PSLE Mathematics tuition for Serangoon North Avenue 2 can teach an important distinction: removing a rectangular corner decreases the area of a board, yet its outside perimeter may stay unchanged when the cut creates replacement edges of the same total length.
The weekday-versus-weekend parent choice should follow the pupil’s first attempt. Did they fail to subtract the missing corner, overlook a side length, or count an internal construction line? A focused lesson should repair that exact decision.
eduKateSG’s three-pupil teaching approach should connect clear diagrams, exact arithmetic and a second method of checking. All dimensions are fictional and do not announce a local tuition outlet.
Contents: L-shape area, perimeter and checks
A removed corner changes the shaded region · Syllabus and assessment objectives · Calculate the enclosing area · Subtract the missing eight-by-six corner · Derive every exposed boundary length · Why the new perimeter equals the old perimeter
A removed corner changes the shaded region
A fictional rectangular board measures 24 cm long and 16 cm wide. A smaller 8 cm by 6 cm rectangle is removed from its upper-right corner, leaving an L-shape. Find the new area and perimeter.
The original rectangle covers 24 × 16 = 384 cm². The missing corner covers 8 × 6 = 48 cm². Thus the remaining L-shaped material has area 336 cm².
The exposed perimeter still totals 80 cm, the same as the original rectangle, because the two lost outer edges are replaced by two inner notch edges of equal lengths.
For Serangoon North Avenue 2 parents choosing weekday or weekend PSLE Mathematics tuition, the first diagnostic is whether the learner traces the actual outside boundary rather than adding every printed line.
The dimensions are original instructional examples, not architectural measurements of a real local facility.
Syllabus and assessment objectives
Composite geometry problems rely on concepts of area, perimeter, rectangles and careful diagram interpretation developed through the MOE Primary Mathematics progression.
The revised SEAB 2026 Standard Mathematics assessment emphasises understanding, application and reasoning in both written papers. A composite diagram can practise those decisions without predicting any particular national item.
An L-shape may be solved by subtracting a corner from its enclosing rectangle or by adding two non-overlapping rectangles. Both methods must describe precisely the same shaded region.
The diagram should not be assumed to scale. Use the labelled dimensions and show how any missing lengths are derived.
A tutor should inspect whether errors begin in arithmetic or in choosing what belongs to the region and boundary.
Calculate the enclosing area
The complete rectangle measures 24 cm by 16 cm, so its original area is 24 × 16 = 384 square centimetres.
This total includes the upper-right corner that will be removed. It is useful as a starting whole for a subtraction approach.
An area is a two-dimensional measurement, so the answer uses cm² rather than cm.
The complete rectangle perimeter would be 2 × (24 + 16) = eighty centimetres, which is a different type of quantity from the area.
Before subtracting, ask the learner to shade the full 384-cm² shape and then mark the smaller region that is no longer present.
Subtract the missing eight-by-six corner
The removed upper-right rectangle has dimensions eight centimetres along the horizontal direction and six along the vertical direction.
Its area is 8 × 6 = 48 cm². Subtract from the original 384 cm² to obtain 336 cm² of L-shaped material.
Check the answer must be smaller than 384 because material has been removed, and larger than zero because most of the original board remains.
A wrong result of 432 cm² comes from adding the removed corner instead of subtracting it. The calculation reflects the wrong action rather than a multiplication problem.
The same geometry can be verified by dividing the L into two simple rectangles without overlap.
Derive every exposed boundary length
Removing eight centimetres from the top-right end leaves a top horizontal segment of 24 − 8 = 16 cm.
The inward vertical notch edge measures six centimetres and its horizontal notch edge measures eight. The remaining outer right vertical edge is 16 − 6 = 10 cm.
The bottom of the L is the full twenty-four centimetres and the left side is the full sixteen.
Trace the six boundary segments in order: sixteen, six, eight, ten, twenty-four and sixteen. Their sum is 80 cm.
A child who adds the removed original top and right segments as though they still exist double-counts part of the boundary.
Why the new perimeter equals the old perimeter
The original full rectangle has perimeter 2 × (24 + 16) = eighty centimetres.
