Simple Inequalities

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Lessons

Standards in this Lesson

Common Core Math Standards

6.EE.B: Reason about and solve one-variable equations and inequalities.
6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
HSF.BF.A: Build a function that models a relationship between two quantities.
HSF.BF.A.1: Write a function that describes a relationship between two quantities.
HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
HSF.IF.B: Interpret functions that arise in applications in terms of the context.

CSTA Standards

3B-AP-10: Use and adapt classic algorithms to solve computational problems.

Alabama Standards

AL.6.EE.B: Reason about and solve one-variable equations and inequalities.
AL.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
AL.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
AL.HSF.BF.A: Build a function that models a relationship between two quantities.
AL.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
AL.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
AL.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Arkansas Standards

AR.6.EE.B: Reason about and solve one-variable equations and inequalities.
AR.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
AR.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
AR.HSF.BF.A: Build a function that models a relationship between two quantities.
AR.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
AR.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
AR.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

California Standards

CA.6.EE.B: Reason about and solve one-variable equations and inequalities.
CA.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
CA.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
CA.HSF.BF.A: Build a function that models a relationship between two quantities.
CA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
CA.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
CA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Colorado Standards

CO.6.EE.B: Reason about and solve one-variable equations and inequalities.
CO.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
CO.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
CO.HSF.BF.A: Build a function that models a relationship between two quantities.
CO.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
CO.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
CO.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Connecticut Standards

CT.6.EE.B: Reason about and solve one-variable equations and inequalities.
CT.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
CT.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
CT.HSF.BF.A: Build a function that models a relationship between two quantities.
CT.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
CT.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
CT.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Delaware Standards

DE.6.EE.B: Reason about and solve one-variable equations and inequalities.
DE.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
DE.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
DE.HSF.BF.A: Build a function that models a relationship between two quantities.
DE.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
DE.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
DE.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Delaware Standards

GA.6.EE.B: Reason about and solve one-variable equations and inequalities.
GA.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
GA.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
GA.HSF.BF.A: Build a function that models a relationship between two quantities.
GA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
GA.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
GA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Hawaii Standards

HI.6.EE.B: Reason about and solve one-variable equations and inequalities.
HI.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
HI.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
HI.HSF.BF.A: Build a function that models a relationship between two quantities.
HI.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
HI.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
HI.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Idaho Standards

ID.6.EE.B: Reason about and solve one-variable equations and inequalities.
ID.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
ID.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
ID.HSF.BF.A: Build a function that models a relationship between two quantities.
ID.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
ID.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
ID.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Illinois Standards

IL.6.EE.B: Reason about and solve one-variable equations and inequalities.
IL.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
IL.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
IL.HSF.BF.A: Build a function that models a relationship between two quantities.
IL.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
IL.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
IL.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Iowa Standards

IA.6.EE.B: Reason about and solve one-variable equations and inequalities.
IA.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
IA.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
IA.HSF.BF.A: Build a function that models a relationship between two quantities.
IA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
IA.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
IA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Kansas Standards

KS.6.EE.B: Reason about and solve one-variable equations and inequalities.
KS.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
KS.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
KS.HSF.BF.A: Build a function that models a relationship between two quantities.
KS.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
KS.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
KS.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Kentucky Standards

KY.6.EE.B: Reason about and solve one-variable equations and inequalities.
KY.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
KY.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
KY.HSF.BF.A: Build a function that models a relationship between two quantities.
KY.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
KY.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
KY.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Louisiana Standards

LA.6.EE.B: Reason about and solve one-variable equations and inequalities.
LA.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
LA.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
LA.HSF.BF.A: Build a function that models a relationship between two quantities.
LA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
LA.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
LA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Maine Standards

ME.6.EE.B: Reason about and solve one-variable equations and inequalities.
ME.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
ME.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
ME.HSF.BF.A: Build a function that models a relationship between two quantities.
ME.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
ME.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
ME.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Michigan Standards

MI.6.EE.B: Reason about and solve one-variable equations and inequalities.
MI.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
MI.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
MI.HSF.BF.A: Build a function that models a relationship between two quantities.
MI.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MI.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
MI.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Maryland Standards

