Measuring with different units
Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen
What a learner can do afterwards
- Measure the same object in centimetres and inches and record each number with its unit
- Explain why a smaller unit needs more copies to cover the same length
- Predict whether the number of centimetres will be greater or less than the number of inches for the same length
- Find a total length by adding equal unit lengths placed end to end without gaps or overlaps.
- Find how much longer one object is than another when both lengths use the same unit.
- Find one unit's length when a known number of equal units covers a given total length exactly.
1 · Read
You have used rulers and tapes to measure length. Now keep the length the same and change the unit size. Shorter units need more copies to cover that length. Longer units need fewer copies. Changing units changes the number you record, without changing the object.
An inch is longer than a centimetre. A metre is longer than a centimetre too. For the same length, the centimetre number is larger than the inch or metre number. A 50 cm strip measures about 20 inches to the nearest whole inch. Keep each reading beside its unit. Say about when a reading is rounded.
Add equal unit lengths to find a total. Three 2 cm tiles cover 2 + 2 + 2 = 6 cm. To find how many units cover a length, count equal hops to the end. A 20 cm length needs five 4 cm hops: 4, 8, 12, 16, 20. Leave no gaps or overlaps.
Different objects can have different lengths. Compare their numbers directly only when the units match. A 20 cm strip is 2 cm longer than an 18 cm strip: 20 - 18 = 2. Equal numbers with different units need care. A 7-inch string is longer than a 7-centimetre string because each inch is longer.
Counts can help you find a unit's size. Three equal units cover 15 cm exactly. Try equal hops: 5 + 5 + 5 = 15, so each unit is 5 cm long. For the same length, a unit needing more copies is shorter. Accurate measurements using equal-sized units should give matching counts.
To test how unit size changes the count, keep the object and its length unchanged. Change only the unit size. Stretching a string changes its length. Another object might have the same length or a different one. Keeping the same unstretched object helps you control the length. The shorter-unit rule compares equal lengths.
Knowing that a unit is longer does not tell its exact size. A 10 cm line needs five 2 cm units or two 5 cm units. Both units are longer than 1 cm, but their counts differ. To find an exact count, you need the unit's length or a measurement using that unit.
Two readings of one object describe one length. A strip measuring 40 cm is about 16 inches to the nearest whole inch. Do not add these readings. They measure the same strip twice, not separate parts, and use different units. Keep each number with its unit.
Same object, different units: the smaller the unit, the bigger the number you count.
Lesson, questions and flashcards written for this dataset.
Questions, readings and flashcards written for this dataset. Referenced videos are by Khan Academy.
More to read
Keep the length unchanged
Cover one strip with equal short units. Cover that same strip with equal longer units. Place the units end to end without gaps or overlaps each time.
The longer units reach farther with each copy, so you need fewer. The strip has not changed. To test unit size, do not stretch the strip, cut it or swap it for another one.
Predict before finding an exact count
An inch is longer than a centimetre. For the same length, the inch number is smaller than the centimetre number.
That fact tells you which number is larger. It does not give an exact conversion by itself. To find an exact count, you need to know the unit's size or measure using it. Keep supplied readings beside their units, and mark rounded readings with about.
Check units before comparing
Two length numbers can match even when the objects do not. A strip of 8 inches is longer than a strip of 8 centimetres because each inch is longer.
When both measurements use centimetres, compare the numbers directly. A 14 cm strip is longer than a 10 cm strip. Subtract 10 from 14 to find the difference: 4 cm.
Find the missing measurement
Equal units let you work in either direction. If four tiles are each 3 cm long, add four lengths of 3 cm to find their total.
If you know the total and the number of equal units, try equal hops to find one unit's length. Check that every hop is the same size and the last hop reaches the end. Counts from unequal units cannot be used this way.
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