# 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

Work through the warm up section below with your children and then try the worksheet before moving on to the main part of the lesson.

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

### Pre-assessment worksheet

Have your children try the assessment worksheet below before starting the main lesson . If they get less than 12 out of the 15 questions correct they should review the information in the warm up section above before moving on.

## Main Lesson: Word Problems With Distance, Time, & Mass

There are six examples of word problems that involve distance, time, or mass. Work through these with your children and have them try the word problem worksheets as they go.

### 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.

Help your children make connections to metric measurements by using it in their everyday life. Ask them, "How many meters or kilometers do you think it is from home to school?" "How many kilometers did you walk today?"

### 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)

### 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

Elapsed time is an easy skill to practice at home. Suppose your children asks"What time dinner will be served?" You can say, "It's 4:30 now, dinner will be ready at 6:00. That is 1 hour and 30 minutes from now." Explain to them how you solved the problem.

### 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

Remind your children to count minutes first, then hours. If the minutes go over 60, they must convert these into hours, and minutes. For example, 75 minutes equals 1 hour, 15 minutes.

#### 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
• When going from a large unit to a small unit, you multiply:
• Convert 7 kilograms into grams?
• 7 x 1,000 = 7,000 g

### 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

Your child may be confused by the idea of mass and how it is different than weight. Explain that mass is never affected by anything like gravity. Your weight may change when you are under water in a pool but your mass remains the same!

### 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.

### Test Questions

Have your children try the 10 questions in the Post-assessment worksheet below. Check their answers and review this lesson with them if necessary.

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