Same length, different units
Connect mm, cm, m and km as different representations of the same length.
Begin with the activity ↓Does 1.2 m get longer when written as 120 cm?
A smaller unit produces a larger count for the same length. Compare numbers together with their units.
Recall measuring one ribbon with small and large sticks. Their counts differed. Shared units let different people communicate the same length.
One centimetre is 10 millimetres, one metre is 100 centimetres, and 1000 metres make one kilometre. The symbols are mm, cm, m and km.
In 1.2 m, the whole metre is 100 cm and the 0.2 m part is 20 cm, making 120 cm. The ribbon did not grow; you counted it in a smaller unit.
Rewriting 35 mm in centimetres gives 3.5 cm: three full groups of 10 mm and half another. A larger unit reduces the number, not the length.
Do not add 2 m and 35 cm as 37 m. In centimetres use 200+35=235 cm; in metres use 2+0.35=2.35 m.
Do not assume every named step is a factor of ten. Metres and centimetres differ by 100; kilometres and metres by 1000. Write the relationship first, then explain the new unit count.
Listen one paragraph at a time
Hold on to this distinction
Start with 1 m=100 cm and recount the same length in smaller units. A length cannot be converted into litres or kilograms.
Change it and check
Choose a length and two units. Read the converted value alongside the reference-unit length and check that the quantity is unchanged.
1.2 m = 120 cm
1 m = 100 cm
Check the same quantity in a reference unit: 1200 mm
The quantity is unchanged. Units of a different quantity type cannot be converted directly.
Screen diagrams are scaled illustrations, not physical centimetres. Unit conversions are exact relationships, distinct from measurement error.
Try with paper and objects
Draw a strip labelled 1 m and divide it into ten parts. Label each 10 cm and connect it to 0.1 m. The paper diagram need not measure an actual metre.
Check and explain another example
Check your idea 1
Check your idea 2
Apply it in a new setting
Connect the answer to its unit
Return to the explanationCompare with a solution
45 · mm
Since 1 m=1000 mm, multiply 0.045 by 1000.
Does your explanation include these ideas?
Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.
Continue, or pause here
Connect g with kg and mL with L, without confusing mass with volume.