The room looks simple until somebody asks where a desk should be placed. A rectangle on paper is not yet a feasible seating plan: a correct answer must keep units, scale, sight lines and constraints together. This Mathematics guide takes the physics question from Volume 0805 and turns it into a sequence of G3 problems that can be checked rather than guessed.
You will use scale drawings, coordinates, right-angled triangles, angles, distances, inequalities and data tables to compare hypothetical classroom positions. Every numerical example is invented for teaching and does not assert measurements, legal building standards or school-approved seating conditions. The goal is mathematical reasoning under explicit assumptions, not a promise that a particular desk layout will remove all glare.
**Quick route:** draw and label the floor plan; convert scale correctly; use perpendicular distances and the right triangle that actually exists; identify which inequality each position must satisfy; test units and rounding; distinguish modelled lines from measured observations; and do not turn subjective glare scores into physical light measurements.
1. Use the correct 2027 SEC G3 mathematics paper
The official 2027 SEC G3 Mathematics subject is K310, replacing the earlier reference code 4052. SEAB lists Paper 1 as two hours 15 minutes, 90 marks, 50%, and Paper 2 as two hours 15 minutes, 90 marks, 50%. Both require all questions to be answered. The final Paper 2 question focuses on using mathematics in a real-world scenario. The syllabus emphasises mathematical processes, applications, reasoning and communication; it does not prescribe this particular glare case as an examination question.
The official 2027 K310 Mathematics syllabus includes geometry, measurement, similarity, scale drawings, trigonometry and statistical interpretation. It also specifies that non-exact numerical answers should generally be given to three significant figures, or one decimal place for angles in degrees, unless the question says otherwise. Essential working must be shown. These are official requirements worth building into every solution.
This guide uses the G3 framework and deliberately leaves some details of real-world optical engineering outside the Mathematics syllabus. An examination candidate should solve the mathematical relationships actually given, not import advanced optics formulas or assume a physical measurement that the question never supplied.
2. Build a consistent floor-plan model
Imagine a rectangular room eight metres long and six metres wide. Put the origin at the lower-left corner, with the horizontal axis running along the eight-metre wall and the vertical axis along the six-metre wall. A desk location can then be represented by a point such as (2.0, 1.5), where both coordinates are in metres. The brackets indicate position, not length. To find distance between two points, a separate calculation is required.
State these assumptions before answering: the floor plan is a horizontal projection, furniture sizes are simplified, the relevant points are measured from the same origin and the coordinate units are metres. A window, a reflecting tabletop and an observer may require different heights in the full physical problem. A two-dimensional plan can still answer a limited horizontal-layout question if that simplification is made explicit.
Always sketch the room boundary before plotting points. If a candidate writes coordinates in centimetres halfway through a solution while the axes remain in metres, the final answer may be numerically plausible and physically absurd. The model’s units are part of its meaning.
3. Read scales in both directions
At scale 1:100, one centimetre on paper represents 100 centimetres in the room, which is one metre. An eight-by-six metre room becomes an eight-by-six centimetre drawing. A two-metre gap becomes two centimetres. At scale 1:50, the same two-metre gap becomes four centimetres. The ratio must be applied consistently to every length.
A useful check is to ask which object should be larger: the real room or its plan. Converting a scale-drawing length into an actual distance requires multiplying by the scale factor in matching units. Converting actual distance into a drawing length requires dividing by that factor. Write the unit conversion explicitly instead of trusting a memorised multiply-or-divide rule.
Areas do not scale by the same linear factor. At 1:100, lengths change by 100 but areas by 10,000. A three-centimetre by two-centimetre rectangle on such a plan represents a three-metre by two-metre area, or six square metres. It does not represent six square centimetres of real floor area.
4. Straight-line distance is not walkway distance
Put one point at (1, 1) and another at (4, 5), using metres. Their horizontal separation is three metres and vertical separation is four metres. The direct straight-line distance is five metres by Pythagoras’ theorem. This is a geometric model of direct separation, not automatically a walking route around furniture.
