In a lesson about area and perimeter, a child suggests covering a desk with…
2026
In a lesson about area and perimeter, a child suggests covering a desk with equal-sized tiles to find out how 'big' the desk is. Which mathematical concept is the child intuitively applying, and how should the teacher extend this activity to introduce the concept of unit?
Answer: A. The child is applying area measurement; the teacher should emphasize use of same-sized tiles as units — ConceptTo measure any quantity is to choose a unit and then find how many copies of that unit fit the thing being measured. Area is the attribute that tells…
- A.
The child is applying area measurement; the teacher should emphasize use of same-sized tiles as units
- B.
The child is applying perimeter measurement; the teacher should count the edges of the desk
- C.
The child is applying length measurement; the teacher should use a tape to measure sides
- D.
The child is applying volume measurement; the teacher should stack tiles for depth
Attempted by 12 students.
Show answer & explanation
Correct answer: A
Concept
To measure any quantity is to choose a unit and then find how many copies of that unit fit the thing being measured. Area is the attribute that tells how much flat, two-dimensional surface a region covers, so it is measured by tiling: the surface is covered completely, without gaps or overlaps, by identical shapes, and those shapes are counted. The count carries meaning only when every copy of the unit is the same size, because unequal copies make one surface give different numbers and destroy any comparison.
Applying the idea to the child's suggestion
The desk top is a flat, two-dimensional surface, and the child proposes to cover it and see how many tiles it takes. Covering and counting is the procedure for the surface a region covers, not for any single one-dimensional extent.
Each tile is therefore serving as one unit, and the number of tiles is the measure. By insisting that the tiles are equal-sized, the child has already grasped informally the requirement that a unit must be uniform.
The teacher extends the activity by making that requirement explicit: let the class cover the same desk again with a larger tile, then with a smaller tile, and record both counts.
Ask the class why one desk produced two different numbers although the desk itself never changed. They arrive at the rule that a measure is meaningless until the unit is named, so the same desk must be reported as so many large tiles and so many small tiles.
Finally, let two groups measure two different desks with two different tiles and try to decide which desk is bigger. Being unable to compare motivates a single unit agreed by everyone, which is the step from informal tiles to standard square units.
Comparing the four measures
Quantity | What it tells | How it is found | Unit |
|---|---|---|---|
Length | The extent between two points along one dimension | Matching a scale such as a tape against one side | cm, m |
Perimeter | The total length of the boundary of a flat figure | Adding the lengths of all the edges | cm, m |
Area | The amount of flat surface a region covers | Covering it with identical shapes and counting them | cm2, m2 |
Volume | The amount of space a solid occupies | Filling it with identical cubes | cm3, m3 |
The other suggested extensions answer different questions. Working along the edges of the desk leads to its boundary, but perimeter is obtained only by measuring each edge and adding those lengths, so merely counting the edges yields a number of sides rather than a measure. Measuring the sides with a tape gives the extent of one side. Stacking tiles for depth introduces a third dimension that the child's single flat covering never had.
So the child is intuitively applying area measurement with an informal unit, and the teacher extends the activity by making the equal-sized tile the explicit unit and then moving the class on to a standard unit.