Inverse Relationship Teacher Resources
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In this algebra worksheet, students find the inverse of an equations. They graph their solutions and analyze it. There are 8 questions.
In this transformation activity, students identify a series of transformations and sketch them. They use inversion mapping to establish a one-to-one correspondence between nonzero points. This four-page activity contains approximately eight problems, with examples.
The major goal of this lesson is to collect data from a variety of experiments, and then determine what type of model best fits the data, and explain why. Students will explore a variety of relationships using pennies, pressure, temperature, light, and pe
Help the class determine missing factors in equations by creating arrays. Through modeling and practice, they come to see the inverse relationship between multiplication and division. As an assessment, individuals build their own array and write corresponding equations.
The relationship between multiplication and division is explained with a touch of humor in the third of five videos on understanding properties of operations. Scaffolding begins the lesson with a review of the relationship between addition and subtraction and an explanation of how this is different for dividing and multiplying. A thorough and well-illustrated discussion follows as the inverse relationship between these two operations is explained.
Pupils, after identifying and examining the relationship of temperature and air masses in association with smog and pollution, create a temperature inversion in a long aquarium jar. They experience what happens when smog builds up and no mixing of air masses occurs.
Eleventh graders investigate the inverse of a function. In this Algebra II instructional activity, 11th graders graph a function and its inverse and determine if the inverse is in fact a function.
This activity presents a real-world problem that gives learners practice in analyzing data, plotting the data on a graph, and using the graph to draw conclusions. The basic task is to determine how long it will take varying numbers of people to complete a leaf-raking job, given the time it takes one person to do the job. The task is extended to include questions that require interpreting the graph within the context of the problem. Plotting the data generates the graph of a hyperbola and introduces a discussion about inverse relationships. A second part of the activity asks learners to apply the same techniques used in the leaf-raking activity to a similar one about shoveling snow.
Learners are given a logarithmic function and its inverse exponential function. The task, which is to graph both compositions of the two functions, uses the inverse nature of exponents and logarithms to generalize about the properties of any two inverse functions. This activity is the second in a series of two. Note that the resource itself references only Common Core standard F-BF.4. This review, however, includes Common Core standard F-BF.5 because the task is very dependent on understanding the inverse relationship between exponents and logarithms.
Students investigate pressure and temperature relationship by conducting an experiment. In this chemistry instructional activity, students collect data using Vernier computer interface. They plot and analyze the resulting graphs.
Ninth graders access a database and open a spreadsheet. In this oxygen and water temperature lesson plan students save the database, sort it and generate scatter plot graphs.
Sal illustrates the all-important relationships between pKa and pKb in this chemistry video. This relationship is what determines whether an acid is considered to be "weak," or "strong." The mathematics behind figuring out these relations are presented in a clear fashion.
Here is a great set of worksheets that can be used as an entire lesson! Kids build a data table for an inverse relationship and construct a graph illustrating the data. Then they determine the domain and range of the data and write a function rule that fits the data. There are 5 handouts total, which include learning goals, problems to solve, a graph, and follow-up questions.
This exit ticket contains four items that provide learners an opportunity to demonstrate their knowledge of the inverse relationship between exponents and logarithms. Items include converting from one form to the other and solving a logarithmic equation. The single sheet contains three copies of the same ticket.
Second graders explore fact families and inverse relationships between addition and subtraction. They use flashcards to model the inverse relationships. Students complete the equations for each fact family.
Explore the concept of "how many times" where the word "times" is defined. Learners will determine the product and quotient in a word problem. Then use manipulatives to solve the problem. Finally, they will write in their math journals to explain their understanding of the process. There are not a lot of directions or steps to this activity, but the idea could be easily adapted by adding more sample problems.
Hopefully you have a sensor interface for your physics class to use with graphing calculators when collecting data with a light sensor. If so, read on. Use this resource for learners to predict and then test whether or not the intensity of light is directly related to the distance from the point light source. After the investigation, they associate findings to the forces of gravity and electricity. This is an outstanding activity for introducing the inverse square law.
Learners explore the characteristics of logarithmic functions and their relationship to exponential functions. Using the subscriber website Explorelearning.com, pupils observe changes in the input variable and its effect on the graph of the functions, examine reflections over the line y = x, and examine the restrictions associated with each function. Explore the compound interest equation as a real world application.
Students study operations with real numbers using mental computation or paper-and-pencil calculations. They judge the reasonableness of numerical computations and their results. They set up and solve proportions for direct and inverse variation of simple quantities.
High schoolers solve problems identifying the functions and inverses. For this algebra lesson, students identify a one-to-one function, and perform the horizontal line test. They analyze data and graph their results on a graph.