ALEX Classroom Resource

  

Algebra I Module 5, Topic A: Elements of Modeling

  Classroom Resource Information  

Title:

 Algebra I Module 5, Topic A: Elements of Modeling

URL:

 https://www.engageny.org/resource/algebra-i-module-5-topic-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

Module 5, Topic A focuses on the skills inherent in the modeling process: representing graphs, data sets, or verbal descriptions using explicit expressions (F-BF.A.1a) when presented in graphic form in Lesson 1, as data in Lesson 2, or as a verbal description of a contextual situation in Lesson 3. They recognize the function type associated with the problem (F-LE.A.1b, F-LE.A.1c) and match to or create 1- and 2-variable equations (A-CED.A.1, A-CED.2) to model a context presented graphically, as a data set, or as a description (F-LE.A.2). Function types include linear, quadratic, exponential, square root, cube root, absolute value, and other piecewise functions. Students interpret features of a graph in order to write an equation that can be used to model it and the function (F-IF.B.4, F-BF.A.1) and relate the domain to both representations (F-IF.B.5). This topic focuses on the skills needed to complete the modeling cycle and sometimes uses purely mathematical models, sometimes real-world contexts.

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Algebra I
5 ) Define appropriate quantities for the purpose of descriptive modeling. [N-Q2]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.Q.HS.5- Recognize units of weight (ounces, pounds, grams, kilograms), length (inch, foot, mile, centimeter, meter, kilometer), area (square inches in^2, square feet ft^2, square centimeters cm^2, square meters m^2) and capacity (cubic inches in^3, cubic feet ft^3, cubic centimeters cm^3, cubic meters m^3).
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
11. Create equations and inequalities in one variable and use them to solve problems in context, either exactly or approximately. Extend from contexts arising from linear functions to those involving quadratic, exponential, and absolute value functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given a contextual situation that may include linear, quadratic, exponential, or rational functional relationships in one variable.
  • Model the relationship with equations or inequalities and solve the problem presented in the contextual situation for the given variable.
Teacher Vocabulary:
  • Variable
  • Equation
  • Inequality
  • Solution Set
  • Identity
  • No solution for a given domain
  • Approximate solutions
Knowledge:
Students know:
  • When the situation presented in a contextual problem is most accurately modeled by a linear, quadratic, exponential, or rational functional relationship.
Skills:
Students are able to:
  • Write equations in one variable that accurately model contextual situations.
Understanding:
Students understand that:
  • Features of a contextual problem can be used to create a mathematical model for that problem.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.11.1: Solve the equation represented by the real-world situation.
ALGI.11.2: Set up an equation to represent the given situation, using correct mathematical operations and variables.
ALGI.11.3: Given a contextual situation, interpret and defend the solution in the context of the original problem.
ALGI.11.4: Define equation, expression, variable, equality and inequality.
ALGI.11.5: Create inequalities with one variable (Exponential, Quadratic, Linear).
ALGI.11.6: Create equalities with one variable (Exponential, Quadratic, Linear).
ALGI.11.7: Solve two-step equations and inequalities.
ALGI.11.8: Solve one-step equations and inequalities using the four basic operations.
ALGI.11.9: Compare and contrast equations and inequalities.
ALGI.11.10: Recognize inequality symbols including greater than, less than, greater than equal to and less than equal to.

