Course 2 Online!
Henrico County Public Schools, Virginia
7.12 - Functions & Relations
Number, Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

SOL Review Materials
Patterns, Functions, and Algebra
Focus: Linear Equations

The student will represent relationships with tables, graphs, rules, and words. 
Essential Knowledge and Skills 
  • Describe and represent relations and functions, using tables, graphs, rules, and words. Given one representation, students will be able to represent the relation in another form.
Essential Understandings
  • What are the different ways to represent the relationship between two sets of numbers? Rules that relate elements in two sets can be represented by word sentences, equations, tables of values, graphs or illustrated pictorially.
Vertical Articulation
  • SOL 8.14 - make connections between any two representations (tables, graphs, words, rules)
  • SOL A.7abcdef - investigate/analyze functions (linear/quadratic) families and characteristics (algebraically/graphically) - a) determine relation is function; b) domain/range; c) zeros; d) x- and yintercepts; e) find values of function for elements in domain; f) make connect between/among multiple representation of functions (concrete/verbal/numeric/graphic/algebraic)
Instructional Materials
  1. VDOE Enhanced Scope and Sequence Lesson: Relationships Round Robin (PDF) - Representing relationships with tables, graphs, rules, and words (Word)
  2. Notes: Coordinate Plane (ppt)
  3. Notes: Relations (flipchart)
  4. Activity: Relations Foldable (doc)
  5. Notes: Input/Output Tables (flipchart)
  6. Notes: Graphing Equations (flipchart)
  7. Notes: Function Review (flipchart)
  8. Guided Practice: Function Table Warm-up (flipchart)
  9. Activity: Paper Tearing (pdf)
  10. Project: Graphing a Line (doc)
  11. Activity: Matching Functions, Graphs, Tables and Words (doc)
  12. VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)
Real World Lessons
  1. Activity: Penny Jar Investigation (flipchart)
  2. Mathalicious: Big Foot Conspiracy - Do people with small feet pay too much for shoes, and what would happen if Nike charged by weight?
  3. Mathalicious: Fat Burner - What's the best way to exercise for fat burning?
  1. Worksheet: Graphing Equations (doc)
  2. Worksheet: Graphing Linear Functions (pdf)
  3. Worksheet: Solve and Graph Linear Functions (pdf)
  4. Worksheet: Function Word Problems (doc)
  5. Worksheet: Solving Linear Functions #1 (pdf) | Functions #2 (pdf) | Functions #3 (pdf) | Functions #4 (pdf)
  6. Worksheet: Graphing Equations (doc) | Graphing Equations #2 (doc)
  7. Activity: Representing Relationships (flipchart)
SOL Mini Quiz
  1. SOL 7.12 Mini Quiz: Relations and Functions (pdf) | (doc)
  1. Mathematics Assessment Project
    • A08:Buses - Apprentice - In this task, you will work with a distance-time graph describing a bus journey.
    • A09:Sugar Prices - Apprentice - In this task, you must use a graph showing the prices and weights of bags of sugar to find the bag offering the best value for money.
    • A02:Patchwork - Apprentice - Kate makes patchwork cushions using right triangles made from squares of material. In this task, you must investigate number patterns and to find a rule, or a formula, that will help Kate figure out the number of squares she needs for cushions of different sizes.
  2. Representations: Crawling Crayfish (doc)
  1. PH Determining a Reasonable Domain and Range for a Situation
  2. PH Modeling a Function Using Three Views
  3. PH Identifying Functions using a Mapping
  4. PH Identifying Functions using a Vertical Line Test
  5. PH Making a Table from a Function Rule
  6. PH Finding the Range of a Function Given the Domain
  7. PH Graphing a function using a table
Explore Learning
  1. ntroduction to Functions: Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation.
  1. Rent-a-Car Activity
  2. Game: General Coordinates - investigate the coordinate system through identifying or requesting coordinates at
  3. Game: Maze- Investigate the coordinate system by directing a robot through a mine field at
  4. Interactive: Function Machine - explore the concept of a function machine by inputting values and observing the output in a table at
  5. Interactive: Function Machine - investigate simple linear functions by trying to guess the algebraic form from inputs and outputs at
  6. Interactive: Function Machine - investigate simple linear functions by trying to guess the algebraic form from inputs and outputs at
  7. Interactive: Vertical Line Test - discovery activity that determines if a graph is a function at
  8. Interactive: Graphs and Functions- view images of graphs at Shodor.organd determine if they represent a function
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. Additionally, students learn to solve equations and inequalities, first by using manipulatives and then by working with symbols. They use modeling to collect data, and they learn to record data so that they can see the
    relationship that exists among tables, graphs, words, and equations. (pdf)
Common Core Standards