Patterns, Functions, and Algebra
Focus: Variable Equations and Properties
The student will identify and extend geometric and arithmetic sequences. 


Essential Knowledge and Skills 
 Investigate and apply strategies to recognize and describe the change between terms in arithmetic patterns.
 Investigate and apply strategies to recognize and describe geometric patterns.
 Describe verbally and in writing the relationships between consecutive terms in an arithmetic or geometric sequence.
 Extend and apply arithmetic and geometric sequences to similar situations.
 Extend arithmetic and geometric sequences in a table by using a given rule or mathematical relationship.
 Compare and contrast arithmetic and geometric sequences.
 Identify the common difference for a given arithmetic sequence.
 Identify the common ratio for a given geometric sequence.

Essential Understandings 
 What is the difference between an arithmetic and a geometric sequence? While both are numerical patterns, arithmetic sequences are additive and geometric sequences are multiplicative.


Vertical Articulation 
 SOL 4.15  recognize/create/extend
numerical/geometric patterns
 SOL 5.17  describe/express the
relationship in a number pattern
 SOL
7.2  describe/represent
arithmetic/geometric sequences
using variable expressions

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: Growing Patterns and Sequences (PDF)  Identifying and extending arithmetic and geometric sequences (Word)
 Notes: Arithmetic and Geometric Sequences (flipchart)  13 slides with notes and interactive practice
 Notes: Arithmetic and Geometric Sequences #2 (flipchart)  7 slides with notes and a few practice problems
 Notes: Patterns (ppt)  notes, examples, and SOL practice questions
 Guided Notes: Sequences (doc)  fill in the blank notes
 Activity: Pattern Match (doc)  small group activity to find different patterns using given numbers
 Activity: Exploring Patterns (zip)  flipchart and student worksheet to explore different questions involving different patterns (14 questions)
 ActivEngage: Patterns (flipchart)  11 questions using ActivEngage
 Game: Arithmetic and Geometric Sequences (flipchart)  21 question board game
 VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)

Real World Lessons 
 Incredible Shrinking Dollar  What will the dollar bill look like after getting reduced that many times?
 Mathalicious: Family Tree  Can we use exponential growth to prove that everyone on the planet is related?

Practice 
 Worksheet: Patterns  Arithmetic and Geometric (doc)  16 practice problems
 Worksheet: Sequences (doc)  14 practice problems including filling in a table

SOL Mini Quiz 
 SOL 6.17 Mini Quiz: Sequences (pdf)

Skills 

Videos 
 YouTube: Arithmetic vs. Geometric Sequences
 PH Finding terms of an arithmetic sequence
 PH Finding terms of a 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 
 IXL: Identify Arithmetic and Geometric Sequences
 WyzAnt: Algebraic and Geometric Patterns
 Sadlier: Fibonacci Sequence
 BrainGenie: Finding info about sequences
 BrainGenie: Calculating terms in arithmetic 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 
