Download Unit 5: Expressions and Equations

Math Unit 5 Overview
MATH
Grade 6
Essential Questions:
Unit 5: Expressions and Equations
Time Frame: 24 days

How are real world situations expressed and recorded in mathematics?

How are mathematical expressions, equations, and inequalities used to represent and
solve real-world and mathematical problems?
Key Vocabulary: algebraic expression, evaluate
an expression, expression, numerical expression,
order of operations, term, variable, base,
exponent, power, equivalent expressions,
associative property of addition, commutative
property of addition, coefficient, like terms,
associative property of multiplication,
commutative property of multiplication, simplify,
distributive property, greatest common factor,
double number line, dependent variable,
independent variable, inequality, solution of an
equality, solution, solve, inverse operations,
multiplication inverse

How are expressions manipulated to suit various purposes and help solve problems?
Big Ideas:

Writing, Interpreting and Analyzing Expressions

Equivalent Expressions

Representing and Describing Quantitative Relationships

Solving Equations and Inequalities
Suggested Mentor Texts:
N/A
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards
Teaching Points/Lesson Activity Description
Assessment

Understand the meanings of variable, expression, and term

Use the Order of Operations to simplify numerical expressions

Evaluate algebraic expressions for given values of the variables
6.EE.2 Write, read, and evaluate expressions in
which letters stand for numbers.

Interpret whole number exponents as indicating repeated
multiplication
6.EE.3
Apply the properties of operations to generate
equivalent expressions.

Write and simplify numerical expressions involving exponents
Lesson 1: page 422

Evaluate algebraic expressions involving exponents
Lesson 2: page 432
6.EE.4
Identify when two expressions are equivalent
(i.e., when the two expressions name the same
number regardless of which value is substituted
into them).

Use expressions with exponents to represent figures
Lesson 3: page 442

Translate between algebraic expressions and words
Lesson 4: page 452

Analyze algebraic expressions by applying the order of operations
6.EE.5
Understand solving an equation or inequality as a
process of answering a question: which values
from a specified set, if any, make the equation or
inequality true? Use substitution to determine
whether a given number in a specified set makes
an equation or inequality true.

Lesson 5: page 459
(Quick Quiz 1)
Draw diagrams that represent the structure of algebraic
expressions
Lesson 6: page 474

Identify and write expressions for dot diagrams
Lesson 7: page 488

Make dot diagrams to match algebraic expressions
Lesson 8: page 500

Analyze and evaluate algebraic expressions
Lesson 9: page 510
(Quick Quiz 2)
6.EE.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.

Write expressions for areas of complex figures

Write expressions for surface areas of rectangular prisms based
on their nets

Understand the meaning of equivalent expressions

Write and recognize equivalent expressions

Connect real world situations, models and expressions
Mathematical Content
6.EE.1 Write and evaluate numerical expressions
involving whole-number exponents.
6.EE.B.7
Solve real-world and mathematical problems by
writing and solving equations of the form x + p =
Initial Assessment –
Form A pre-test
Formative
Assessments–Quick
quizzes
Lesson 10: page 520
Lesson 11: page 532
Lesson 12: page 542
Lesson 13: page 550
(Quick Quiz 3)
Lesson 14: page 562
q and px = q for cases in which p, q and x are all
nonnegative rational numbers.

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.

Simplify expressions by combining like terms

Identify coefficients of terms

Understand and apply the distributive property

Use the properties of arithmetic to identify and write equivalent
expressions
6.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
variables using graphs and tables, and relate
these to the equation.

Simplify and evaluate expressions

Use properties to write and recognize equivalent expressions

Write expressions for real world situations

Recognize quantities that vary together

Define variables for quantities

Use tables, diagrams, and equations to represent relationships
between quantities that vary together

Investigate how the rate of motion relates to tables, graphs, and
equations relating time and distance

Use different representations to find or estimate distances traveled
in given amounts of time

Make a table and a graph based on an equation

Relate equations, graphs and tables for constant-change situations

Write and relate cost equations to situations

Make tables to identify the company that offers the lowest price for
different numbers of items

Find solutions of inequalities
6.G.1 Find the area of right triangles, other
triangles, special quadrilaterals, and polygons by
composing into rectangles or decomposing into
triangles and other shapes; apply these
techniques in the context of solving real-world
and mathematical problems.
6.G.4 Represent three-dimensional figures using
nets made up of rectangles and triangles, and
use the nets to find the surface area of these
figures. Apply these techniques in the context of
solving real-world and mathematical problems.
6.NS.4 Find the greatest common factor of two
whole numbers less than or equal to 100 and the
least common multiple of two whole numbers
less than or equal to 12. Use the distributive
Understand and apply the commutative and associative properties
of addition and multiplication
Lesson 15: page 572
Lesson 16: page 582
Lesson 17: page 594
Math Writing Prompts
End of Unit
Assessment – Form
A assessment
Performance Task if
created.
property to express a sum of two whole numbers
1-100 with a common factor as a multiple of a
sum of two whole numbers with no common
factor.

Graph one-variable inequalities

Write and graph inequalities that represent real world situations

Determine whether a given value is a solution of an equation or
inequality

Solve equations by reasoning about which value of the variable will
make the sides equal

Model and solve addition and subtraction equations

Model and solve multiplication and division equations

Apply mathematical concepts and skills in meaningful contexts

Reinforce the common core mathematical content standards and
mathematical practices with a variety of problem-solving situations
Mathematical Practices
CC.K-12.MP.1 Make sense of problems and
persevere in solving them
CC.K-12.MP.2 Reason abstractly and
quantitatively
CC.K-12.MP.3 Construct viable arguments and
critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
CC.K-12.MP.5 Use appropriate tools
CC.K-12.MP.6 Attend to precision
CC.K-12.MP.7 Look for and make use of
structure
CC.K-12.MP.8 Look for and express regularity in
repeated reasoning