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 
 SOL 7.12  represent relationships with tables,
graphs, rules, and words
 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 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 
 VDOE Enhanced Scope and Sequence Lesson: Matching Representations (PDF)  Making connections between representations (Word)
 Functions Unit Overview (doc)  Functions Unit Planner (doc)
 Notes: Functions (ppt)
 Guided Notes: Continuous and Discrete Functions (doc)
 Activity: Functions Sort (flipchart)
 Activity: Functions Sort #2 (doc)
 Notes: Linear Functions (ppt)
 Activity: Matching Functions, Graphs, and Tables (flipchart)
 Activity: Matching Functions, Graphs, and Tables (doc)
 Notes: Writing Function Rules (ppt)
 Notes: Writing Linear Equations from Tables (ppt)
 VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)

Real World Lessons 

Dan Meyer: Taco Cart  Who will reach the taco cart first?

Practice 
 Worksheet: Functions Vocabulary (doc)
 WarmUp: Functions (doc)
 Worksheet: Functions (doc)
 Quiz Review: Functions and Relations (doc)
 Quiz: Functions and Relations (doc)
 Worksheet: Writing Linear Equations (doc)
 Worksheet: Functions and Graphs Review (doc)
 Quiz: Comparing Graphs, Tables, and Rules (doc)
 Worksheet: Functions Practice (doc)
 Worksheet: Functions, Tables, and Graphs Practice (doc)

SelfAssessments 
 SOL 8.14 MiniQuiz: Connections between Representations

Skills 
 Mathalicious: Sweet Tooth  When you go trickortreating 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!)?
 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 distancetime graph to represent it.
 Functions: Designing Patios (doc)
 Functions: Growing Tomato Plants (doc)

Videos 

Explore
Learning 
 DistanceTime Graphs: Create a graph of a runner's position versus time and watch the runner complete a 40yard 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 realworld meaning to the intersection of two graphs.
 DistanceTime and VelocityTime Graphs: Create a graph of a runner's position versus time and watch the runner run a 40yard 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 realworld 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.
 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.
 SlopeIntercept 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.
 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 
 Numerical, Graphical and Analytical Math Problem Solving  Garden Task

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. 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 
FIF.1 