MD.6.EE.B: Reason about and solve one-variable equations and inequalities.
MD.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
MD.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
MD.HSF.BF.A: Build a function that models a relationship between two quantities.
MD.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MD.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
MD.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Massachusetts Standards

MA.6-8.CT.a.2: Define a simple function that represents a more complex task/problem and can be reused to solve similar tasks/problems.
MA.6-8.CT.b.2: Use logical reasoning to predict outputs given varying inputs.
MA.6-8.CT.d.2: Use functions to hide the detail in a program.
MA.6-8.CT.d.5: Trace programs step-by-step in order to predict their behavior.
MA.6.EE.B: Reason about and solve one-variable equations and inequalities.
MA.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
MA.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
MA.9-12.CT.b.2: Represent algorithms using structured language, such as pseudocode.
MA.HSF.BF.A: Build a function that models a relationship between two quantities.
MA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MA.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
MA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Mississippi Standards

MS.6.EE.B: Reason about and solve one-variable equations and inequalities.
MS.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
MS.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
MS.HSF.BF.A: Build a function that models a relationship between two quantities.
MS.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MS.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
MS.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Missouri Standards

MO.6.EE.B: Reason about and solve one-variable equations and inequalities.
MO.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
MO.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
MO.HSF.BF.A: Build a function that models a relationship between two quantities.
MO.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MO.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
MO.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Montana Standards

MT.6.EE.B: Reason about and solve one-variable equations and inequalities.
MT.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
MT.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
MT.HSF.BF.A: Build a function that models a relationship between two quantities.
MT.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
MT.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
MT.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

New Hampshire Standards

NH.6.EE.B: Reason about and solve one-variable equations and inequalities.
NH.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
NH.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
NH.HSF.BF.A: Build a function that models a relationship between two quantities.
NH.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NH.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
NH.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Nevada Standards

NV.6.EE.B: Reason about and solve one-variable equations and inequalities.
NV.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
NV.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
NV.HSF.BF.A: Build a function that models a relationship between two quantities.
NV.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NV.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
NV.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

New Jersey Standards

NJ.6.EE.B: Reason about and solve one-variable equations and inequalities.
NJ.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
NJ.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
NJ.HSF.BF.A: Build a function that models a relationship between two quantities.
NJ.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NJ.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
NJ.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

New Mexico Standards

NM.6.EE.B: Reason about and solve one-variable equations and inequalities.
NM.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
NM.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
NM.HSF.BF.A: Build a function that models a relationship between two quantities.
NM.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NM.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
NM.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

North Carolina Standards

NC.6.EE.B: Reason about and solve one-variable equations and inequalities.
NC.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
NC.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
NC.HSF.BF.A: Build a function that models a relationship between two quantities.
NC.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NC.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
NC.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

North Dakota Standards

ND.6.EE.B: Reason about and solve one-variable equations and inequalities.
ND.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
ND.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
ND.HSF.BF.A: Build a function that models a relationship between two quantities.
ND.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
ND.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
ND.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

New York Standards

NY.6.EE.B: Reason about and solve one-variable equations and inequalities.
NY.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
NY.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
NY.HSF.BF.A: Build a function that models a relationship between two quantities.
NY.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
NY.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
NY.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Oklahoma Standards

OK.6.A.3.1: Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.
OK.7.A.3.3: Represent real-world or mathematical situations using equations and inequalities involving variables and rational numbers.
OK.PA.A.4.3: Represent real-world situations using equations and inequalities involving one variable.