A school floor plan may require a route that changes direction around desks. If the problem asks for a route made of horizontal and vertical segments, add those segments rather than using the diagonal. In our example the simplest axis-aligned route without obstacles totals seven metres. The straight-line answer and the route answer are both valid for different questions.
Examination errors often begin with the right calculation for the wrong quantity. Underline whether the question says direct distance, shortest path in an unobstructed plane, walking route or horizontal separation. Do not silently replace one by another.
5. Draw the triangle before using trigonometry
A diagram may give the horizontal displacement and the difference in height between a lamp and an observer. If the horizontal displacement is three metres and vertical difference is two metres, the straight segment between them has length square root of thirteen metres, approximately 3.61 metres. The angle above the horizontal is arctangent of two divided by three, approximately 33.7 degrees.
This calculation assumes a right triangle in a vertical plane and a direct line segment. It does not, by itself, provide the angle of reflection at the desk. For that angle you need the orientation of the surface normal and the directions of incident and outgoing rays. Mathematics offers the triangles; Physics specifies the reflection rule.
A student who can calculate a tangent ratio but cannot say what the opposite and adjacent sides represent is not in control of the model. Label the sides with meanings before writing a formula. When given a new orientation, rebuild the triangle rather than copying the old arrangement.
6. Complementary angles matter
For a horizontal desktop, the normal is vertical. A ray making twenty degrees with the surface makes seventy degrees with the normal. This geometric fact is independent of how complicated the room looks. If a question gives the incidence angle to the normal, do not convert it unnecessarily; if it gives an angle to the surface, subtract from ninety degrees.
A floor-plan angle measured from an east-west wall may not equal an optical angle measured from a surface normal in a vertical section. The planes may differ. If the question switches between plan and elevation, draw two sketches and label them. A number carried across dimensions without its reference line is a common source of errors.
A complete solution shows why the chosen angle is the one required. One short sentence explaining the reference can prevent a long incorrect computation.
7. Set up feasible positions as inequalities
Suppose a simplified exercise gives a desk-centre rule: the x-coordinate must be between 1.0 and 7.0 metres, and the y-coordinate must be between 1.0 and 5.0 metres. Those numbers are invented problem constraints, not official minimum clearances. The feasible region is the intersection of both conditions. A point can satisfy one axis condition and still fail the other.
If a second fictional requirement says x must be at least 2.5 metres, combine it with the first to obtain 2.5 at most x at most 7.0. Avoid describing the first condition as a safety regulation. The examiner’s given conditions are the only authority in the problem.
This is the heart of a real-world mathematical task: compute a number, then check whether it is allowed. A mathematically exact coordinate that violates a stated constraint is not an acceptable design solution.
8. Compare candidate positions fairly
Suppose candidate A is (2, 2), B is (4, 2), and C is (6, 2). These positions have the same y-coordinate but different horizontal distances from a window at x=0. If the question defines an inverse relationship or an observed score, apply the given definition separately to each position. Do not invent an inverse-square law merely because distance changes.
One way to organise the answer is a table containing position, distance, predicted sight-line status, walking-route condition and final admissibility. Keep measured observations separate from predicted categories. If a table reports ‘reflection seen’ at one station, that is not equivalent to ‘highest illuminance’ unless the measurement system supports that interpretation.
The best mathematical comparison is transparent enough for another student to reproduce. Label units at the column headings, preserve extra digits during calculations and round only the result required by the question.
9. Coordinate changes must preserve geometry
A desk point may be represented by (2, 3) metres from the lower-left origin. If the origin moves to the lower-right corner of an eight-metre-wide room, the same physical point is (6, 3) in the new coordinate system, assuming the horizontal axis is measured leftwards. The numbers change; the physical position does not.
This distinction is useful when two planning diagrams use different origins. Do not compare raw x-coordinates until you know which direction the axes point. A reflection diagram may also use a normal drawn in a local coordinate system. Each drawing should say what its references mean.
