Did you know? A twelve-square-metre room can require exactly forty-eight half-metre square tiles in a simple grid. But if those tiles come only in packs of ten, a pupil must calculate five packs, not forty-eight packs and not 4.8 packs. Floor-plan Mathematics brings together geometry, unit conversion and whole-number decisions.
For Bukit Timah families seeking a Secondary 1 G2 Mathematics tutor, this guide explains how to calculate rectangular and L-shaped floor areas, count exact-fit tile grids, distinguish tile count from pack count, and apply fictional material or skirting prices. A real cutting layout can require more tiles than an area calculation suggests, so the assumptions matter.
Quick method: check units, calculate the exact floor region, identify tile dimensions and whether they fit an aligned grid, then apply any stated spare allowance and whole-pack restriction before calculating cost. These examples extend the MOE G2 syllabus on mensuration and everyday floor-plan contexts. The unchanged eduKateSG Secondary 1 small-group reference describes three-student weekly tuition near Sixth Avenue MRT.
Floor-plan Mathematics in one minute
- Rectangle floor area = length×width in consistent units.
- One square metre equals 10,000 square centimetres.
- For a square tile, face area = tile-side length squared.
- For an exact-fit grid, tile count = whole rows×whole columns.
- Area÷tile area gives a lower bound when a cutting layout is not known.
- Whole packs needed = round up required whole tiles ÷ tiles per pack.
- A specified spare allowance is applied before pack rounding.
- A composite L-shaped floor can be a big rectangle minus a corner.
- Perimeter measures edge trim; area measures surface covering.
- Prices per pack and per square metre use different units.
One floor, two whole-number steps
Consider a hypothetical 3 m by 4 m rectangular room and square tiles 50 cm on each side, aligned to the walls with no gaps. Three metres fits six tiles and four metres fits eight tiles, giving 6×8=48 exact-fit tiles. Each tile covers 0.25 m², and forty-eight cover the room’s 12 m².
Suppose the tiles are supplied in whole packs of ten, at a fictional $18 per pack. Four packs contain only forty tiles, so five packs are needed. They contain fifty tiles, leaving two spare pieces after the exact-fit layout. The fictional material bill is 5×$18=$90. This example does not require any cutting allowance; a different layout may.
32 first-principles ideas for room plans and tile quantities
1. A floor plan models a two-dimensional region
A mathematical plan is a simplified picture of a real or hypothetical floor. To calculate its area, use the lengths and geometric conditions given, rather than estimating a sketch by eye. Rooms need not be rectangles, but a rectangle is a useful starting model.
Worked connection: A 4 m by 3 m rectangular model has floor area 12 m².
Checking question: Use stated dimensions, not guessed measurements from an illustration.
2. Area is different from the outside boundary
Area tells how much two-dimensional surface is covered. Perimeter measures the length around that surface, which may be useful for edge strips or skirting. The two quantities have different units and different formulas.
Worked connection: A 4 m by 3 m rectangle has area 12 m² and perimeter 14 m.
Checking question: Underline ‘cover’, ’tile’, ‘border’ and ‘skirting’ before choosing a formula.
3. Convert lengths before calculating area
Multiplying measurements in unlike units without conversion produces an incorrect dimension. Express both sides of a rectangle in metres or both in centimetres before using length×width.
Worked connection: A fictional room is 300 cm by 4 m. Convert 300 cm to 3 m and obtain area 12 m².
Checking question: Check a second route using 300 cm×400 cm=120,000 cm².
4. A square metre is ten thousand square centimetres
A metre has one hundred centimetres along each side, so a one-square-metre area contains 100×100=10,000 square centimetres. Confusing length and area conversions causes hundredfold errors.
Worked connection: 12 m² is 120,000 cm².
Checking question: Explain where each factor one hundred comes from.
5. Square tile area is the side length squared
A square tile of side s has face area s². Both side measurements must use compatible length units. Real grout gaps are ignored unless a task explicitly provides them.
Worked connection: A 50 cm square tile covers 2500 cm², equivalent to 0.25 m².
Checking question: Check 0.5 m×0.5 m=0.25 m².
6. Rectangular tile area is length times width
When tiles are rectangular rather than square, count along length and width separately. A tile’s area is the product of its two side lengths.
Worked connection: A 20×40 cm rectangle covers 800 cm².
Checking question: Do not square twenty just because the word tile appears.
7. Exact grid tiling uses row count times column count
If room dimensions are whole multiples of the tile side and square tiles are placed in an aligned rectangular grid with no gaps, divide each room dimension by tile side to find rows and columns.
Worked connection: A 300×400 cm floor with 50 cm square tiles needs 6×8=48 exact-fit tiles.
Checking question: This is stronger than a mere area-based estimate because the dimensions fit the grid.
8. Area divided by tile area is an area lower bound
If a region requires A square metres and each tile covers a square metres, at least A/a whole tiles are needed in total area. However, for shapes requiring cuts, area coverage alone may not guarantee that the number can actually tile the geometry without unusable offcuts.
Worked connection: A floor of 4.5 m² with 0.25 m² tiles has an area-equivalent of 18 tiles; cutting geometry may still matter.
Checking question: State any exact-fit assumption before calling the quotient the actual required tile count.
9. Rounding a partial tile may require an extra whole tile
Purchasing or placing a count of complete tiles is a whole-number decision. An area-equivalent calculation of 18.4 means at least 19 intact tiles’ worth of area, though a layout and cutting plan may need more.
Worked connection: An area equivalent of 18.4 tiles gives an area lower bound of 19 whole tiles.
Checking question: Do not mistake a lower bound for a guaranteed workable layout.
10. Not all offcuts can be reused
When dimensions do not divide evenly by tile size, cutting patterns influence material use. An offcut may be useful elsewhere, or it may be too small or have the wrong orientation. The task must state assumptions for an exact count.
Worked connection: A 2.5 m by 1.8 m room with 0.3 m tiles cannot be counted solely by rounding the area quotient and declaring a guaranteed minimal layout.
Checking question: Use an explicitly given cutting plan or report a necessary area bound.
