Constructing a square or rectangle from its side lengths

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What to assume they know

The two properties that define a rectangle, and the one more a square needs — R1, R2, S1 and S2, the four conditions
Naming corners in order, and why a rotated square is still a square — how the corners of a figure are named in order
Reading and drawing an angle with a protractor — setting and reading an angle of 90°
Every curve in these figures is part of a circle — a compass carries a length from one place to another

What they should be able to do

Construct a square of a given side using a ruler and a right angle
Say, for each step of the construction, which property makes that step necessary
Transfer a length with a compass instead of re-measuring it, and explain why that is more reliable
Construct a rectangle from its two side lengths
Predict the length and the angles at the fourth corner before drawing it
Check a finished figure against R1 and R2 rather than assuming it is right
Construct a square inside a rectangle so that the two share a centre
Decide whether a stated set of conditions can be met at all

Where it usually goes wrong

"Measure all four sides and you get a square." Four correct lengths with no control of the angles gives a shape with equal sides that is not a square. The perpendiculars are not decoration.
"Step 5 is where you measure the fourth corner." It is where you stop measuring. Three corners already determine the fourth; measuring it again only adds a chance to be wrong.
"The compass and the ruler are interchangeable at Step 3." They give the same point, but the compass carries the length you already have, while the ruler asks you to read a scale a second time. The chapter offers both.
"A long thin rectangle is a harder construction." The 2 cm by 10 cm case uses exactly the same five decisions as the 4 cm by 6 cm one.
"If the figure looks right, it is right." The chapter ends each Construct item with an instruction to check the properties, p.197.
"The inner square in the 8 by 4 rectangle can be any size." Sharing the centre and touching both long sides pins it to 4 cm.
"Falling Squares is just three squares." The corner-to-corner contact is the constraint; the chapter says explicitly that the alignment must match.

Questions to check understanding

Construct a square of side 6 cm and check both square properties
Draw a rectangle with sides 4 cm and 6 cm, then verify R1 and R2 (asked at p.197)
Draw a rectangle with sides 2 cm and 10 cm and verify the same (asked at p.197)
After three corners are placed, state the length of the remaining side without measuring it
Is a 4-sided figure with all angles 90° and unequal opposite sides possible? (asked at p.197)
Construct a rectangle 8 cm by 4 cm and a square inside it with the same centre; state the square's side and the gap at each end
Reproduce the Falling Squares arrangement with squares of 3 cm, 5 cm and 7 cm

Examples worth working on the board

The square PQRS of side 6 cm, pp.195–196. The chapter prints six numbered steps. Step 1: the side PQ, 6 cm. Step 2: at P, a line rising perpendicular to PQ, set with a protractor in the printed figure. Step 3: mark the point 6 cm up that perpendicular — Method 1 uses a ruler, Method 2 a compass. Step 4: a perpendicular to PQ through Q. Step 5: with the compass already set to 6 cm, the fourth corner is marked without re-measuring. Step 6: the completed square, with 6 cm marked on three sides and 90° at P and at Q. Checked against pp.195 and 196.
The closing question, p.196. The chapter asks how long the last side is and what the angles at the two upper corners are. The construction has already forced the answers: the last side is 6 cm and both angles are 90°. Nothing was measured to make that happen, which is the point.
The two rectangles, p.197. Sides 4 cm and 6 cm; then sides 2 cm and 10 cm. In each case the chapter asks the student to check R1 and R2 afterwards. The second one is deliberately long and thin — a good case for showing that the method does not care about the proportions.
The impossible one, p.197. Can a 4-sided figure have all its angles 90° while its opposite sides are unequal? Treat it as a genuine question; the answer is no, and the reasoning belongs in The two properties that define a rectangle, and the one more a square needs.
A Square within a Rectangle, p.201. A rectangle 8 cm by 4 cm, with a square inside sharing its centre. The printed figure shows the square spanning the full 4 cm height, so its side is 4 cm and a 2 cm strip is left at each end. Checked against p.201; the two internal division lines are drawn, and no numbers are printed on them. The chapter's hint asks for exactly these two quantities and gives neither.
Falling Squares, p.202. Three squares of side 4 cm, each set so that it touches the next at a single corner and steps down and to the left. Then the same arrangement with squares of side 3 cm, 5 cm and 7 cm, largest at the bottom. The book's instruction is that the alignment shown must be reproduced. Checked against p.202.
Shadings, p.202. An outer square subdivided into smaller squares of two sizes, most of them carrying a hatched triangle over one diagonal half, with one plain large square filling the bottom-left quarter. No measurements are given; the chapter says to choose your own, and states only that the outer figure and the smaller ones are all squares. Checked against p.202.
Square with more Holes and Square with Curves, p.203. The first is a square cut into four equal smaller squares with a circle drawn inside each. The second is a square of side 8 cm with four arcs drawn inside it, one bulging inwards from each side, all four meeting at the square's corners. The 8 cm is printed; the arc radius is not, and the chapter asks the student to work out where the compass tip must go. Checked against p.203.

Figures to have open

The six construction steps of the 6 cm square, shown in order. This is the spine of the topic. Redraw rather than reproduce the printed figures, and see the note below about the corner labels.
A side-by-side of the ruler and compass methods for Step 3.
The 8 cm by 4 cm rectangle with its centred 4 cm square and the two 2 cm strips dimensioned.
The Falling Squares arrangement at both sets of sizes.
The 8 cm square with its four inward arcs.
No photograph or dataset is required.

Where this sits in the book

NCERT Ganita Prakash, Class 6, Chapter 8 "Playing with Constructions", §8.3 "Constructing Squares and Rectangles", pp.195–197 — the six steps on pp.195–196, the closing question on p.196, and the three Construct items on p.197
§8.4 "An Exploration in Rectangles", pp.201–203 — A Square within a Rectangle on p.201, Falling Squares and Shadings on p.202, Square with a Hole, Square with more Holes and Square with Curves on p.203
§8.2, p.193, for the R and S conditions the steps are answering to
Summary, p.216, for the statement that a rectangle can be constructed from its side lengths