MA.912.GR.4.4

This task is the first in a series of three tasks that assess the students’ understanding of informal derivations of the formulas for the area and circumference of a circle. In this task, students are shown a regular n-gon inscribed in a circle. They are asked to use the formula for the area of the n-gon to derive an equation that describes the relationship between the area and circumference of the circle.

Type: Formative Assessment

Students are asked to solve a design problem in which a softball complex is to be located on a given tract of land subject to a set of specifications.

Type: Formative Assessment

Students are asked to determine an estimate of the density of trees and the total number of trees in a forest.

Type: Formative Assessment

Students are asked to determine the population of the state of Utah given the state’s population density and a diagram of the state’s perimeter with boundary distances labeled in miles.

Type: Formative Assessment

Students are asked to select appropriate geometric shapes to model a lake and then use the model to estimate the surface area of the lake.

Type: Formative Assessment

This task is the third in a series of three tasks that assess the students’ understanding of informal derivations of the formulas for the area and circumference of a circle. In this task, students are given the definition of pi as the area of the unit circle, A(1), and are asked to use this representation of pi along with the results from the two previous tasks to generate formulas for the area and circumference of a circle.

Type: Formative Assessment

This task is the second in a series of three tasks that assesses the students’ understanding of informal derivations of the formulas for the area and circumference of a circle. In this task, students show that the area of the circle of radius r, A(r), can be found in terms of the area of the unit circle, A(1) [i.e., A(r) = r² · A(1)].

Type: Formative Assessment

Students apply concepts of density to situations that involve area (2-D) and volume (3-D).

Type: Lesson Plan

The lesson introduces area of sectors of circles then uses the areas of circles and sectors to approximate area of 2-D figures. The lesson culminates in using the area of circles and sectors of circles as spray patterns in the design of a sprinkler system between a house and the perimeter of the yard (2-D figure).

Type: Lesson Plan

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Go behind the scenes and learn about science museum exhibits, design constraints, and engineering workflow! Produced with funding from the Florida Division of Cultural Affairs.

Type: Perspectives Video: Professional/Enthusiast

See and see far into the future of arts and manufacturing as a technician explains computer numerically controlled (CNC) machining bit by bit.

Type: Perspectives Video: Professional/Enthusiast

Dr. David McNutt explains how a simple do-it-yourself quadrat and a transect can be used for ecological sampling to estimate population density in a given area.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Set sail with this math teacher as he explains how kites were used for lessons in the classroom.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea