Rising Temperatures:
Algebra Worksheet
9th-12th Grades
Targeted Skill: Rational and Radical Equations | |
CCSS.MATH.CONTENT.HSA.REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. |
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Climate Change Connection | |
As the need for climate awareness increases, it is important to provide students with opportunities to explore climate topics in their day-to-day learning. Using climate change scenarios to practice math skills is a great way to integrate climate education into what they are already doing. While this activity focuses on rising temperatures, the same process can be done with a variety of topics. For more context about rising temperatures, consider exploring the following resources: |
Teaching Tips | |
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Name: Date:
Rising Temperatures Algebra
As global temperatures rise due to climate change, it's important to understand the mathematical models that describe this phenomenon. This worksheet will focus on solving rational and radical equations that relate to temperature increases over time.
Part 1: Rational Equations
Average Temperature Increase
The average global temperature increase T (in °C) per year is inversely proportional to the number of years y since 2000. If the rate of yearly increase of global temperature is 0.05°C/year, how many years did it take to increase global temperatures by 0.2°C?
Set up the rational equation based on the given information.
Solve for y when T = 0.05
Verify your solution and discuss if there are any extraneous solutions.
Temperature Increase Rate
The rate of temperature increase R (in °C per decade) is inversely proportional to the number of actions A taken to reduce carbon emissions. If taking 5 significant actions results in a temperature increase of 0.2°C per decade, determine how many actions are needed to reduce the temperature increase rate to 0.1°C per decade.
Set up the rational equation based on the given information where k is a constant.
Use the given values to find k.
Solve the rational equation for A when R = 0.1.
Long-Term Temperature Model
The long-term temperature increase I (in °C) over n years since 2000 can be described by the equation
√n + 4 = I - 1. If the temperature increase is 5°C, solve for n.
Set up the radical equation based on the given information.
Solve for n.
Verify your solution and discuss if there are any extraneous solutions.
Part 2: Radical Equations
Projected Temperature Rise
The projected rise in temperature R (in °C) over t years can be modeled by the equation √ 2t + 1 = R.
If the projected rise is 3°C, find t. In this example, the equation represents a simplified climate model of the climate system where the constants 2 and 1 represent other aspects of the climate system.
Set up the radical equation based on the given information.
Solve for t.
Verify your solution and discuss if there are any extraneous solutions.
Name: Date:
ANSWER KEY
Rising Temperatures Algebra
As global temperatures rise due to climate change, it's important to understand the mathematical models that describe this phenomenon. This worksheet will focus on solving rational and radical equations that relate to temperature increases over time.
Part 1: Rational Equations
Average Temperature Increase
The average global temperature increase T (in °C) per year is inversely proportional to the number of years y since 2000. If the rate of yearly increase of global temperature is 0.05°C/year, how many years did it take to increase global temperatures by 0.2°C?
Set up the rational equation based on the given information.
Solve for y when T = 0.05
Verify your solution and discuss if there are any extraneous solutions.
Temperature Increase Rate
The rate of temperature increase R (in °C per decade) is inversely proportional to the number of actions A taken to reduce carbon emissions. If taking 5 significant actions results in a temperature increase of 0.2°C per decade, determine how many actions are needed to reduce the temperature increase rate to 0.1°C per decade.
Set up the rational equation based on the given information where k is a constant.
Use the given values to find k.
Solve the rational equation for A when R = 0.1.
Long-Term Temperature Model
The long-term temperature increase I (in °C) over n years since 2000 can be described by the equation
√n + 4 = I - 1. If the temperature increase is 5°C, solve for n.
Set up the radical equation based on the given information.
Solve for n.
Verify your solution and discuss if there are any extraneous solutions.
Part 2: Radical Equations
Projected Temperature Rise
The projected rise in temperature R (in °C) over t years can be modeled by the equation √ 2t + 1 = R.
If the projected rise is 3°C, find t. In this example, the equation represents a simplified climate model of the climate system where the constants 2 and 1 represent other aspects of the climate system.
Set up the radical equation based on the given information.
Solve for t.
Verify your solution and discuss if there are any extraneous solutions.
ANSWER KEY
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Authors |
Elizabeth Ward Maia Huang |
Scientist Reviewer |
Archibong Akpan, PhD Colin Evans, PhD |
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