Reach for the Star

Circles arcs and sectors · Optional extension

L034 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

A sector has radius 9 cm and angle 80°. Find arc length and area exactly.

Reveal a worked check after attempting

Arc=80/360×18π=4π cm; area=80/360×81π=18π cm².

Deep challenge

A learner finds the perimeter of a semicircle of radius 5 cm as 5π cm. Explain the missing part.

Reveal a worked check after attempting

5π is curved arc only; full perimeter includes diameter 10, so 5π+10 cm.

Recall & Review: feedback and extension integration

Lesson L034: Circles arcs and sectors

Objective: Calculate circle circumference and area, arc length and sector area, distinguishing curved length from the full sector perimeter.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.

Even Better If (EBI)

I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.

Stretch and deep challenge

Stretch: A sector has radius 9 cm and angle 80°. Find arc length and area exactly.

Deep challenge: A learner finds the perimeter of a semicircle of radius 5 cm as 5π cm. Explain the missing part.