Subject: Math
Grade: 8
Unit #: 4
Title: Say it with Symbols
UNIT OVERVIEW
8.EE.2
8.EE.7a,7b
8.EE.8a, 8b, 8c
8.F.1
8.F.2
8.F.3
8.F.4
8.F.5
8.G.9
STAGE ONE: Identify Desired Results
Long-Term Transfer Goal
At the end of this unit, students will use what they have learned to independently…
The Say it with Symbols unit will focus on making sense of symbolic expression and
equations. Scholars will understand that there are different ways of reasoning about a
situation that can lead to different but equivalent expressions. They will use mathematical
properties of equality, distributive and communicative number properties to rewrite
expressions. Using equivalent expressions, they will understand that problems can be
thought about in different ways. Scholars will further develop their strategies to solve
equations, including problems related to volumes of cylinders, cones and spheres. They will
also continue their work using multiple representations, including graphs, tables, and
symbolic representations.
Enduring Understandings
Meaning
Essential Questions
Established Goals/Standards
Students will understand that…
Algebra provides ideas and symbols for
expressing information about quantitative
variables and relationships. Students will
solve problems designed to develop their
understanding and skill in symbolic
expressions and equations.
East High School, Rochester, NY
Students will consider such questions as…
How can expressions and equations be
rewritten into equivalent expressions?
How can equivalent expressions be
used to solve problems?
Students will understand
(Equivalence)
 How to represent patterns and
relationships in symbolic form
 Determining when different symbolic
expression are mathematically
equivalent
 Writing algebraic expressions in
useful equivalent forms
 Combining symbolic expressions
using algebraic operations to form
new expressions
 Solving linear equations using
symbolic reasoning
 Using algebraic reasoning to validate
generalizations and conjecture
(Functions)
 Identifying and representing
relationships expressed in problem
contexts with linear and non linear
functions and use these relationships
to solve problems
 How to analyze equations to
determine the patterns of change in
a table and graph that an equation
Based on UbD (ASCD) by G. Wiggins and J. McTighe
Subject: Math
Grade: 8
Unit #: 4


Title: Say it with Symbols
represents
How to relate parts of a symbolic
statement or expression to the
underlying properties of the
relationship they represent and to
the context of the problem
Determine characteristics of a graph
of an equation looking at its symbolic
representation
Acquisition
What knowledge will students learn as part
of this unit?
What expressions or equations represent the
pattern or relationship in a context?
Can you write an equivalent expression for a
given expression to provide new information
about a relationship?
What operations can transform a given
equation or expression into an equivalent
form that can be used to answer a question?
How can symbolic reasoning help confirm a
conjecture?
Criteria for to assess
understanding: (This is
used to build the scoring
tool.)
What skills will students learn as part of this
unit?
Five aspects of symbolic representation:
creating and interpreting equivalent
expressions, combining expressions, solving
equations, observing patterns of change, and
reasoning with symbols.
STAGE TWO: Determine Acceptable Evidence
Assessment Evidence
Performance Task focused on Transfer:
Unit test
Unit project (if time permits)
Other Assessment Evidence:
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East High School, Rochester, NY
Check ups
Partner Quiz (post investigation 2)
Self-assessments of learning targets
Teacher observations
Unit Test
Common assessment (task to be determined at 20 weeks)
Based on UbD (ASCD) by G. Wiggins and J. McTighe
Subject: Math
Grade: 8
T, M, A
(Code for Transfer,
Unit #: 4
Title: Say it with Symbols
STAGE THREE: Plan Learning Experiences
Meaning Making and
Acquisition)
Learning Events:
Evidence of learning:
Investigation 1:Equivalent Expressions (3 days)
Scholars will use their selected strategies to generate and justify
equivalence of two or more symbolic expressions for the same situation.
Equivalence will be discussed in terms of tables, graphs, and the validity
of reasoning each expression or equation represents. Scholars will be
reintroduced to the properties of equality and commentaries and
distributive number properties.
(formative assessment)
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Reflection questions
Ace questions
Class work
Student journals
Teacher observations
 Problem 1.1: Tiling pools-writing equivalent expressions (A)
LT: I can develop expressions to represent the number of border tiles
needed to surround a square poll with side length s.
 Problem 1.2: Thinking in different ways- deterring equivalence
(M)
LT: I can determine if two or more expressions are equivalent.
 Problem 1.4: Diving in- revisiting the distributive property
(M/T)
LT: I can use the distributive and commutative property of show that
two expressions are equivalent.
Investigation 2: Combining Expressions (5 days)
Scholars will combine expressions to write new expressions by either
adding or subtracting expressions or by substituting an equivalent
expression for a given quantity in an expression or equation. They will
also explore, describe and develop formulas for the relationship
between the volumes of cylinders, cones and spheres.
 Problem 2.1: Walking together- adding expressions (M)
LT: I can identify the advantages and disadvantages of using one
equation rather than two or more equations to represent a situation.
 Problem 2.2: Predicting Profit- substituting expression (T)
LT: I can apply what I know to combine one or more expressions (or
equations) to create a new expression (or equation)
 Problem 2.3: Making candles- volumes of cylinders, cones, and
spheres (M)
LT: I can use equations to represent the relationships among the
volumes of cylinders, cones, and spheres.
 Problem 2.4: Selling ice cream- solving volume problems (T)
LT: I can determine which formulas are useful in solving problems
involving volumes of cylinders, cones, and spheres.
Investigation 3: Solving Equations (2 days)
Scholars will continue to use distributive and commutative number
properties and properties of equality to solve linear equations with
parentheses.
 Problem 3.1: Selling greeting cards-solving linear equations (M)
LT: I can use strategies I know to solve equations that contain
East High School, Rochester, NY
Based on UbD (ASCD) by G. Wiggins and J. McTighe
Subject: Math
Grade: 8
Unit #: 4
Title: Say it with Symbols
parentheses.
 Problem 3.2: Comparing costs-solving more linear equations (T)
LT: I can use strategies I know to find a solution that is common to two
variable linear equations.
?Filling and Wrapping Investigation 4 (3 days)
*to extend work on 8.G.9*
Using generalizations from particular cylinders to find the formulas for
the volume and surface area of any cylinder. They will see that the
volume of a cylinder can be calculated by multiplying area of the base by
the height. Relationships between volumes of cylinders, spheres, and
cones lead to constructing formulas for these other figures. These
formulas will be applied to solve problems.
 Problem 4.2: Wrapping paper-Volume of cylinders (A)
LT: I can calculate the volume of a cylinder and apply my understanding
to develop how calculate the volume of a prism.
 Problem 4.4: Filling cones and spheres (M)
LT: Using a sphere and a cone with the same dimensions as a cylinder,
can compare the volumes of these objects.
I can derive the for the volume of a sphere and the volume of a cone
 Problem 4.5: Comparing volumes of sphere, cylinders, and
cones (M)
I can explore relationships involving a cone, sphere, and a cylinder with
the same dimensions.
East High School, Rochester, NY
Based on UbD (ASCD) by G. Wiggins and J. McTighe