2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 2
6 days
Module 12: Sequences and Series
Learning Goal
Students will learn about arithmetic and
geometric sequences.
Essential Questions
1.
2.
3.
4.
How do sequences and series help to solve real-world
problems?
What are algebraic ways to define an arithmetic sequence?
How can you define a geometric sequence algebraically?
How do you find the sum of a finite geometric series?
Approximate Time:
Unit Overview
This unit focuses on using exponential and logarithmic functions,
arithmetic and geometric sequences, exponential growth and
decay, and the base 𝑒.
Vertical Progression
MAFS.912.A-CED.1.2, MAFS.912.A-SSE.1.2, MAFS.912.F-BF.1.1a, MAFS.912.F-IF.3.7: In previous curriculum, students understand inverses of functions, square root functions, and
radical expressions and equations. In future curriculum, students will study the unit circle, radian measure, and graphing and transforming trigonometric functions.
Module Focus Standards
Module Topics
Essential Vocabulary
Algebra 2 Item Specs (Reference sheet located at end)
High School Flip Book
MAFS.912.A-CED.1.2: (DOK 2) Create equations in two or more variables to represent
relationships between quantities; graph equations on coordinate axes with labels and
scales. (conceptual, procedural, application)
 Identify the quantities in a mathematical problem or real-world situation that
should be represented by distinct variables and describe what quantities the
variables represent.
 Graph one or more created equations on coordinate axes with appropriate
labels and scales.
 Justify which quantities in a mathematical problem or real-world situation are
dependent and independent of one another and which operations represent
those relationships.
 Determine appropriate units for the labels and scale of a graph depicting the
relationship between equations created in two or more variables.
Arithmetic Sequences (F-BF.1.2, A-CED.1.2, FIF.1.3, F-BF.1.1a, F-LE.1.2)
Core Resource:
 Lesson 12.1 (HMH Book)
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MAFS.912.A-SSE.1.2: (DOK 2) Use the structure of an expression to identify ways to
rewrite it. For example, see 𝑥 4 − 𝑦 4 as (𝑥 2 )2 − (𝑦 2 )2 , thus recognizing it as a
difference of squares that can be factored as (𝑥 2 − 𝑦 2 )(𝑥 2 + 𝑦 2 ). (conceptual)
 Identify ways to rewrite expressions, such as difference of squares, factoring out a
common monomial, and regrouping.
 Identify various structures of expressions.
 Use the structure of an expression to identify ways to rewrite it.
 Classify expressions by structure and develop strategies to assist in classification.
Additional Resource:
 Algebra 1 Module 3 Lesson 1 – Engage NY
 Algebra 1 Module 3 Lesson 2 – Engage NY
 Algebra 1 Unit 2 - Georgia
Formative Assessments:
 Lesson Performance Task (HMH 596)
Geometric Sequences (F-BF.1.2, F-IF.1.3, FIF.3.7e, F-BF.1.1a, F-LE.1.2)
Core Resource:
 Lesson 12.2 (HMH Book)
Additional Resource:
 Algebra 1 Module 3 Lesson 3 – Engage NY
 Module 3 Lesson 25 – Engage NY
 Algebra 1 Unit 2 - Georgia
Formative Assessments:
 Lesson Performance Task (HMH pg. 612)
arithmetic sequence
explicit rule
finite geometric series
geometric sequence
recursive rule
sequence
series
Higher Order Question Stems
 What properties could we use to find a
solution?
 How do the important quantities in your
problem relate to each other?
Writing Connections
 Compare and contrast two strategies
used to solve the problem.
 Write to explain your interpretation of
the results of a mathematical situation.
Link to Webb’s DOK Guide
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Algebra 2
Module 12: Sequences and Series
MAFS.912.A-SSE.2.4: (DOK 3) Derive the formula for the sum of a finite geometric series
(when the common ratio is not 1), and use the formula to solve problems. For example,
calculate mortgage payments. (conceptual, procedural, application)
 Find the first term in a geometric sequence given at least two other terms.