Prior Knowledge Skills:
  • Test the found number or number set for accuracy by substitution.
  • Set up equations and inequalities to represent the given situation, using correct mathematical operations and variables.
  • Define equation, inequality, and variable.
  • Convert mathematical terms to mathematical symbols and numbers.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.11 Select an equation or inequality involving one operation (limit to addition or subtraction) with one variable that represents a real-world problem. Solve the equation.
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
12. Create equations in two or more variables to represent relationships between quantities in context; graph equations on coordinate axes with labels and scales and use them to make predictions. Limit to contexts arising from linear, quadratic, exponential, absolute value, and linear piecewise functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given a contextual situation expressing a relationship between quantities with two or more variables,
  • Model the relationship with equations and graph the relationship on coordinate axes with labels and scales.
  • Make predictions about the contextual situation using the graphs of the equations.
Teacher Vocabulary:
  • Piecewise functions
Knowledge:
Students know:
  • When a particular two variable equation accurately models the situation presented in a contextual problem.
Skills:
Students are able to:
  • Write equations in two variables that accurately model contextual situations.
  • Graph equations involving two variables on coordinate axes with appropriate scales and labels.
  • Make predictions about the context using the graph.
Understanding:
Students understand that:
  • There are relationships among features of a contextual problem, a created mathematical model for that problem, and a graph of that relationship.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.12.1: Solve the equations represented by real-world situations.
ALGI.12.2: Set up an equation to represent the given situation, using correct mathematical operations and variables.
ALGI.12.3: Given a contextual situation, interpret and defend the solution in the context of the original problem.
ALGI.12.4: Explain how to draw informal inferences from data distributions.
ALGI.12.5: Define ordered pair and coordinate plane.
ALGI.12.6: Create equations with two variables (exponential, quadratic and linear).
ALGI.12.7: Graph equations on coordinate axes with labels and scales (exponential, quadratic, and linear).
ALGI.12.8: Identify an ordered pair and plot it on the coordinate plane.

Prior Knowledge Skills:
  • Demonstrate how to plot points on a coordinate plane using ordered pairs from a table.
  • Plot independent (input) and dependent (output) values on a coordinate plane.
  • Draw and label a coordinate plane.
  • Define dependent variable, independent variable, ordered pairs, input, output, and coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.11.11 Select an equation or inequality involving one operation (limit to addition or subtraction) with one variable that represents a real-world problem. Solve the equation.
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
28. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries; and end behavior. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and linear piecewise functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given a function that models a relationship between two quantities, produce the graph and table of the function and show the key features (intercepts. intervals where the function is increasing, decreasing, positive, or negative. relative maximums and minimums. symmetries. end behavior. and periodicity) that are appropriate for the function.


Given key features from verbal description of a relationship,
  • Sketch a graph with the given key features.
  • Know periodicity.
Teacher Vocabulary:
  • Function
  • Periodicity
  • x-intercepts
  • y-intercepts
  • Intervals of Increasing
  • Intervals of decreasing
  • Function is positive
  • Function is negative
  • Relative Maximum
  • Relative Minimum
  • y-axis symmetry
  • Origin symmetry
  • End behavior
Knowledge:
Students know:
  • Key features of function graphs (i.e., intercepts. intervals where the function is increasing, decreasing, positive, or negative. relative maximums and minimums. symmetries. end behavior. and periodicity).
  • Methods of modeling relationships with a graph or table.
Skills:
Students are able to:
  • Accurately graph any relationship.
  • Interpret key features of a graph.
Understanding:
Students understand that:
  • The relationship between two variables determines the key features that need to be used when interpreting and producing the graph.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.28.1: Define intercepts, intervals, relative maxima, relative minima, symmetry, end behavior, and periodicity.
ALGI.28.2: For a function that models a relationship between two quantities, find the periodicity.
ALGI.28.3: For a function that models a relationship between two quantities, find the end behavior.
ALGI.28.4: For a function that models a relationship between two quantities, find the symmetry.
ALGI.28.5: For a function that models a relationship between two quantities, find the intervals where the function is increasing, decreasing, positive, or negative.
ALGI.28.6: For a function that models a relationship between two quantities, find the relative maxima and minima.
ALGI.28.7: For a function that models a relationship between two quantities, find the x and y intercepts.

Prior Knowledge Skills:
  • Identify parts of the Cartesian plane.
  • Graph a function given the slope-intercept form of an equation.
  • Demonstrate how to plot points on a coordinate plane using ordered pairs from table.
  • Recall how to plot ordered pairs on a coordinate plane.
  • Name the pairs of integers and/or rational numbers of a point on a coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.12.28 Given graphs that represent linear functions, identify key features (limit to y intercept, x-intercept, increasing, decreasing) and/or interpret different rates of change (e.g., Which is faster or slower?).
Tags: arithmetic sequence, description, descriptive modeling, equation, Exponential function, expression, function, geometric sequence, graph, input, linear function
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Author: Hannah Bradley
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