Curriculum Development Overview
th
Unit Planning for 6 Grade Mathematics
Unit Title
Very Variable
Focusing Lens(es)
Structure
Modeling
Inquiry Questions
(EngagingDebatable):
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Unit Strands
Expressions and Equations
Concepts
exponents, multiplication, symbolizing, base, substitution, variable, inequalities, equations, solutions, values, order of operations, commutative, associate,
distributive, equivalent, numeric expressions, algebraic expressions, characteristics, term, coefficient, sum, factor, quotient, product, constraint, condition,
infinite, number line diagram, independent, dependent
Length of Unit
Standards and Grade
Level Expectations
Addressed in this Unit
6 weeks
MA10-GR.6-S.2-GLE.1
MA10-GR.6-S.2-GLE.2
Why do we call letters meant to symbolize unknown quantities variables, do they always vary? (MA10-GR.6-S.2-GLE.2-EO.b)
Generalizations
My students will Understand that…
Guiding Questions
Factual
Conceptual
Exponents symbolize repeated multiplication; the base
represents the quantity being repeatedly multiplied and
the exponent defines the number of repeated
multiplications. (MA10-GR.6-S.2-GLE.1-EO.a)
What does a base and exponent represent?
In order of operations, which comes should be
performed first exponents or multiplication and
division?
How is multiplication symbolizing repeated addition
similar and different from exponents symbolizing
repeated multiplication?
Why isn’t (2+3)3 equal to 23+ 33?
Using order of operations and the commutative,
associate, and distributive properties generates
equivalent expressions. (MA10-GR.6-S.2-GLE.1-EO.b.iv, c)
Which property justifies that 2k+6 is equivalent to
2(k+3)?
How do you simplify a given expression?
Why do the order of operations exist? (MA10-GR.6-S.2GLE.1-IQ.4)
Algebraic expressions contain variables that represent
either a single unknown or a quantity that varies
(changes). (MA10-GR.6-S.2-GLE.1-EO.b.i, c)
What is the difference between an algebraic and
numeric expression?
If we didn’t have variables, what would we use? (MA10GR.6-S.2-GLE.1-IQ.1)
What purpose do algebraic expressions serve? (MA10GR.6-S.2-GLE.1-IQ.2)
Why is it helpful to record operations with numbers and
letters standing for numbers?
Why are there advantages to being able to describe
a pattern using variables? (MA10-GR.6-S.2GLE.1-IQ.3)
Authors of the Sample: Sara Gust (Sangre De Cristo RE-22J); Shirley Martinson (Thompson R-2J), Crystal Schmidt (Otis R3)
Complete Sample Curriculum – Posted: February 15, 2013
6th Grade, Mathematics
Page 13 of 20
Curriculum Development Overview
th
Unit Planning for 6 Grade Mathematics
The structure and characteristics of mathematical
expressions (term, coefficient, sum, factor, quotient and
product and equations) help predict mathematical
behaviors and model mathematical situations. (MA10GR.6-S.2-GLE.1-EO.b.ii)
What does the word term mean in relation to
expressions?
How can you determine the number of terms in an
expression?
What is a coefficient?
What is a constant?
How does understanding the structure of expressions
support the simplification of expressions?
Why is it helpful to sometimes view terms of an
expression as a single entity and other times as
separate entities?
Mathematicians can ascertain the equivalence of two
algebraic expressions if, for any value substituted for the
variable, the values of two expressions are equal. (MA10GR.6-S.2-GLE.1-EO.d) and (MA10-GR.6-S.2-GLE.2-EO.a)
How can you determine if two expressions are
equivalent?
If an equation has multiple instances of the same
variable, does the same value need to be substituted
for all of them?
Do all equations have one unique solution? (2.2.IQ1)
Why is only one counter-example (a value for the
variable that yields unequal results for the two
expressions) needed to disprove the equivalence of
two expressions?
How might simplifying two expressions help determine if
they are equivalent?
Why is a solution(s) to an equation or inequality the
value(s) that make them true?
An inequality of the form x > c or x < c represents a
constraint or condition in a real-world or mathematical
problem and inequalities of this form have infinitely many
solutions. (MA10-GR.6-S.2-GLE.2-EO.e, f)
How can you show an infinite amount of solutions on a
number line?
Why does an inequality have an infinite number of
solutions?
Dependent and independent variables represent two
quantities that change in relationship to one another.
(MA10-GR.6-S.2-GLE.2-EO.g)
How can you represent the relationship between
dependent and independent variables in a table?
graph?
Why are coordinate pairs used to represent solutions to
two variable equations?
How can you determine if a variable is independent or
dependent? (MA10-GR.6-S.2-GLE.2-IQ.2)
Authors of the Sample: Sara Gust (Sangre De Cristo RE-22J); Shirley Martinson (Thompson R-2J), Crystal Schmidt (Otis R3)
Complete Sample Curriculum – Posted: February 15, 2013
6th Grade, Mathematics
Page 14 of 20
Curriculum Development Overview
th
Unit Planning for 6 Grade Mathematics
Key Knowledge and Skills:
My students will…
What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics
samples what students should know and do are combined.
Authors of the Sample: Sara Gust (Sangre De Cristo RE-22J); Shirley Martinson (Thompson R-2J), Crystal Schmidt (Otis R3)
Complete Sample Curriculum – Posted: February 15, 2013
6th Grade, Mathematics
Page 15 of 20
Curriculum Development Overview
th
Unit Planning for 6 Grade Mathematics
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Write and evaluate numerical expressions involving whole-number exponents. (MA10-GR.6-S.2-GLE.1-EO.a)
Evaluate numbers raised to a power
Write expressions using exponents (use exponential notation)
Write expressions that record operations with numbers and with letters standing for numbers. (MA10-GR.6-S.2-GLE.1-EO.b.i)
Write expressions of mathematical operations with numbers and variables
Create expressions using numbers and variables to describe a quantity

