Course 1 Online!
Henrico County Public Schools, Virginia
Number and Number Sense

Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
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
  1. SOL 4.15 - recognize/create/extend numerical/geometric patterns
  2. SOL 5.17 - describe/express the relationship in a number pattern
  3. SOL 7.2 - describe/represent arithmetic/geometric sequences using variable expressions
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Growing Patterns and Sequences (PDF) - Identifying and extending arithmetic and geometric sequences (Word)
  2. Notes: Arithmetic and Geometric Sequences (flipchart) - 13 slides with notes and interactive practice
  3. Notes: Arithmetic and Geometric Sequences #2 (flipchart) - 7 slides with notes and a few practice problems
  4. Notes: Patterns (ppt) - notes, examples, and SOL practice questions
  5. Guided Notes: Sequences (doc) - fill in the blank notes
  6. Activity: Pattern Match (doc) - small group activity to find different patterns using given numbers
  7. Activity: Exploring Patterns (zip) - flipchart and student worksheet to explore different questions involving different patterns (14 questions)
  8. ActivEngage: Patterns (flipchart) - 11 questions using ActivEngage
  9. Game: Arithmetic and Geometric Sequences (flipchart) - 21 question board game
  10. VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)
Real World Lessons
  1. Incredible Shrinking Dollar - What will the dollar bill look like after getting reduced that many times?
  2. Mathalicious: Family Tree - Can we use exponential growth to prove that everyone on the planet is related?
Practice
  1. Worksheet: Patterns - Arithmetic and Geometric (doc) - 16 practice problems
  2. Worksheet: Sequences (doc) - 14 practice problems including filling in a table
SOL Mini Quiz
  1. SOL 6.17 Mini Quiz: Sequences (pdf)
Skills
Videos
  1. YouTube: Arithmetic vs. Geometric Sequences
  2. PH Finding terms of an arithmetic sequence
  3. PH Finding terms of a geometric sequence
Explore Learning
  1. 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.
  2. 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.
  3. 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
  1. IXL: Identify Arithmetic and Geometric Sequences
  2. WyzAnt: Algebraic and Geometric Patterns
  3. Sadlier: Fibonacci Sequence
  4. BrainGenie: Finding info about sequences
  5. BrainGenie: Calculating terms in arithmetic sequences
VDOE Interventions
  1. 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
F-BF.1a
F-BF.1b