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Arc Length or Sector Area?

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Arc Length or Sector Area?

Connect what students know about area and circumference of circles to match to diagrams representing sector areas and arc lengths.

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Bicycle Wheel

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Bicycle Wheel

From the Illustrative Mathematics website, "the purpose of this task is to introduce radian measure for angles in a situation where it arises naturally."
 

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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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Circles and Segments

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Circles and Segments

These four parts are designed to support students in making connections between chord, secant, and tangent line relationships in circles and creating proofs of these relationships using triangle similarity.

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Circles and Squares

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Circles and Squares

In this task, you must solve a problem about circles inscribed in squares.

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Elmo's Microwave Travel

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Elmo's Microwave Travel

 

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End of Unit Assessment (Geometry, Unit 7)

Geometry
Unit 7: Circles
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End of Unit Assessment (Geometry, Unit 7)

After this unit, how prepared are your students for the end-of-course Regents examination?  The end of unit assessment is designed to surface how students understand the mathematics in the unit.  It includes spiralled multiple choice and constructed response questions, comparable to those on the end-of-course Regents examination.  A rich task, that allows for multiple entry points and authentic assessment of student learning, may be available for some units and can be included as part of the end of unit assessment.  All elements of the end of unit assessment are aligned to the NYS Mathematics Learning Standards and PARCC Model Frameworks prioritization. 

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Find the Center (Geometry)

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Find the Center (Geometry)

Connect to what students know about the Pythagorean theorem and reading coordinates to find the center of a circle.

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Find the Other Point (Geomtry)

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Find the Other Point (Geomtry)

Use what students know about symmetry and coordinates to find a coordinate on a circle.

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Inscribing and Circumscribing Right Triangles

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Inscribing and Circumscribing Right Triangles

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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Inscribing a Triangle in a Circle

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Inscribing a Triangle in a Circle

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter. 

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Instructions for Square Peg

Geometry
Unit 7: Circles
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Instructions for Square Peg

This page contains instructions on how to use the initial task, Square Peg, to find out what your students already know about calculating the areas of squares and circles, and using the Pythagorean theorem and/or trigonometry.

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