Math Word Problems: Distance, Time, Volume, Mass
In this lesson, students will solve different types of word problems. Distance word problems will involve converting metric units (for example, centimeters to meters). Time word problems will involve elapsed time (for example, how much time has gone by between 3:30 pm and 5:00 pm?). Mass word problems will involve converting mass units (for example, grams to kilograms).
Learning Outcomes
After this lesson your child will be able to:
 Convert between metric units of distance measurement
 Find elapsed time
 Convert between metric units of mass
Warm Up
Distance tells you how far apart objects are and is measured in metric units. The chart below shows you metric distance units from smallest to largest.
Unit Name  Unit Abbreviation 
Millimeter  mm 
Centimeter  cm 
Decimeter (rarely used)  dm 
Meter  m 
Kilometer  km 
Converting metric distances
The chart below shows you common metric conversions.
10 mm = 1 cm  50 mm = 5 cm  3 cm = 30 mm 
100 cm = 1 m  500 cm = 5 m  3 m = 300 cm 
1,000 m = 1 km  5,000 m = 5 km  3 km = 3,000 m 
Elapsed Time
The chart below shows you common time conversions
1 minute  60 seconds 
1 hour  60 minutes 
Quarter of an hour  15 minutes 
Half and hour  30 minutes 
Solving Elapsed Time Problems
Break the problem into workable part

3:30  5:15
 3:30  4:30 = 1 hour
 4:30  5:00 = 30 minute
 5:00  5:15 = 15 minutes
 Total: 1 hour, 45 minutes
Add minutes to get to a whole hour

3:17  5:15
 3:17  4:00 = 43 minutes
 4:00  5:00 = 1 hour
 5:00  5:15 = 15 minutes
 Total: 1 hour, 58 minutes
An hour is only 60 minutes so if you go over 60 minutes, convert into hours and minutes
 85 minutes = 85  60 (1 hour) = 25 minutes left over minutes
 Total: 1 hour, 25 minutes
Mass
Mass is the amount of material in an object. Mass is not weight! Weight is how heavy an object is and can be affected by forces such as gravity. You may weigh less on the moon, where there no gravity but your mass is the same!
The chart below shows you the metric mass units from smallest to largest.
Unit Name  Unit Abbreviation 
Milligram  mg 
Centigram (rarely used)  cg 
Decigram (rarely used)  dg 
Gram  g 
Kilogram  kg 
Operations and Key Words in Word Problems
The chart below shows common operations ( + ,  , x , ÷ ) and associated key words that are found in many math word problems.
Add  Subtract  Multiply  Divide 
Total  Difference  Each  Each 
In all  Less than  Row  Split 
Together/ All together  How many more  
And  
Sum 
Main Lesson: Word Problems With Distance, Time, & Mass
Example 1 of 6: Distance Word Problem
John rode {2 kilometers} on his bike. His sister Sally rode {3000 meters} on her bike. Who rode the farthest and how much farther did they ride (answer in km)?
 Step 1: Underline important information and {bracket} important numbers.
 Step 2: Ask: What is this question asking me to do? (Determine who rode the farthest and by how much).
 Step 3: When going from a large unit to a small unit, you multiply. When going from a small unit to a large unit, you divide.
 Step 4: Since the question is asking for the answer in km, convert Sally’s distance to km: 3,000 m = 3 km because there are 1,000 m in 1 km; 2,000 m in 2 km etc.
 Step 5: Solve: Sally rode farther because she rode 3 km and John only rode 2 km. Subtract to find the difference: 3km  2km = 1 km.
Example 2 of 6: Distance Word Problem
Jessica is measuring two line segments. The first line segment is {30 cm long}. The second line segment is {500 mm long}. How long are the two line segments together? (answer in cm)
 Step 1: Underline key words and {bracket} important numbers.
 Step 2: Ask: What is this question asking me to do? (Find the length of both line segments together).
 Step 3: Since the line segments are in different units, convert mm into cm. 500 mm = 50 cm because there are 10 mm in 1 cm, 20 mm in 2 cm, 30 mm in 3 cm, 40 mm in 4 cm etc.
 Step 4: Add to solve since together is an addition word (50 cm + 30 cm = 80 cm)
 Distance Word Problems Worksheet  Converting between mm, cm, m, & km
Example 3 of 6: Elapsed Time Word Problem
Steven wakes up for school at {6:30} in the morning. If school starts at {8:00} am, how long does he have from the time he wakes up until school starts?
 Step 1: Underline key words/phrases and bracket important numbers.
 Step 2: Ask: What is this question asking me to do? (find the elapsed time between wake up and the start of school).
 Step 3: Find the number of minutes between partial hours (6:30) to the next whole hour (7:00) 6:30  7:00 = 30 minutes
 Step 4: Find the amount of time between whole hours 7:00  8:00 = 1 hour
 Step 5: Add the hours and minutes (hours always come first) 1 hour, 30 minutes
Example 4 of 6: Elapsed Time Word Problem
Stephanie and her best friend Brianne went to see a movie. It started at {1:45} and ended at {4:00}. How long was the movie?
 Step 1: Underline key words/ phrases and bracket important numbers.
 Step 2: Ask: What is this question asking me to do? (find the elapsed time between the start and end of the movie).
 Step 3: Find the number of minutes from 1:45 to the next whole hour (2:00). 45 + 15 = 60 so there are 15 minutes until 2:00
 Step 4: Find the amount of time between 2:00 and 4:00 2:00, 3:00, 4:00 = 2 hours
 Step 5: Add the hours and minutes (hours always come first) 2 hours, 15 minutes
Time Word Problems Worksheet  Elapsed time and converting between minutes and hours
Converting Metric Mass Units
 Milligrams (mg) is the smallest commonly used mass unit and kilograms (kg) is the largest.
 1,000 mg = 1 g; 1,000 g = 1 kg

