# ALEX Learning Activity

## The Spread of a Virus: Which Virus Is More Virulent?

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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This learning activity provided by:
 Author: David Dai System: Mobile County School: Alma Bryant High School
General Activity Information
 Activity ID: 2621 Title: The Spread of a Virus: Which Virus Is More Virulent? Digital Tool/Resource: Which Virus is More Virulent? (Exit Slip) Web Address – URL: https://drive.google.com/file/d/13K1VNSxEPjAz26n_Dt0Qo9BVYWzCPsj4/view?usp=sharing Overview: This activity allows teachers to formatively assess students' understanding of multiplicative rates of change from different representations. The activity presents four different viruses of different spread rates, and students are to determine which virus is the most virulent and justify their responses.This activity results from the ALEX Resource Development Summit.
Associated Standards and Objectives
Content Standard(s):
 Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability 24. Distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions. a. Show that linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals. b. Define linear functions to represent situations in which one quantity changes at a constant rate per unit interval relative to another. c. Define exponential functions to represent situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Unpacked Content Evidence Of Student Attainment:Students: Given a linear or exponential function, Create a sequence from the functions and examine the results to demonstrate that linear functions grow by equal differences, and exponential functions grow by equal factors over equal intervals. Use slope-intercept form of a linear function and the general definition of exponential functions to justify through algebraic rearrangements that linear functions grow by equal differences, and exponential functions grow by equal factors over equal intervals. Given a contextual situation modeled by functions, determine if the change in the output per unit interval is a constant being added or multiplied to a previous output, and appropriately label the function as linear, exponential, or neither.Teacher Vocabulary:Linear functions Exponential functions Constant rate of change Constant percent rate of change Intervals Percentage of growth Percentage of decayKnowledge:Students know: Key components of linear and exponential functions. Properties of operations and equalitySkills:Students are able to: Accurately determine relationships of data from a contextual situation to determine if the situation is one in which one quantity changes at a constant rate per unit interval relative to another (linear). Accurately determine relationships of data from a contextual situation to determine if the situation is one in which one quantity grows or decays by a constant percent rate per unit interval relative to another (exponential).Understanding:Students understand that: Linear functions have a constant value added per unit interval, and exponential functions have a constant value multiplied per unit interval. Distinguishing key features of and categorizing functions facilitates mathematical modeling and aids in problem resolution.Diverse Learning Needs: Essential Skills:Learning Objectives: ALGI.24.1: Define linear function and exponential function. ALGI.24.2: Distinguish between graphs of a line and an exponential function. ALGI.24.3: Identify the graph of an exponential function. ALGI.24.4: Identify the graph of a line. ALGI.24.5: Plot points on a coordinate plane from a given table of values. a. ALGI.24.6: Divide each y-value in a table of values by its successive y-value to determine if the quotients are the same, to prove an exponential function. ALGI.24.7: Subtract each y-value in a table of values by its successive y-value to determine if the differences are the same, to prove a linear function. ALGI.24.8: Apply rules for adding, subtracting, multiplying, and dividing integers. b. ALGI.24.9: Define constant rate of change as slope. ALGI.24.10: Subtract each y-value in a table of values by its successive y-value to determine if the differences are the same, to prove a linear function. ALGI.24.11: Recognize the calculated difference is the constant rate of change. ALGI.24.12: Apply rules for adding, subtracting, multiplying, and dividing integers. c. ALGI.24.13: Define exponential growth and decay. ALGI.24.14: Divide each y-value in a table of values by its successive y-value to determine if the quotients are the same, to prove an exponential function. ALGI.24.15: Apply the rules of multiplication and division of integers. Prior Knowledge Skills:Recognize ordered pairs. Identify ordered pairs. Recognize linear equations. Recall how to solve problems using the distributive property. Define linear and nonlinear functions, slope, and y-intercept. Analyze the graph to determine the rate of change. Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.12.24 Given a simple linear function on a graph, select the model that represents an increase by equal amounts over equal intervals. Mathematics MA2019 (2019) Grade: 9-12 Algebra I with Probability 27. Interpret the parameters of functions in terms of a context. Extend from linear functions, written in the form mx + b, to exponential functions, written in the form abx. Example: If the function V(t) = 19885(0.75)t describes the value of a car after it has been owned for t years, 1985 represents the purchase price of the car when t = 0, and 0.75 represents the annual rate at which its value decreases. Unpacked Content Evidence Of Student Attainment:Students: Given a contextual situation that may be modeled by a linear or exponential function, Create a function that models the situation. Define and justify the parameters (all constants used to define the function) in terms of the original context. Teacher Vocabulary:ParametersKnowledge:Students know: Key components of linear and exponential functions.Skills:Students are able to: Communicate the meaning of defining values (parameters and variables) in functions used to model contextual situations in terms of the original context. Understanding:Students understand that: Sense making in mathematics requires that meaning is attached to every value in a mathematical expression. Diverse Learning Needs: Essential Skills:Learning Objectives: ALGI.27.1: Recall the formula of an exponential function. ALGI.27.2: Recall the slope-intercept form of a linear function. ALGI.27.3: Define b as growth or decay factor in the context of an exponential problem. ALGI.27.4: Define k as the initial amount in the context of an exponential problem. ALGI.27.5: Define m as the rate of change in the context of a linear problem. ALGI.27.6: Define b as the initial amount in the context of a linear problem. Prior Knowledge Skills:Solve problems with exponents. Discuss strategies for solving real-world and mathematical problems. Recognize ordered pairs. Identify parts of the Cartesian plane. Recall how to plot points on a Cartesian plane. Distinguish the difference between linear and nonlinear functions. Define qualitative, increase, and decrease. Recall how to name points from a graph (ordered pairs). Recall how to find the rate of change (slope) in a linear equation. Recall how to complete an input/output function table. Analyze real-world situations to identify the rate of change and initial value from a table, graph, or description. Define function, rate of change, and initial value. Alabama Alternate Achievement Standards AAS Standard: M.A.AAS.12.24 Given a simple linear function on a graph, select the model that represents an increase by equal amounts over equal intervals.
Learning Objectives:

