Support
Answer and teaching response
304 · The three metres contribute 300 cm; the four leftover centimetres give 304 cm. The answer preserves both parts of the measurement.
Compare metric records written in different units
Build a common-unit record before comparing lengths, masses or capacities, and explain why changing the unit changes the number but preserves the measurement.
Get student and teacher materialsPrepare the lesson
Learning goal: Convert a measurement expressed in larger and smaller metric units into the smaller unit, retain every leftover unit and justify a comparison using matching units.
You will need: Paper and pencil. Copy this exact conversion key: 1 m = 100 cm; 1 kg = 1000 g; 1 L = 1000 mL. All records are invented examples of exact measurements.
Start with a diagnostic
A length record says 1 m 8 cm. Using 1 m = 100 cm, write the same length entirely in centimetres. Explain where each part of your number comes from.
Check the reasoning and choose a starting point
108 cm: 100 cm from the metre and 8 cm more. · This distinguishes conversion followed by addition from treating 1 m 8 cm as 18 cm or 180 cm. The 8 is a count of centimetres, not tens of centimetres.
Start with support: If the learner writes 18 or 180, or cannot explain 108, draw a box labelled 100 cm and eight separate centimetre marks. Have the learner combine them, complete p1 with a partner and recheck with 2 m 6 cm = 206 cm before joining the comparison task.
Ready for core: If the learner gives 108 cm and identifies the 100 cm and 8 cm parts, start the two-record comparison. Ask the learner to check that a partner has used the same unit before comparing numerals.
Work through an example
Strip A is recorded as 2 m 35 cm. Strip B is recorded as 228 cm. Using 1 m = 100 cm, which strip is longer, and by how many centimetres?
A is 7 cm longer. Its two metres are 200 cm, so its total length is 235 cm. Comparing 235 cm with 228 cm gives a difference of 7 cm.
- Copy a record with three columns: object, original measurement and measurement in centimetres. Both records describe length, so centimetres can be a common comparison unit.
- Replace each of A's two metres with 100 cm: 2 × 100 = 200 cm. Add the remaining 35 cm once to obtain 235 cm. Keep the original mixed-unit record beside the converted record.
- Copy B as 228 cm; it already uses the chosen unit. Compare 235 with 228, then subtract 235 − 228 = 7. State both the longer strip and the size of the difference.
- Check A by separating 235 cm into 200 cm and 35 cm, which reconstructs 2 m 35 cm. A change of unit changes the count of units, while the strip's length stays the same.
Run the 40-minute lesson
- 5 minutes. Give the diagnostic individually and ask learners to label the source of every centimetre. Sort responses using the support and ready routes; collect a brief explanation as well as the number.
- 10 minutes. Model the A/B record. In pairs, one learner converts A and the other reconstructs its mixed-unit form. Swap roles and agree on the longer strip and its difference. Ask why comparing the original numerals alone fails.
- 15 minutes. Use p1 for the support group, then recheck 2 m 6 cm. Ready learners complete p2 and explain their mass comparison. Pairs examine p3 as an error report, identify the unit represented by the leftover 5 and write a corrected equality. Bring one corrected report to discussion.
- 10 minutes. Have every learner complete e1 without a partner for four minutes. Use three minutes to compare the conversion and reverse check, then three minutes for the transfer. Learners who lose the leftover unit return to a larger-unit box plus smaller-unit marks; learners who preserve units explain the transfer's missing conversion information.
A useful error to discuss
A learner might say: Compare 2 with 228, or write 2 m 35 cm as 235 cm simply by joining the printed digits.
Have the learner label the unit beside every number. Replace the metres using the conversion key and add the leftover centimetres. Test the digit-joining rule on 2 m 5 cm: it is 205 cm, because the two metres still contribute 200 cm.
Practise at your level, then check independently
Use the diagnostic to choose support or core practice, then try the challenge. Complete the independent check without help. Enter a number, fraction or mixed number. The number check does not assess your drawing or explanation.
Core
Answer and teaching response
100 · A has mass 1080 g and B has mass 980 g. Their difference is 100 g; comparing the numerals 1 and 980 would compare unlike units.
Challenge
Answer and teaching response
495 · The correct measurement is 2005 mL. The reported 2500 mL exceeds it by 495 mL. Five millilitres remains five millilitres after converting the two litres; it does not become 500 mL.
Independent check
Answer and teaching response
9 · C is 407 cm, so 407 − 398 = 9 cm. Splitting 407 into 400 and 7 reconstructs four metres and seven centimetres.
Transfer the idea
A new card says a strip is 2 large units and 5 small units long. No relationship between those units is supplied. Can you record its exact length entirely in small units? What information would make the conversion possible?
Discuss a possible response
An exact number cannot be determined yet. We need the number of small units in one large unit. If that relationship is 100, the record becomes 205 small units; if it is 1000, it becomes 2005. Unit names and their relationship must be established before converting.
Choose the next teaching step
- Uses the stated conversion relationship and adds the smaller-unit remainder exactly once.
- Records both measurements in the same unit before comparing them.
- Names the longer object and gives a difference with a length unit.
- Reconstructs the original mixed-unit measurement as a check.
Support: Keep one box for each larger unit and label its equivalent smaller-unit count. Write the leftover smaller units outside those boxes. Add the groups, then test 2 m 6 cm = 206 cm before removing the boxes.
Extend: Make two different-looking records for exactly 3050 mL, such as 3 L 50 mL and 2 L 1050 mL. Explain why the second record is equivalent even though its smaller-unit part can be regrouped into another litre.
Materials for your group
Student pages and teacher answers are separate. Keep the HTML files or print them in your browser.
Revisit a prerequisite
Missing Number Bridges is a prerequisite for using a multiplicative relationship to rename an equivalent quantity. Its full lesson concerns equivalent fractions; the metric conversion key and mixed-unit comparisons are taught here.