11. Tile packs introduce a second rounding step
If a pack contains P whole tiles, the number of packs required to buy at least N tiles is the smallest whole number no less than N/P. This is ceiling division, distinct from finding the exact-fit grid count.
Worked connection: 48 required tiles sold in packs of 10 need five packs, providing 50 tiles.
Checking question: Check four packs would contain only forty tiles, which is insufficient.
12. Extra purchased tiles are purchased minus required
If the pack system forces a purchase larger than the exact count, leftover tiles equal whole tiles bought minus those allocated. This calculation presumes a known exact required count.
Worked connection: Five packs of ten contain fifty tiles; if forty-eight are used, two remain.
Checking question: Do not call these two necessarily wasted: they may remain usable spares.
13. A specified spare allowance changes the target
Some mathematics exercises explicitly request extra tiles, for example ten percent beyond the exact-fit count. Apply the stated allowance to the count and round up to whole tiles if the result is not integral.
Worked connection: For forty-eight exact-fit tiles plus ten percent, calculate 48×1.1=52.8, so at least 53 whole tiles are targeted.
Checking question: The ten percent is an example condition, not a universal rule for real flooring purchases.
14. Pack rounding follows the allowance calculation
When both a spare allowance and pack size are specified, calculate the target whole-tile count first, then the number of packs. Rounding only once at the beginning can produce an insufficient purchase.
Worked connection: If 48 tiles need ten percent extra, target 53. In packs of ten, purchase six packs, or 60 tiles.
Checking question: Verify five packs would give only fifty, less than the target fifty-three.
15. A per-pack rate differs from a per-tile rate
A pack price includes a stated number of tiles. The effective unit cost is pack price divided by number of tiles, but the actual bill is number of packs purchased times pack price.
Worked connection: Five packs at a fictional $18 per pack cost $90, even if only forty-eight of fifty tiles are used.
Checking question: Do not multiply required tile count by per-pack price.
16. A per-square-metre rate uses the covered area
A price stated in dollars per square metre should be multiplied by the area measured in square metres, not by a bare count of centimetre squares. The result is an idealised material-rate cost.
Worked connection: A 12 m² floor at a fictional $24/m² has a calculated cost of $288.
Checking question: State whether the fictional rate includes any additional charges; do not invent fees.
17. A tile price and an installation price are distinct
If a question gives separate material and work rates, calculate each using its supplied basis and combine them. A material rate per pack cannot be treated as a labour rate per square metre.
Worked connection: Four packs at $20 each plus $10 per m² across 6 m² total $80+$60=$140.
Checking question: Check each rate’s units before multiplication.
18. A fixed charge is added exactly once
A fictional installation story may include a fixed setup amount plus a variable rate based on area. The fixed term is not multiplied by the floor area.
Worked connection: A hypothetical fee of $15 plus $8/m² on 6 m² gives $15+$48=$63.
Checking question: Write the model as fixed+rate×area before substituting.
19. An L-shaped floor can be measured by subtraction
An L-shaped region is often easier to model as a large rectangle with a small corner rectangle removed. Subtract the missing area from the full enclosing area.
Worked connection: An outer 5×4 m rectangle with a 2×1 m cut-out has area 20−2=18 m².
Checking question: Check that the cut-out really is removed and does not overlap a second subtracted area.
20. An L-shaped floor can also be split into nonoverlapping pieces
Instead of subtraction, split the L into two rectangles whose interiors do not overlap. Their areas should add to the same answer as the outer-minus-cutout method.
Worked connection: The same 5×4 outer with a 2×1 removed top corner may be decomposed into a 5×3 rectangle plus a 3×1 rectangle, totaling 18 m².
Checking question: Two independent decompositions provide a useful check.
21. Composite tiled areas need a common grid assumption
If an L-shaped plan is aligned to square tiles and every boundary lies along tile-grid lines, the number of exact-fit tiles equals the sum of the grid cells retained. This is not guaranteed for arbitrary diagonal or off-grid boundaries.
Worked connection: A 5×4 tile-unit rectangle with a 2×1 corner removed retains eighteen unit-square tile positions.
Checking question: Draw the grid and count cells to validate the subtraction.
22. An internal wall or opening may change the plan
A room may include a region not to be covered. Such a region needs to be excluded from the floor area only if the problem specifies it as unavailable or un-tiled.
Worked connection: A 6×4 m floor excluding a 1×1 m square fixture base has tiled area 23 m².
Checking question: Label exactly which regions are included or excluded.
23. Border length comes from perimeter not area
A skirting or edge-trim question asks for length along a boundary. For a simple rectangular model, perimeter is 2(l+w). Openings may be omitted only if the problem explicitly says not to trim across them.
Worked connection: A 4×3 m room has perimeter 14 m. With one 0.9 m doorway omitted, skirting length is 13.1 m.
Checking question: Do not multiply floor area by a price per metre of skirting.
24. A doorway gap changes trim, not the floor’s area
Removing a segment from the border trim does not cut a hole out of the rectangular floor. The floor area remains the same unless the doorway creates a described excluded floor region.
Worked connection: A 4×3 m floor remains 12 m² while 0.9 m may be deducted from 14 m of perimeter for trim.
Checking question: Separate the area diagram from the edge-trim diagram.
25. Unequal floor dimensions can still have the same area
Different rectangles may cover the same area but require different border lengths or tile layouts. Area alone does not determine all dimensions.
Worked connection: A 2×6 m room and 3×4 m room each have area 12 m², but perimeters 16 m and 14 m.
Checking question: Use both dimensions when the question asks for an edge or exact-fit tile grid.
26. The ratio of tile dimensions to room dimensions matters
A tile that covers a certain area may fail to fit an exact arrangement if the boundary lengths are not compatible. Tile orientation can also matter with rectangular tiles.
Worked connection: A 20×40 cm tile can cover a 40×60 cm region with a suitable layout, but not every region of equal area has an equally easy arrangement.
Checking question: Avoid claiming that equal area automatically guarantees identical installation counts.
