Comparing lengths by measuring

Activities to try

1. 1

   How much taller? Measure, align, and find the overhang

   Why it works: The difference is a real, measurable piece of length — the overhang between two lengths aligned at a common baseline — not just the fact that one object 'wins'. The answer must be an amount with a unit.

   1. Place two objects of clearly different height/length (e.g. a desk and a bookshelf) so both stand on the SAME baseline, with a ruler, metre stick or tape measured from zero at that baseline.
   2. Measure both in the same unit (e.g. desk 118 cm, shelf 125 cm) and write each measurement with its unit.
   3. Identify the strip of the longer object that sticks up above the top of the shorter one — this overhang is the answer to 'how much taller?'
   4. Find the difference by subtracting the smaller measurement from the larger (125 − 118) and state the answer with its unit: 'the bookshelf is 7 cm taller.'
   5. In a word-problem round, both measures are given (for example, stated in the problem's words in the same unit rather than read from the ruler), and the DIFFERENCE is the unknown: draw a comparison bar/tape diagram with two bars from a common baseline, mark the difference as the missing part, then write an equation with a symbol for the unknown difference (e.g. 32 + ? = 45, or 45 − 32 = ?) and solve it.
2. 2

   Same unit first: the mixed-unit trap

   Why it works: You can only subtract lengths once they are expressed in the same unit; comparing bare numbers across different units gives a meaningless answer.

   1. Take a pair of objects measured in different units (e.g. a shelf labelled 1 m and a desk labelled 80 cm).
   2. Before subtracting, re-express both in one common unit (e.g. 1 m = 100 cm).
   3. Then subtract smaller from larger in that common unit and state the difference with its unit (100 cm − 80 cm = 20 cm taller).
   4. Say aloud why '1 − 80' is wrong: the numbers are in different units and cannot be subtracted as bare numbers.
3. 3

   Check questions: comparison word problems and 'by how much?'

   Why it works: A correct answer to a comparison problem is an amount with a unit, obtained by subtracting in a common unit — not a choice of 'which one'.

   1. Answer 'how much longer/taller?' items where you enter the amount (fill-in or slider), not just which object is longer.
   2. Work at least one item that gives the two measures in different units, so you must convert to a common unit before subtracting.
   3. For a comparison word problem, pick the correct equation with the unknown difference and justify it with a bar diagram.