Converting measurement units

Activities to try

1. 1

   One length, two scales: seeing why larger→smaller multiplies

   Why it works: Why larger→smaller multiplies: because a larger unit holds many of the smaller unit, the smaller-unit count is always the bigger number — the inverse relationship between unit size and count, observed rather than memorised. The exact multiplier depends on the pair (100 for cm↔m, 1000 for m↔km).

   1. Look at one physical length laid against two scales stacked together — e.g. a metre scale and a centimetre scale — each with its own counter showing how many of that unit fit the length
   2. Make the length longer and watch BOTH counts rise, then say which count rises faster and which is always the bigger number
   3. Explain in your own words why the smaller unit always gives the bigger count (one large unit holds many small units, so the multiplier equals how many small units fit one large unit — e.g. 100 cm in a metre)
   4. Feed a value through a '×/÷' gate to convert between a larger and a smaller unit and back; use the km↔m case where the factor is ×1000/÷1000 because 1 km = 1000 m, and note that a different pair has a different factor (100 for cm per m)
   5. Deliberately pick the wrong gate once and describe why the answer is an absurd size (e.g. 3 km wrongly divided to 0.003 m)
2. 2

   Known-facts reference: metric vs time

   Why it works: Correct conversion depends on knowing the right relationship securely, and on recognising that time is not base-ten; metric and time must be kept separate.

   1. Build and keep a reference of the relationships as secure known facts: 1000 m = 1 km, 60 seconds = 1 minute, 60 minutes = 1 hour, 7 days = 1 week
   2. Sort the facts into two groups — metric (base-ten, follows place value: kilo = 1000) and time (60s and 7s, NOT powers of ten)
   3. Reveal the meaning of metric prefixes (e.g. kilo = 1000, centi = one hundredth) and tie each to a worked equivalent
   4. Answer 'which is bigger, 90 cm or 1 m?' and explain how you know, so a bigger number does not fool you
   5. Test yourself: 'How many minutes in 2 hours?' — then explain why the answer is 120, not 100
3. 3

   Compound measures: convert before combining

   Why it works: A compound measure like 2 m 30 cm is not a single number; its parts must be converted to a common unit before they can be combined.

   1. Write 2 m 30 cm all in centimetres: convert the metres first (2 m = 200 cm), then add the 30 cm to get 230 cm — explaining each step
   2. Notice that adding the numbers across units (2 + 30 = 32) or writing 2.30 cm does NOT give the length; say why (2.30 m is a correct way to write it, but only with the metre unit)
   3. Work a mixed set and check equivalences, e.g. decide true/false for '32 cm + 1.05 m = 150 cm − 0.13 m' by converting everything to one unit first
   4. Combine two lengths given in different units, e.g. a '1.2 m' ribbon and a '90 cm' ribbon, by converting to a common unit before adding