Part+II+-+Teaching+Circles+and+Pi

Major parts to consider when teaching Circles and pi:

According to the GPS, students should build their knowledge of circles in three main parts: properties of the circle, circumference and pi, and area of a circle. Students are first introduced to circles as a geometric shape in the third grade. During this time, they begin to form vocabulary for circles' properties including: center, radius, and diameter. The second idea of circles students learn includes circumference and pi. In this section, students will need to find the relationship between a circle's circumference and diameter is pi which can be used to derive the formula of circumference. Finally, students should explore the area of a circle with both estimation and precision. Teaching circles can be easily taught in three sections that apply students prior knowledge to learn new concepts of the properties of circles.

In the first stage of learning circles, students are introduced to identifying parts of the circle in the third grade. At this stage, students are building their knowledge of geometric figures including circles and their parts. Bringing up these ideas are crucial for students to be able to dig in and explore properties. The properties of a circle are unique, and students need to know them in order to understand how to formulate bigger ideas like area of formula for circumference. Going over key terms is important for having a discussion so that students are able to practice using proper vocabulary and thinking more about each idea as an individual component. Important concepts in this stage students need to learn includes:
 * center, radius, diameter, circumference
 * In geometry, students will use a circle's radius for many concepts including constructions.
 * focus on the idea that a circle is made from multiple points an equal distance from a center point.

The second stage of circles covers discussing circumference and pi. In this area of learning, students should be able to relate their understanding of perimeter to the circle specific, circumference. Because this portion of conceptual growth is derived from measurement and finding formulas, we want to prioritize having a hands-on approach to finding how pi applies to circles. Using a hands on method for measuring allows students to manufacture meaning from the lesson and the derivation will hopefully create an almost permanent recognition of the concept of pi.
 * Students can use their prior knowledge of perimeter to understand circumference. A circle's perimeter is called a circumference and the students can use the relationship between it and the circle's diameter to come up with the formula for circumference.
 * Circumference/diameter = pi
 * Circumference = diameter x pi or 2 x pi x r

Finally, the students will learn about circle's area. Area is an important concept to apply to spacial understanding. Most figures at this point have a specific formula for finding their area. Circles use the concept of pi just as in circumference to find the area. Students should learn to find and derive the area formula just as they did the circumference. As teachers, you are going to have a hard time doing much to supplement student formation besides allowing them to use prior knowledge to derive the area formula. The circle is very different from other shapes and has an individual method to find its area, which is abstract in comparison to most other area formulas that the students may have previously encountered.
 * estimating area
 * finding area
 * Area = pi x radius squared