Compare metric records written in different units

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.

Answer: 108 cm: 100 cm from the metre and 8 cm more.

Teacher response: 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.

model. 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?

1. 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.
2. 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.
3. 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.
4. 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.

Worked example: 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.

p1. Support: using 1 m = 100 cm, convert 3 m 4 cm entirely to centimetres. Enter the number of centimetres and draw the three metre-sized groups plus the leftover centimetres.

Answer: 304

Teacher response: The three metres contribute 300 cm; the four leftover centimetres give 304 cm. The answer preserves both parts of the measurement.

p2. Core: parcel A has mass 1 kg 80 g and parcel B has mass 980 g. Using 1 kg = 1000 g, enter how many grams heavier A is. Record both masses in grams before subtracting.

Answer: 100

Teacher response: 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.

p3. Challenge: a record claims 2 L 5 mL = 2500 mL. Using 1 L = 1000 mL, enter how many millilitres too large the right-hand record is. Write the corrected equality and explain the error.

Answer: 495

Teacher response: 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.

e1. Independent check: strip C is 4 m 7 cm and strip D is 398 cm. Using 1 m = 100 cm, enter how many centimetres longer C is. Show the common-unit record and reverse the conversion to check C.

Answer: 9

Look for:

• 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.

Teacher response: C is 407 cm, so 407 − 398 = 9 cm. Splitting 407 into 400 and 7 reconstructs four metres and seven centimetres.

transfer. 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?

Answer: 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.

teach-1. 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.

teach-2. 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.

teach-3. 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.

teach-4. 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.

misconception. Compare 2 with 228, or write 2 m 35 cm as 235 cm simply by joining the printed digits.

Teacher response: 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.

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.

support-route. 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-route. 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.