Maryland Math 4.GR.A.4
The Standard
Relate the area of a triangle to the area of a rectangle using decomposition and visual models. Derive and apply the formula to solve problems in contexts involving triangles positioned within or formed from the decomposition of rectangles
Maryland College and Career Ready Standards for Mathematics (2025) · SOLVE PROBLEMS INVOLVING MEASUREMENT CONVERSION, AREA, AND PERIMETER.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students split rectangles to show why a triangle with the same base and perpendicular height has half the rectangle's area. They use base times height divided by 2 to solve problems.
What Mastery Looks Like
- A student can mark the base and perpendicular height, even when the triangle's top point is not at a rectangle corner. They can explain why the triangle covers half the rectangle and give its area in square units.
Common Misconceptions
- Students may use a slanted side as the height or forget to divide by 2. Some think any triangle inside a rectangle covers half its area, even when the triangle does not span the rectangle's full base and height.
How to Assess It
- Exit ticket: Draw an 8-by-6 rectangle. Put a point on its top edge and connect it to both bottom corners. Find the triangle's area and show why your answer makes sense.
Lesson moves
Ways to Teach It
Have students cut an 8-by-6 grid-paper rectangle along its diagonal, then fit the two triangles together to check their areas.
Draw a rectangle with a triangle's tip halfway along its top edge, and ask students why the triangle still covers half the rectangle.
Give pairs cards showing 8-by-6 and 10-by-4 rectangles and matching triangles; have them match each pair and calculate the triangle's area.
Draw a triangular flower bed with its base along the bottom of an 8-by-6-foot plot and its tip on top; find its area.
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Printable 4.GR.A.4 Worksheet
A ready-to-print activity worksheet aligned to 4.GR.A.4, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 5.NOS.B.5.d
Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of division.
- 4.NOS.B.6.d
Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of division.
- 6.GR.A.1
Find the area of triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and quadrilaterals to solve problems.
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