Math Example: Comparing Area: Example 6

Topic

Geometry

Description

This example compares the areas of a circle (Figure A) and a square (Figure B) drawn on a grid. The circle has a radius of 2 units, while the square has a side length of 4 units. Using the formula for the area of a circle (π r²) and a square (s²), we calculate that the circle has an area of π * 2² = 4π square units, and the square has an area of 4² = 16 square units. Comparing these results, we can conclude that A < B, meaning the square has a larger area than the circle.

This example is part of a series designed to teach students about comparing areas of different geometric shapes. By introducing a comparison between a circle and a square, students learn to apply different area formulas and make comparisons between dissimilar shapes. This approach helps reinforce the concept that area calculation methods vary for different shapes, and that direct comparison of numbers may involve comparing a value involving π with a whole number.

Exposing students to multiple worked-out examples is essential for developing a deep understanding of area comparison across different shapes. Each example provides a unique scenario, allowing students to apply their knowledge to new situations. This repetition helps solidify the concept and improves students' ability to tackle various area-related problems independently, especially when dealing with different types of shapes.

Teacher Script: "Now we're comparing a circle and a square. This is interesting because we need to use different formulas for each shape. Can you recall the formulas for the area of a circle and a square? Let's calculate their areas together. What do you notice about the results? The circle's area involves π, while the square's doesn't. How can we compare these? This example shows us that comparing areas can sometimes involve comparing different types of numbers. In real life, when might we need to compare circular and square areas?"

For a complete collection of math examples related to Geometry click on this link: Math Examples: Comparing Areas Collection.