A reliable student can translate a solution into another labelled coordinate system without changing the physical conclusion. That is a strong test of understanding.
10. Sensitivity: a small position error can matter
A marked desk centre at x=3.0 metres may actually be placed at x=3.1 metres. Whether that changes a decision depends on the threshold. If the allowed interval ends at x=3.5 metres, both are acceptable. If it ends at x=3.05 metres, one placement satisfies the condition and the other does not.
Do not report a design as ‘definitely feasible’ just because the calculated centre is close to the boundary. State measurement precision, compare the full possible range and decide whether the conclusion survives the uncertainty. In mathematics this is a bounds question before it is a design opinion.
For instance, if a distance is recorded as 3.0 metres to the nearest tenth of a metre, the actual value is at least 2.95 and less than 3.05 metres under ordinary rounding assumptions. A boundary inside that interval cannot be settled from the rounded value alone.
11. Distinguish exact and approximate answers
Square root of thirteen metres is exact; 3.61 metres is a rounded approximation. The official K310 guidance on non-exact answers usually calls for three significant figures unless a different accuracy is instructed. Keep the exact or calculator value during intermediate steps, then round only when reporting the final answer. Premature rounding can change a decision near a threshold.
Angles in degrees are normally reported to one decimal place unless specified otherwise. If the answer is an angle of 33.690… degrees, 33.7 degrees is appropriate under that default. If the question explicitly demands the nearest whole degree, follow that direction. Always include the unit when needed.
For a design comparison, explain what the rounded answer means. A desk width of 0.995 metres is not the same as a one-metre clearance requirement merely because a one-significant-figure display looks the same. The precision of a decision must be appropriate to the condition being tested.
12. Avoid false precision from subjective scores
Suppose four observers use categories 0, 1 and 2 for absent, faint and clear highlights. You can tabulate the frequencies. But the categories are ordinal labels, not calibrated units of light. A mean category score may summarise responses for a stated protocol; it must not be called an average light intensity.
If one location receives category scores 2, 2, 1 and 1, the arithmetic mean label is 1.5. That is a description of coded responses only. Another station with four scores of 1.5 would not even be possible if observers must choose integer categories. A mathematically correct calculation is not proof that the measured quantity is continuous.
Before using any statistical comparison, ask what the numbers represent and what operations make sense for them. That question protects both scientific and mathematical accuracy.
13. Use the right figure for the evidence
A floor plan is useful for showing positions and distances. A bar chart is useful for comparing categories or counts. A line graph may help with ordered measurements across distance when the measured variable is meaningful. A scale drawing and a statistical graph are not interchangeable just because both use axes.
If a graph omits a baseline or changes vertical scales, it may exaggerate a difference. If a plan is not to scale, do not measure real distances from the printed drawing. A labelled diagram can still illustrate relationships, but its numerical use must match its stated status.
The SEC Mathematics syllabus includes interpreting statistical diagrams and identifying misleading presentations. This connects to the classroom case without requiring a new advanced statistical model.
14. Problem-solving under Paper 2 conditions
A multi-stage question can combine floor dimensions, candidate positions, a budget and a line-of-sight rule. Write a compact working table. First calculate necessary distances. Next apply coordinate or geometric constraints. Then check any whole-number requirements. Finally give a recommendation tied to the options that survive.
Students sometimes select the option with the smallest cost before checking whether it meets the physical constraint. Others calculate the shortest distance even when the question asks for the greatest feasible separation. In both cases, arithmetic is not the only challenge. The verb in the question tells you what to optimise.
The final sentence should be mathematical: ‘Option B is feasible because it meets all stated boundaries and has the lowest given cost among feasible options.’ Avoid saying the design is safe in a real building unless actual applicable standards have been checked.
15. A worked location comparison
Assume a fictitious floor plan with candidate points A=(2,2), B=(4,3), and C=(6,4). A lamp is represented by the plan point L=(1,1). Their direct plan distances from L are square root of two, square root of thirteen and square root of fifty metres respectively. These are horizontal plan distances, not the full three-dimensional optical distances to a ceiling lamp.
