CCSS.Math.Content.3.MD.C.7d
The standard
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
Common Core State Standards for Mathematics
What this standard means
Students need to split an L-shaped or other rectilinear figure into rectangles, find each rectangle’s area, then add the parts. They should label side lengths, use multiplication for each rectangle, and show that different splits can still give the same total area.
Mastery looks like a clear drawing with non-overlapping rectangles, correct missing side lengths, multiplication equations, and a final answer in square units. Students often get stuck counting edge lengths as area, overlapping their rectangles, or forgetting to add all parts after multiplying.
Ways to teach it
- Hands-on: Give students grid paper L-shapes, have them cut along one line into rectangles, then label and calculate each area.
- Prompt: Show two different ways to split the same shape, then write which is easier and why.
- Quick check: Project one rectilinear figure with side lengths and ask students to write the total area on a sticky note.
- Real-world: Use a simple floor plan of a bedroom and closet, then find the total carpet area needed.
Plan a lesson for CCSS.Math.Content.3.MD.C.7d
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- CCSS.Math.Content.3.MD.C.7b
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Apply the area and perimeter formulas for rectangles in real world and mathematical problems.