Reference / Curriculum / 3B / Chapter 11

3B · Chapter 11 · Lesson 7

Word Problems

Choose operations and units in multistep measurement contexts.

MATH-3B-C11-L07Independent and tutor-supported

Today's mathematical question

A route is 5 km 875 m long. A walker finishes 880 m of the route. How far remains? Express in km and m.

Learning target

Choose operations and units in multistep measurement contexts.

Before starting: Prior lesson: Kilograms and Grams. 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

    Express 2,020 g as kg and g.

    Reveal explanation

    Answer: 2 kg 20 g

    Partition 2,020 into 2 full groups of 1,000 plus 20.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. P2

    Convert 4 kg 125 g into g.

    Reveal explanation

    Answer: 4,125 g

    4 kg = 4,000 g; add 125 to make 4,125 g.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. P3

    Express 8,040 g as kg and g.

    Reveal explanation

    Answer: 8 kg 40 g

    Partition 8,040 into 8 full groups of 1,000 plus 40.

    1 kg1000 g each=1,000 g
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Learn and understand

Measurement problems may involve several changes to a distance, mass, or capacity. Before calculating, identify the initial quantity, each change, and the requested unit. Translate every quantity to one shared unit so you do not accidentally add kilometers to raw meters. Regroup only when presenting the final answer. A route is 2 km 300 m, and a walker travels 450 m. Convert or regroup to subtract correctly: 2,300 − 450 = 1,850 m. Then write 1 km 850 m.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Draw a before-and-after bar. Label the amount that was used or traveled and the amount that remains, with the same units on every segment.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

initial amount
quantity at the start
remaining
quantity after a change
convert
rename with equivalent units

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

A route is 5 km 875 m long. A walker finishes 880 m of the route. How far remains? Express in 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. The route is 5875 m. Subtract 880 m to get 4995 m; regroup into kilometers and meters.
  3. Check that the answer uses the right units and makes sense.

Answer: 4 km 995 m

Check your understanding 1

A route is 3 km 65 m long. A walker finishes 273 m of the route. How far remains? Express in km and m.

Reveal answer and explanation

2 km 792 m — The route is 3065 m. Subtract 273 m to get 2792 m; regroup into kilometers and meters.

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

A route is 2 km 40 m long. A walker finishes 541 m of the route. How far remains? Express in 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. The route is 2040 m. Subtract 541 m to get 1499 m; regroup into kilometers and meters.
  3. Check that the answer uses the right units and makes sense.

Answer: 1 km 499 m

Check your understanding 2

A route is 2 km 20 m long. A walker finishes 491 m of the route. How far remains? Express in km and m.

Reveal answer and explanation

1 km 529 m — The route is 2020 m. Subtract 491 m to get 1529 m; regroup into kilometers and meters.

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

A route is 8 km 40 m long. A walker finishes 160 m of the route. How far remains? Express in 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. The route is 8040 m. Subtract 160 m to get 7880 m; regroup into kilometers and meters.
  3. Check that the answer uses the right units and makes sense.

Answer: 7 km 880 m

Check your understanding 3

A route is 6 km 20 m long. A walker finishes 2851 m of the route. How far remains? Express in km and m.

Reveal answer and explanation

3 km 169 m — The route is 6020 m. Subtract 2851 m to get 3169 m; regroup into kilometers and meters.

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

    A route is 7 km 480 m long. A walker finishes 1005 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 6 km 475 m

    The route is 7480 m. Subtract 1005 m to get 6475 m; regroup into kilometers and meters.

    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

    A route is 4 km 650 m long. A walker finishes 98 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 4 km 552 m

    The route is 4650 m. Subtract 98 m to get 4552 m; regroup into kilometers and meters.

    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

    A route is 3 km 65 m long. A walker finishes 265 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 2 km 800 m

    The route is 3065 m. Subtract 265 m to get 2800 m; regroup into kilometers and meters.

    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

    A route is 2 km 20 m long. A walker finishes 322 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 1 km 698 m

    The route is 2020 m. Subtract 322 m to get 1698 m; regroup into kilometers and meters.

    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

    A route is 2 km 55 m long. A walker finishes 978 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 1 km 77 m

    The route is 2055 m. Subtract 978 m to get 1077 m; regroup into kilometers and meters.

    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

    A route is 4 km 480 m long. A walker finishes 477 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 4 km 3 m

    The route is 4480 m. Subtract 477 m to get 4003 m; regroup into kilometers and meters.

    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

    A route is 2 km 375 m long. A walker finishes 301 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 2 km 74 m

    The route is 2375 m. Subtract 301 m to get 2074 m; regroup into kilometers and meters.

    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

    A route is 2 km 480 m long. A walker finishes 600 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 1 km 880 m

    The route is 2480 m. Subtract 600 m to get 1880 m; regroup into kilometers and meters.

    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

    A route is 8 km 375 m long. A walker finishes 2630 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 5 km 745 m

    The route is 8375 m. Subtract 2630 m to get 5745 m; regroup into kilometers and meters.

    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

    A route is 7 km 875 m long. A walker finishes 1529 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 6 km 346 m

    The route is 7875 m. Subtract 1529 m to get 6346 m; regroup into kilometers and meters.

    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

    A route is 3 km 480 m long. A walker finishes 108 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 3 km 372 m

    The route is 3480 m. Subtract 108 m to get 3372 m; regroup into kilometers and meters.

    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

    A route is 2 km 65 m long. A walker finishes 958 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 1 km 107 m

    The route is 2065 m. Subtract 958 m to get 1107 m; regroup into kilometers and meters.

    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

    A route is 2 km 55 m long. A walker finishes 426 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 1 km 629 m

    The route is 2055 m. Subtract 426 m to get 1629 m; regroup into kilometers and meters.

    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 7 km exactly the same length as 7,000 m?

    Reveal explanation

    Answer: 1 km = 1,000 m

    Each of the 7 kilometers contains 1,000 meters. The unit changes, not the distance.

  2. C2

    A path is 7 km 200 m. After walking 450 m, what remains? Explain the exchange.

    Reveal explanation

    Answer: 6 km 750 m

    Rename as 6 km 1,200 m, then subtract 450 m to get 6 km 750 m.

Exit · 3 questions

Exit check

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

  1. E1

    A route is 3 km 40 m long. A walker finishes 44 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 2 km 996 m

    The route is 3040 m. Subtract 44 m to get 2996 m; regroup into kilometers and meters.

    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

    A route is 3 km 125 m long. A walker finishes 209 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 2 km 916 m

    The route is 3125 m. Subtract 209 m to get 2916 m; regroup into kilometers and meters.

    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

    A route is 6 km 875 m long. A walker finishes 2647 m of the route. How far remains? Express in km and m.

    Reveal explanation

    Answer: 4 km 228 m

    The route is 6875 m. Subtract 2647 m to get 4228 m; regroup into kilometers and meters.

    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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