# ALEX Learning Activity

## The Spread of a Virus: Does Social Distancing Matter?

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: 2620 Title: The Spread of a Virus: Does Social Distancing Matter? Digital Tool/Resource: Virus Outbreak Behavior Task Sheet Web Address – URL: https://drive.google.com/file/d/1C6RKqLukzvOyl3PT_WgBOSCLmevUTh-H/view?usp=sharing Overview: This exploration provides students the opportunity to actively engage in creating their own knowledge about exponential models. They are given the support to conduct their own simulation and record the information, make predictions using the data that they have collected, and compare their predictions to the technology generated models. Additionally, the technology element is necessary to make sense of the data in a more efficient manner as compared to hand calculations of procedures. The emphasis is to produce a deep conceptual understanding of rates of change of exponential functions in multiple representations and use that information to build up procedural fluency.This activity results from the ALEX Resource Development Summit.
Associated Standards and Objectives
Content Standard(s):
 Mathematics MA2015 (2016) Grade: 9-12 Algebra I 45 ) Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [S-ID6] a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [S-ID6a] b. Informally assess the fit of a function by plotting and analyzing residuals. [S-ID6b] c. Fit a linear function for a scatter plot that suggests a linear association. [S-ID6c] Alabama Alternate Achievement Standards AAS Standard: M.AAS.SP.HS.45- Given a scatter plot with data with a line of best fit that can be represented by a linear function, describe what is happening to the y-values in reference to the x-values (x- and y- values limited positive numbers). 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 25. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Unpacked Content Evidence Of Student Attainment:Students: Given a contextual situation shown by a graph, a description of a relationship, or two input-output pairs, Create a linear or exponential function that models the situation. Create arithmetic and geometric sequences from the given situation. Justify the equality of the sequences and the functions mathematically and in terms of the original sequence.Teacher Vocabulary:Arithmetic and geometric sequences Arithmetic sequence Geometric sequence Exponential functionKnowledge:Students know: That linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Properties of arithmetic and geometric sequences.Skills:Students are able to: Accurately recognize relationships within data and use that relationship to create a linear or exponential function to model the data of a contextual situation.Understanding:Students understand that: Linear and exponential functions may be used to model data that is presented as a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Linear functions have a constant value added per unit interval, and exponential functions have a constant value multiplied per unit interval.Diverse Learning Needs: Essential Skills:Learning Objectives: ALGI.25.1: Define linear function and exponential function. ALGI.25.2: Define arithmetic sequence, geometric sequence, and input-output pairs. ALGI.25.3: Define sequences and recursively-defined sequences. ALGI.25.4: Recognize that sequences are functions whose domain is the set of all positive integers and zero. ALGI.25.5: Given a chart, write an equation of a line. ALGI.25.6: Given a graph, write an equation of a line. ALGI.25.7: Given two ordered pairs, write an equation of a line. Prior Knowledge Skills:Given a function, create a rule. Recognize numeric patterns. Recall how to complete input/output tables. Demonstrate how to plot points on a Cartesian plane using ordered pairs. Define function, ordered pairs, input, output. Graph a linear equation given the slope-intercept form of an equation. Graph a function given the slope-intercept form of an equation. Identify the slope-intercept form (y=mx+b) of an equation where m is the slope and y is the y-intercept. Generate the slope of a line using given ordered pairs. Recall the rules for multiplying integers. Define quotient, divisor, and integer. Solve addition and subtraction of multi-digit whole numbers. Solve addition and subtraction of multi-digit decimal numbers (emphasis on alignment). Recall basic multiplication and division facts. Solve multiplication problems involving multi-digit whole numbers and decimal numbers. Solve division problems involving multi-digit whole numbers and decimal numbers. 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 simulate the spread of disease and represent the spread using multiple representations (table, graph, algebraic model).

Students will interpret the rate of change for their models and compare them to their predictions.

Students will develop an understanding of the virulent spread of disease in terms of their model's rate of change.

Strategies, Preparations and Variations