Describing a room you cannot see: a grid as a shared language for position

What to assume they know

• Reading a plan or map drawn to scale, and converting between model and reality
• Measuring in feet, and the meaning of a written dimension such as 12 ft × 10 ft
• Area of a rectangle, for the floor-space arithmetic
• That a solid object has three independent measurements — length, breadth and height
• Where coordinates came from: grid cities, meridians, and the road to the Cartesian plane — that a coordinate system is an agreement about directions, a starting point and a unit

What they should be able to do

• State the difference between the shape of an object and its position, and say which of the two a wool outline can carry on its own
• Read the printed floor plan of Fig. 1.1 and report each stated dimension
• Convert between the model and the room using the stated scale of 1 cm to 1 foot
• Compute the floor area of each room from its printed dimensions
• Explain why a window cannot be placed on this floor plan, and name the measurement the plan discards
• List what two people must agree on before either can describe a position to the other, and check each item against Shalini's model
• Explain why the same room can be described with wall names or with numbers, and what the numbers add

Where it usually goes wrong

• "A map shows you where things are, full stop." It shows where things are relative to the frame it was drawn in. Change the corner you measure from and every number changes while the room does not.
• "The wool outlines already tell Reiaan where the wardrobe is." They tell him its shape and size. He knows where it is only once he can relate it to something fixed — the grid, an edge, a corner he has already found.
• "Position is a property of the object." It is a relation. This is the whole reason a coordinate system has to be agreed before it can be used, and the reason the chapter's model has a grid under the pins.
• "The scale is a formality." Without it the model is only a shape. With it, every measured length in the model is a claim about the room, which is what makes the model checkable.
• "Windows are left out because they are not important." They are left out because the drawing has already discarded height. The same limitation returns in Exercise Set 1.2, which asks for the table's width and length and then asks whether its height can be made out at all (p. 8, item 1).
• "A tactile map is a special case for a blind reader." It is the general case made visible. The chapter's grid works for exactly the same reason a printed graph works, and only the channel differs.

Questions to check understanding

• Given a floor plan and its scale, report a stated dimension and convert a measured model length into a real one
• Compute the floor area of a room from its printed dimensions, and the fraction of it a piece of furniture occupies
• Explain, in two lines, why a floor plan cannot record a window
• Given a description in words ("the wardrobe is against the bottom wall"), say what further information is needed before it can be drawn in one definite place
• The chapter's own reflection prompts (p. 5): what is a standard width for a room door, and are the doors around you usable by a person in a wheelchair
• Design task: describe your own room to someone who cannot see it, stating exactly what you asked them to agree on first

Examples worth working on the board

Values marked verified are worked out here on the printed inputs.

• Fig. 1.1, the room sketch (p. 3). Read off the printed page: a bathroom on the left, printed 6 ft × 9 ft, coloured blue, with a Bathing Area labelled in its upper part and bounded by two straight segments — one running from the top wall down to an interior point, one from that point across to the left wall. To its right, the bedroom, printed 12 ft × 10 ft, with a bed drawn against the wall shared with the bathroom, a bedside table and lamp at the top of that wall, a potted plant in the far corner, and a wardrobe printed 4 ft × 2 ft standing against the bottom wall. Three walls are named in type: Left Wall of the Bathroom at the far left, Left Wall of the Room on the wall the two rooms share, and Right Wall of the Room at the far right.
• The two doorways (Fig. 1.1, p. 3). Both are labelled Door along the bottom of the drawing, and each carries a red dashed arc showing the leaf swinging. One doorway sits in the wall shared with the bathroom, hinged low and sweeping into the bedroom; the other sits in the bedroom's bottom wall towards the right, hinged at its right-hand edge and sweeping up into the room. Because both printed labels sit along the bottom edge, the drawing alone does not settle which is which — Figs. 1.3 and 1.5 do, by giving them coordinates (see Two axes, an origin, and why the order of the pair matters and The four quadrants, and reading a point's signs off its position).
• The stated scale (p. 3): 1 cm : 1 foot. Verified consequences worth showing: the bedroom's 12 ft wall is 12 cm of thread; the wardrobe's 4 ft face is 4 cm; a 2 mm error in placing a pin is about 2.4 inches of real room.
• Floor areas from the printed dimensions. Verified: bedroom 12 × 10 = 120 sq ft; bathroom 6 × 9 = 54 sq ft; the two together 174 sq ft; the wardrobe's footprint 4 × 2 = 8 sq ft, which is about 6.7 % of the bedroom floor. None of these products is printed; the chapter prints only the dimensions.
• The window question (p. 3). The chapter closes §1.2 by asking the reader why this drawing has no place for the windows, and leaves it open. The answer to build the section on: a window is a hole in a wall. Its horizontal position along the wall is recordable, but its footprint on the floor is a segment inside the wall thickness, and the thing that distinguishes a window from a doorway — its height above the floor — is the one measurement this drawing has no room for. A plan is a two-measurement record of a three-measurement room. The doors survive on the plan only because they reach the floor.
• A cross-check to use. The printed bathroom dimension of 6 ft × 9 ft is independently confirmed two figures later, where the same bathroom is drawn against numbered axes and its corners fall 6 units to the left of the origin and 9 units up (Fig. 1.5, p. 7). Verified by reading the checked figure against its own axis ticks. Use this as the moment the story's model and the mathematics meet.
• A naming change to watch. The region labelled Bathing Area inside Fig. 1.1 (p. 3) is the one the exercise calls the showering area at p. 8, where its corners are lettered SHWR. Fig. 1.5 (p. 7) prints its own name for the region inside it and letters those four corners individually, so the parallel is tighter than a label against a letter string: both figures print a name for the region in the same place, and the two names differ.
• The two figures do not draw that region identically — flag this before any redraw. Verified against each figure's own printed dimensions: in Fig. 1.5 the boundary running in to the left wall is horizontal, both of its ends 6 ft up from the bottom wall. In Fig. 1.1 the same boundary slopes — its interior corner sits about 5 ft up while the end on the left wall sits about 6 ft up, a drop of roughly one foot across the segment. Anyone who carries Fig. 1.5's flat boundary back into a redraw of Fig. 1.1 will straighten a line the page draws slanted, and one who does the reverse will slant a line the page draws flat. Redraw each figure from itself.

Figures to have open

• A redrawn schematic of Fig. 1.1 (p. 3) carrying all three printed dimensions, the two rooms, the wardrobe, the bathing area and the two doorways with their swing arcs. This is the chapter's own figure and the topic cannot be taught without it; redraw it as a clean plan rather than reproducing the printed artwork.
• A tactile-model illustration: a grid board with pins and thread, and a hand tracing one edge. Standard schematic.
• One three-dimensional cutaway of the same bedroom showing a window in a wall, with the height measurement highlighted and then removed as the view flattens to the plan. Standard schematic; the chapter prints nothing like it, and it is what makes section 7 land.
• A scale strip: 1 cm of model against 1 foot of room. Standard schematic.

Where this sits in the book

• NCERT Ganita Manjari Class 9 (Part I), printed Chapter 1, §1.2 "Settling In", pp. 2–3, including Fig. 1.1 "Sketch of Reiaan's room" and its caption
• The window question is the closing line of §1.2, p. 3
• The same room appears with axes at Fig. 1.3 (p. 5) and with the bathroom and its surroundings at Fig. 1.5 (p. 7); the dimensions printed in Fig. 1.1 are what those two figures are consistent with
• The height-cannot-be-read point returns at Exercise Set 1.2 item 1(iii), p. 8
• The accessibility prompts sit in the Think and Reflect box at p. 5