Use compound measurement units

What you will learn

• Use compound measurement units

Models used: number sentences, stories, tables.

Before you start

• Measure length in kilometres and liquid volume in millilitres

One length can use two units

A ribbon is 2 metres and 35 centimetres long. What do the two parts mean?

1. The complete bar is the whole. Each labelled section is one part of it.

   One metre contains 100 centimetres. Two complete metres therefore contain 200 centimetres.

   2 m = 200 cm

   Smaller units are needed in greater numbers. The named unit relationship, rather than a universal decimal rule, determines the factor.

   200

   1001 metre1001 metre

2. The complete bar is the whole. Each labelled section is one part of it.

   The ribbon has those two metres and another 35 centimetres. The second number counts the smaller-unit part.

   2 m 35 cm = 200 cm + 35 cm

   235

   100100 cm100100 cm3535 cm

3. The complete bar is the whole. Each labelled section is one part of it.

   Together the parts are 235 centimetres. The ribbon did not change; we described all of it using one unit.

   2 m 35 cm = 235 cm

   235

   200two metres35extra centimetres

Worked example: A new example, together

Convert 4400 ml to litres and ml.

1. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   Write the relationship between the two units and track complete units plus any remainder.

   Changing units changes the number we count, while the measured amount stays the same.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   4 litres	4000 ml

2. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   1 litres = 1000 ml.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   4 litres	4000 ml

   Convert 4400 ml to litres and ml.

   4 litres 400 ml

3. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   1 litres = 1000 ml.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   4 litres	4000 ml

4. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   4 litres = 4000 ml.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   4 litres	4000 ml

5. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   4000 + 400 = 4400 ml; this is 4.4 litres.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   4 litres	4000 ml

6. The unit changes; the quantity stays the same. Read each value with the heading above its column.

   Check the result against the question we started with.

   4400 ÷ 1000 = 4.4 litres.

   We found 4 litres 400 ml. Changing units changes the number we count, while the measured amount stays the same.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   4 litres	4000 ml

Common mistakes to discuss

• One multiplier for every unit. The pairs differ: 100 cm in a metre, 1000 m in a kilometre, 1000 g in a kilogram, 1000 ml in a litre. 2 m 30 cm is 230 cm, and 1 km 50 m is 1050 m.

Check your understanding

• Use compound measurement units
• justify a conversion while preserving the measured quantity
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.