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Algebra I Support - Linear vs Exponential vs Quadratics

What
Algebra I Support - Linear vs Exponential vs Quadratics
When
3/23/2023

Unit 7 Comparing and Contrasting All Functions

Standards Addressed:

  • MGSE9-12.F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
  • MGSE9-12.F.LE.1a Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be shown by algebraic proof, with a table showing differences, or by calculating average rates of change over equal intervals).
  • MGSE9-12.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
  • MGSE9-12.F.LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
  • MGSE9-12.F.LE.2 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).
  • MGSE9-12.F.LE.5 Interpret the parameters in a linear (f(x) = mx + b) and exponential (f(x)=a•dx ) function in terms of context. (In the functions above, “m” and “b” are the parameters of the linear function, and “a” and “d” are the parameters of the exponential function.) In context, students should describe what these parameters mean in terms of change and starting value.
  • MGSE9‐12.F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. (Focus on vertical translations of graphs of linear and exponential functions. Relate the vertical translation of a linear function to its y‐intercept.)
  • MGSE9-12.F.IF.4 Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior;
  • MGSE9-12.F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
  • MGSE9-12.F.IF.7 Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.
  • MGSE9-12.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one function and an algebraic expression for another, say which has the larger maximum.
  • MGSE9-12.F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. MGSE9-12.F.IF.7 & 9 – Comparing Functions (graphs & rates of change)

Learning Targets:

  • ·        I can determine whether a function is linear, quadratic or exponential using data from a table.
  • ·        I can determine how a graph will be affected by changing parameters.
  • ·        I can determine function type by looking a graph of the function.
  • ·        I can determine when to use a linear function, when to use a quadratic function and when to use an exponential function.
  • ·        I can find the average rate of change for a function.
  • ·        I can determine maximum values on an interval.
  • ·        I can determine minimum values on an interval

Success Criteria

  • ·        I know that linear functions have a constant first difference
  • ·        I know that quadratic functions have a constant second difference
  • ·        I know that exponential functions have a common ratio
  • ·        I can identify a vertical shift on a function from the graph regardless of function type
  • ·        I can determine type of function from  graph of the function
  • ·        I can identify stretches and shrinks of quadratic functions
  • ·        I can write a linear equation for a given situation that shows constant rate of change
  • ·        I can write a quadratic equation to model motion of an object being thrown or dropped
  • ·        I can write an exponential equation to model percentage increase or percentage decrease of a quantity
  • ·        I can use an exponential equation to model change by a constant ratio
  • ·        I know that slope is the measure of rate of change for a linear function
  • ·        I know that average rate of change can be calculated for a quadratic or exponential function by using a linear approximation
  •   I can find average rate of change algebraically using rate of change formula
  • ·        I can find average rate of change graphically using rise over run
  • ·        I know that either the maximum or minimum value for a quadratic equation occurs at the vertex
  • ·        I know that an exponential function will eventually grow at a much greater rate than any other function
  • ·        I know end behavior for quadratic functions
  • ·        I know end behavior for both positive and negative slopes for linear functions
  • ·        I know end behavior for exponential growth and exponential decay
  • ·        I can determine intervals of increase and intervals of decrease for any function

Introduction:

  • Daily 10

Instructional Strategies:

  • Opening (I do) – Students will be given Unit 7 packet and will be placed in groups, these groups will work thought the packet all week.  unit 7 basically summarizes Unit 2 - 6 and compares all functions.  
  • Work Session (We do-You do): During the work sessions we will work in groups to determine the characteristics for each and also this will allow students to determine what they know and What the still need to learn.       
  • Closing (We check): At the end of each class we will go over one page in packet to review and will assign groups the next days based on learning targets and success criteria met each day.      

Differentiation Strategies: Scaffolding throughout lesson and applications will be provided for rigor. Students will work with pairs at some points throughout the assignment.

Formative/Summative Assessment(s) (We check): teacher will walk around room helping groups who seem to be struggling on their unit review.

Summarizer:

  • Review solutions to the test review

Assignment/Homework: On Google Classroom

Copy to Google Calendar  •  Download iCal Event