- Students may add side lengths and report perimeter, multiply unrelated dimensions, or use a slanted side as a triangle's height. They may also double-count pieces, forget to subtract cutouts, or omit square units.
How to Assess It
- Exit ticket: A 12 cm by 8 cm rectangle has a 4 cm by 3 cm corner removed. Split the remaining shape into two rectangles and find its area.
Lesson moves
Ways to Teach It
Cut L-shaped figures from grid paper, then have pairs draw two different decompositions and verify that both produce the same area.
Writing prompt: Which decomposition makes the given floor plan easiest to solve, and why?
Run a matching game where students pair composite-figure cards with decomposition diagrams, area expressions, and correct totals.
Measure the classroom floor and a rectangular cabinet footprint, then calculate the exposed floor area available for new tile.
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Related Standards
- MA.8.GR.2.4
Solve mathematical and real-world problems involving proportional relationships between similar triangles.
- MA.912.GR.4.4
Solve mathematical and real-world problems involving the area of two-dimensional figures.
- MA.6.GR.2.2
Solve mathematical and real-world problems involving the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles.
- MA.3.GR.2.4
Solve mathematical and real-world problems involving the perimeter and area of composite figures composed of non-overlapping rectangles with whole-number side l...
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