Rate of Change Word Problems

Strategies for Word Problems

1.

Read carefully, annotate
a.

What is the problem asking you to
do? (Find… Analyze… Solve…
Write… etc.)

b.

What are the numbers
representing? Are any of the
numbers unnecessary? (distractors)

c.

What are the unknown quantities?
Write a sentence stem for your
answer. “She will have _____
sweaters.”

2.Draw a picture. It will help you
think.
3. Pretend the problem has easier
numbers. (whole numbers, no
negatives) How would you solve the
easier problem?

The answer to a multiplication problem.
Key words: of, as in 1/2 of the 20 cupcakes are blue. 1/2 x 20/1 = 10

Product

The answer to a division problem.
Quantities that are split into equal groups.

Quotient

Important Words to Notice

Descending (diver, airplane, etc.) ex. A plane descends 600 feet/min --> -600 ft/min
Removing, consuming (gas tank, water pump, etc.) ex. A water pump removes 5 gallons per minute --> -5 gallons per minute

Negative Number

​Ascending, increasing, (airplane, hot air baloon, stock price)

ex. The price is increasing an average of 10% per month --> 10% per month

Positive Number

Strategies: Read, annotate, draw a picture.

A diver is 30 feet below sea level. She descends 100 feet in the next 5 minutes. What quotient represents her rate of change? ____ ft/min

Find the quotient for the rate of change. Find the rate.

Multiple Choice

A hot air baloon is at 1,000 feet elevation and is descending at a rate of 100 feet per 4 minutes. What is its rate of change?

• -25 feet per minute.

• 20 feet per minute

• 100 feet per minute

Multiple Choice

A hot air baloon is at 1,000 feet elevation and is descending at a rate of 100 feet per 4 minutes. Which quotient represents its rate of change?

• 100/4

• 1000/4

• 1,000/100

Multiple Choice

A diver descends 25 feet in 5 minutes. What quotient best represents their rate of change?

• 25 feet per minute

• 25/5 feet per minute

• -25/5 feet per minute

• 5/1 feet per minute

Fill in the Blanks

A diver descends 50 feet in 10 minutes. What quotient represents their rate of change?

ft/min

Multiple Choice

An industrial water storage tank is being drained to be cleaned. It holds 5,000 gallons. A pump can remove 200 gallons in 5 minutes. What is the change in the amount of water in 1 minute?

• 40 gallons per minute

• -40 gallons per minute

• 200 gallons per minute

• -25 gallons per minute

Multiple Choice

An industrial water storage tank is being drained to be cleaned. It holds 5,000 gallons. A pump can remove 200 gallons in 5 minutes. Which quotient represents the rate of change?

• 200/5

• -200/5

• 5,000/200

• -5,000/5