**Title:** Arc Lengths and Sector Areas

**Description:**
Students will work in cooperative groups to discover the relationships between arc length, central angle measure, and circumference. They will also discover the relationship between circle area, central angle measures, and sector area. Students will share their discoveries and create formulas for calculating arc length and sector area. Then they will practice these skills in a journal entry and solving a real-life extension.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
**Standard(s): **

[MA2015] GEO (9-12) 28: Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. [G-C5]

**Subject:**Mathematics (9 - 12)

**Title:**Arc Lengths and Sector Areas

**Description:**Students will work in cooperative groups to discover the relationships between arc length, central angle measure, and circumference. They will also discover the relationship between circle area, central angle measures, and sector area. Students will share their discoveries and create formulas for calculating arc length and sector area. Then they will practice these skills in a journal entry and solving a real-life extension. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

**Title:** Soda Cans

**Description:**
This reproducible activity sheet, from an Illuminations lesson, guides students through a simulation in which they try different arrangements to make the most efficient use of space and thus pack the most soda cans into a rectangular packing box.
**Standard(s): **

[MA2015] ALC (9-12) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama)

**Subject:**Mathematics

**Title:**Soda Cans

**Description:**This reproducible activity sheet, from an Illuminations lesson, guides students through a simulation in which they try different arrangements to make the most efficient use of space and thus pack the most soda cans into a rectangular packing box.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Circle Packing and Curvature

**Description:**
In this lesson, one of a three-part unit from Illuminations, students investigate the curvature of circles. Students apply definitions and theorems regarding curvature to solve circle problems. In addition, there are links to an online activity sheet and other related resources.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Circle Packing and Curvature

**Description:**In this lesson, one of a three-part unit from Illuminations, students investigate the curvature of circles. Students apply definitions and theorems regarding curvature to solve circle problems. In addition, there are links to an online activity sheet and other related resources.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12

**Title:** Soccer Problem

**Description:**
This student interactive, from an Illuminations lesson, allows students to investigate a soccer problem by changing the location of a soccer player as well as the distance between the player and the goal posts. The angle changes as the player is moved, and students must therefore determine the player s position so that the angle is maximized.
**Standard(s): **

[MA2015] GEO (9-12) 41: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost, working with typographic grid systems based on ratios).* [G-MG3]

**Subject:**Mathematics

**Title:**Soccer Problem

**Description:**This student interactive, from an Illuminations lesson, allows students to investigate a soccer problem by changing the location of a soccer player as well as the distance between the player and the goal posts. The angle changes as the player is moved, and students must therefore determine the player s position so that the angle is maximized.

**Thinkfinity Partner:**Illuminations

**Grade Span:**9,10,11,12