The corner removal deletes eight centimetres of the original top boundary and six centimetres of the original right boundary, a combined fourteen centimetres.
The notch exposes a replacement horizontal edge of eight centimetres and a vertical edge of six, also fourteen in total.
Therefore the boundary length is unchanged. The area decreases but the perimeter stays eighty under this specific axis-aligned corner-cut model.
Do not infer that cutting away any region always leaves perimeter unchanged. A notch placed inside a side can expose additional boundary length.
More worked variations and independent checks
A second area method: split the L into rectangles · Another way to split the same L-shape · Find the missing notch width from the remaining area · A side notch does not preserve perimeter · Second original L-shape: a 30-by-18 board · An attached rectangle requires addition instead · A perimeter number cannot substitute for an area · Do not invent a missing dimension from appearance
A second area method: split the L into rectangles
The L-shaped figure can be divided into a bottom band 24 cm wide and 10 cm high and a smaller upper-left band 16 cm wide and six centimetres high.
The bottom band area is 24 × 10 = 240 cm². The upper-left band covers 16 × 6 = 96 cm².
These regions meet along one edge and have no overlapping area, so their sum is 240 + 96 = 336 cm².
This independently confirms the enclosing-rectangle subtraction of 384 − 48 = 336.
A tutor can ask the child to shade the two rectangles in different patterns. Every piece of the remaining L should be included once, with none counted twice.
Another way to split the same L-shape
Instead of separating top and bottom, take a left strip 16 cm wide and the entire 16 cm tall, then a lower-right strip 8 cm wide and 10 cm high.
The left strip area is 16 × 16 = 256 cm². The lower-right piece covers 8 × 10 = 80 cm².
Together they give 256 + 80 = 336 cm², a third valid route to the same shaded region.
The split must ensure the left strip and lower-right strip do not overlap. Adding an entire bottom rectangle and an entire left strip without adjusting overlap would double-count a region.
Comparing multiple valid decompositions helps the pupil distinguish a geometric choice from an arithmetic coincidence.
Find the missing notch width from the remaining area
Suppose the full rectangle still measures 24 cm by 16 cm. A rectangular corner notch is six centimetres high, and the remaining L-shaped area is given as 336 cm².
The original full area is 384, so the missing notch area must be 384 − 336 = 48 cm².
Divide the notch area by its given height: 48 ÷ 6 = 8 cm for its horizontal width.
Check forwards: a notch 8 × 6 has area forty-eight, leaving 384 − 48 = 336, exactly as required.
A child who treats 336 as the notch area rather than the remaining area has misidentified the reference region. Shading the given final shape prevents that error.
A side notch does not preserve perimeter
Imagine the same 24-by-16 rectangle, but an 8-by-6 rectangular notch is removed from the middle of its right side rather than from a corner.
Assume four centimetres of right boundary remains above the notch and six centimetres below it, since 4 + 6 + 6 = 16.
The area still decreases by 8 × 6 = 48 cm², leaving the same 336 cm².
But the perimeter now increases: the original six-centimetre right segment is replaced by a six-centimetre inner vertical edge and two eight-centimetre horizontal edges.
Thus the perimeter is 80 − 6 + (8 + 6 + 8) = 96 cm. The sixteen-centimetre increase is twice the notch depth eight.
This contrast shows why the corner-cut perimeter shortcut cannot be applied to every removed region.
Second original L-shape: a 30-by-18 board
A fictional rectangular board measures 30 cm by 18 cm. A 9-by-5 rectangular corner is removed at the top-right.
The complete rectangle area is 30 × 18 = 540 cm², and the notch area is 9 × 5 = 45 cm².
The remaining L-shaped region covers 540 − 45 = 495 cm².
The original perimeter is 2 × (30 + 18) = 96 cm. The matching horizontal and vertical replacement edges leave that perimeter unchanged after a rectangular corner cut.
Ask the pupil to find the visible top twenty-one centimetres and right thirteen centimetres, then trace the full L to confirm ninety-six.
An attached rectangle requires addition instead
Consider the original 24-by-16 rectangle, but now the 8-by-6 rectangle is attached to its top-right outside edge rather than removed from the inside.
