In this unit, students build on prior knowledge of solving one and two step equations and extend it to solving inequalities. This is the students’ first time learning about multiplication and division properties of inequalities, including those of negative numbers. The majority of the work is centered around solving inequalities in context and determining whether the context calls for a discrete or continuous solution set. Common misconceptions include the idea that the boundary, c, of x < c is the solution to the inequality and a lack of understanding that inequalities can have an infinite number of solutions. An idea that students will likely struggle with is that inequalities can be solved such that the variable is on the left or right of the relation. This may result in students misunderstanding whether the solution is less than or greater that the boundary found.
Key Concepts:
 Two expressions, a and b, have one of three relationships: either ab, or a=b
 In the case of variable expressions, it may be possible to write equivalent equations or inequalities in order to determine the set of values that makes the equation or inequality true
 There may be infinitely many solutions for an inequality, and the set of solutions may be shown on a number line
Prior Knowledge Needed:
 Understand solutions are values which make a relationship true; Grade 6, Unit 9; 6.EE.B.5
 Understand a variable can represent any value in a specific set; Grade 6, Unit 9; 6.EE.B.6
 Solve equations and inequalities with nonnegative numbers; Grade 6, Unit 9; 6.EE.B.7
 Represent solutions to inequalities on a number line; Grade 6, Unit 9; 6.EE.B.8
 Understanding ordering of rational numbers; Grade 6, Unit 6; 6.NS.C.7.a,b
 Compute fluently with decimals and fractions; Grade 6, Units 4, Unit 5; 6.NS.B.3, 6.NS.A.1
 Solve equations; Grade 7, Unit 6; 7.EE.B.4.a
Units on the Horizon:
 Solving Linear Equations; Grade 8, Unit 10
 Systems of Linear Equations Grade 8, Unit 11
Lessons

Lesson objective: Understand that an expression doesn't have to be equal to another. It can be less than or greater than another. Students bring prior knowledge of inequalities from 6.EE.B.7. This prior knowledge is extended to algebraic expressions as ...

Lesson objective: Write algebraic inequalities to match a written verbal description. This lesson helps to build procedural skill with writing inequalities. This work develops students' understanding that an algebraic expression can be less than, greate...

Lesson objective: Apply skills of writing inequalities to compare the inequalities resulting from different written verbal descriptions. This lesson provides an opportunity for students to apply their knowledge and understanding of writing inequalities ...

Lesson objective: Understand that inequalities can be solved using inverse operations to write equivalent inequalities leading to a solution. Students bring prior knowledge of solving equations from 7.EE.B.4.a. This prior knowledge is extended to inequa...

Lesson objective: Fluently solve multistep inequalities in one variable. This lesson helps to build fluency with solving inequalities. The number line is used here because it helps students to visualize the relationships and prepares them for graphing ...

Lesson objective: Solve multistep inequalities in one variable with negative coefficients. This lesson helps to build procedural skill with solving inequalities with negative coefficients. The number line is used here because it helps students to visua...

Lesson objective: Apply skills of writing and solving inequalities to problem solve. This lesson provides an opportunity for students to apply their knowledge and understanding of inequalities to a reallife situation. Students are asked to find the bes...

Lesson objective: Understand that there are multiple values that make an inequality true and they can be shown on the number line. Students bring prior knowledge of graphing inequalities from 6.EE.B.8. This prior knowledge is extended to discrete and co...

Lesson objective: Graph the solutions to inequalities on a number line. This lesson helps to build procedural skill with graphing the solutions to inequalities. The number line is used here because it is the appropriate place to graph a solution set in ...

Lesson objective: Apply skills of writing, solving, and graphing the solutions to inequalities to compare situations leading to discrete and continuous graphs. This lesson provides an opportunity for students to apply their knowledge and understanding o...