Circles: Circumference, Area, Arc Length and Sectors

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Mathematics · Geometry
SP-GEOM-007 · Free to print and use in your classroom · substituteplans.com
Page 2
Circles: Circumference, Area, Arc Length and
Sectors
Mathematics · Geometry · Grades 9-10 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Write the circle formulas on the board.
Technology
None. A basic calculator is optional.
Student
independence
High. Students work alone with a calculator if available.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet, Whiteboard or chalkboard, Calculators (optional)
Goal for today: Students will use the circumference and area formulas, and the fraction-of-a-circle idea, to find arc
lengths and sector areas.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: d = 2r. Circumference C = 2πr = πd. Area A = πr². Arc length = (angle ÷ 360) × 2πr.
Sector area = (angle ÷ 360) × πr².
☐ Keep the answer key on your desk. You do not need to solve anything yourself.
Say this to start
Good morning! Today’s geometry practice is about circles. Students will use a few formulas, which are on the board, to
find the distance around a circle, the space inside, and parts of a circle. They may leave answers with the symbol π or
round using 3.14. A calculator is useful but not required.
Run of show
Minutes
What you do
What students do
0–5
Take attendance. Hand out the worksheet face down.
Settle in and take out a pencil.
5–13
Read the formulas from the board aloud. Then read this
example: a circle with radius 3 has circumference 2π(3) =
6π and area π(3²) = 9π. An arc of 90° is one quarter of the
circle, so its length is 6π ÷ 4 = 1.5π.
Follow along and copy the example.
13–38
Tell students to work questions 1–10 in the work boxes.
Say they may leave answers in terms of π or round using π
≈ 3.14. Walk around. If students are stuck on arcs, ask:
“What fraction of the whole circle is this angle?”
Write the formula, substitute, and solve.
38–44
Tell students to answer question 11 and fill in the Fraction
Table (not numbered).
Choose an answer and fill in the table.
44–50
Read the answers aloud from the key while students check.
Collect all worksheets.
Check their work and hand in the
worksheet.

SubstitutePlans.com
Mathematics · Geometry
SP-GEOM-007 · Free to print and use in your classroom · substituteplans.com
Page 3
If things go wrong
• If students confuse radius and diameter, remind them: the diameter goes all the way across; the radius is half
of that.
• If a student asks whether to use 3.14 or the π button, tell them either is fine, but they should say which one
they used.
• If students are confused by arcs, tell them an arc is a fraction of the circumference. Set up the fraction first
(angle over 360).
• If the class is noisy, remind them this is independent work.
Early finishers
• A circle has a circumference of 10π. Find its radius, then its area.
• Find the area of a ring with outer radius 6 and inner radius 4 (answer: 20π).
• Explain in a sentence why doubling the radius makes the area 4 times larger.
Support and challenge
• Support: Allow calculators and have students complete questions 1, 2, 3, 5 and 6 only.
• Challenge: Ask students to find the length of an arc of 150° in a circle with radius 12 (answer: 10π, about
31.42).
Notes for the teacher (you fill this in)
Jot a few lines before you leave. A full Daily Sub Report is in the free Sub Survival Kit at SubstitutePlans.com.
How far the class got / what to pick up next:
Students who were especially helpful:
Anything the teacher should know: