Convert km and m; m and cm; kg and g; litres and ml

What you will learn

• Convert km and m; m and cm; kg and g; litres and ml

Models used: number sentences, stories, tables.

Before you start

• Use compound measurement units

A new unit for the same amount

One m contains 100 cm. We can measure the same amount using either unit.

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

   One m contains 100 cm. We can measure the same amount using either unit.

   The amount does not grow when we change its name. Smaller units simply need a bigger count.

   100

   1001 m = 100 cm

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

   Two m contain two groups of 100 cm.

   2 × 100 = 200 cm

   First convert the larger-unit part by multiplying by 100.

   200

   1001 m1001 m

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

   Add another 50 cm. The complete amount is 250 cm.

   200 + 50 = 250 cm

   The last part is already in small units. Add it after converting the larger units.

   250

   1001 m1001 m5050 cm
   Why do we need more small units than large units?

   Each small unit measures less, so more of them are needed to describe the same amount.

Worked example: A new example, together

Convert 2300 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
   2 litres	2000 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
   2 litres	2000 ml

   Convert 2300 ml to litres and ml.

   2 litres 300 ml

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

   2 litres = 2000 ml.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   2 litres	2000 ml

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

   2000 + 300 = 2300 ml; this is 2.3 litres.

   The unit changes; the quantity stays the same

   Larger unit	Smaller unit
   1 litres	1000 ml
   2 litres	2000 ml

5. 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.

   2300 ÷ 1000 = 2.3 litres.

   We found 2 litres 300 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
   2 litres	2000 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

• Convert km and m; m and cm; kg and g; litres and ml
• 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.