Standard: 3.MD.C7d – 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.
Grade level: Grade 3
Subject: Mathematics
Domain: Measurement & Data
Teacher Overview
This standard focuses on understanding that the area of a shape can be found by decomposing it into smaller, non-overlapping rectangles. This skill is crucial for solving real-world problems and sets the foundation for more advanced geometric concepts. Students need to have a solid grasp of basic multiplication and the concept of area. They should also be comfortable measuring sides of rectangles.
After mastering this standard, students will be able to calculate the area of more complex shapes and will be prepared to understand volume in three-dimensional figures.
Common Misconception 1
A common misconception is that overlapping parts of decomposed figures should be included in the total area. This is incorrect because overlapping areas are counted twice, leading to an inaccurate total.
Intervention 1
Use visual aids and hands-on activities to show that overlapping areas should not be counted twice. Practice with clear examples and gradually increase complexity.
Common Misconception 2
Another misconception is that students may think they cannot find the area if the sides are not whole numbers. This is incorrect because area calculations can include fractions and decimals.
Intervention 2
Provide practice problems involving non-whole number side lengths and demonstrate the multiplication of fractions and decimals to find the area.
Prerequisite Knowledge
Students should understand basic concepts of area and multiplication, and be able to identify and measure the sides of rectangles.
Subsequent Knowledge
Students will develop skills in calculating the area of more complex shapes and understanding the concept of volume in three-dimensional figures.
Instructional Activities
- Create a floor plan for a dream house using rectilinear shapes.
- Design a garden layout and calculate the area of each section.
- Solve real-world problems involving the area of playground sections.
- Use graph paper to draw and decompose rectilinear figures.