27. A floor-plan scale is a separate extension
Some drawings give a scale that links plan lengths with actual lengths. Convert the plan sides to real-world lengths first, then calculate area. Formal map-scale topics may appear later in G2, so this is an optional application.
Worked connection: At a clearly stated 1:100 drawing scale, 4 cm represents 4 m and 3 cm represents 3 m, giving real area 12 m².
Checking question: Do not multiply plan area by one hundred when both length dimensions scale by one hundred.
28. A dimension in a diagram can be an algebraic unknown
A floor perimeter or area problem may describe one side as x+2 and the other as x. A given perimeter then creates a one-variable equation, which supplies both dimensions.
Worked connection: Rectangle width x, length x+2, perimeter 20 m: 2x+2(x+2)=20, so x=4 and length 6.
Checking question: After solving, compute area 24 m² only if that is requested.
29. Money rounding and tile rounding follow different rules
An amount of money may be reported to cents, while a quantity of whole tiles or packs must be an integer. Rounding a price to the nearest dollar and rounding a needed pack count down can give invalid results.
Worked connection: An exact need of 51 tiles in packs of ten requires six packs, never five by nearest-integer rounding.
Checking question: Read whether a quantity represents currency, area, tiles or packs.
30. Estimating checks unit mistakes
A 3 m by 4 m floor covers about twelve square metres. A calculation of 1200 m² suggests a conversion or misplaced-zero error. Estimation helps locate such mistakes before trusting a final cost.
Worked connection: If tiles are 0.5 m squares, roughly four tiles per square metre give about 48 tiles for 12 m².
Checking question: Use a simple square-metre benchmark before calculation.
31. Prices are mathematical models, not current quotations
Fictional flooring costs can teach rates without claiming current local retailer prices, labour charges or installation recommendations. Only supplied rates belong in the calculation.
Worked connection: At an illustrative $20 per pack, three packs cost $60. No claim about any actual merchant follows.
Checking question: Do not add assumed taxes, waste or contractor fees unless the word problem states them.
32. A later unfamiliar plan tests independent mastery
A learner may reproduce a 4×3 rectangle calculation by memory yet fail on an L-shaped plan or a different tile size. A fresh model checks whether they can choose the right area, count and rate relationships.
Worked connection: Move from exact-fit 50 cm square tiles to a different room with 25 cm tiles, then an L shape.
Checking question: Record the first misread length, unit or rounding decision for a later retest.
84 worked tile-grid, pack, L-shape and cost clinics
Cover each answer. These are idealised hypothetical floor plans and fictional material rates. The exact-fit examples explicitly have compatible tile grids; other questions distinguish an area lower bound from a workable cutting layout. No retailer, contractor or real building measurements are represented.
Floor clinic 1: Fictional rectangular floor 300×400 cm, exact-fit 50-cm square tiles, 10 tiles/pack at $18.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 12 m²; 48 tiles; 5 packs; 2 purchased extra; cost $90.00.. Method: Tile grid 6 rows×8 columns gives 48. Packs=round up 48/10 to 5; total price 5×$18.00.
Independent check: Check area coverage 48×(50/100)²=12 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 2: Fictional rectangular floor 200×350 cm, exact-fit 50-cm square tiles, 8 tiles/pack at $15.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 7 m²; 28 tiles; 4 packs; 4 purchased extra; cost $60.00.. Method: Tile grid 4 rows×7 columns gives 28. Packs=round up 28/8 to 4; total price 4×$15.00.
Independent check: Check area coverage 28×(50/100)²=7 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 3: Fictional rectangular floor 250×500 cm, exact-fit 25-cm square tiles, 12 tiles/pack at $24.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 12.5 m²; 200 tiles; 17 packs; 4 purchased extra; cost $408.00.. Method: Tile grid 10 rows×20 columns gives 200. Packs=round up 200/12 to 17; total price 17×$24.00.
Independent check: Check area coverage 200×(25/100)²=12.5 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 4: Fictional rectangular floor 400×600 cm, exact-fit 50-cm square tiles, 10 tiles/pack at $22.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 24 m²; 96 tiles; 10 packs; 4 purchased extra; cost $220.00.. Method: Tile grid 8 rows×12 columns gives 96. Packs=round up 96/10 to 10; total price 10×$22.00.
Independent check: Check area coverage 96×(50/100)²=24 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 5: Fictional rectangular floor 300×500 cm, exact-fit 25-cm square tiles, 10 tiles/pack at $16.50. Find area, exact tile count, packs and fictional material bill.
Answer: Area 15 m²; 240 tiles; 24 packs; 0 purchased extra; cost $396.00.. Method: Tile grid 12 rows×20 columns gives 240. Packs=round up 240/10 to 24; total price 24×$16.50.
Independent check: Check area coverage 240×(25/100)²=15 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 6: Fictional rectangular floor 500×700 cm, exact-fit 50-cm square tiles, 12 tiles/pack at $30.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 35 m²; 140 tiles; 12 packs; 4 purchased extra; cost $360.00.. Method: Tile grid 10 rows×14 columns gives 140. Packs=round up 140/12 to 12; total price 12×$30.00.
Independent check: Check area coverage 140×(50/100)²=35 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 7: Fictional rectangular floor 200×300 cm, exact-fit 20-cm square tiles, 10 tiles/pack at $9.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 6 m²; 150 tiles; 15 packs; 0 purchased extra; cost $135.00.. Method: Tile grid 10 rows×15 columns gives 150. Packs=round up 150/10 to 15; total price 15×$9.00.
Independent check: Check area coverage 150×(20/100)²=6 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 8: Fictional rectangular floor 600×800 cm, exact-fit 100-cm square tiles, 6 tiles/pack at $18.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 48 m²; 48 tiles; 8 packs; 0 purchased extra; cost $144.00.. Method: Tile grid 6 rows×8 columns gives 48. Packs=round up 48/6 to 8; total price 8×$18.00.
Independent check: Check area coverage 48×(100/100)²=48 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 9: Fictional rectangular floor 300×450 cm, exact-fit 50-cm square tiles, 8 tiles/pack at $16.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 13.5 m²; 54 tiles; 7 packs; 2 purchased extra; cost $112.00.. Method: Tile grid 6 rows×9 columns gives 54. Packs=round up 54/8 to 7; total price 7×$16.00.
