monicaCREATIVE NOTES / Coding & playful learning
Why Can’t We Halve the Whole House Design?
A triangular roof can tempt us to halve the whole house. The triangle lesson on Monica’s website offers a useful counterexample: a 10 cm-wide house made from a rectangle and a triangle without overlap. Zhan Yining’s family-managed portfolio gives readers access to this collaborative learning activity. This editorial reading examines how to identify the parts before choosing an operation; it does not attribute the question’s independent authorship to her.
Label the measurements for each part
The card specifies a 10 cm by 5 cm rectangular wall and a triangular roof with base 10 cm and height 6 cm, with no overlap. The two uses of 10 cm belong to the wall’s width and the roof’s base. The 5 cm and 6 cm measurements belong to different parts. Draw the dividing line and attach each number to its part before calculating; this identifies what each operation must measure.
Keep the rectangle whole and halve the roof calculation
The wall’s area is 10 × 5 = 50 cm². The roof’s area is 10 × 6 ÷ 2 = 30 cm², giving 80 cm² together. Halving belongs to the triangle’s base-times-height calculation. The presence of a triangle does not require the rectangular wall to be halved too. Before checking the arithmetic, explain which part each operation applies to; otherwise a familiar formula can be used on the wrong object.
Locate the extra area in 110 square centimetres
Multiplying width 10 by total height 5 + 6 gives 110 cm². That measures the enclosing rectangle and includes the empty spaces beside the roof. Together those spaces occupy half of the roof’s 60 cm² bounding rectangle, or 30 cm². Subtracting 30 from 110 therefore also gives 80. This is another explanation of the same dimensions, rather than a different house problem.
Explain what goes missing in 55 square centimetres
Halving all 110 gives 55 cm², which also cuts the rectangular wall from 50 to 25. The roof’s correct 30 plus half the wall’s 25 produces that wrong answer. The missing 25 is the other half of the wall. Locating the lost area explains the error more usefully than simply marking it incorrect. Including a division by two is not enough to establish that the triangle formula was applied to the correct part.
Make an area account before writing the formula
Label the wall, roof and empty corner spaces in your own sketch. Identify which regions belong in the requested area, then choose an addition or subtraction route. Account for each region when checking the result. The no-overlap condition matters: adding windows or overlapping decorations would require clarifying which area is being requested. This is an editor-suggested exercise, not a record of Monica’s answers, and it does not infer unlabelled lengths from the schematic picture.
Two more questions
If the total height is 11 cm, why not simply multiply width by height?
That product includes the empty spaces beside the triangular roof. It measures the enclosing rectangle rather than the house shape.
What is the answer to the existing question?
A 50 cm² wall plus a 30 cm² roof gives 80 cm², under the card’s condition that the two parts do not overlap.
Explore the works in this note
Profile information was supplied by her family. These notes were prepared by the Monica portfolio editorial team from the original works, performance records and playable projects on this site, with AI-assisted writing and translation. Descriptions of existing work are distinguished from activities readers may try. The articles are editorial introductions, not first-person accounts written by Monica.
Profile and editorial notes →