Course 3 Online!
Henrico County Public Schools, Virginia
8.14 - Relations and Functions
Number and Number Sense, Computation and Estimation

Measurement and Geometry

Probability, Statistics, Patterns, Functions, and Algebra

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


The student will make connections between any two representations (tables, graphs, words, and rules) of a given relationship. 
Essential Knowledge and Skills 
  • Graph in a coordinate plane ordered pairs that represent a relation.
  • Describe and represent relations and functions, using tables, graphs, words, and rules. Given one representation, students will be able to represent the relation in another form.
  • Relate and compare different representations for the same relation.
Essential Understandings
  • What is the relationship among tables, graphs, words, and rules in modeling a given situation? Any given relationship can be represented by all four.
Vertical Articulation
  1. SOL 7.12 - represent relationships with tables, graphs, rules, and words
  2. SOL A.7 - investigate/analyze functions (linear/quadratic) families and characteristics (algebraically/graphically) - a) determine relation is function; b) domain/range; c) zeros; d) x- and y-intercepts; 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: Matching Representations (PDF) - Making connections between representations (Word)
  2. Functions Unit Overview (doc) | Functions Unit Planner (doc)
  3. Notes: Functions (ppt)
  4. Guided Notes: Continuous and Discrete Functions (doc)
  5. Activity: Functions Sort (flipchart)
  6. Activity: Functions Sort #2 (doc)
  7. Notes: Linear Functions (ppt)
  8. Activity: Matching Functions, Graphs, and Tables (flipchart)
  9. Activity: Matching Functions, Graphs, and Tables (doc)
  10. Notes: Writing Function Rules (ppt)
  11. Notes: Writing Linear Equations from Tables (ppt)
  12. VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)
Real World Lessons
  1. Dan Meyer: Taco Cart - Who will reach the taco cart first?
Practice
  1. Worksheet: Functions Vocabulary (doc)
  2. Warm-Up: Functions (doc)
  3. Worksheet: Functions (doc)
  4. Quiz Review: Functions and Relations (doc)
  5. Quiz: Functions and Relations (doc)
  6. Worksheet: Writing Linear Equations (doc)
  7. Worksheet: Functions and Graphs Review (doc)
  8. Quiz: Comparing Graphs, Tables, and Rules (doc)
  9. Worksheet: Functions Practice (doc)
  10. Worksheet: Functions, Tables, and Graphs Practice (doc)
Self-Assessments
  1. SOL 8.14 Mini-Quiz: Connections between Representations
Skills
  1. Mathalicious: Sweet Tooth - When you go trick-or-treating on Halloween, how much enjoyment do you get from each additional piece of candy? Do you get the same amount of satisfaction from each piece of candy, or do you start to get sick of it (maybe even literally!)? 
  2. Mathematics Assessment Project:
    • 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.
    • A06:Bike Ride - Apprentice - In this task, you interpret a distance/time graph describing a bike ride.
    • A16:Journey - Apprentice - In this task, you will read a description of a car journey and draw a distance-time graph to represent it.
  3. Functions: Designing Patios (doc)
  4. Functions: Growing Tomato Plants (doc)
Videos
Explore Learning
  1. Distance-Time Graphs: Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs.
  2. Distance-Time and Velocity-Time Graphs: Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.
  3. Linear Functions: Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear.
  4. Slope-Intercept Form of a Line - Activity A: Compare the slope‑intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
  5. Points, Lines and Equations : Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change.
Websites
  1. Numerical, Graphical and Analytical Math Problem Solving - Garden Task
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. 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
7.RP.2c
7.RP.2d
8.EE.5
8.F.1
8.F.2
8.F.3
8.F.4
8.F.5
F-IF.1