Independent check: Check area coverage 54×(50/100)²=13.5 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 10: Fictional rectangular floor 400×500 cm, exact-fit 25-cm square tiles, 12 tiles/pack at $21.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 20 m²; 320 tiles; 27 packs; 4 purchased extra; cost $567.00.. Method: Tile grid 16 rows×20 columns gives 320. Packs=round up 320/12 to 27; total price 27×$21.00.
Independent check: Check area coverage 320×(25/100)²=20 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 11: Fictional rectangular floor 250×400 cm, exact-fit 50-cm square tiles, 6 tiles/pack at $12.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 10 m²; 40 tiles; 7 packs; 2 purchased extra; cost $84.00.. Method: Tile grid 5 rows×8 columns gives 40. Packs=round up 40/6 to 7; total price 7×$12.00.
Independent check: Check area coverage 40×(50/100)²=10 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 12: Fictional rectangular floor 600×900 cm, exact-fit 50-cm square tiles, 15 tiles/pack at $35.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 54 m²; 216 tiles; 15 packs; 9 purchased extra; cost $525.00.. Method: Tile grid 12 rows×18 columns gives 216. Packs=round up 216/15 to 15; total price 15×$35.00.
Independent check: Check area coverage 216×(50/100)²=54 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 13: Fictional rectangular floor 800×500 cm, exact-fit 100-cm square tiles, 8 tiles/pack at $24.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 40 m²; 40 tiles; 5 packs; 0 purchased extra; cost $120.00.. Method: Tile grid 8 rows×5 columns gives 40. Packs=round up 40/8 to 5; total price 5×$24.00.
Independent check: Check area coverage 40×(100/100)²=40 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 14: Fictional rectangular floor 400×400 cm, exact-fit 40-cm square tiles, 10 tiles/pack at $17.50. Find area, exact tile count, packs and fictional material bill.
Answer: Area 16 m²; 100 tiles; 10 packs; 0 purchased extra; cost $175.00.. Method: Tile grid 10 rows×10 columns gives 100. Packs=round up 100/10 to 10; total price 10×$17.50.
Independent check: Check area coverage 100×(40/100)²=16 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 15: Fictional rectangular floor 300×600 cm, exact-fit 30-cm square tiles, 12 tiles/pack at $18.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 18 m²; 200 tiles; 17 packs; 4 purchased extra; cost $306.00.. Method: Tile grid 10 rows×20 columns gives 200. Packs=round up 200/12 to 17; total price 17×$18.00.
Independent check: Check area coverage 200×(30/100)²=18 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 16: Fictional rectangular floor 500×800 cm, exact-fit 50-cm square tiles, 10 tiles/pack at $22.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 40 m²; 160 tiles; 16 packs; 0 purchased extra; cost $352.00.. Method: Tile grid 10 rows×16 columns gives 160. Packs=round up 160/10 to 16; total price 16×$22.00.
Independent check: Check area coverage 160×(50/100)²=40 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 17: Fictional rectangular floor 200×500 cm, exact-fit 25-cm square tiles, 8 tiles/pack at $12.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 10 m²; 160 tiles; 20 packs; 0 purchased extra; cost $240.00.. Method: Tile grid 8 rows×20 columns gives 160. Packs=round up 160/8 to 20; total price 20×$12.00.
Independent check: Check area coverage 160×(25/100)²=10 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 18: Fictional rectangular floor 600×600 cm, exact-fit 50-cm square tiles, 10 tiles/pack at $19.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 36 m²; 144 tiles; 15 packs; 6 purchased extra; cost $285.00.. Method: Tile grid 12 rows×12 columns gives 144. Packs=round up 144/10 to 15; total price 15×$19.00.
Independent check: Check area coverage 144×(50/100)²=36 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 19: Fictional rectangular floor 400×700 cm, exact-fit 100-cm square tiles, 6 tiles/pack at $23.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 28 m²; 28 tiles; 5 packs; 2 purchased extra; cost $115.00.. Method: Tile grid 4 rows×7 columns gives 28. Packs=round up 28/6 to 5; total price 5×$23.00.
Independent check: Check area coverage 28×(100/100)²=28 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 20: Fictional rectangular floor 750×500 cm, exact-fit 25-cm square tiles, 12 tiles/pack at $21.00. Find area, exact tile count, packs and fictional material bill.
Answer: Area 37.5 m²; 600 tiles; 50 packs; 0 purchased extra; cost $1050.00.. Method: Tile grid 30 rows×20 columns gives 600. Packs=round up 600/12 to 50; total price 50×$21.00.
Independent check: Check area coverage 600×(25/100)²=37.5 m²; this exact-fit model assumes aligned grid boundaries and no grout gaps. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 21: An exact-fit layout uses 48 tiles. The exercise specifies 10% extra and tiles are sold in packs of 10. How many whole tiles should be targeted and how many packs bought?
Answer: Target 53 tiles, buy 6 packs (60 tiles), 7 beyond the allowance target.. Method: First calculate 48×(1+10/100)=52.800000000000004, round upward to 53; then packs=ceil(53/10)=6.
Independent check: Check 5 packs would contain 50 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 22: An exact-fit layout uses 24 tiles. The exercise specifies 10% extra and tiles are sold in packs of 8. How many whole tiles should be targeted and how many packs bought?
Answer: Target 27 tiles, buy 4 packs (32 tiles), 5 beyond the allowance target.. Method: First calculate 24×(1+10/100)=26.400000000000002, round upward to 27; then packs=ceil(27/8)=4.
Independent check: Check 3 packs would contain 24 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 23: An exact-fit layout uses 63 tiles. The exercise specifies 5% extra and tiles are sold in packs of 12. How many whole tiles should be targeted and how many packs bought?
Answer: Target 67 tiles, buy 6 packs (72 tiles), 5 beyond the allowance target.. Method: First calculate 63×(1+5/100)=66.15, round upward to 67; then packs=ceil(67/12)=6.
