Number and Number Sense
Focus: Proportional Reasoning
The student will describe and represent arithmetic and geometric sequences, using variable expressions. 


Essential Knowledge and Skills 
 Analyze arithmetic and geometric sequences to discover a variety of patterns.
 Identify the common difference in an arithmetic sequence.
 Identify the common ratio in a geometric sequence.
 Given an arithmetic or geometric sequence, write a variable expression to describe the relationship between two consecutive terms in the sequence.

Essential Understandings 
 When are variable expressions used? Variable expressions can express the relationship between two consecutive terms in a sequence.


Vertical Articulation 
 SOL 5.17  describe/express the
relationship in a number pattern
 SOL 6.17  identify/extend geometric/arithmetic
sequences

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Arithmetic and Geometric Sequences (PDF)  Describing arithmetic and geometric sequences (Word)
 Notes: Sequences (ppt)
 Notes: Sequences (flipchart)
 Notes: Sequences Review (flipchart)
 Activity: Pattern Sort (doc)
 Activity: Exploring Patterns and Sequences (flipchart)
 VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)

Real World Lessons 

Practice 
 Worksheet: Sequence Match (pdf)
 Quiz: Sequences (doc)

SOL Mini Quiz 
 SOL 7.2 Mini Quiz: Sequences (pdf)  (doc)

Skills 

Videos 
 PH Finding terms of an arithmetic sequence
 PH Finding terms of a geometric sequence
 YouTube: Arithmetic vs Geometric Sequences
 YouTube: Writing a Formula from a Sequence
 Virtual Nerd: Arithmetic or Geometric Sequence?

Explore
Learning 
 Arithmetic Sequences: Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response.
 Arithmetic and Geometric Sequences: Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response.
 Geometric Sequences: Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas.

Websites 
 Math Guide: Arithmetic Sequences
 Math Guide: Geometric Sequences
 Algebra Lab: Arithmetic and Geometric Sequences
 IXL Math: Identify Arithmetic and Geometric Sequences

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra  The lessons focus on algebraic reasoning. Students explore the relationships found in
number patterns through arithmetic and geometric sequences using variables expressions. (pdf)

Common Core
Standards 
5.OA.3 
FBF.1a 
FBF.1b 
F.BF.2 
