- 1. Lesson 1: What Is a Circle? Definition and Real-World Connections
Students can state the mathematical definition of a circle, identify its centre and circumference, and connect the shape to real-world contexts.
- 2. Lesson 2: Semicircles and Quadrants — Dividing the Circle
Students can identify a semicircle and a quadrant, explain what fraction of a full circle each represents, and count their straight and curved edges.
- 3. Lesson 3: Radius and Diameter — The Inside Lines
Students can define and identify the radius and diameter, state the relationship $d = 2r$, and apply this rule to calculate one from the other.
- 4. Chord, Tangent, and Arc — Three More Key Parts
Students can define and identify the chord, tangent, and arc; distinguish an arc from the full circumference; and identify major and minor arcs.
- 5. Sector and Segment — The Two Regions
Students can define and identify a sector and a segment, distinguish major and minor versions of each, and compare their boundaries.
- 6. Pi — The Ratio That Defines All Circle Calculations
Students can explain what $\pi$ represents (the ratio of circumference to diameter), know that $\pi \approx 3.14159$, and understand why it is an irrational number.
- 7. Circumference Formula $C = \pi d$ — From Ratio to Formula
Students can apply $C = \pi d$ to find the circumference of a circle given its diameter, providing answers in both exact form (in terms of $\pi$) and approximate decimal form.
- 8. Circumference from the Radius
Students can derive and use $C = 2\pi r$ to find the circumference when given the radius, and move fluently between radius, diameter, and circumference.
- 9. Arc Length of a Semicircle and Quadrant
Students can find the arc length of a semicircle and quadrant using fraction reasoning (without needing a new formula), and calculate the total perimeter of these shapes.
- 10. Finding Radius from Arc Length — Reverse Arc Problems
Students can find the radius or diameter of a semicircle or quadrant when given its arc length by using algebraic rearrangement and inverse operations.
- 11. Area Formula & square derivation
Students can state and apply the area formula A = πr², understanding that it arises because exactly π lots of r² squares fill a circle.