Independent check: Check 5 packs would contain 60 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 24: An exact-fit layout uses 72 tiles. The exercise specifies 10% extra and tiles are sold in packs of 10. How many whole tiles should be targeted and how many packs bought?
Answer: Target 80 tiles, buy 8 packs (80 tiles), 0 beyond the allowance target.. Method: First calculate 72×(1+10/100)=79.2, round upward to 80; then packs=ceil(80/10)=8.
Independent check: Check 7 packs would contain 70 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 25: An exact-fit layout uses 80 tiles. The exercise specifies 10% extra and tiles are sold in packs of 12. How many whole tiles should be targeted and how many packs bought?
Answer: Target 88 tiles, buy 8 packs (96 tiles), 8 beyond the allowance target.. Method: First calculate 80×(1+10/100)=88, round upward to 88; then packs=ceil(88/12)=8.
Independent check: Check 7 packs would contain 84 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 26: An exact-fit layout uses 36 tiles. The exercise specifies 15% extra and tiles are sold in packs of 8. How many whole tiles should be targeted and how many packs bought?
Answer: Target 42 tiles, buy 6 packs (48 tiles), 6 beyond the allowance target.. Method: First calculate 36×(1+15/100)=41.4, round upward to 42; then packs=ceil(42/8)=6.
Independent check: Check 5 packs would contain 40 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 27: An exact-fit layout uses 120 tiles. The exercise specifies 5% extra and tiles are sold in packs of 15. How many whole tiles should be targeted and how many packs bought?
Answer: Target 126 tiles, buy 9 packs (135 tiles), 9 beyond the allowance target.. Method: First calculate 120×(1+5/100)=126, round upward to 126; then packs=ceil(126/15)=9.
Independent check: Check 8 packs would contain 120 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 28: An exact-fit layout uses 50 tiles. The exercise specifies 12% extra and tiles are sold in packs of 8. How many whole tiles should be targeted and how many packs bought?
Answer: Target 57 tiles, buy 8 packs (64 tiles), 7 beyond the allowance target.. Method: First calculate 50×(1+12/100)=56.00000000000001, round upward to 57; then packs=ceil(57/8)=8.
Independent check: Check 7 packs would contain 56 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 29: An exact-fit layout uses 44 tiles. The exercise specifies 10% extra and tiles are sold in packs of 6. How many whole tiles should be targeted and how many packs bought?
Answer: Target 49 tiles, buy 9 packs (54 tiles), 5 beyond the allowance target.. Method: First calculate 44×(1+10/100)=48.400000000000006, round upward to 49; then packs=ceil(49/6)=9.
Independent check: Check 8 packs would contain 48 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 30: An exact-fit layout uses 96 tiles. The exercise specifies 8% extra and tiles are sold in packs of 10. How many whole tiles should be targeted and how many packs bought?
Answer: Target 104 tiles, buy 11 packs (110 tiles), 6 beyond the allowance target.. Method: First calculate 96×(1+8/100)=103.68, round upward to 104; then packs=ceil(104/10)=11.
Independent check: Check 10 packs would contain 100 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 31: An exact-fit layout uses 30 tiles. The exercise specifies 10% extra and tiles are sold in packs of 12. How many whole tiles should be targeted and how many packs bought?
Answer: Target 33 tiles, buy 3 packs (36 tiles), 3 beyond the allowance target.. Method: First calculate 30×(1+10/100)=33, round upward to 33; then packs=ceil(33/12)=3.
Independent check: Check 2 packs would contain 24 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 32: An exact-fit layout uses 64 tiles. The exercise specifies 10% extra and tiles are sold in packs of 8. How many whole tiles should be targeted and how many packs bought?
Answer: Target 71 tiles, buy 9 packs (72 tiles), 1 beyond the allowance target.. Method: First calculate 64×(1+10/100)=70.4, round upward to 71; then packs=ceil(71/8)=9.
Independent check: Check 8 packs would contain 64 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 33: An exact-fit layout uses 84 tiles. The exercise specifies 15% extra and tiles are sold in packs of 12. How many whole tiles should be targeted and how many packs bought?
Answer: Target 97 tiles, buy 9 packs (108 tiles), 11 beyond the allowance target.. Method: First calculate 84×(1+15/100)=96.6, round upward to 97; then packs=ceil(97/12)=9.
Independent check: Check 8 packs would contain 96 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 34: An exact-fit layout uses 100 tiles. The exercise specifies 7% extra and tiles are sold in packs of 20. How many whole tiles should be targeted and how many packs bought?
Answer: Target 107 tiles, buy 6 packs (120 tiles), 13 beyond the allowance target.. Method: First calculate 100×(1+7/100)=107, round upward to 107; then packs=ceil(107/20)=6.
Independent check: Check 5 packs would contain 100 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 35: An exact-fit layout uses 42 tiles. The exercise specifies 10% extra and tiles are sold in packs of 10. How many whole tiles should be targeted and how many packs bought?
Answer: Target 47 tiles, buy 5 packs (50 tiles), 3 beyond the allowance target.. Method: First calculate 42×(1+10/100)=46.2, round upward to 47; then packs=ceil(47/10)=5.
Independent check: Check 4 packs would contain 40 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 36: An exact-fit layout uses 55 tiles. The exercise specifies 20% extra and tiles are sold in packs of 12. How many whole tiles should be targeted and how many packs bought?
Answer: Target 66 tiles, buy 6 packs (72 tiles), 6 beyond the allowance target.. Method: First calculate 55×(1+20/100)=66, round upward to 66; then packs=ceil(66/12)=6.
Independent check: Check 5 packs would contain 60 tiles, less than required. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 37: A fictional L-shaped floor is an outer 5×4 m rectangle with a 2×1 m corner removed. Tile size 1 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 18 m² and 18 whole tiles.. Method: Outer area 20 m² minus missing corner 2 m² gives 18 m². Each exact-fit tile covers 1 m².
Independent check: Check 20 outer grid positions minus 2 removed positions equals 18. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 38: A fictional L-shaped floor is an outer 6×4 m rectangle with a 2×2 m corner removed. Tile size 1 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 20 m² and 20 whole tiles.. Method: Outer area 24 m² minus missing corner 4 m² gives 20 m². Each exact-fit tile covers 1 m².
