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 
 VDOE Enhanced Scope and Sequence Lesson: Relationships Round Robin (PDF)  Representing relationships with tables, graphs, rules, and words (Word)
 Notes: Coordinate Plane (ppt)
 Notes: Relations (flipchart)
 Activity: Relations Foldable (doc)
 Notes: Input/Output Tables (flipchart)
 Notes: Graphing Equations (flipchart)
 Notes: Function Review (flipchart)
 Guided Practice: Function Table Warmup (flipchart)
 Activity: Paper Tearing (pdf)
 Project: Graphing a Line (doc)
 Activity: Matching Functions, Graphs, Tables and Words (doc)
 VDOE Algebra Readiness Curriculum Companion: Investigating Patterns, Functions, and Algebra (pdf)

Real World Lessons 
 Activity: Penny Jar Investigation (flipchart)
 Mathalicious: Big Foot Conspiracy  Do people with small feet pay too much for shoes, and what would happen if Nike charged by weight?
 Mathalicious: Fat Burner  What's the best way to exercise for fat burning?

Practice 
 Worksheet: Graphing Equations (doc)
 Worksheet: Graphing Linear Functions (pdf)
 Worksheet: Solve and Graph Linear Functions (pdf)
 Worksheet: Function Word Problems (doc)
 Worksheet: Solving Linear Functions #1 (pdf)  Functions #2 (pdf)  Functions #3 (pdf)  Functions #4 (pdf)
 Worksheet: Graphing Equations (doc)  Graphing Equations #2 (doc)
 Activity: Representing Relationships (flipchart)

SOL Mini Quiz 
 SOL 7.12 Mini Quiz: Relations and Functions (pdf)  (doc)

Skills 
 Mathematics Assessment Project
 A08:Buses  Apprentice  In this task, you will work with a distancetime 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.
 Representations: Crawling Crayfish (doc)

Videos 
 PH Determining a Reasonable Domain and Range for a Situation
 PH Modeling a Function Using Three Views
 PH Identifying Functions using a Mapping
 PH Identifying Functions using a Vertical Line Test
 PH Making a Table from a Function Rule
 PH Finding the Range of a Function Given the Domain
 PH Graphing a function using a table

Explore
Learning 
 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.

Websites 
 RentaCar Activity
 Game: General Coordinates  investigate the coordinate system through identifying or requesting coordinates at Shodor.org
 Game: Maze Investigate the coordinate system by directing a robot through a mine field at Shodor.org
 Interactive: Function Machine  explore the concept of a function machine by inputting values and observing the output in a table at matti.usu.edu.
 Interactive: Function Machine  investigate simple linear functions by trying to guess the algebraic form from inputs and outputs at Shodor.org.
 Interactive: Function Machine  investigate simple linear functions by trying to guess the algebraic form from inputs and outputs at Shodor.org.
 Interactive: Vertical Line Test  discovery activity that determines if a graph is a function at Shodor.org.
 Interactive: Graphs and Functions view images of graphs at Shodor.organd determine if they represent a function

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. 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 
6.RP.3a 
6.EE.9 
7.RP.2a 
7.RP.2b 
7.RP.2c 
7.RP.2d 
8.F.1 
8.F.2 