 Define a geometric series as a series with a constant ratio between successive terms.
 Use the formula S + a (1-rn)/(1-r) to solve problems.
 Derive a formula [i.e. equivalent to the formula S + a (1-rn)/(1-r) ] for the sum of a
finite geometric series (when the common ratio is not 1).
MAFS.912.F-BF.1.1a: (DOK 3) Write a function that describes a relationship between
two quantities. (a) Determine an explicit expression, a recursive process, or steps for
calculation from a context. (conceptual, application)
 Define explicit function and recursive process.
 Write a function that describes a relationship between two quantities by
determining an explicit expression, a recursive process, or steps for calculation from
a context.
MAFS.912.F-BF.1.2: (DOK 2) Write arithmetic and geometric sequences both recursively
and with an explicit formula, use them to model situations, and translate between the
two forms. (conceptual, procedural, application)
 Identify arithmetic and geometric patterns in given sequences.
 Generate arithmetic and geometric sequences from recursive and explicit formulas.
 Given an arithmetic or geometric sequence in recursive form, translate into the
explicit formula.
 Given an arithmetic or geometric sequence as an explicit formula, translate into the
recursive form.
 Use given and constructed arithmetic and geometric sequences, expressed both
recursively and with explicit formulas, to model real-life situations.
 Determine the recursive rule given arithmetic and geometric sequences.
 Determine the explicit formula given arithmetic and geometric sequences.
 Justify the translation between the recursive form and explicit formula for arithmetic
and geometric sequences.
MAFS.912.F-IF.1.3: (DOK 2) Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers. For example, the Fibonacci
sequence is defined recursively by 𝑓(0) = 𝑓(1) = 1, 𝑓(𝑛 + 1) = 𝑓(𝑛) + 𝑓(𝑛 − 1) for
𝑛 ≥ 1. (conceptual)
Geometric Series (A-SSE.2.4, A-SSE.1.2)
Core Resource:
 Lesson 12.3 (HMH Book)
Additional Resource:
 Module 3 Topic E Lesson 29-33 – Engage NY
Formative Assessments:
 Lesson Performance Task (HMH pg. 628)
Approximate Time:
6 days
2016-2017 Curriculum Blueprint
Grade: 9-12
Module 12: Sequences and Series
 Recognize that sequences are functions, sometimes defined recursively, whose
domain is a subset of the integers.
MAFS.912.F-IF.3.7e: (DOK 2) Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using technology for more
complicated cases. (e) Graph exponential and logarithmic functions, showing intercepts
and end behavior, and trigonometric functions, showing period, midline, and
amplitude, and using phase shift. (conceptual, procedural)
 Graph exponential functions, by hand in simple cases or using technology for more
complicated cases, and show intercepts and end behavior.
 Determine the differences between simple and complicated linear and exponential
functions and know when the use of technology is appropriate.
 Compare and contrast the domain and range of exponential, logarithmic, and
trigonometric functions with linear, quadratic, absolute value, step- and piecewisedefined functions.
 Select the appropriate type of function, taking into consideration the key features,
domain, and range, to model a real-world situation.
MAFS.912.F-LE.1.2: (DOK 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). (conceptual, procedural,
application)
 Recognize that arithmetic sequences can be expressed as linear functions.
 Recognize that geometric sequences can be expressed as exponential functions.
 Construct linear functions, including arithmetic sequences, given a graph, a
description of a relationship, or two input-output pairs (include reading these from a
table).
 Construct exponential functions, including geometric sequences, given a graph, a
description of a relationship, or two input-output pairs (include reading these from a
table).
 Determine when a graph, a description of a relationship, or two input-output pairs
(include reading these from a table) represents a linear or exponential function in
order to solve problems.
Mathematical Practice Standards
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.2.1: Reason abstractly and quantitatively.
Course: Algebra 2
Approximate Time:
6 days
2016-2017 Curriculum Blueprint
Grade: 9-12
Module 12: Sequences and Series
MAFS.K12.MP.7.1: Look for and make use of structure.
Course: Algebra 2
Approximate Time:
6 days