The two flat regions share only an edge and do not overlap in area. Their combined area is 384 + 48 = 432 cm².
The boundary calculation requires tracing the actual attachment. One cannot blindly apply the corner-removal perimeter rule because the visible shared edge may become internal.
Ask the learner to shade the target region and identify which construction action occurred: adding a piece, removing a piece or moving a piece.
The sign of the area operation follows that geometric action, not simply the presence of two rectangles in the picture.
A perimeter number cannot substitute for an area
The original full rectangle’s perimeter is eighty centimetres while its area is 384 square centimetres. The L-shaped region has perimeter eighty centimetres and area 336 square centimetres.
Despite the coincidence that the two perimeters equal eighty, the areas differ. A number of centimetres along a boundary cannot be added directly to a number of square centimetres covering a region.
A pupil who calculates 336 and attaches cm instead of cm² has the correct subtraction but incomplete answer presentation.
An independent check traces the exposed sides for perimeter and shades the material for area. These actions represent different measurements before any numbers are written.
Do not invent a missing dimension from appearance
If a diagram gives the overall 24-by-16 rectangle but says only that a rectangular corner was removed, without supplying either its width, height or area, the exact remaining area cannot generally be determined.
A large-looking notch in a drawing is not a numerical measurement. Different notch sizes would leave different shaded regions.
The student should identify what extra condition is needed, such as the missing rectangle’s dimensions or its area, before producing an exact answer.
Recognising insufficient information is valid problem solving. A tutor should not reward guesses that happen to resemble a sketch drawn without scale.
More reasoning problems and alternative checks
Two independent perimeter calculations · A square corner cut has the same area and boundary principle · What fraction of the original board remains? · Worked variation: 30-by-18 with 9-by-5 corner removed · Recover a missing notch dimension from the area · A notch cut inside an edge increases boundary length · An attached rectangular extension requires adding area · An unlabelled diagram cannot supply every missing length
Two independent perimeter calculations
Trace the L-shaped outline in order: top visible length sixteen, inward edge six, notch edge eight, lower right length ten, bottom twenty-four and left side sixteen.
Adding yields 16 + 6 + 8 + 10 + 24 + 16 = 80 cm.
Alternatively start from the outer 24-by-16 rectangle’s perimeter, eighty centimetres, remove eight plus six of original exterior and add the same eight plus six of newly exposed notch boundary.
Both routes give eighty and confirm why the area decrease does not force a decrease in perimeter.
Independent checks should use a different geometric interpretation, not merely repeat the same six-term addition.
A square corner cut has the same area and boundary principle
Imagine a 20-by-15-centimetre rectangular sheet with a five-by-five square removed from one corner.
The full area is 300 cm², and the missing square area is twenty-five, so 275 cm² remain.
The original perimeter is 2 × (20 + 15) = 70 cm. The two five-centimetre exterior edges removed are replaced by the two five-centimetre notch edges, preserving seventy centimetres.
This example confirms that the boundary result depends on a rectangular corner cut rather than a particular 8-by-6 shape.
An unseen variation should prompt the child to explain the replacement-edge reasoning without being told the final perimeter.
What fraction of the original board remains?
The original 24-by-16 board covers 384 cm² and the L-shaped remainder covers 336 cm².
The fraction remaining is 336/384. Divide numerator and denominator by forty-eight to obtain 7/8.
Seven eighths is 87.5 percent, so the removed corner represents the complementary one eighth, or 12.5 percent, of the original area.
Check directly: the missing 48 cm² divided by the original 384 equals one eighth.
A student who reports eighty-seven and a half centimetres instead of percent has confused a proportion with a measurement unit.
Worked variation: 30-by-18 with 9-by-5 corner removed
An original rectangular board has length thirty and height eighteen centimetres. A rectangular corner nine centimetres wide and five high is removed.
Original area is 30 × 18 = 540 cm². The notch removes 9 × 5 = 45 cm², leaving 495 cm².
The original rectangle perimeter is 2 × (30 + 18) = 96 cm, and the rectangular corner cut preserves that perimeter.
