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Many Class 6 students can draw a neat circle but freeze when asked to "construct a rectangle with one side 5 cm and a diagonal 7 cm". The compass feels like a drawing toy, not a thinking tool. This post covers the chapter's ideas, two constructions step by step, common slips and a home practice routine, for students and parents.
Where is this chapter in the new book?
In the current NCERT book Ganita Prakash for Grade 6 (reprint 2026-27), Chapter 8 is titled "Playing with Constructions". The chapter PDF has six sections: Artwork, Squares and Rectangles, Constructing Squares and Rectangles, An Exploration in Rectangles, Exploring Diagonals of Rectangles and Squares, and Points Equidistant from Two Given Points. Check with your school which sections are set for your tests.
What does a compass actually do?
The chapter starts with a question: mark lots of points that are exactly 4 cm from a point P. What shape do they make? A circle. That is the big idea of the whole chapter. A circle is the set of all points at one fixed distance, the radius, from the centre.
So when you open a compass to 4 cm and swing it, you are not just drawing a curve. You are drawing every point that is 4 cm from the centre, all at once. Each construction in the chapter uses this to find a point without trial and error.
What makes a rectangle or square?
The chapter lists the properties you must check.
A rectangle: opposite sides are equal (R1) and all angles are 90° (R2).
A square: all sides are equal (S1) and all angles are 90° (S2).
A rectangle must be named by going round its corners in order: ABCD or DCBA, never ABDC. And a tilted square is still a square: turning it does not change its sides or angles.
Worked construction 1: a rectangle with side 5 cm and diagonal 7 cm
This is one of the chapter's solved examples. Here is the plan.
Rough figure. Draw a quick sketch of rectangle ABCD. Mark DC = 5 cm and the diagonal DB = 7 cm.
Draw the base. With a ruler, draw DC = 5 cm.
Perpendicular at C. Draw a line through C at 90° to DC. Point B must lie somewhere on this line.
Use the compass, not guesswork. B is also 7 cm from D. Open the compass to 7 cm, put the point on D and draw an arc that cuts the perpendicular line. Where they meet is B. The chapter shows that you only need a small arc near the line, not a full circle.
Finish. Draw perpendiculars at D and at B. They meet at A. Check that AB equals DC and that all four angles are 90°.
Measure BC when you are done. It should come out a little under 5 cm, about 4.9 cm. You will learn later, with Pythagoras' theorem, why it must be exactly the square root of 24 cm.
Worked construction 2: the "House"
In Section 8.6 the chapter asks you to recreate a house whose border lines are all 5 cm: a square with a pointed roof. The hard part is finding the roof's top point A, which must be 5 cm from both B and C, the top corners of the square.
Construct the 5 cm square first.
Open the compass to 5 cm. With the point on B, draw an arc above the square.
Keep the same opening. With the point on C, draw another arc that crosses the first.
The crossing point is A. It is 5 cm from B (it is on the first arc) and 5 cm from C (it is on the second).
Join AB and AC.
This is the key trick of the chapter: two arcs find a point that is a given distance from two places at once.
What mistakes do students usually make?
The compass slips. If the opening changes mid-arc, the point is wrong. Hold the compass by the top knob and tighten the hinge if it is loose.
Measuring the opening from the ruler's edge. Put the metal point on the 0 mark, not at the end of the ruler.
Naming shapes in the wrong order. The chapter's own question asks which of PQSR, SPQR, RSPQ and QRSP is not a name for square PQRS. The answer is PQSR.
Rubbing out construction arcs. Teachers want to see the arcs. They prove you constructed rather than guessed.
Skipping the check. After drawing, measure all sides and angles against R1 and R2 or S1 and S2.
Why practise this at all?
Constructions train spatial skills, the ability to picture and move shapes in your head. A large review of 217 studies, Uttal and colleagues (2013), found that spatial skills improve with training, with an average effect size of 0.47, and that the gains lasted and carried over to spatial tasks that were not practised. The authors note that good spatial skills strongly predict success in science, technology, engineering and maths.
A practice routine for one week
Day 1: Draw five circles of different radii. Mark three points on each and check with a ruler that each is the right distance from the centre.
Day 2: Construct a 6 cm square using the chapter's steps. Check S1 and S2.
Day 3: Construct a rectangle with one side 4 cm and a diagonal 8 cm (one of the chapter's exercises). Measure the other side.
Day 4: Recreate the House. Then try it with 4 cm sides.
Day 5: Construct a rectangle where a diagonal splits the corner angles into 60° and 30°, as in the chapter.
For more on angles, see our guide to Lines and Angles in Class 6, and for the shapes you just drew, Symmetry in Class 6.
If your child gets stuck on why an arc finds the right point, Fermi's AI tutor draws the figure and checks understanding as it goes, so they can see the reasoning rather than copy steps.
Tonight, take a compass and try the House construction once, keeping every arc on the page.
