9 Components
Big Ideas
End of Unit Assessments
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Big Ideas
End of Unit Assessments
Big Idea:

### There is a constant proportional relationship between an angle and its arc measures on a circle.

1 week

Evidence of Understanding

• describe proportional relationships between angles, arcs, and sectors of a circle
• create visuals to describe a central angle in terms of the fraction of the circle it represents
• Example: show an angle measuring 72° is equivalent to ⅕ of the circle
• investigate the constant ratio between an angle’s arc length and a circle’s circumference
• explain the proportional relationship with the radius
• use similarity to derive the length of the arc intercepted by an angle
• use tools to verify the relationship between an angle’s degree and radian measure
• apply the relationship between degrees and radians to find a missing measure
• determine and justify the length of 1 radian
• explain how sectors are related to area of a circle using similarity relationships
• derive and use the formula for determining the area of a sector

• analyze and apply the relationships between the angles and arcs used to describe a circle
• use examples and nonexamples to distinguish central, inscribed, and circumscribed angles
• define and classify angles using radii, chords, and tangents
• investigate relationships between angle and arc measure for a central, inscribed, or circumscribed angle and use them to solve problems
• prove inscribed angles open to the same arc are congruent (and vice versa)
• prove parallel chordsintercept congruent arcs
• prove that a triangle inscribed in a circle with a leg through the center of the circle is a right triangle (hypotenuse is the diameter)
• describe patterns relating the angle and arc measures on a circle by two tangents, two secants, a secant and a tangent, or a chord and a tangent
• describe patterns relating the angle and arc measures resulting from two intersecting chords
• calculate the value of an unknown angle or arc measure

Develop conceptual understanding:

central angle, arc length, circumference, degrees, radians, sector,  inscribed angle, circumscribed angle

Supporting terms to communicate:

equivalent, ratio, proportion, similarity, scale factor, dilation, angle, radius, diameter, area, chord, tangent, secant, parallel, alternate interior angles, hypotenuse

Core Resource
A core resource supports multiple days of instruction. COMING SOON!
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate.
• Pacman
Connect what students know about perpendicular lines and symmetry in order to calculate the area of a sector.
Resource:
Pacman

Connect what students know about perpendicular lines and symmetry in order to calculate the area of a sector.

All Resources From:
• Unit 7

#### Circles

Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.
• 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.
Resource:
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.

All Resources From:
• Unit 7