Check by tracing visible edges: top 21, notch down 5, notch across 9, right remainder 13, bottom 30 and left 18. Their sum is ninety-six.
A child should recover each unknown length from the full dimensions rather than measure the drawing by eye.
Recover a missing notch dimension from the area
Suppose a 24-by-16 rectangle has a rectangular upper-right corner removed. The notch height is known to be six centimetres and the remaining L-shaped area is 336 cm².
The full area is 384, so the missing notch area is 384 − 336 = 48 cm².
Divide the notch area by its six-centimetre height to obtain 8 cm for the notch width.
Check forwards by computing 8 × 6 = 48 and subtracting from 384 to recreate 336.
The learner must distinguish the known remaining area from the missing area before dividing by a dimension.
A notch cut inside an edge increases boundary length
Suppose the same 8-by-6 rectangular notch is cut into the middle of the right edge, with four centimetres of the original right boundary above it and six below.
The shaded area still falls by forty-eight to 336 cm², because the removed region has the same dimensions.
The perimeter differs. The removed straight six-centimetre segment is replaced by an inward eight, vertical six, and outward eight, creating sixteen additional centimetres of boundary.
The new perimeter is 80 + 2 × 8 = 96 cm.
That contrast shows why an L-shape’s perimeter should be traced rather than inferred from area change alone.
An attached rectangular extension requires adding area
If an 8-by-6 rectangle were attached outside the 24-by-16 board, meeting only along an edge and without interior overlap, the area would increase by forty-eight rather than decrease.
The combined region would have area 384 + 48 = 432 cm².
The perimeter cannot be found by simply adding both full rectangle perimeters, because their shared attachment edge becomes internal.
To calculate its boundary, the learner must know precisely which sides touch and how long their shared edge is, then trace only the exposed outside.
Ask the child to distinguish a corner removal, a side notch and an attachment using shaded diagrams before writing an operation.
An unlabelled diagram cannot supply every missing length
Some school figures are schematic rather than drawn to exact scale. A drawn notch that appears one third the width of a rectangle does not prove that proportion without a stated relationship.
If the full rectangle is 24-by-16 but the notch has no dimensions and its area is unknown, the remaining L-shaped area cannot generally be determined uniquely.
Many 24-by-16 rectangles with differently sized removed corners would satisfy the given outer dimensions yet have different shaded areas.
An accurate pupil identifies what extra dimension or area condition is needed rather than selecting a number because the drawing looks convenient.
Recognising insufficient information is a valid mathematical conclusion.
More geometry, PSLE preparation and parent answers
The corner-cut perimeter can be explained symbolically · Removing material does not dictate the boundary change · Find the hidden lengths without measuring the sketch · Another inverse question from the boundary and area · The L-shape can be divided more than one way · Why squared units matter in structured working · A sketch may lack enough information for exact area · Five first mistakes point to five different repairs · When weekday PSLE Mathematics tuition fits · When weekend tutoring can support a diagram model · Focused three-pupil tuition should show different needs · Four checkpoints before timed composite-geometry practice · Answers for Serangoon North Avenue 2 parents · Official syllabus and connected eduKate learning
The corner-cut perimeter can be explained symbolically
Let a rectangle have length L and height B. Remove a rectangular corner whose horizontal width is w and vertical height is h, with both smaller than the corresponding original dimensions.
The new top external segment measures L − w, while the new horizontal notch segment measures w. Those two horizontal lengths add back to L.
Likewise the right external segment measures B − h and the new vertical notch segment measures h, which together add back to B.
The untouched bottom and left boundaries measure L and B. The complete exposed boundary therefore totals L + B + L + B = 2(L + B).
This explains why the corner-cut rectangle has the original perimeter. The formula depends on the axis-aligned corner geometry, not merely the act of removing an area.
Removing material does not dictate the boundary change
In the original 24-by-16 example, removing the 8-by-6 corner takes away forty-eight square centimetres of material but leaves the outer perimeter at eighty centimetres.
An 8-by-6 notch cut from the interior of the right edge removes the same area of forty-eight yet increases the perimeter to ninety-six because two additional eight-centimetre horizontal edges appear.
