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IM 7.5.16 Lesson: Representing Contexts with Equations

Author:GeoGebra Classroom Activities, IM 6 - 8 Math

Is the solution positive or negative?

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Check my answer (3)

Select all that apply
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Select all that apply
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  • B
Check my answer (3)

Select all that apply
  • A
  • B
Check my answer (3)

You may use this applet for the below questions if you find it helpful.

For each situation: Find two equations that could represent the situation from the bank of equations.

For each situation,

  • Explain what the variable  represents in the situation.
  • Determine the value of the variable that makes the equation true, and explain your reasoning.
Situation 1

Situation 2

Situation 3

Situation 4

Situation 5

Match each situation with a diagram.

Next, write an equation to represent each animal's situation and answer the question. Be prepared to explain your reasoning.

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?

Your teacher will assign your group one of situations below. 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
Situations:
  1. As a inch candle burns down, its height decreases inch each hour. How many hours does it take for the candle to burn completely?
  2. On Monday 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 descents 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 degrees every hour and the current temperature is . How many hours ago was the temperature ?
  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?

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