If a question sets a fictional rule that the plan distance must exceed three metres, A fails, while B and C pass. If a second rule sets x at most five metres, B passes and C fails. B alone satisfies both conditions. Do not interpret the rules as actual lighting guidance; they are numerical assumptions that demonstrate intersection of constraints.
Show the process rather than guessing from the drawing. A roughly sketched point may look far enough even when the exact distance is slightly below a boundary. Calculations and labelled conditions make the conclusion auditable.
16. A worked route comparison
Suppose the same room has a rectangular obstacle. A point-to-point Euclidean distance may pass through that obstacle. If the question asks for a usable route, construct paths around the obstacle and add segment lengths. A neat diagonal is not automatically an admissible route. This is the same distinction that appears in school-layout and delivery-route problems.
If two permitted routes have lengths 6.4 metres and 6.8 metres, the shorter is 6.4 metres. But if the first route fails an expressly stated width constraint, it is not a feasible option. The correct comparison is among feasible routes, not among all drawn lines.
This extends Volume 0800 on classroom geometry. Here the new question is how observer positions and modelled light paths affect the choice after the room layout has already been represented.
17. A diagnostic ladder for errors
If the learner converts scales incorrectly, return to one-centimetre intervals and explicit units. If Pythagoras is misapplied, draw the right triangle and name its hypotenuse. If the trigonometric ratio is wrong, label opposite and adjacent sides relative to the angle. If the numerical answer is sound but the decision breaks a constraint, practise reading inequalities and evaluating candidate points.
If the student keeps confusing horizontal plan distance with actual lamp-to-eye distance, draw a side elevation beside the plan. The two pictures answer different geometric questions. That visual distinction can correct several downstream mistakes at once.
Do not treat every wrong final answer as a need for more practice papers. Identify the first failed step, repair it with a smaller task, then return to the complete problem. This is how mathematical fluency becomes reliable under timed conditions.
18. Connection to Physics and English
The previous Physics Volume 0805 explains why reflected rays follow particular directions. This Mathematics volume takes the given geometry and uses numerical tools to compare feasible positions. Mathematics cannot by itself prove that a room is comfortable or that a glossy reflection harms learning.
The English companion will examine a public claim based on the same fictitious study. For example, a poster saying ‘the new seating plan removes every reflection’ is stronger than a few observations at specified points. The Mathematics learner’s responsibility is to make the numerical assumptions visible so that an English reader can check the claim.
This is a useful habit beyond school: distinguish what the model calculates, what the observer records and what a decision-maker chooses.
19. Primary-to-SEC continuity
At PSLE, pupils learn measurement, unit conversion, angles and word problems. The secondary step asks for more explicit reasoning across multiple representations and constraints. A student who can find a rectangle’s area may still struggle when a scale drawing, coordinate position and a feasibility rule occur in the same question. The improvement is to slow down at the modelling stage, not merely memorise more formulae.
See the PSLE Maths word-problem route, the Sengkang Mathematics owner, and Volume 0802 on matched force records and constrained budgets. They approach different mathematical demands but reinforce the same discipline of stating a quantity before manipulating it.
20. Five quick test questions
One: at scale 1:100, what does 4.5 centimetres on the plan represent? Answer: 4.5 metres. Two: what is the direct separation of points (1,1) and (4,5) metres? Answer: five metres. Three: if a ray makes 30 degrees with the horizontal surface, what angle does it make with the vertical normal? Answer: 60 degrees.
Four: a point must satisfy x at least 2 and x at most 5. Does x=5.2 qualify? No. Five: a distance shown as 2.0 metres to the nearest tenth may be between 1.95 metres inclusive and 2.05 metres exclusive. Can you decide with certainty that it exceeds 2.01 metres? No. Explain why, rather than merely giving ‘no’.
Redo the questions with different values. If the student can change the scale, origin, boundary and triangle orientation while preserving the method, the understanding is becoming transferable.
