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Algebra I Module 3, Topic A: Linear and Exponential Sequences

  Classroom Resource Information  

Title:

 Algebra I Module 3, Topic A: Linear and Exponential Sequences

URL:

 https://www.engageny.org/resource/algebra-i-module-3-topic-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 3, Topic A, students explore arithmetic and geometric sequences as an introduction to the formal notation of functions (F-IF.A.1, F-IF.A.2). They interpret arithmetic sequences as linear functions with integer domains and geometric sequences as exponential functions with integer domains (F-IF.A.3, F-BF.A.1a). Students compare and contrast the rates of change of linear and exponential functions, looking for structure in each and distinguishing between additive and multiplicative change (F-IF.B.6, F-LE.A.1, F-LE.A.2, F-LE.A.3).

Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Algebra I
26 ) Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [F-IF2]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.F.HS.26- Substitute x-values into one-step linear equations in two variables (y = x + p or y = px) and solve for the y-values. (this could include the original information listed above and have students represent in data table)
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
15. Define a function as a mapping from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range.

a. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Note: If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.

b. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Limit to linear, quadratic, exponential, and absolute value functions.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given input/output relations between two variables in graphical form, verbal description, set of ordered pairs, or algebraic model, distinguish between those that are functions and non-functions.


Using functional notation,
  • Evaluate functions for inputs.
  • Interpret statements in terms of context.


Given a contextual relationship that may be represented as a function,
  • Determine that exactly one element of the range (output) is assigned to each element of the domain (input) by the function.
  • Relate the domain to its graph and to the quantitative relationship it describes.
Teacher Vocabulary:
  • Domain
  • Range
  • Function
  • Relation
  • Function notation
  • Set notation
Knowledge:
Students know:
  • Distinguishing characteristics of functions.
  • Conventions of function notation.
  • In graphing functions the ordered pairs are (x,f(x)) and the graph is y = f(x).
Skills:
Students are able to:
  • Evaluate functions for inputs in their domains.
  • Interpret statements that use function notation in terms of context.
  • Accurately graph functions when given function notation.
  • Accurately determine domain and range values from function notation.
Understanding:
Students understand that:
  • A function is a mapping of the domain to the rangeFunction notation is useful in contextual situations to see the relationship between two variables when the unique output for each input relation is satisfied.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.15.1: Define domain, range, relation, function, table of values, input, and output.
ALGI.15.2: Understand the graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
ALGI.15.3: Understand that a function is a rule that assigns to each input exactly one output.
ALGI.15.4: Identify the equation of a function, given its graph.
ALGI.15.5: Find the range of a function given its domain.
ALGI.15.6: Recognize that f(x) and y are the same.
ALGI.15.7: Recall how to complete input/output tables.
ALGI.15.8: Recall how to read/interpret information from a table.
ALGI.15.9: Define function notation.
ALGI.15.10: Translate a simple word problem into function notation.
ALGI.15.11: Evaluate function when given x-value.

Prior Knowledge Skills:
  • Analyze the graph to determine the rate of change.
  • Generate the slope of a line using given ordered pairs.
  • Define linear functions, nonlinear functions, slope, and y-intercept
  • Identify ordered pairs.
  • Plot points on a coordinate plane., then connect points for the vertices to sketch a polygon.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.12.15 Use the vertical line test to determine if a given relation is a function.
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
22. Define sequences as functions, including recursive definitions, whose domain is a subset of the integers.

a. Write explicit and recursive formulas for arithmetic and geometric sequences and connect them to linear and exponential functions.

Example: A sequence with constant growth will be a linear function, while a sequence with proportional growth will be an exponential function.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given a sequence, generate and justify a function that relates the number of the term to the value of the term in the sequence.
Teacher Vocabulary:
  • Sequence
  • Recursively
  • Domain
  • Arithmetic sequence
  • Geometric sequence
Knowledge:
Students know:
  • Distinguishing characteristics of a function.
  • Distinguishing characteristics of function notation.
  • Distinguishing characteristics of generating sequences.
Skills:
Students are able to:
  • Relate the number of the term to the value of the term in a sequence and express the relation in functional notation.
Understanding:
Students understand that:
  • Each term in the domain of a sequence defined as a function is unique and consecutive.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.22.1: Define proportions and proportional relationships.
ALGI.22.2: Write equations to represent a proportional relationship.
ALGI.22.3: Discuss the use of variables in proportional relationships.
ALGI.22.4: Define sequences and recursively-defined sequences.
ALGI.22.5: Recognize that sequences are functions whose domain is the set of all positive integers and zero.

Prior Knowledge Skills:
  • Recall that a proportion is the comparison of two ratios.
  • Identify the appropriate equation from a proportion.
  • Solve an equation to find an unknown quantity.
  • Identify patterns in number sequences.
Alabama Alternate Achievement Standards
AAS Standard:
M.A.AAS.12.22 Given a sequence of numbers, identify the rule that will give you the next number in the sequence. [Limit to expressions with simple arithmetic (adding or subtracting) or geometric (multiplying or dividing) operations.]
Tags: arithmetic, domain, evaluate, function, geometric, inputs, integer, range, sequences
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Comments

There are seven lessons on this topic.

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Author: Hannah Bradley
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