Independent check: Check 24 outer grid positions minus 4 removed positions equals 20. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 39: A fictional L-shaped floor is an outer 8×5 m rectangle with a 3×2 m corner removed. Tile size 1 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 34 m² and 34 whole tiles.. Method: Outer area 40 m² minus missing corner 6 m² gives 34 m². Each exact-fit tile covers 1 m².
Independent check: Check 40 outer grid positions minus 6 removed positions equals 34. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 40: A fictional L-shaped floor is an outer 7×6 m rectangle with a 2×3 m corner removed. Tile size 1 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 36 m² and 36 whole tiles.. Method: Outer area 42 m² minus missing corner 6 m² gives 36 m². Each exact-fit tile covers 1 m².
Independent check: Check 42 outer grid positions minus 6 removed positions equals 36. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 41: A fictional L-shaped floor is an outer 10×6 m rectangle with a 4×2 m corner removed. Tile size 1 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 52 m² and 52 whole tiles.. Method: Outer area 60 m² minus missing corner 8 m² gives 52 m². Each exact-fit tile covers 1 m².
Independent check: Check 60 outer grid positions minus 8 removed positions equals 52. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 42: A fictional L-shaped floor is an outer 9×7 m rectangle with a 3×3 m corner removed. Tile size 1 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 54 m² and 54 whole tiles.. Method: Outer area 63 m² minus missing corner 9 m² gives 54 m². Each exact-fit tile covers 1 m².
Independent check: Check 63 outer grid positions minus 9 removed positions equals 54. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 43: A fictional L-shaped floor is an outer 6×5 m rectangle with a 2×1 m corner removed. Tile size 0.5 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 28 m² and 112 whole tiles.. Method: Outer area 30 m² minus missing corner 2 m² gives 28 m². Each exact-fit tile covers 0.25 m².
Independent check: Check 120 outer grid positions minus 8 removed positions equals 112. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 44: A fictional L-shaped floor is an outer 8×4 m rectangle with a 1×2 m corner removed. Tile size 0.5 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 30 m² and 120 whole tiles.. Method: Outer area 32 m² minus missing corner 2 m² gives 30 m². Each exact-fit tile covers 0.25 m².
Independent check: Check 128 outer grid positions minus 8 removed positions equals 120. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 45: A fictional L-shaped floor is an outer 5×6 m rectangle with a 2×2 m corner removed. Tile size 0.5 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 26 m² and 104 whole tiles.. Method: Outer area 30 m² minus missing corner 4 m² gives 26 m². Each exact-fit tile covers 0.25 m².
Independent check: Check 120 outer grid positions minus 16 removed positions equals 104. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 46: A fictional L-shaped floor is an outer 7×5 m rectangle with a 3×1 m corner removed. Tile size 0.5 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 32 m² and 128 whole tiles.. Method: Outer area 35 m² minus missing corner 3 m² gives 32 m². Each exact-fit tile covers 0.25 m².
Independent check: Check 140 outer grid positions minus 12 removed positions equals 128. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 47: A fictional L-shaped floor is an outer 10×8 m rectangle with a 2×4 m corner removed. Tile size 1 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 72 m² and 72 whole tiles.. Method: Outer area 80 m² minus missing corner 8 m² gives 72 m². Each exact-fit tile covers 1 m².
Independent check: Check 80 outer grid positions minus 8 removed positions equals 72. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 48: A fictional L-shaped floor is an outer 9×6 m rectangle with a 3×2 m corner removed. Tile size 0.5 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 48 m² and 192 whole tiles.. Method: Outer area 54 m² minus missing corner 6 m² gives 48 m². Each exact-fit tile covers 0.25 m².
Independent check: Check 216 outer grid positions minus 24 removed positions equals 192. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 49: A fictional L-shaped floor is an outer 8×8 m rectangle with a 4×3 m corner removed. Tile size 1 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 52 m² and 52 whole tiles.. Method: Outer area 64 m² minus missing corner 12 m² gives 52 m². Each exact-fit tile covers 1 m².
Independent check: Check 64 outer grid positions minus 12 removed positions equals 52. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 50: A fictional L-shaped floor is an outer 12×6 m rectangle with a 5×2 m corner removed. Tile size 1 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 62 m² and 62 whole tiles.. Method: Outer area 72 m² minus missing corner 10 m² gives 62 m². Each exact-fit tile covers 1 m².
Independent check: Check 72 outer grid positions minus 10 removed positions equals 62. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 51: A fictional L-shaped floor is an outer 10×5 m rectangle with a 3×1 m corner removed. Tile size 0.5 m square; boundaries align with one common tile grid. Find area and exact tile positions.
Answer: 47 m² and 188 whole tiles.. Method: Outer area 50 m² minus missing corner 3 m² gives 47 m². Each exact-fit tile covers 0.25 m².
