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Calculating Arcs and Areas of Sectors of Circles

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Calculating Arcs and Areas of Sectors of Circles

 
This lesson unit is intended to help you assess how well students are able to solve problems involving area and arc length of a sector of a circle using radians. It assumes familiarity with radians and should not be treated as an introduction to the topic. This lesson is intended to help you identify and assist students who have difficulties in:
Computing perimeters, areas, and arc lengths of sectors using formulas.
Finding the relationships between arc lengths, and areas of sectors after scaling.

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Completing the Square #2

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Completing the Square #2

Connect standard form and vertex form of a quadratic to an area model representation to see how negative values of h in the vertex form impact the visual and the standard form.

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Lines and Linear Equations

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Lines and Linear Equations

A Classroom Challenge (aka formative assessment lesson) is a classroom-ready lesson that supports formative assessment. The lesson’s approach first allows students to demonstrate their prior understandings and abilities in employing the mathematical practices, and then involves students in resolving their own difficulties and misconceptions through structured discussion.

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Lucky Cow

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Lucky Cow

3 Acts activity about the area of a sector.

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MARS FAL: Evaluating Statements about Length and Area

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MARS FAL: Evaluating Statements about Length and Area

This lesson unit is intended to help you assess how well students can:
Understand the concepts of length and area.
Use the concept of area in proving why two areas are or are not equal.
Construct their own examples and counterexamples to help justify or refute conjectures.

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Obscure Geometry

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Obscure Geometry

Videos that explore the relationship between the area of triangles formed by the diagonals of squares.

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Setting Up Sprinklers

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Setting Up Sprinklers

This task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7). 

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Sprinkler Task

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Sprinkler Task

Website and video that uses sprinklers to model the area of circles in context.

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Super Venn Diagram
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Super Venn Diagram

In the Super Venn protocol, a team of teachers creates a large Venn diagram to show the overlap between an initial task, intended to assess student knowledge and skills at the beginning of a unit of study, and a final task, intended to assess student knowledge and skills at the end of a unit.

Tennis Balls in a Can

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Tennis Balls in a Can

Task that models real world situations using spheres and cylinders.

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Tilted Square

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Tilted Square

Make connections between the structure of a shape and ways to efficiently count the number of objects within the shape.

Toilet Paper Roll

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Toilet Paper Roll

Task that uses a cylinder to model a roll of toilet paper.

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