Unit Design
Content Area
Grade/Course
Unit Title
Duration of Unit
Warren County Public Schools
Math
9th/ Algebra I
Unit 4: Linear Equations & Inequalities
30 Days
Insert unit priority standards(s) below (include numerical and letter codes). Underline the skills (verbs)
students must master and circle the concepts (nouns) that students need to know.
1) A-CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
2) A-REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).
3) A-REI.D.12: Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary
in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the
intersection of the corresponding half-planes.
4) F-IF.B.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table)
over a specified interval. Estimate the rate of change from a graph.★
5) F-IF.C.7a: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases
and using technology for more complicated cases.★
a) Graph linear and quadratic functions and show intercepts, maxima, and minima.
6) S-ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of
the data.
7) F-LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential
functions.
a) Prove that linear functions grow by equal differences over equal intervals, and that exponential functions
grow by equal factors over equal intervals.
b) Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
c)
Recognize situations in which a quantity grows or decays by a constant percent rate perunit interval relative to
another.
8) F-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a
graph, a description of a relationship, or two input-output pairs (include readingthese from a table)
9) F-LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity
increasing linearly, quadratically, or (more generally) as a polynomial function.
Insert unit supporting standards in italics below (Include numerical and letter codes)
1) F-IF.C.7b: Graph functions expressed symbolically and show key features of the graph, by hand insimple cases
and using technology for more complicated cases.★
b) Graph square root, cube root, and piecewise- defined functions, including step functions and absolute value
functions.
2) F-BF.A.1a: Write afunction that describes a relationship between two quantities. ★
a) Determine an explicit expression, a recursive process, orsteps for calculationfrom a context.
3) F-BF.A.2: Write arithmetic and geometric sequences both recursively andwith an explicitformula, use them to
model situations, and translate between the two forms.★
Unit Design
Warren County Public Schools
4) F-BF.3: Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k
(both positiveand negative); find the valueof k given the graphs. Experiment with cases and illustrate an
explanationof the effects on the graph using technology. Include recognizing even and odd functions from their
graphs and algebraic expressions for them.
5) F-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
6) A-REI.A.1: Explaineach step in solving a simple equation as following from the equality of numbers asserted at the
previous step, starting from the assumptionthat the originalequation has a solution. Construct a viable argument to
justify a solution method.
7) A-REI.D.11: Explainwhy the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x)
intersect are the solutions of the equation f(x)=g(x); find thesolutions approximately, e.g., using technology to
graph the functions, make tablesof values,or find successive approximations. Include cases where f(x) and/or g(x)
are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
8) F-IF.C.7b: Graph functions expressed symbolically and show key features of the graph, by hand insimple cases
and using technology for more complicated cases.★
b) Graph square root, cube root, and piecewise- defined functions, including step functions and absolute value
functions.
Unwrap Priority Standards
Concepts (nouns)
Equations
Equations
Graph Set of All Solutions
Linear Inequality Solutions
Solution Set
Average Rate of Change
Average Rate of Change
Rate of Change
Functions
Key Features
Linear Functions
Intercepts
Slope
Intercepts
Situations
Linear Functions
One Quantity at Constant
Rate
Quantity Grows or Decays
Linear
Graphs and Tables
Skills (verbs)
Create
Graph
Understand
Graph
Graph
Calculate
Interpret
Estimate
Graph
Show
Graph
Show
Interpret
Interpret
Distinguish
Prove
Recognize
Bloom’s Level (verb)
Create
Analyze
Understand
Analyze
Analyze
Apply
Analyze
Apply
Analyze
Apply
Analyze
Apply
Analyze
Analyze
Analyze
Evaluate
Remember
Recognize
Construct
Observe
Remember
Create
Remember
Combine priority standards Skills and Concepts columns above to write Learning Targets below. Add
Bloom’s level (number) after each learning target.
Create and graph an equation of two or more variables. (6)
Understand that a graph is the set of all of its solutions. (2)
Graph a linear inequality in two variables as a half-plane. (4)
Graph the solution set of a system of inequalities. (4)
Calculate and interpret the average rate of change. (3)
Estimate the rate of change from a graph. (3)
Unit Design
Warren County Public Schools
Graph functions and show key features. (4)
Graph linear functions and show intercepts.(4)
Interpret the slope and intercept of a linear equation using data. (4)
Distinguish between linear and exponential functions. (6)
Prove that linear functions change at a constant rate. (5)
Recognize that linear functions grow and decay at a constant rate. (1)
Construct linear functions using multiple representations. (6)
Observe graphs and tables, then distinguish the differences between linear, quadratic, and exponential functions. (1)
Determine Big Ideas (lifelong understandings)
Differentiating between situations that have linear
growth and decay and those that do not.
Formative Assessment Lessons.
Write Essential Questions (Answer Big Idea, hook student
interest.
Would you rather get a dollar everyday or get a penny and
have your total doubled everyday?
Finding Equations of Parallel and Perpendicular Lines
The teacher leaders for the Gates grant work recommend that Warren County Administration adopt the
practice that Warren County Math teachers do a minimum of one Formative Assessment Lesson per
quarter. Choices for formative assessment lessons may be found at
http://map.mathshell.org/materials/lessons.php
Create assessments.
Create engaging learning experiences.