Grade 7 › G7U07 Circles & Area

Grade 7 › G7U07 Circles & Area › L4
GRADE 7 · ALBERTAOUTCOME AB-G7-SS1

L4 · Constructing circles

Learning goal

“I can construct a circle with a compass and straightedge for a given radius or diameter: I know the compass opening equals the radius, I can state the steps in order, and I can check a finished circle by measuring its diameter across the centre.”

Compass — the drawing tool with a sharp point and a pencil leg; the point stays fixed at the centre while the pencil leg swings around it.
Compass opening (setting) — the distance between the compass point and the pencil tip. For drawing a circle, the opening is set to the RADIUS.
Construction — a drawing made with compass and straightedge following exact steps, so lengths are built in, not eyeballed.
Concentric circles — two or more circles that share the same centre but have different radii.
Worked example

Construct a circle with radius 4 cm. Step 1: Mark the centre point O on the paper. Step 2: Set the compass opening to 4 cm: place the compass point at 0 on a ruler and open the pencil leg until the tip reaches the 4 cm mark. The opening IS the radius - every point the pencil draws will be exactly 4 cm from O. Step 3: Plant the compass point on O. Do not change the opening. Step 4: Swing the pencil leg in one full turn around O, keeping the point fixed and the opening unchanged. The pencil traces the circle of radius 4 cm. Say it plainly: the compass opening is the radius, the point marks the centre, and a steady single turn does the rest. If the opening slips, the "circle" is wrong.

Check yourself — explain it

The compass opening must be set to the radius because...

Paired problem — example still visible

To construct a circle with radius 6 cm, what compass opening do you set? -> 6 cm

Faded completion — last step is yours

"Construct radius 3 cm: 1) mark the centre; 2) set the opening to ___ cm; 3) plant the point on the centre; 4) ___." -> 3 cm; swing the pencil leg in one full turn without changing the opening

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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