

Unit 3 Expressions,
Equations, and Inequalities Grade 7 Math 

Unit
Length and Description: 36
days Unit
3 consolidates and expands students’ previous work with generating equivalent
expressions and solving equations and inequalities. By the end of this unit
students should fluently solve multistep
problems posed with positive and negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools strategically. This work is
the culmination of many progressions of learning in arithmetic, problem
solving and mathematical practices. In
solving word problems leading to onevariable equations of the form px +
q = r and p(x + q) = r, as well as
px + q < r and px + q > r, students should solve these equations
fluently. This will require fluency with rational number arithmetic, as well
as fluency to some extent with applying properties of operations to rewrite
linear expressions with rational coefficients. Students use the properties of
operations and the relationships between addition and subtraction, and
multiplication and division, as they formulate expressions, equations, and
inequalities in one variable and use these to solve problems. They solve real‐life and mathematical
problems using numerical and algebraic expressions, equations, and
inequalities. At the end of the unit students’ work with expressions and
equations is applied to finding unknown angles in a figure. By using facts about supplementary,
complementary, vertical, and adjacent angles, students are able to write and
solve simple equations to solve for the unknown angle. The work and required fluency expectations
in this unit are a major capstone leading to the mathematical development
necessary to perform operations with linear equations in Grade 8. 

Standards: 7.EE.A.1 Apply properties of
operations as strategies to add, subtract, factor, and expand linear
expressions with rational coefficients. 7.EE.A.2 Understand that rewriting an
expression in different forms in a problem context can shed light on the
problem and how the quantities in it are related. For
example, a + 0.05a = 1.05a means that “increase by 5%” is the same as
“multiply by 1.05.” o
Standards
Clarification: Students will apply
their conceptual understanding and procedural skill in rearranging
expressions to make them more meaningful within a particular context. 7.EE.B.3 Solve multistep reallife
and mathematical problems posed with positive and negative rational numbers
in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of
operations to calculate with numbers in any form; convert between forms as
appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies.
For example: If a woman making $25 an hour gets a 10%
raise, she will make an additional 1/10 of her salary an hour, or $2.50, for
a new salary of $27.50. If you want to
place a towel bar 9 3/4 inches long in the center of a door that is 27 ½
inches wide, you will need to place the bar about 9 inches from each edge;
this estimate can be used as a check on the exact computation. o
Standards
Clarification: The equations and
inequalities in this unit should provide the students an opportunity to work
with all types of rational numbers, not just integers. 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. a. Solve word problems leading
to equations of the form px + q = r and p(x + q) = r, where p, q,
and r, are specific rational
numbers. Solve equations of these
forms fluently. Compare an algebraic
solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. For example, the perimeter of a rectangle
is 54 cm. Its length is 6 cm. What is its width? o Standards Clarification: It
is not necessary nor is it encouraged to use the distributive property to
solve the multistep equations in this unit.
The equations in this unit should provide the students an opportunity
to work with all types of rational numbers, not just integers. b. Solve word problems leading
to inequalities of the form px + q >
r or px + q < r, where p, q,
and r are specific rational
numbers. Graph the solution set of the
inequality and interpret it in the context of the problem. For
example: As a salesperson, you are
paid $50 per week plus $3 per sale.
This week you want your pay to be at least $100. Write an inequality for the number of sales
you need to make, and describe the solutions. o Standards
Clarification: Although the
mathematical examples in the standard only show the less than and greater
than signs, it is appropriate to use the less than or equal to and the
greater than or equal to signs as well.
The inequalities in this unit should provide the students an
opportunity to work with all types of rational numbers, not just integers. 7.G.B.5 Use facts about
supplementary, complementary, vertical, and adjacent angles in a multistep
problem to write and use them to solve simple equations for an unknown angle
in a figure. o
Standards
Clarification: Students will be
expected to write and solve equations for an unknown angle in a figure. This
provides an opportunity to reinforce students’ fluency in solving equations;
also, this unit provides an opportunity to model realworld situations
involving angles with equations and inequalities. The standards do not
explicitly address at any grade level the measure of a straight angle. It may
need to be discovered by applying the students’ understanding of right angles
and angle addition. Focus Standards of
Mathematical Practice: MP.1 Make
sense of problems and persevere in solving them. MP.2 Reason
abstractly and quantitatively. MP.3
Construct viable arguments and critique the reasoning of others. MP.4 Model
with mathematics. MP.5 Use
appropriate tools strategically. MP.6 Attend
to precision. MP.7 Look for
and make use of structure. MP.8 Look for
and express regularity in repeated reasoning. Instructional
Outcomes: Full Development of the Major Clusters,
Supporting Clusters, Additional Clusters and Mathematical Practices for this
unit could include the following instructional outcomes: 7.EE.A.1 ·
I can combine like
terms with rational coefficients. ·
I can factor and expand linear expressions with rational
coefficients using the distributive property. ·
I can apply properties of operations as strategies to
add, subtract, factor, and expand linear expressions with rational
coefficients. 7.EE.A.2 ·
I can write equivalent expressions with fractions,
decimals, and
integers. ·
I can rewrite an expression in an equivalent form in
order to provide insight about how quantities are related in a problem
context. 7.EE.B.3 ·
I can convert between numerical forms as appropriate. ·
I can solve multistep reallife and mathematical
problems posed with positive and negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools strategically. ·
I can apply properties of operations to calculate with
numbers in any form. ·
I can assess the reasonableness of answers using mental
computation and estimation strategies. 7.EE.B.4a ·
I can identify the sequence of operations used to solve
an algebraic equation of the form px +
q=r and p(x + q) = r. ·
I can fluently solve equations of the form px + q=r and p(x + q) = r with speed and accuracy. ·
I can solve word problems leading to equations of the
form px + q=r and p(x + q) = r, where p, q, and r are specific rational numbers. ·
I can compare an algebraic solution to an arithmetic
solution by identifying the sequence of the operations used in each approach.
For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm.
What is the width? This can be answered algebraically by using only the
formula for perimeter (P=2l+2w) to isolate w or by finding an arithmetic
solution by substituting values into the formula. 7.EE.B.4b ·
I can graph the solution set of the inequality of the
form px + q>r or px + q<r, where p, q, and r are
specific rational numbers. ·
I can use variables and construct equations to represent
quantities of the form px + q=r and p(x + q) = r from
realworld and mathematical problems. ·
I can solve word problems leading to inequalities of the
form px + q>r or px + q<r, where p, q, and r
are specific rational numbers. ·
I can interpret the solution set of an inequality in the
context of the problem. 7.G.B.5 ·
I can identify and recognize types of angles:
supplementary, complementary, vertical, adjacent. ·
I can determine complements and supplements of a given
angle. ·
I can determine unknown angle measures by writing and
solving algebraic equations based on relationships between angles. 