Independent check: Check 200 outer grid positions minus 12 removed positions equals 188. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 52: A fictional 3×4 m floor has a supplied material rate $20.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 12 m²; cost $240.00; perimeter 14 m.. Method: Area=3×4=12; multiply by $20.00 per m² to get $240.00. Boundary length=2(3+4)=14 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 53: A fictional 2×6 m floor has a supplied material rate $25.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 12 m²; cost $300.00; perimeter 16 m.. Method: Area=2×6=12; multiply by $25.00 per m² to get $300.00. Boundary length=2(2+6)=16 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 54: A fictional 5×5 m floor has a supplied material rate $18.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 25 m²; cost $450.00; perimeter 20 m.. Method: Area=5×5=25; multiply by $18.00 per m² to get $450.00. Boundary length=2(5+5)=20 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 55: A fictional 4×7 m floor has a supplied material rate $22.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 28 m²; cost $616.00; perimeter 22 m.. Method: Area=4×7=28; multiply by $22.00 per m² to get $616.00. Boundary length=2(4+7)=22 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 56: A fictional 6×8 m floor has a supplied material rate $15.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 48 m²; cost $720.00; perimeter 28 m.. Method: Area=6×8=48; multiply by $15.00 per m² to get $720.00. Boundary length=2(6+8)=28 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 57: A fictional 3×5 m floor has a supplied material rate $40.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 15 m²; cost $600.00; perimeter 16 m.. Method: Area=3×5=15; multiply by $40.00 per m² to get $600.00. Boundary length=2(3+5)=16 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 58: A fictional 8×10 m floor has a supplied material rate $12.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 80 m²; cost $960.00; perimeter 36 m.. Method: Area=8×10=80; multiply by $12.00 per m² to get $960.00. Boundary length=2(8+10)=36 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 59: A fictional 7×4 m floor has a supplied material rate $30.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 28 m²; cost $840.00; perimeter 22 m.. Method: Area=7×4=28; multiply by $30.00 per m² to get $840.00. Boundary length=2(7+4)=22 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 60: A fictional 5×9 m floor has a supplied material rate $16.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 45 m²; cost $720.00; perimeter 28 m.. Method: Area=5×9=45; multiply by $16.00 per m² to get $720.00. Boundary length=2(5+9)=28 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 61: A fictional 12×3 m floor has a supplied material rate $20.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 36 m²; cost $720.00; perimeter 30 m.. Method: Area=12×3=36; multiply by $20.00 per m² to get $720.00. Boundary length=2(12+3)=30 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 62: A fictional 10×6 m floor has a supplied material rate $18.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 60 m²; cost $1080.00; perimeter 32 m.. Method: Area=10×6=60; multiply by $18.00 per m² to get $1080.00. Boundary length=2(10+6)=32 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 63: A fictional 9×8 m floor has a supplied material rate $14.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 72 m²; cost $1008.00; perimeter 34 m.. Method: Area=9×8=72; multiply by $14.00 per m² to get $1008.00. Boundary length=2(9+8)=34 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 64: A fictional 6×6 m floor has a supplied material rate $27.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 36 m²; cost $972.00; perimeter 24 m.. Method: Area=6×6=36; multiply by $27.00 per m² to get $972.00. Boundary length=2(6+6)=24 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 65: A fictional 4×9 m floor has a supplied material rate $21.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 36 m²; cost $756.00; perimeter 26 m.. Method: Area=4×9=36; multiply by $21.00 per m² to get $756.00. Boundary length=2(4+9)=26 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 66: A fictional 8×5 m floor has a supplied material rate $33.00/m². Find area, ideal material cost and boundary perimeter.
Answer: 40 m²; cost $1320.00; perimeter 26 m.. Method: Area=8×5=40; multiply by $33.00 per m² to get $1320.00. Boundary length=2(8+5)=26 m.
Independent check: Area and perimeter answer different questions; this cost excludes unspecified installation charges. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 67: A 4×3 m floor with 50-cm square tiles: exact count?
Answer: 48 tiles. Method: 400/50=8 columns, 300/50=6 rows; 8×6=48.
Independent check: 0.25 m² per tile; 48×0.25=12 m². Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 68: 48 exact-fit tiles in packs of 10: packs and extras?
Answer: 5 packs and 2 extras. Method: Round 48/10 up to five.
Independent check: Fifty purchased minus forty-eight used is two. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 69: 48 required with an explicitly stated 10% spare allowance and 10 per pack: packs?
Answer: 6 packs. Method: Target ceil(48×1.10)=53; ceil(53/10)=6.
Independent check: Five packs only provide fifty. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 70: A 4×3 m floor with 0.9-m doorway omitted from skirting: trim length?
Answer: 13.1 m. Method: Perimeter 14 m minus doorway 0.9 m.
Independent check: Floor area remains 12 m². Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 71: A 5×4 m rectangle loses a 2×1 m corner: area?
Answer: 18 m². Method: 20−2=18.
Independent check: A 5×3 plus 3×1 split also gives eighteen. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 72: A 2×6 m rectangle and 3×4 m rectangle: same area?
Answer: Yes, both 12 m². Method: 2×6=3×4=12.
Independent check: Their perimeters differ, 16 versus 14 m. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 73: Tile side 50 cm: area in m²?
Answer: 0.25 m². Method: 0.5×0.5=0.25.
Independent check: Four such tiles cover one square metre in an exact grid. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 74: 1 m² in cm²?
Answer: 10,000 cm². Method: 100 cm×100 cm.
Independent check: Area conversion squares the length factor. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 75: A tiled region has area 4.6 m² and tiles cover 0.25 m² each: area lower bound on whole tiles?
Answer: 19 tiles. Method: 4.6/0.25=18.4; ceiling is nineteen.
Independent check: An actual cutting layout might need more. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 76: A real cutting layout is unspecified; can the exact minimal tile count always be deduced from area alone?
Answer: No. Method: Offcuts and boundary geometry matter.
Independent check: An area quotient alone is a necessary coverage bound, not always sufficient. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 77: Six packs at a fictional $18 each: amount payable?
Answer: $108. Method: 6×18.
Independent check: Pack count, not tile count, multiplies pack rate. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 78: A floor area 6 m² at $10/m² plus $15 fixed: total?
Answer: $75. Method: 6×10+15=75.
Independent check: Fixed fifteen is added once. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 79: A room width x and length x+2 has P=20 m: dimensions and area?
Answer: 4×6 m; area 24 m². Method: 2x+2(x+2)=20 gives x=4.
Independent check: Check perimeter 20 m. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 80: Is a scale drawing 1:100 with plan sides 4 cm and 3 cm an actual 4 m×3 m rectangle?
Answer: Yes, under that stated length scale. Method: 4 cm×100=400 cm; 3×100=300 cm.
Independent check: Area 12 m² is not plan area multiplied by only 100. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 81: Does a gap in skirting length automatically reduce floor area?
Answer: No. Method: Border trim and surface covering are different quantities.
Independent check: Subtract an area only if an untiled region is specified. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 82: Can a pack of eight tiles be purchased as 6.25 packs in ordinary whole-pack sales?
Answer: No. Method: Round pack count upward if packs are sold only whole.
