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3B · Chapter 11 · Lesson 5

Liters and Milliliters

Model capacity and convert liters to milliliters and vice versa.

MATH-3B-C11-L05Independent and tutor-supported

Today's mathematical question

Convert 4 L 480 mL into mL.

Learning target

Model capacity and convert liters to milliliters and vice versa.

Before starting: Prior lesson: Subtracting from Kilometers. Try the warm-up independently.

Prerequisite · 3 questions

Check earlier skills first

These are earlier ideas you need for today; revisit them if they are difficult.

  1. P1

    Subtract 697 m from 2 km 650 m. Give mixed units.

    Reveal explanation

    Answer: 1 km 953 m

    Exchange one km for 1000 m, then subtract: 2650 − 697 = 1953 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. P2

    Subtract 605 m from 4 km 375 m. Give mixed units.

    Reveal explanation

    Answer: 3 km 770 m

    Exchange one km for 1000 m, then subtract: 4375 − 605 = 3770 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. P3

    Subtract 981 m from 6 km 375 m. Give mixed units.

    Reveal explanation

    Answer: 5 km 394 m

    Exchange one km for 1000 m, then subtract: 6375 − 981 = 5394 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Learn and understand

Capacity describes how much liquid a container can hold. One liter equals 1,000 milliliters. When you mix liters and milliliters, convert to the same unit before adding or subtracting; then rewrite the result if needed. The amount of liquid does not change when its unit name changes. One liter is 1,000 milliliters. A bottle with 1 L 250 mL contains 1,250 mL. Notice that the letters L and mL label volume rather than weight.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Represent one liter with a measuring container marked from zero to 1,000 mL. Match each full liter to 1,000 mL.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

liter
metric capacity unit equal to 1,000 mL
milliliter
one thousandth of a liter
capacity
amount a container holds

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

Convert 4 L 480 mL into mL.

1 L1000 mL each=1,000 mL
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  1. Identify the whole, the units, and what the question asks.
  2. 4 L = 4,000 mL; add 480 to make 4,480 mL.
  3. Check that the answer uses the right units and makes sense.

Answer: 4,480 mL

Check your understanding 1

Convert 8 L 480 mL into mL.

Reveal answer and explanation

8,480 mL — 8 L = 8,000 mL; add 480 to make 8,480 mL.

1 L1000 mL each=1,000 mL
One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Worked example 2

Explore, calculate, verify

Express 3,480 mL as L and mL.

1 L1000 mL each=1,000 mL
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  1. Identify the whole, the units, and what the question asks.
  2. Partition 3,480 into 3 full groups of 1,000 plus 480.
  3. Check that the answer uses the right units and makes sense.

Answer: 3 L 480 mL

Check your understanding 2

Express 6,375 mL as L and mL.

Reveal answer and explanation

6 L 375 mL — Partition 6,375 into 6 full groups of 1,000 plus 375.

1 L1000 mL each=1,000 mL
One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Worked example 3

Explore, calculate, verify

Convert 8 L 65 mL into mL.

1 L1000 mL each=1,000 mL
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  1. Identify the whole, the units, and what the question asks.
  2. 8 L = 8,000 mL; add 65 to make 8,065 mL.
  3. Check that the answer uses the right units and makes sense.

Answer: 8,065 mL

Check your understanding 3

Express 5,875 mL as L and mL.

Reveal answer and explanation

5 L 875 mL — Partition 5,875 into 5 full groups of 1,000 plus 875.

1 L1000 mL each=1,000 mL
One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Guided · 5 questions

Guided practice

Keep the model and earlier examples visible while practising.

  1. G1

    Convert 2 L 250 mL into mL.

    Reveal explanation

    Answer: 2,250 mL

    2 L = 2,000 mL; add 250 to make 2,250 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. G2

    Express 4,875 mL as L and mL.

    Reveal explanation

    Answer: 4 L 875 mL

    Partition 4,875 into 4 full groups of 1,000 plus 875.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. G3

    Convert 7 L 65 mL into mL.

    Reveal explanation

    Answer: 7,065 mL

    7 L = 7,000 mL; add 65 to make 7,065 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  4. G4

    Express 5,250 mL as L and mL.

    Reveal explanation

    Answer: 5 L 250 mL

    Partition 5,250 into 5 full groups of 1,000 plus 250.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  5. G5

    Convert 2 L 20 mL into mL.

    Reveal explanation

    Answer: 2,020 mL

    2 L = 2,000 mL; add 20 to make 2,020 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Independent · 8 questions

Independent practice

Work these without hints and explain the method used. Write answers on paper.

  1. I1

    Convert 7 L 480 mL into mL.

    Reveal explanation

    Answer: 7,480 mL

    7 L = 7,000 mL; add 480 to make 7,480 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. I2

    Convert 5 L 875 mL into mL.

    Reveal explanation

    Answer: 5,875 mL

    5 L = 5,000 mL; add 875 to make 5,875 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. I3

    Express 3,375 mL as L and mL.

    Reveal explanation

    Answer: 3 L 375 mL

    Partition 3,375 into 3 full groups of 1,000 plus 375.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  4. I4

    Convert 8 L 125 mL into mL.

    Reveal explanation

    Answer: 8,125 mL

    8 L = 8,000 mL; add 125 to make 8,125 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  5. I5

    Express 4,375 mL as L and mL.

    Reveal explanation

    Answer: 4 L 375 mL

    Partition 4,375 into 4 full groups of 1,000 plus 375.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  6. I6

    Convert 5 L 125 mL into mL.

    Reveal explanation

    Answer: 5,125 mL

    5 L = 5,000 mL; add 125 to make 5,125 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  7. I7

    Express 7,125 mL as L and mL.

    Reveal explanation

    Answer: 7 L 125 mL

    Partition 7,125 into 7 full groups of 1,000 plus 125.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  8. I8

    Convert 6 L 40 mL into mL.

    Reveal explanation

    Answer: 6,040 mL

    6 L = 6,000 mL; add 40 to make 6,040 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Challenge · 2 questions

Challenge and error analysis

Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.

  1. C1

    Explain why 5 L 250 mL equals 5,250 mL.

    Reveal explanation

    Answer: 5,250 mL

    Each L is 1,000 mL. Add the remaining 250 mL.

  2. C2

    A measurement is 5,125 mL. Explain why its mixed-unit form is 5 L 125 mL.

    Reveal explanation

    Answer: 5 L 125 mL

    There are 5 full groups of 1,000 mL and 125 leftover mL.

Exit · 3 questions

Exit check

Solve independently, then return on another day to check retention.

  1. E1

    Convert 8 L 40 mL into mL.

    Reveal explanation

    Answer: 8,040 mL

    8 L = 8,000 mL; add 40 to make 8,040 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. E2

    Express 4,125 mL as L and mL.

    Reveal explanation

    Answer: 4 L 125 mL

    Partition 4,125 into 4 full groups of 1,000 plus 125.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. E3

    Convert 7 L 125 mL into mL.

    Reveal explanation

    Answer: 7,125 mL

    7 L = 7,000 mL; add 125 to make 7,125 mL.

    1 L1000 mL each=1,000 mL
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
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