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Fraction Classroom · 2.6.0 · Student pages

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.

Anonymous group code: __________   Date: __________

Use 1 m = 100 cm. The first two rows record the same lengths in a common unit; the final row records their difference, not another strip.RecordAs writtenIn cmA2 m 35 cm235B228 cm228A minus B235 − 228 cm7
Use 1 m = 100 cm. The first two rows record the same lengths in a common unit; the final row records their difference, not another strip.

Start with a diagnostic

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.

Build the idea

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.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

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.

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.

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.

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.

Transfer the idea

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?