Enduring
Understandings: ·
Variables can be used to represent numbers in any type of
mathematical problem. ·
Understand the difference between an expression and an equation. ·
Understand the difference between an equation and an inequality. ·
Properties of operations allow us to add, subtract, factor, and
expand linear expressions. ·
There are precise terms and sequences to describe operations with
rational numbers. ·
Expressions can be manipulated to suit a particular purpose to solve
problems efficiently. ·
Mathematical expressions, equations, inequalities, and graphs are
used to represent and solve realworld and mathematical problems. ·
Properties, order of operations, and inverse operations are used to
simplify expressions and solve equations and inequalities efficiently. ·
Generating equivalent, linear expressions with rational
coefficients using the properties of operations will lead to solving linear
equation. ·
Discovering that rewriting expressions in different
forms in a problem context leads to understanding that the values are
equivalent. ·
The ability to solve and explain real life and
mathematical problems involving rational numbers using numerical and
algebraic expressions is important in preparation for algebra concepts in
future math courses. ·
Constructing simple equations and inequalities to solve
real life word problems is a necessary concept. ·
Writing and solving reallife and mathematical problems
involving simple equations for an unknown angle in a figure helps students as
they engage in higher geometry concepts. ·
Reason about relationships among twodimensional
figures, which leads to gaining familiarity with the relationships between
angles formed by intersecting lines. 
Essential
Questions: ·
How can I apply the order of operations and the
fundamentals of algebra to solve problems involving equations and
inequalities? ·
How can I justify that multiple representations in the
context of a problem are equivalent expressions? ·
How do I assess the reasonableness of my answer? ·
How can I use and relate facts about special pairs of
angles to write and solve simple equations involving unknown angles? ·
What is the total number of degrees in supplementary and
complementary angles? ·
What is the relationship between vertical and adjacent
angles? ·
When and how are expressions, equations, and
inequalities applied to real world situations? ·
What are some possible reallife situations to which
there may be more than one solution? ·
How does the ongoing use of decimals apply to
reallife situations? ·
How can geometry be used to solve problems about
realworld situations, spatial relationships, and logical reasoning? 
