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Course: 6th grade mathematics
Unit: 6 Expressions, Equations, and Inequalities
Unit Length:22 days
Unit Overview:
Next Generation Content Standards and Objectives:
M.6.EE.5 (CCSS6.EE.B.5) Understand solving an equation or inequality as a process of
answering a question: Which values from a specific set, if any, make the equation or
inequality true? Use substitution to determine whether a given number in a specified set
makes an equation true.
M.6.EE.6 (CCSS6.EE.B.6) Use variables to represent numbers and write expressions when
solving a real world or mathematical problem; understand that a variable can represent an
unknown number or depending on the purpose at hand, any number in a specified set.
M.6.EE.7 (CCSS6.EE.B.7) Solve real world and mathematical problems by writing and solving
equations of the form x + p = q and px= q for cases in which p, q, and x are all nonnegative
rational numbers.
M.6.EE.8 (CCSS6.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
each inequalities on number line diagrams.
M.6.EE.9 (CCSS6.EE.C.9) Use variables to represent two quantities in a real world problem
that change in relationship to one another. Write an equation to express one quantity
thought of as the dependent variable in terms of the other quantity thought of as the
independent variable. Analyze the relationship between the dependent and independent
variable using graphs and tables and relate these to the equation.
Standards for Mathematical Practices:
Math Practice 1: Make sense of problems and persevere in solving them.
Students will be faced with expressions, equations, inequalities, and real world scenarios. Students must
use their reasoning skills and algebraic thinking to determine what steps are needed to evaluate or solve
each problem.
Math Practice 2: Reason abstractly and quantitatively.
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Students must use their knowledge of expressions, equations, and inequalities and apply them abstractly to
solve real world scenarios and problems.
Math Practice 3: Construct viable arguments and critique the reasoning of others.
Students will construct arguments to determine if a value or set of values is the solution or solution set to
equations and inequalities. Then, students must justify their answers and be able to interpret other students’
responses.
Math Practice 4: Model with mathematics.
Students will represent mathematical real world scenarios by writing expressions, equations, and
inequalities.
Math Practice 5: Use appropriate tools strategically.
Students will use paper, pencil, graph paper, and TI -73 calculators to evaluate expressions and solve
equations and inequalities.
Math Practice 6: Attend to precision.
Students must attend to precision when evaluating expressions. Students must also attend to precision when
solving equations for a specific value. Finally, students must be precise when interpreting inequalities
because a wrong interpretation will lead to a solution set that is inaccurate.
Math Practice 7: Look for and make use of structure.
Students will look for structure when learning how to evaluate expressions and solve equations and
inequalities through the use of inverse operations.
Math Practice 8: Look for and express regularity in repeated reasoning.
Through the use of repeated reasoning, students will apply the properties of inverse operations to solve
equations and inequalities.
Driving question: How are equations and inequalities used to represent situations in the
real world?
Overview script: Unit 6 is based on the driving question: How are equations and inequalities
used to represent situations in the real world? In this unit, you will be learning content
standards and objectives 6.EE.5-9.
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Think back to Unit 5, in the previous unit, you defined variables as letters that represent
unknown numbers. You also replaced variables with given values to evaluate expressions.
In this unit, you will apply your knowledge of writing and evaluating numerical expressions
to write expressions, equations, and inequalities.
You will also solve equations from real world scenarios. For example, if Sally purchases 2
pairs of jeans for 100.00, how much will each pair of jeans cost? First, let’s make the cost of
each pair of jeans the variable, x. If 2 pairs of jeans cost 100.00, then the equation would be
set up as 2x = 100. You can now apply the division property of equality to isolate x. 2x =
100, (Divide both side by 2), x = 50.
After writing equations, you will learn how to write inequalities. For example, look at the
expression: the maximum height for a roller coaster’s rider is 6 feet. Let x stand for the
possible heights of the riders. Then, choose the appropriate symbol to place in between x
and 6. x ≤ 6.
You will also graph the inequalities on a number line like the example provided.
Why are these skills important? Expressions, equations, and inequalities are everywhere,
but sometimes they are hidden in signs and labels. Take a look at the sale signs in the mall
or the height and weight requirements at amusement parks.
Expressions, equations, and inequalities are also used in a variety of career fields including
architecture and construction, business management, tourism, human services, marketing
and manufacturing, medical, and science, technology, and engineering.
What students will know and do:
The students will know that variables represent unknown values. Students will define
equations and inequalities and make comparisons between them.
The students will do: Students will substitute values to determine the solution or solution
set to an equation or inequality. Students will write expressions, equations, and inequalities
from mathematical and real world problems. Students will solve one step equations
involving addition and multiplication. Students will write and graph an inequality to
represent a real world situation.
In the previous unit, you explored variables and numerical expressions. In this set of
lessons, you will understand that variables represent unknown values. You will also define
equations and inequalities and make comparisons between them. You will be able to
substitute values into equations and inequalities to calculate solutions and solution sets.
You will also write expressions, equations, and inequalities from mathematical and real
world problems. You will develop and solve one step equations involving addition and
multiplication. In the final lesson, you will write inequalities based on real world scenarios
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and provide a graphical representation of the inequality.