Students will interpret the rate of change for different viruses and compare them to see which virus is more virulent.

Strategies, Preparations and Variations
 Phase: After/Explain/Elaborate Activity: The activity linked above and provided here should be given to students to complete individually. As students are completing this after activity, the teacher should move around the classroom monitoring student responses. After students complete the activity, the teacher should collect student responses and assess the student responses to prepare for the next class period. Assessment Strategies: Teachers need to attend to how students made sense of the different virus spread representations to determine the rate of change in each representation. Teachers should offer comments on student strategies that provided the rate of change for each representation or suggestion for how students can move toward thinking about determining the rates of change for each representation. The correct response is the virus represented as a graph, but students should be able to justify their response by demonstrating that this virus has the greatest rate of change. Student answers and strategies may vary, and teachers should analyze responses according to students' demonstration of their understanding of comparing multiplicative rates of change. Advanced Preparation: Teachers should answer the after activity before class in as many strategies as possible to effectively assess student responses to the activity. The after activity is again linked here. Variation Tips (optional): Notes or Recommendations (optional): ALCOS 201924. Distinguish between situations that can be modeled with linear functions and those that can be modeled with exponential functions. a. Show that linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals. b. Define linear functions to represent situations in which one quantity changes at a constant rate per unit interval relative to another. c. Define exponential functions to represent situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.27. Interpret the parameters of functions in terms of a context. Extend from linear functions, written in the form mx + b, to exponential functions, written in the form ab^x. Example: If the function V(t) = 19885(0.75)^t describes the value of a car after it has been owned for t years, 19885 represents the purchase price of the car when t = 0, and 0.75 represents the annual rate at which its value decreases.
Keywords and Search Tags
 Keywords and Search Tags: Disease, Exponential Functions, Social Distancing, Virus