Ohio Standards

OH.6.EE.B: Reason about and solve one-variable equations and inequalities.
OH.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
OH.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
OH.HSF.BF.A: Build a function that models a relationship between two quantities.
OH.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
OH.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
OH.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Oregon Standards

OR.6.EE.B: Reason about and solve one-variable equations and inequalities.
OR.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
OR.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
OR.HSF.BF.A: Build a function that models a relationship between two quantities.
OR.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
OR.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
OR.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Pennsylvania Standards

PA.6.EE.B: Reason about and solve one-variable equations and inequalities.
PA.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
PA.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
PA.HSF.BF.A: Build a function that models a relationship between two quantities.
PA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
PA.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
PA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Rhode Island Standards

RI.6.EE.B: Reason about and solve one-variable equations and inequalities.
RI.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
RI.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
RI.HSF.BF.A: Build a function that models a relationship between two quantities.
RI.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
RI.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
RI.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

South Dakota Standards

SD.6.EE.B: Reason about and solve one-variable equations and inequalities.
SD.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
SD.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
SD.HSF.BF.A: Build a function that models a relationship between two quantities.
SD.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
SD.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
SD.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Tennessee Standards

TN.6.EE.B: Reason about and solve one-variable equations and inequalities.
TN.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
TN.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
TN.HSF.BF.A: Build a function that models a relationship between two quantities.
TN.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
TN.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
TN.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Utah Standards

UT.6.EE.B: Reason about and solve one-variable equations and inequalities.
UT.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
UT.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
UT.HSF.BF.A: Build a function that models a relationship between two quantities.
UT.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
UT.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
UT.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Vermont Standards

VT.6.EE.B: Reason about and solve one-variable equations and inequalities.
VT.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
VT.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
VT.HSF.BF.A: Build a function that models a relationship between two quantities.
VT.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
VT.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
VT.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Washington Standards

WA.6.EE.B: Reason about and solve one-variable equations and inequalities.
WA.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
WA.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
WA.HSF.BF.A: Build a function that models a relationship between two quantities.
WA.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
WA.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
WA.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

West Virginia Standards

WV.6.EE.B: Reason about and solve one-variable equations and inequalities.
WV.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
WV.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
WV.HSF.BF.A: Build a function that models a relationship between two quantities.
WV.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
WV.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
WV.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Wisconsin Standards

WI.6.EE.B: Reason about and solve one-variable equations and inequalities.
WI.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
WI.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
WI.HSF.BF.A: Build a function that models a relationship between two quantities.
WI.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
WI.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
WI.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Wyoming Standards

WY.6.EE.B: Reason about and solve one-variable equations and inequalities.
WY.6.EE.B.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
WY.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
WY.HSF.BF.A: Build a function that models a relationship between two quantities.
WY.HSF.BF.A.1: Write a function that describes a relationship between two quantities.
WY.HSF.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
WY.HSF.IF.B: Interpret functions that arise in applications in terms of the context.

Textbook Alignment

IM Algebra 1

IM.Alg1.2.18: Representing Situations with Inequalities

IM 6 Math™

IM.6.7.10: Interpreting Inequalities
IM.6.7.9: Solutions of Inequalities
IM 6.7.8: Writing and Graphing Inequalities

Practices in this Lesson

Math

MP.1: Make sense of problems and persevere in solving them
MP.4: Model with mathematics
MP.6: Attend to precision

Math Lang. Routines

MLR.5: Co-Craft Questions and Problems

(Also available in Pyret)

Students identify solutions and non-solutions of inequalities using an interactive starter file. This lesson also reviews the Boolean datatype.

Lesson Goals

Students will be able to:

Describe the solution set of a simple inequality

Student-Facing Lesson Goals

I can find solutions and non-solutions to an inequality

Materials

Supplemental Resources

Booleans Review

Key Points for the Facilitator

A Boolean is just another data type, like Numbers or Images. But unlike those types, there are only two values: true and false. While simple to explain, this different behavior can be confusing for some students.
Boolean-producing functions are essentially yes-or-no questions, so the names of the functions in this lesson read like questions.
For example, odd? and even? (pronounced "odd-huh?" and "even-huh?" in Scheme) are both functions that ask if a given number is odd or even. }

Glossary

Boolean: a type of data with two values: true and false
data type: a way of classifying values, such as: Number, String, Image, Boolean, or any user-defined data structure
equation: a mathematical description of the relationship between two variables or quantities, in which they are equal
inequality: a mathematical description of the relationship between two variables or quantities, in which they are not necessarily equal
solution set: the set of all values or coordinate pairs that will make an equation, inequality, set of equations or set of inequalities true

🔗Introducing Booleans 20 minutes

Launch

Students should be logged into WeScheme.