When going from a small unit to a large unit, you divide:.

Convert 5,000 milligrams into grams.
 5,000 ÷ 1,000 = 5 g

Convert 5,000 milligrams into grams.

When going from a large unit to a small unit, you multiply:

Convert 7 kilograms into grams?
 7 x 1,000 = 7,000 g

Convert 7 kilograms into grams?
Example 5 of 6: Metric Mass Units Word Problem
Ezra's stuffed animal has a mass of {300 grams}. How many milligrams is the stuffed animal?
 Step 1: Underline the important information and bracket the numbers.
 Step 2: Decide whether you convert the units by multiplying or dividing.
 Step 3: Remember that grams are larger than milligrams so you multiply. 300 x 1,000 = 300,000 mg
Example 6 of 6 :Metric Mass Units Word Problem
Skylar goes to a pumpkin patch and picks out a pumpkin that has a mass {6,000 grams}. How many kilograms is the pumpkin?
 Step 1: Underline the important information and bracket the numbers.
 Step 2: Decide whether you convert the units by multiplying or dividing.
 Step 3: Remember that grams are smaller than kilograms so you divide. 6,000 ÷ 1,000 = 6 kg
Metric Mass Word Problems Worksheet  Converting between mg, g, & kg.
Recap

Word Problems
 Bracket numbers and underline important information
 Determine what the question is asking you to do

Converting Metric Units
 When going from a large unit to a small unit, you multiply
 When going from a small unit to a large unit, you divide

Elapsed Time
 Bring minutes to the whole hour
 Count whole hours
 Add hours and minutes
Measurement Word Problems: Worksheets
Listed below at the 3 worksheets included in the above lesson.
 Distance Word Problems Worksheet  Converting between mm, cm, m, & km
 Time Word Problems Worksheet  Elapsed time and converting between minutes and hours
 Metric Mass Word Problems Worksheet  Converting between mg, g, & kg.