Maryland Math 7.GR.B.4.c
The Standard
- 7.GR.B.4
- Solve mathematical problems with and without context involving area, surface area, and volume of two- and three-dimensional objects.
Interpret and justify solutions in context by comparing different geometric representations, estimating or checking for reasonableness, and explaining how the result applies to the context.
Maryland College and Career Ready Standards for Mathematics (2025) · REASON WITH AND ABOUT GEOMETRIC FORMULAS TO SOLVE PROBLEMS AND JUSTIFY SOLUTIONS IN CONTEXT.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare a gridded drawing with a calculation for the same shape. They check that the area fits the drawing, then use it to decide how much material to buy.
What Mastery Looks Like
- For a 6-by-4-foot board with a 2-by-3-foot triangular corner removed, a student finds 21 square feet and shows why on a grid. They explain why the area is less than 24 square feet and why three paint pots are needed if each covers 7 square feet.
Common Misconceptions
- Students may subtract the full 2-by-3 rectangle instead of half of it. They may write 21 feet instead of 21 square feet, or choose two paint pots without checking their total coverage.
How to Assess It
- Exit ticket: A 6 ft by 4 ft board has a 2 ft by 3 ft triangular corner removed. Draw a grid model, calculate the paintable area, and explain whether two pots covering 7 square feet each are enough.
Lesson moves
Ways to Teach It
Cut a 2-by-3 triangle from a 6-by-4 grid-paper rectangle, then compare the remaining area with 24 minus 3.
Ask: Why must the board's paintable area be less than 24 square feet, and how does your sketch show that?
Give pairs cards with cut-corner sketches, area equations, and answers; have them match sets and reject any answer larger than the original rectangle.
Hand out a mock paint label marked 7 square feet per pot; have students decide how many pots the cut-corner board needs.
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Related Standards
- 6.AT.C.10
Solve problems in context by writing and solving inequalities and interpreting solution sets in context.
- 7.AT.C.7
Analyze contextual situations to determine whether an equation or inequality best represents the relationship between quantities. Justify the choice based on th...
- 6.AT.C.8
Solve problems in context by writing and solving equations and interpreting the solutions in context.
- 7.NOS.A.3.b
Evaluate the reasonableness of solutions using estimation, mental math, and understanding of the context.
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