21. Conclusion
A mathematically responsible seating plan is not the prettiest diagram. It is a model with consistent units, correct geometry, clearly stated constraints, appropriate rounding and conclusions that survive the supplied information. Use Mathematics to establish what is numerically feasible; use Physics to interpret reflection paths; and use English to communicate the difference between a result and an overclaim.
Continue with the next English and EMS learner guides, and verify all future examination changes through SEAB’s current syllabus listing. This page is independent educational guidance rather than an official examination notice.
Practice case 1: scale mismatch
Read the given information without immediately selecting a formula: a room is 7.2 metres wide but a student draws it as 7.2 centimetres on a 1:50 plan. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: the correct drawing width is 14.4 centimetres, since 720 centimetres divided by fifty is 14.4. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that the student has silently used a 1:100 conversion in a 1:50 task. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
Practice case 2: right triangle orientation
Read the given information without immediately selecting a formula: a lamp is 2 metres above the eye level and 5 metres horizontally displaced. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: the straight-line segment is square root of twenty-nine metres and the elevation angle is arctangent of two fifths. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that this is a geometric line-of-sight estimate, not by itself a reflection angle. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
Practice case 3: constraint intersection
Read the given information without immediately selecting a formula: an option requires x between 2 and 6 metres and y between 1 and 4 metres. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: point (5,4) satisfies both inclusive boundaries; point (5,4.2) does not. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that do not inspect one coordinate and assume the full constraint is satisfied. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
Practice case 4: rounding boundary
Read the given information without immediately selecting a formula: a computed clearance is 0.994 metres against a required 1.00 metres. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: the calculation is below the threshold, even though rough rounding could display one metre. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that use enough precision to make the decision before rounding the reported answer. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
Practice case 5: three-dimensional versus plan distance
Read the given information without immediately selecting a formula: horizontal separation is 4 metres while the vertical height difference is 3 metres. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: the direct three-dimensional separation in the corresponding vertical plane is 5 metres. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that do not report four metres as the full source-to-observer distance. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
Practice case 6: inverse conversion
Read the given information without immediately selecting a formula: one-centimetre on a drawing represents 0.5 metres in reality. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: the drawing scale is 1:50 when both are expressed in centimetres. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that do not mix metres and centimetres inside one scale ratio. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
Practice case 7: different origins
Read the given information without immediately selecting a formula: the same object is two metres from the west wall of an eight-metre room. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: its coordinate from the east wall is six metres if the new positive direction runs west. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that coordinate values change with the origin, not with the physical position. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
Practice case 8: misleading graph
Read the given information without immediately selecting a formula: two categories have counts 17 and 19 but a bar chart begins its vertical axis at 16. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: the chart can visually exaggerate a difference of only two counts. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that restate the numerical difference before drawing a conclusion. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
Practice case 9: subjective category
Read the given information without immediately selecting a formula: four pupils report glare scores of 0, 1, 1 and 2. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: the mean code is one but it is not one lux or one unit of calibrated brightness. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that the scoring scale defines category labels, not physical illuminance. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
Practice case 10: conditional recommendation
Read the given information without immediately selecting a formula: option A is shortest but violates a stated width rule, while B is slightly longer and satisfies it. Name the required quantity and write its unit. Draw a small labelled sketch or table that makes the positions, scale and boundaries explicit. The first decision is whether this is a distance, angle, scale, coordinate or feasibility question. A correct calculation using the wrong kind of quantity does not answer the task.
Work the calculation and compare with this result: B may be the feasible choice even though its raw distance is larger. State the relationship that justifies the step and keep enough digits for the last comparison. If a numerical condition is present, test it as an inequality rather than relying on how large or small the answer looks in the picture. The method should be reproducible by a reader who has not seen the original classroom.
The principal trap is that optimise only among candidates that satisfy every relevant condition. Write a one-sentence error diagnosis and a one-sentence repair. Then ask what remains unverified in the original physical room. A diagram or model can identify mathematical feasibility under supplied assumptions, but it does not establish the comfort or safety of a real classroom without the relevant observations and requirements.
