Subject: Math
Grade Level: 7 Compacting
Big Idea/Theme: Algebra
Unit 2 Title: What’s Your Function?
Timeframe Needed for Completion: 10 weeks
Grading Period: 1st & 2nd 9 wks.
Understandings:
 Relationships between verbal and mathematical expressions and equations
 Evaluate expressions, equations, and inequalities (solving one and two step equations/inequalities)
 Fluency in problem solving skills- convert to algebra, venn diagrams, look for a pattern (See “Crossing the River with Dogs”)
 Representations of expressions, equations, and inequalities (graphs, tables, diagrams, written descriptions)
 Operations with integers
 Functions and Relations
 Linear or Nonlinear
 Slope
 Intercepts
 Linear Equations
 Linear Inequalities
Curriculum Goals/Objectives:
Essential Questions:
 What is the function of a function?
Common Core Standards
 How is an equation like a balance?
Solve real-life mathematical problems using numerical and  What is a variable? How is it used in math? Science? Life?
algebraic expression and equations.
 How does solving equations apply to the real world?
7.EE.4 Use variables to represent quantities in a real world or
 What is the best way to represent a function?
mathematical problem, and construct simple equations and
inequalities to solve problems by reasoning about the
 How do you use patterns to help you make decisions?
quantities.
 How can you use Algebra outside of class?
Understanding the connections between proportional
 How has equality or inequality shaped your life?
relationships, lines, and linear equations
8.EE.5 Graph proportional relationships, interpreting the unit
 Equality or inequality? Explain.
rate as the slope of the graph. Compare two different
 What distinguishes one line from another?
proportional relationships represented in different ways.
8.EE.6 Use similar triangles to explain why the slope m is the
 What is the difference between a function and a relation?
same between any two distinct points on a non-vertical line in
 Are all functions relations?
the coordinate plane; derive the equation y = mx for a line
through the origin and the equations y = mx + b for a line
 Are all relations functions?
intercepting the vertical axis at b.
 How can you determine when a relation is not a function?
8.EE.7 Solve linear equations in one variable.
 What are the different ways you can model/represent a function or relation?
a. Give examples of linear equations in one variable with
one solution, infinitely many solutions, or no solutions. Show
 What are the advantages/disadvantages to looking at a table as opposed to the
which of these possibilities is the case by successively
graphic representation?
transforming the given equation into simpler forms, until an
equivalent equation of the form x = a, a = a, or a = b results
 What are the advantages/disadvantages to looking at a graph as opposed to the
(where a and b are different numbers).
algebraic representation?
Define, evaluate, and compare functions.
 Is there any representation that is more beneficial than the others? (verbal,
8.F.1 Understand that a function is a rule that assigns to each
input exactly one output. The graph of a function is the set of
ordered pairs consisting of an input and the corresponding
output.
8.F.2 Compare properties of two functions each represented in
a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions).
8.F.3 Interpret the equation y = mx + b as defining a linear
function, whose graph is a straight line; give examples of
functions that are not linear.
Use functions to model relationships between quantities.
8.F.4 Construct a function to model a linear relationship
between two quantities. Determine the rate of change and
initial value of the function from a description of a relationship
or from two (x,y) values, including reading these from a table
or from a graph. Interpret the rate of change and initial value
of a linear function in terms of the situation it models, and in
terms of its graph or a table of values.
8.F.5 Describe qualitatively the functional relationship
between two quantities by analyzing a graph (e.g., where the
function is increasing or decreasing, linear or nonlinear).
Sketch a graph that exhibits the qualitative features of a
function that has been described verbally.
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tabular, graphic and algebraic) Explain.
Explain how you can create the other three representations given one
representation to start with.
What is the difference between linear and nonlinear?
How can you determine if a situation represents a linear or nonlinear relation?
What is slope?
How can slope be represented?
Is it possible to have no slope?
Is zero slope and no slope the same?
Is undefined slope and no slope the same?
How can you determine when lines have the same slope?
How can you determine which line is steeper?
What is the x and y intercept?
What is the significance of the x- and y- intercept in problem situations?
If the x-intercept stays the same but the slope changes how is the line affected
line?
If the slope stays the same but the x-intercept or y-intercept changes, how does
that affect the line?
What determines if a line moves along the vertical axis?
What determines if a line moves along the horizontal axis?
Why do most linear equations have two variables?
What kinds of lines only have one variable?
How would you graph linear equations given: the slope and a point, two points,
the equation in standard form, the equation in slope-intercept form?
How would you write the equation of a line in slope-intercept form given: the
slope and a point or two points.
How can you take an equation in standard form and put it in slope-intercept
form?
Compare and contrast equations and inequalities?
How is the graph of an inequality different from an equation?
Looking at the graph of an equation how can you determine a solution for the
inequality?
How do you determine when an inequality has a solid line or a broken line?
What is the significance of the broken line or solid line?
Assessment Tasks:
 Algebraic foldables
 Quickwrites
 Flow charts
 Venn diagrams (algebraic relationships)
 Word Wall
 Four Color Activity for Functions (see AVID Math 2 book)
 Integer Computation Triangle Puzzle (Grade 7 Classroom Strategies-DPI)
 ClassScape
 Lining up Dominoes-Distributive Property (located in the 7th grade Objective
tasks)
 Algebraic Expressions Square Puzzle (located in the 7th grade Objective tasks)
 Inequality Match (located in the 7th grade Objective tasks)
Essential Skills/Vocabulary:
Vocabulary:
Variable
Expression
Equivalent
Function
Equivalent
Equation
expressions
Inequality
Coefficient
Solution
Constant
Linear Expression Formulas
Slope
Linear Equation
Intercepts
Input
Slope Intercept
Output
Function Rule
Relation
Materials Suggested:
NCDPI Resources:
http://www.ncpublicschools.org/curriculum/mathematics/middlegrades/grade08/
http://mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=5149151
National Library of Manipulatives
http://nlvm.usu.edu/en/nav/vlibrary.html
NCTM Illuminations
http://illuminations.nctm.org/
Lesson Plan sites and Activities:
http://www.lessonplanspage.com/Math.htm
http://www.ilovemath.org
Skills:
Graphing on coordinate plane
Naming solutions
Solving multiple types of
equations/inequalities
Math Graphic Organizers
http://www.enchantedlearning.com/graphicorganizers/math/
Common Core Standards
http://www.dpi.state.nc.us/acre/
AVID Library/Write Path Books
SMART Board Lessons
exchange.smarttech.com