How this resource helps
Complete 35-slide NC Math 3 Grades 9–12 lesson deriving arc and sector formulas from similarity and radian measure, with editable original circular diagrams. Standard NC.M3.G-C.5: Using similarity, demonstrate that the length of an arc, s, for a given central angle is proportional to the radius, r, of the circle. Define radian measure of the central angle as the ratio of the length of the arc to the radius of the circle, s/r. Find arc lengths and areas of sectors of circles.
What’s Included
- One editable 16:9 PowerPoint with 35 slides and teacher speaker notes on every slide.
- Full standard and all its subparts, unpacking, essential question, learning goals, warm-up, vocabulary and teaching routine.
- Five worked models, guided practice, partner work, five scored independent items, small-group intervention and an open extension.
- Matched blank/completed guided notes, a three-item exit ticket and reflection.
- Editable mathematical diagrams, tables and graphs where relevant. Graphing calculator or spreadsheet activities are included where required by the standard.
Resource details
- Grade / course
- NC Math 3
- Subject and resource type
- Mathematics · PowerPoint Lesson
- Files
- 0 main PDF pages · 35 editable slides · PPTX
- Estimated completion time
- 45–60 minute lesson
- Answer key
- Teacher answer guidance is included in the speaker notes on every slide.
Standard or objective
NC.M3.G-C.5 — Using similarity, demonstrate that the length of an arc, s, for a given central angle is proportional to the radius, r, of the circle. Define radian measure of the central angle as the ratio of the length of the arc to the radius of the circle, s/r. Find arc lengths and areas of sectors of circles.
Using similarity, demonstrate that the length of an arc, s, for a given central angle is proportional to the radius, r, of the circle. Define radian measure of the central angle as the ratio of the le
Original Saint Pierre Learning Resources lesson aligned to the North Carolina Standard Course of Study for NC Math 3 Mathematics.
Learner directions
Students work through each slide as the teacher directs, completing practice and exit-ticket items.
Teaching suggestions
Project each slide in order. Follow the teacher models, then guide practice as labeled on each slide.