Ask students to evaluate Circles of Evaluation for simple expressions they’ve seen before, and ask them to convert them into code.

+
1 2
(+ 1 2)
-
4 5
(- 4 5)
*
8 0
(* 8 0)

Then show them unfamiliar Circles of Evaluation, and ask them to hypothesize what they think they mean, what they will evaluate to, and what the code would look like.

>
1 2
(> 1 2)
<
4 5
(< 4 5)
=
8 0
(= 8 0)

Have students convert these Circles to code and type them in. What did they evaluate to? What do they think the outputs mean?

Values like true and false obviously aren’t Numbers or Images. But they also aren’t Strings, or else they would have quotes around them. We’ve found a new data type, called a Boolean.

Investigate

Have students open the Boolean Starter File.

Explore the five functions in this starter file: odd?, even?, less-than-one?, continent?, and primary-color?
All five functions produce Booleans. Through your exploration, see if you can come up with an explanation of what a Boolean is.

A Boolean is just another data type, like Numbers or Images. But unlike the others there are only two values: true and false.

Turn to Boolean Functions and use the starter file to complete the questions, identifying inputs that will make each function produce true, and inputs that will make each function false.

Common Misconceptions

Many students - especially traditionally high-achieving ones - will be very concerned about writing examples that are "wrong." The misconception here is that an expression that produces false is somehow incorrect. You can preempt this by explaining that our Boolean-producing functions should sometimes return false.

Synthesize

Students will see functions on this page that they’ve never encountered before! But instead of answering their questions, encourage them to make a guess about what they do, and then type it in to discover for themselves.
Explicitly point out that everything they know still works! They can use their reasoning about Circles of Evaluation and Contracts to figure things out.

🔗Introducing Inequalities 20 minutes

Overview

Students discover (or expand their understanding of) inequalities by identifying solutions and non-solutions and connecting expressions to graphic representations.

Launch

How are equations different from inequalities?

Equations typically have finite solution sets: there’s only one answer for an unknown, or perhaps several answers. Inequalities, on the other hand, can have infinite solutions. Inequality expressions divide all of the numbers in the universe into two categories: solutions and non-solutions.

It is important that students learn to recognize that there are many possible solutions and non-solutions to an inequality and are able to identify whether or not a given number is or isn’t part of the solution set.

We are going to practice identifying whether or not a given number is part of the solution set.
Open the Simple Inequalities Starter File and click "Run".
Analyze the graph that appears (image below), as well as the provided code (lines 10, 18, and 26). 🖼Show image
What do you Notice? What do you Wonder?

Students might observe the following:

This starter file includes a special inequality function that takes in a function (which tests numbers in an inequality) and a list of 8 numbers (to test in the function).
When we click "Run", we see a graph of the inequality on a number line.
The solution set is shaded in blue.
The 8 numbers provided in the list are shown as dots on the numberline. They will appear:
- green when they’re part of the solution set
- red when they are non-solutions

Look at line 18. Edit the list of values by deleting one of the - symbols.
Hit "Run". Examine the graph that appears (sample image below). 🖼Show image
How is this graph different from the one you first produced?

A successful input in this starter file will include 4 solutions and 4 non-solutions; in other words, the image returned will show 4 green dots and 4 red dots.

When students modify the list of numbers, they will see there are now 5 red dots and 4 green dots - along with a message that says, "Challenge yourself: Find 4 true examples and 4 false".

Investigate

Open to the Simple Inequalities and complete it with a partner, identifying solutions and non-solutions to each inequality and testing them in the Simple Inequalities Starter File.
For each inequality, you must find four solutions and four non-solutions.
Try using negatives, positives, fractions and decimals as you generate your lists.

Synthesize

What patterns did you observe in how the inequalities worked?

🔗Additional Exercises:

Word Problem: hot?

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.