The two figures therefore have equal shaded areas of 336 cm² but different boundary lengths. Area does not determine perimeter uniquely.
A pupil who assumes smaller area always means shorter perimeter is relying on an unsupported geometric rule.
Ask the learner to shade a region for area, then trace its exposed boundary in a different colour for perimeter.
Find the hidden lengths without measuring the sketch
The L-shaped boundary has a full rectangle height of sixteen, with a six-centimetre vertical notch. The remaining exposed right side is 16 − 6 = 10 cm.
Likewise the full horizontal length twenty-four includes an eight-centimetre removed top-right portion, leaving 16 cm of visible top edge.
These are subtraction relationships among labelled dimensions. A ruler measurement taken from a diagram that is not stated to scale cannot replace them.
Check that visible top sixteen plus notch horizontal eight returns twenty-four, and right outside ten plus notch vertical six returns sixteen.
The two short checks confirm the missing lengths before they are used in a six-edge perimeter sum.
Another inverse question from the boundary and area
Suppose a rectangular corner cut has height five centimetres and its missing area is forty-five square centimetres. Find the horizontal width of the cut-out.
Divide the area forty-five by the known height five to obtain 9 cm. The answer is a length, not an area.
If the original rectangle measures thirty by eighteen centimetres, the remaining area is 540 − 45 = 495 cm².
Check that the cut-out width nine is smaller than the original thirty and height five is smaller than eighteen. A notch wider or taller than its enclosing board would violate the physical model.
A tutor should distinguish a correct numeric quotient attached to the wrong unit from a misunderstanding of which area was removed.
The L-shape can be divided more than one way
One valid decomposition uses a 24-by-10 bottom rectangle and a 16-by-6 upper-left rectangle. Their areas 240 and 96 sum to 336 cm².
A second uses a 16-by-16 left rectangle and an 8-by-10 lower-right rectangle. Their areas 256 and 80 also sum to 336 cm².
These two routes are genuinely different geometric partitions. Each must cover every part of the final L exactly once without overlap.
A pupil who adds a full 24-by-10 bottom band to a full 16-by-16 left strip would count their overlapping lower-left region twice.
Ask the learner to colour each proposed component and identify its boundaries before accepting the arithmetic.
Why squared units matter in structured working
The notation cm measures a line length; cm² measures a flat area. The L-shaped remaining area of 336 cm² is not the same quantity as its eighty-centimetre perimeter.
A PSLE-style structured question may first request missing lengths, then area, then boundary length. Each answer should be recorded with the correct label so later calculations reuse the intended quantity.
Writing eighty square centimetres for the boundary or 336 centimetres for the region is an answer-format failure even if the arithmetic itself is right.
A tutor can ask the pupil to say aloud what has been measured: exposed edge or shaded material. That verbal check often catches a unit mistake before submission.
Do not combine line lengths and areas in one addition merely because both figures use centimetres somewhere in their dimensions.
A sketch may lack enough information for exact area
Suppose a question gives the original 24-by-16 rectangle but leaves both dimensions of the removed corner unspecified. It does not state the remaining area either.
Many different rectangular corners could be removed while leaving the same outer dimensions, so the exact L-shaped area cannot be uniquely determined.
The pupil should name the missing condition, such as the notch’s width and height, or its total area.
Guessing from the apparent drawing proportions adds information that the problem has not supplied, especially when the sketch is not declared to scale.
Recognising insufficient data is part of mathematical interpretation; it is not a failure to remember an area formula.
Five first mistakes point to five different repairs
A learner may add the forty-eight-square-centimetre removed corner to the original 384 rather than subtract it. That error concerns the meaning of the shaded region.
Another may subtract correctly but call the answer 336 centimetres rather than 336 square centimetres. That is a unit error.
A third may count the two original top-right exterior segments after the corner is removed, inflating the perimeter. A boundary trace helps diagnose that mistake.
A fourth may assume that every cut leaves perimeter unchanged and fail the interior-notch contrast. A fifth may measure an unknown edge from the sketch instead of subtracting dimensions.
These need targeted feedback, not simply another multiplication worksheet. Record the first unsupported decision and check it in a new diagram.
