Reference / Curriculum / 3B / Chapter 11

3B · Chapter 11 · Lesson 3

Kilometers

Represent and convert kilometers and meters in realistic contexts.

MATH-3B-C11-L03Independent and tutor-supported

Today's mathematical question

Convert 4 km 55 m into m.

Learning target

Represent and convert kilometers and meters in realistic contexts.

Before starting: Prior lesson: Subtracting from Meters. 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 73 cm from 5 m 25 cm. Give mixed units.

    Reveal explanation

    Answer: 4 m 52 cm

    Exchange one m for 100 cm, then subtract: 525 − 73 = 452 cm. Regroup the result into m and cm.

    1 m100 cm each=100 cm
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. P2

    Subtract 74 cm from 5 m 65 cm. Give mixed units.

    Reveal explanation

    Answer: 4 m 91 cm

    Exchange one m for 100 cm, then subtract: 565 − 74 = 491 cm. Regroup the result into m and cm.

    1 m100 cm each=100 cm
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. P3

    Subtract 37 cm from 5 m 25 cm. Give mixed units.

    Reveal explanation

    Answer: 4 m 88 cm

    Exchange one m for 100 cm, then subtract: 525 − 37 = 488 cm. Regroup the result into m and cm.

    1 m100 cm each=100 cm
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Learn and understand

A kilometer is 1,000 meters. A distance of 2 km 350 m is 2,350 meters: the full kilometers contribute 2,000 meters and the extra part contributes 350. The base 1,000 must be remembered separately from the meter–centimeter base 100. One kilometer has 1,000 meters. For 3 km 250 m, write 3,000 m + 250 m = 3,250 m. Reversing the conversion restores the original measurement.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Draw a length bar for each kilometer and a shorter remainder bar labeled in meters. Convert all units to meters before calculating.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

kilometer
1,000 meters
meter
standard metric length unit
convert
rename using an equivalent unit

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

Convert 4 km 55 m into m.

1 km1000 m each=1,000 m
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 km = 4,000 m; add 55 to make 4,055 m.
  3. Check that the answer uses the right units and makes sense.

Answer: 4,055 m

Check your understanding 1

Convert 2 km 40 m into m.

Reveal answer and explanation

2,040 m — 2 km = 2,000 m; add 40 to make 2,040 m.

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

Worked example 2

Explore, calculate, verify

Express 2,125 m as 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.
  1. Identify the whole, the units, and what the question asks.
  2. Partition 2,125 into 2 full groups of 1,000 plus 125.
  3. Check that the answer uses the right units and makes sense.

Answer: 2 km 125 m

Check your understanding 2

Express 5,055 m as km and m.

Reveal answer and explanation

5 km 55 m — Partition 5,055 into 5 full groups of 1,000 plus 55.

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

Worked example 3

Explore, calculate, verify

Convert 6 km 375 m into m.

1 km1000 m each=1,000 m
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. 6 km = 6,000 m; add 375 to make 6,375 m.
  3. Check that the answer uses the right units and makes sense.

Answer: 6,375 m

Check your understanding 3

Convert 6 km 40 m into m.

Reveal answer and explanation

6,040 m — 6 km = 6,000 m; add 40 to make 6,040 m.

1 km1000 m each=1,000 m
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 km 875 m into m.

    Reveal explanation

    Answer: 2,875 m

    2 km = 2,000 m; add 875 to make 2,875 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. G2

    Express 4,020 m as km and m.

    Reveal explanation

    Answer: 4 km 20 m

    Partition 4,020 into 4 full groups of 1,000 plus 20.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. G3

    Convert 4 km 375 m into m.

    Reveal explanation

    Answer: 4,375 m

    4 km = 4,000 m; add 375 to make 4,375 m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  4. G4

    Express 2,375 m as km and m.

    Reveal explanation

    Answer: 2 km 375 m

    Partition 2,375 into 2 full groups of 1,000 plus 375.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  5. G5

    Convert 6 km 480 m into m.

    Reveal explanation

    Answer: 6,480 m

    6 km = 6,000 m; add 480 to make 6,480 m.

    1 km1000 m each=1,000 m
    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 4 km 875 m into m.

    Reveal explanation

    Answer: 4,875 m

    4 km = 4,000 m; add 875 to make 4,875 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. I2

    Express 4,125 m as km and m.

    Reveal explanation

    Answer: 4 km 125 m

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

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. I3

    Convert 7 km 480 m into m.

    Reveal explanation

    Answer: 7,480 m

    7 km = 7,000 m; add 480 to make 7,480 m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  4. I4

    Express 6,650 m as km and m.

    Reveal explanation

    Answer: 6 km 650 m

    Partition 6,650 into 6 full groups of 1,000 plus 650.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  5. I5

    Convert 5 km 375 m into m.

    Reveal explanation

    Answer: 5,375 m

    5 km = 5,000 m; add 375 to make 5,375 m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  6. I6

    Express 5,375 m as km and m.

    Reveal explanation

    Answer: 5 km 375 m

    Partition 5,375 into 5 full groups of 1,000 plus 375.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  7. I7

    Convert 5 km 480 m into m.

    Reveal explanation

    Answer: 5,480 m

    5 km = 5,000 m; add 480 to make 5,480 m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  8. I8

    Convert 8 km 250 m into m.

    Reveal explanation

    Answer: 8,250 m

    8 km = 8,000 m; add 250 to make 8,250 m.

    1 km1000 m each=1,000 m
    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

    Why is 3 km exactly the same length as 3,000 m?

    Reveal explanation

    Answer: 1 km = 1,000 m

    Each of the 3 kilometers contains 1,000 meters. The unit changes, not the distance.

  2. C2

    A path is 3 km 200 m. After walking 450 m, what remains? Explain the exchange.

    Reveal explanation

    Answer: 2 km 750 m

    Rename as 2 km 1,200 m, then subtract 450 m to get 2 km 750 m.

Exit · 3 questions

Exit check

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

  1. E1

    Convert 5 km 875 m into m.

    Reveal explanation

    Answer: 5,875 m

    5 km = 5,000 m; add 875 to make 5,875 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. E2

    Express 4,055 m as km and m.

    Reveal explanation

    Answer: 4 km 55 m

    Partition 4,055 into 4 full groups of 1,000 plus 55.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. E3

    Convert 3 km 65 m into m.

    Reveal explanation

    Answer: 3,065 m

    3 km = 3,000 m; add 65 to make 3,065 m.

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