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IM: 7.5.16: Representing Contexts with Equations (Lesson)

By Newsela Staff
Last updated 6 days ago
14 Questions
16.1: Don't Solve It

Is the solution positive or negative?

Positive
Negative
(-8.7)(1.4)=a
-8.7b=1.4
-8.7+c=-1.4
8.7-d=-1.4
16.2: Warmer or Colder than Before?
For each situation,
  • Find two equations that could represent the situation from the bank of equations. (Some equations will not be used.)
  • Explain what the variable v represents in the situation.
  • Determine the value of the variable that makes the equation true, and explain your reasoning.
Bank of equations:

You may use this applet if you find it helpful:

https://curriculum.illustrativemathematics.org/MS/students/2/5/16/index.html
[Scroll to the tool under "16.2: Warmer or Colder than Before?"]

Between 6 a.m. and noon, the temperature rose 12 degrees Fahrenheit to 4 degrees Fahrenheit.

At midnight the temperature was -6 degrees. By 4 a.m. the temperature had fallen to -16 degrees.

The temperature is 0 degrees at midnight and dropping 3 degrees per hour. The temperature is -6 degrees at a certain time.

The temperature is 0 degrees at midnight and dropping 3 degrees per hour. The temperature is 9 degrees at a certain time.

The temperature at 9 p.m. is one third the temperature at midnight.

16.3: Animals Changing Altitudes
Match each situation with a diagram and write an equation to represent each animal's situation and answer the question. Be prepared to explain your reasoning.

Diagram A:

Diagram B:

Diagram C:

Diagram D:

Diagram E:

Diagram F:

A penguin is standing 3 feet above sea level and then dives down 10 feet. What is its depth?

A dolphin is swimming 3 feet below sea level and then jumps up 10 feet. What is its height at the top of the jump?

A sea turtle is swimming 3 feet below sea level and then dives down 10 feet. What is its depth?

An eagle is flying 10 feet above sea level and then dives down to 3 feet above sea level. What was its change in altitude?

A pelican is flying 10 feet above sea level and then dives down reaching 3 feet below sea level. What was its change in altitude?

A shark is swimming 10 feet below sea level and then swims up reaching 3 feet below sea level. What was its change in depth?

16.4: Equations Tell a Story

Your teacher will assign your group one of these situations. Create a visual display about your situation that includes:
  • An equation that represents your situation
  • What your variable and each term in the equation represent
  • How the operations in the equation represent the relationships in the story
  • How you use inverses to solve for the unknown quantity
  • The solution to your equation
  1. As a 7\frac{1}{4} inch candle burns down, its height decreases \frac{3}{4} inch each hour. How many hours does it take for the candle to burn completely?
  2. On Monday \frac{1}{9} of the enrolled students in a school were absent. There were 4,512 students present. How many students are enrolled at the school?
  3. A hiker begins at sea level and descends 25 feet every minute. How long will it take to get to an elevation of -750 feet?
  4. Jada practices the violin for the same amount of time every day. On Tuesday she practices for 35 minutes. How much does Jada practice in a week?
  5. The temperature has been dropping 2\frac{1}{2} degrees every hour and the current temperature is -15\degree F. How many hours ago was the temperature 0\degree F?
  6. The population of a school increased by 12%, and now the population is 476. What was the population before the increase?
  7. During a 5% off sale, Diego pays $74.10 for a new hockey stick. What was the original price?
  8. A store buys sweaters for $8 and sells them for $26. How many sweaters does the store need to sell to make a profit of $990?


Diego and Elena are 2 miles apart and begin walking towards each other. Diego walks at a rate of 3.7 miles per hour and Elena walks 4.3 miles per hour. While they are walking, Elena's dog runs back and forth between the two of them, at a rate of 6 miles per hour. Assuming the dog does not lose any time in turning around, how far has the dog run by the time Diego and Elena reach each other?