Ganita Prakash, period by period — fitted to your timetable.
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From Freehand to Compass: Drawing a Circle
Artwork · Discovery
Watch for students who reposition the compass pivot while drawing — this breaks the equidistance guarantee and produces a spiral rather than a circle; a quick demonstration of keeping the needle fixed corrects this. Students who finish quickly can try estimating the radius needed to draw a circle that just fits inside a 6 cm square drawn on the same sheet.
0–8Students attempt to draw a circle freehand on plain paper, then compare results to discuss what makes a circle precise. The class arrives at the idea that every point on a circle must be exactly the same distance from a fixed centre.
8–22Activity (compass exploration), section 8.1 p.188 ("Students mark a point P, then use a compass set to 4 cm to trace all points….") — each student marks a point P, sets the compass to 4 cm, and traces the full curve, confirming that the resulting shape is a circle with centre P and radius 4 cm.
22–32Students vary the compass opening to 3 cm and 5 cm, draw two more circles from the same centre P, and record what changes (size) and what stays the same (all points equidistant from P). Pairs share observations aloud.
32–40Class discussion: students articulate in their own words what 'radius' means and why the compass guarantees equal distance. Teacher asks: 'Can you draw a circle without lifting the compass point from P?' to consolidate the definition.
Activity (compass exploration), section 8.1 p.188 — Students mark a point P, then use a compass set to 4 cm to trace all points 4 cm from P, discovering that the resulting curve is a circle with centre P and radius 4 cm.
A student wants to draw a circle such that every point on the circle is exactly 3 cm from a fixed point P. To what length should the student open the compass? If the student instead opens the compass to 5 cm from the same point P and draws a second circle, what is the distance between the two circles measured along a straight line from P?
The compass should be opened to 3 cm, because every point on a circle is at a distance equal to the radius from the centre. The first circle has radius 3 cm and the second has radius 5 cm, both centred at P. Along any straight line from P, the first circle is reached at 3 cm and the second at 5 cm, so the gap between the two circles along that line is 5 − 3 = 2 cm.
Also saved as 14 periods or 19 periods.
- 2Building the Wavy Wave with Half-Circles
Artwork - 3Naming, Rotating, and Recognising Squares and Rectangles
Squares and Rectangles - 4Constructing a Square Step by Step
Constructing Squares and Rectangles - 5Rectangles, Right Angles, and the Impossible Figure
Constructing Squares and Rectangles - 6Closest and Farthest: Tracking XY Across a Rectangle
An Exploration in Rectangles - 7Farthest Distance and the Diagonal Connection
An Exploration in Rectangles - 8Breaking Rectangles: Two and Three Identical Squares
An Exploration in Rectangles - 9Construction Challenges: Squares Inside Rectangles
An Exploration in Rectangles - 10Shadings, Holes, and Curves: Creative Construction Challenges
An Exploration in Rectangles - 11Measuring and Predicting Diagonal Properties
Exploring Diagonals of Rectangles and Squares - 12Constructing Rectangles from Diagonal Angle Conditions
Exploring Diagonals of Rectangles and Squares - 13Constructing Rectangles from One Side and the Diagonal
Exploring Diagonals of Rectangles and Squares - 14Finding the Apex: Two Circles, One Intersection
Points Equidistant from Two Given Points - 15Revisiting Artwork and the Rhombus Challenge
Points Equidistant from Two Given Points - 16Artwork Revisited: A Person and Eyes with Precision
Artwork (Revisit) - 17From Construction Steps to Fluent Instrument Use
Constructing Squares and Rectangles (Revisit) - 18Diagonal Laws: From Measurement to General Claim
An Exploration in Rectangles (Revisit) - 19Diagonal Angles and the Square Condition
Exploring Diagonals of Rectangles and Squares (Revisit) - 20Arc Intersections: Extended Practice and the Rhombus
Points Equidistant from Two Given Points (Revisit) - 21Extended Creative Constructions: Shadings and Curved Squares
An Exploration in Rectangles (Revisit) - 22Bringing It Together: Diagonal Constructions and Equidistant Points
Exploring Diagonals of Rectangles and Squares (Revisit) - 23The Compass Controls Distance: Four Problems, One Chapter
Synthesis
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