Independent check: State any exception only if a store explicitly sells partial packs. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 83: Why is buying exactly 48 tiles from 10-tile packs impossible?
Answer: Whole packs give multiples of ten. Method: Four packs give forty; five give fifty.
Independent check: A separate single-tile sales option could change the problem, but is not stated. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Floor clinic 84: A 6×4 m floor at $12 per m²: fictional material cost?
Answer: $288. Method: Area 24 m² times twelve dollars per m².
Independent check: No actual retailer quote is implied. Change the tile dimensions or pack size and explain which earlier result must be recalculated.
Four small design investigations
Draw a 3-by-4-metre grid plan
Use a rectangle representing 300×400 cm and divide it into 50-cm squares. Count six rows and eight columns. Confirm forty-eight tiles and an area of twelve square metres by independent multiplication.
Give a changed sketch after the model is removed and ask the pupil to state what is measured in m, m², tiles and packs.
Separate tile area from package rules
Take a forty-eight-tile exact layout. At ten tiles per pack it needs five packs; at eight per pack it needs six. The covered floor does not change, only the purchase packaging.
Give a changed sketch after the model is removed and ask the pupil to state what is measured in m, m², tiles and packs.
Compare an L-shaped subtraction with a split
Draw a 5×4 m rectangle and remove a 2×1 m corner. Its area is 18 m². Divide the remaining L into a 5×3 and a 3×1 rectangle, also giving 18. This independent decomposition checks the model.
Give a changed sketch after the model is removed and ask the pupil to state what is measured in m, m², tiles and packs.
Add a doorway without changing floor area
A 4×3 m floor has twelve square metres of surface and a perimeter of fourteen metres. For a skirting calculation that excludes a 0.9 m doorway, trim length is 13.1 m, but the floor still occupies twelve square metres.
Give a changed sketch after the model is removed and ask the pupil to state what is measured in m, m², tiles and packs.
Four-week learning sequence
Week 1: area versus perimeter
Calculate simple rectangle and composite floor regions, with consistent lengths in metres or centimetres. Label both area and edge quantities.
Follow the student’s actual school topic order. The main achievement is choosing a geometrically valid model and checking units and whole-number restrictions.
Week 2: exact-fit grids and unit conversion
Convert tile side lengths and count rows and columns where every boundary aligns. Check the count by comparing total tile area with floor area.
Follow the student’s actual school topic order. The main achievement is choosing a geometrically valid model and checking units and whole-number restrictions.
Week 3: packs, allowances and costs
Practise whole-pack rounding, leftover count, explicitly stated spare percentages, fictional per-pack and per-square-metre rates.
Follow the student’s actual school topic order. The main achievement is choosing a geometrically valid model and checking units and whole-number restrictions.
Week 4: mixed models with assumptions
Use L shapes, doorway trim, an optional drawing scale and one case where area alone cannot establish a workable cutting plan. Ask for independent setup and a later retest.
Follow the student’s actual school topic order. The main achievement is choosing a geometrically valid model and checking units and whole-number restrictions.
How small-group tuition finds the real mistake
A pupil might convert a square metre using only a factor of one hundred, another may round 4.8 packs down to four, and a third may treat an area quotient as a guaranteed layout when cutting constraints are unknown. These are not the same misconception and need separate explanation.
The eduKateSG Secondary 1 small-group reference describes weekly 90-minute tutorials with three students near Sixth Avenue MRT. The figures here are fictional classroom problems; parents should confirm suitability and current lesson availability directly.
Frequently asked questions
How do I calculate a rectangular floor’s area?
Multiply its measured length by width, using matching units.
What is the difference between tile count and tile-pack count?
Tile count concerns pieces needed for a defined layout; pack count concerns whole packs purchased to supply at least that many tiles.
Why do I need to round pack numbers upward?
A partial pack cannot be bought when only complete packs are offered, and rounding down would supply too few tiles.
Is area divided by tile area always the exact number of tiles to buy?
No. It gives an area-based lower bound; the room geometry and cutting arrangement may require more pieces.
When can I calculate an exact-fit tile grid?
When the room dimensions, tile dimensions, orientation and no-gap assumption establish whole rows and columns with no cuts.
How do I calculate tiles for an L shape?
Subtract the missing corner from an enclosing rectangle or split the L into nonoverlapping rectangles, then apply the stated exact grid or cutting assumptions.
What if the exercise requests extra tiles?
Apply the stated percentage or whole-count allowance, round to the required tile count and then round up to whole packs.
How do I find leftover purchased tiles?
Subtract the number allocated from the number of tiles actually supplied by purchased packs.
Is skirting charged per square metre?
Not necessarily. A problem may state a cost per metre of boundary, which needs length rather than floor area.
What if a doorway is excluded from skirting?
Deduct the specified doorway width from the relevant border length; it does not automatically subtract floor area.
Are the fictional cost figures local flooring quotes?
No. All prices are hypothetical educational rates, not current Singapore retailer or contractor quotations.
Are floor-plan problems aligned with G2 Secondary 1?
Yes as real-world applications of area, perimeter, unit conversion, rates and composite plane figures in the MOE syllabus.
Is drawing scale an official Secondary 1 G2 topic?
Simple floor plans are a modelling context; formal map-scale and area-scale work is introduced elsewhere in the G2 sequence. Any 1:100 plan here is labelled an extension.
How can a tutor check the first error?
Ask whether the pupil used the wrong area unit, assumed an exact cut layout, rounded packs down or mixed a per-pack charge with a per-square-metre rate.
MOE curriculum and connected geometry guides
See the MOE G2 Mathematics syllabus for area, perimeter, composite figures and real-world floor-plan contexts, and the unchanged eduKateSG tutorial reference for the teaching setting.
- Composite shapes, perimeter and area
- Perimeter equations and unknown sides
- Parallelogram and trapezium area
- Area and volume unit conversions
- Scaling perimeter, area and volume
The most useful conclusion is not a memorised tile formula. It is a careful statement of what is known about the floor, the tile grid, the pack constraint and the price unit, so the calculation can be checked from start to finish.