When weekday PSLE Mathematics tuition fits
A weekday session may help when a newly marked school geometry problem reveals exactly where the pupil misread a composite outline.
Bring the original uncorrected diagram. Ask the tutor whether the first error was classifying the removed region, calculating a missing length or tracing a boundary.
Consider school dismissal, CCAs, a meal, homework, travel to the actual teaching venue and sufficient sleep. A useful lesson requires the child to think clearly.
One focused session can cover the original 24-by-16 L, compare two area methods and finish with the 30-by-18 variation independently.
After several days, give a new unseen corner cut so the learner must find the missing sides without relying on a memorised answer of eighty.
When weekend tutoring can support a diagram model
A weekend lesson can allow a pupil to cut paper rectangles, remove a corner and physically trace the new boundary. That representation makes the replaced side lengths visible.
This is particularly useful when the child calculates area correctly but cannot explain why the exposed boundary does not become shorter.
Weekends may still be crowded with sports, family obligations, other tuition and preparation for school. The potential advantage depends on usable concentration and recovery.
Start with an independent drawing, demonstrate the precise missing relationship and end with a side-notch example whose perimeter really changes.
A short delayed weekday review shows whether the pupil understands the contrast without the physical model.
Focused three-pupil tuition should show different needs
In one small group, a child may struggle to subtract the missing corner area, another may confuse perimeter with area and a third may calculate both correctly but misread a hidden side length.
These students need different supports: a shaded whole-minus-part diagram, a traced boundary or a labelled side-difference model.
An illustrative ninety-minute tutorial might include individual diagnostics, two valid area decompositions, a complete perimeter check and private changed diagrams.
Group discussion can help pupils compare the methods, but no child should be credited with understanding solely because another has given the right answer.
Parents can ask what first hint was needed and whether that hint was still necessary on an unseen drawing later.
Four checkpoints before timed composite-geometry practice
Checkpoint one is interpretation. Identify the complete original region, the cut-out and the final shaded shape before calculating any areas.
Checkpoint two is missing dimensions. Derive shorter exposed sides from the given whole lengths and notch dimensions rather than measuring the picture.
Checkpoint three is verification. Find the area through whole-minus-part and one non-overlapping split, then trace all exposed perimeter edges once.
Checkpoint four is transfer. Change the notch size, place it inside a side instead of at a corner, or ask for an unknown notch dimension from the remaining area.
These checkpoints are flexible diagnostic stages, not promises of four lessons or a particular PSLE score.
Answers for Serangoon North Avenue 2 parents
What is the remaining area? A 24-by-16 rectangle minus an 8-by-6 corner leaves 336 cm².
Why is the perimeter still eighty? The deleted eight- and six-centimetre exterior edges are replaced by notch edges of the same lengths.
Will an interior side notch also preserve perimeter? Not generally. The worked 8-by-6 side notch increases it to 96 cm.
Are two methods useful? Yes, whole-minus-part and a non-overlapping split both give 336 cm².
Is this a predicted PSLE item? No. It is original mathematical reasoning practice.
Is weekday or weekend tuition better? Choose attention, targeted feedback, independent retrieval and rest.
Does this article confirm a tuition venue nearby? No. Verify the actual eduKate location directly.
Official syllabus and connected eduKate learning
The MOE Primary Mathematics syllabus updated October 2025 covers the relevant geometric foundations. For PSLE examination conditions, use the SEAB published formats examined in 2026.
The eduKate Mathematics Learning Hub offers related mathematics explanations. The Serangoon North Avenue 2 Primary 4 guide develops earlier number sense.
To discuss a real eduKate Singapore consultation, bring the child’s own diagram and feasible weekday/weekend windows. Confirm three-pupil class fit, actual teaching venue, fees and travel before attending.
Continue through Serangoon North Avenue 2 Mathematics: Primary 1: Place-Value Subtraction · Primary 2: Odd and Even · Primary 3: Two-Step Sharing · Primary 5: Percentage Remainders · Primary 6: Changed Averages · Exam Prep: Data Tables. Each guide addresses a separate mathematical learning target.