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Lesson 8 of 8 · Grades 3 to 5

Measurement word problems

A measurement word problem mixes a story with units, and the units are the clue to the right operation. This lesson walks through one method for length, mass, capacity, time and money problems.

A method that works

A measurement word problem tells a small story and hides a question inside it. The units in the story tell you what kind of answer to expect, and often they tell you which operation to use. Four steps handle almost every problem: read the question, find the units, change to one unit if you need to, then choose the operation and compute.

Read the question twice: the first read gives the story, the second gives the question. Underline the numbers with their units, and circle the words that ask for something, such as how much longer or how many are left. Those words point to the operation.

Length problems

When lengths share a unit, compute straight away. A rope of 250 cm joined to 1 m 40 cm needs one change first: 1 m 40 cm is 140 cm, and 250 + 140 = 390 cm. A 3 m plank cut into 5 pieces gives 300 ÷ 5 = 60 cm per piece.

50 cm 0 25 50 75 100
A 1 metre plank marked in centimetres. The piece from 25 cm to 75 cm is 50 cm long, which is what 100 ÷ 2 gives.

Mass and capacity problems

A problem about bags and boxes usually asks for a total or a difference. A parcel of 1 kg 200 g and a box of 900 g have a total mass of 1,200 + 900 = 2,100 g. A problem about jugs and bottles usually asks how much is left or how many small containers can be filled. A 2 L can of juice fills eight 250 mL cups, because 2,000 ÷ 250 = 8.

Change two-unit amounts to the smaller unit before computing, then answer in the unit the question asks for.

1 m = 100 cm 1 kg = 1,000 g 1 L = 1,000 mL 1 ft = 12 in
The conversion facts behind the word problems: 100 centimetres in a metre, 1,000 grams in a kilogram, 1,000 millilitres in a litre and 12 inches in a foot.

Time problems

A time problem gives two moments and asks how long is between them, or gives one moment and a duration and asks for the other moment. Count on in jumps: a film from 6:45 p.m. to 8:10 p.m. runs 15 minutes to 7:00, 60 minutes to 8:00 and 10 more minutes, which is 85 minutes in total. When the question asks for the end time, add the duration in the same jumps.

6:45 7:00 8:00 8:10 15 min 60 min 10 min
The film runs from 6:45 p.m. to 8:10 p.m., counted on as 15 + 60 + 10 = 85 minutes.

Money problems and the label

Money problems add prices, then find change by subtracting the total from the note. The label is the last step: an answer of 8 means nothing on its own. Write the unit with the number every time: 8 cups, 8 km, 8 kg or 8 minutes.

Extra numbers sometimes appear to test your choice. Identify the question first, and use only the numbers that answer it.

Watch out for this

Never compute with two different units in the same sum. Adding 2 m to 30 cm as 2 + 30 = 32 gives the wrong answer and the wrong idea. Change the metres to centimetres first: 200 + 30 = 230 cm. The unit is part of the number, so it has to match before the arithmetic can start.

Worked example

A baker uses 1 kg 500 g of flour in the morning and 2 kg 250 g in the afternoon. What is the total mass?

Step 1: read the question and find the units. Both masses use kilograms and grams, so change both to grams.

Step 2: change each mass. 1 kg 500 g = 1,500 g, and 2 kg 250 g = 2,250 g.

Step 3: add the grams. 1,500 + 2,250 = 3,750 g.

Step 4: write the answer in both units and label it. 3,750 g is 3 kg 750 g, so the baker uses 3 kg 750 g of flour in the day.

Answer: 3,750 g, which is 3 kg 750 g.

Remember

  • Read the question twice and find the units.
  • Change to one unit before you compute.
  • The words in the question point to the operation.
  • Every number in the answer needs a unit label.

Try it

Answer the five questions below. Work them out first, then open each answer to check.

  1. A rope is 250 cm long. Another rope is 1 m 40 cm long. What is the total length in centimetres?

    Show answer

    390 cm. 1 m 40 cm = 140 cm, and 250 + 140 = 390 cm.

  2. A recipe needs 500 mL of milk and 250 mL of oil. How much liquid is that in millilitres?

    Show answer

    750 millilitres. 500 + 250 = 750 mL.

  3. You buy 3 kg of apples and use 500 g in a pie. How many grams of apples are left?

    Show answer

    2,500 grams. 3 kg = 3,000 g, and 3,000 - 500 = 2,500 g.

  4. A film starts at 6:45 p.m. and ends at 8:10 p.m. How long is the film in minutes?

    Show answer

    85 minutes. Count 15 minutes to 7:00, 60 minutes to 8:00 and 10 more: 85 min.

  5. A plank is 3 m long. It is cut into 5 equal pieces. How long is each piece in centimetres?

    Show answer

    60 cm. 3 m = 300 cm, and 300 ÷ 5 = 60 cm.

Puzzle · Ribbon cut

Puzzle time

A ribbon is 2 m long. Mia cuts off 75 cm. How long is the piece that is left?

Pick your answer

Show a hint

Change 2 m to centimetres first, then subtract the piece that was cut off: 200 - 75.

Show the answer

Answer: 125 cm. 2 m = 200 cm, and 200 - 75 = 125, so the piece that is left is 125 cm long.