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity (MA10GR.6-S.2-GLE.1-EO.b.ii)

Explain what it means to note that two expressions are equivalent, especially when those expressions include the same variable(s) or different
variables

Evaluate expressions at specific values of their variables; including expressions that arise from formulas used in real-world problems and perform arithmetic operations,
involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order. (MA10-GR.6-S.2-GLE.1-EO.b.iii, b.iv)

Using student white boards, and given 10 numeric expressions, students will correctly compute at least seven of the expressions using the order of
operations.

Apply the properties of operations to generate equivalent expressions. (MA10-GR.6-S.2-GLE.1-EO.c)
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Apply the associative and commutative properties to generate equivalent expressions
Apply the distributive property to generate equivalent expressions
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Identify when two expressions are equivalent. (MA10-GR.6-S.2-GLE.1-EO.d)

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. (MA10-GR.6-S.2-GLE.2-EO.c, c.i)
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Explain what it means to note that two expressions are equivalent, especially when those expressions include the same variable(s) or different
variables
Write expressions of mathematical operations with numbers and variables
Create expressions using numbers and variables to describe a quantity
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem

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 (MA10GR.6-S.2-GLE.2-EO.a)

Show that inequalities of the form x > c or x < c have infinitely many solutions
Graph the solutions of such inequalities on a number line
Describe 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.
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Authors of the Sample: Sara Gust (Sangre De Cristo RE-22J); Shirley Martinson (Thompson R-2J), Crystal Schmidt (Otis R3)
Complete Sample Curriculum – Posted: February 15, 2013
6th Grade, Mathematics
Page 16 of 20
Curriculum Development Overview
th
Unit Planning for 6 Grade Mathematics
 Use substitution to determine whether a given number in a specified set makes an equation or inequality true. (MA10-GR.6-S.2-GLE.2-EO.b)

Given five equations or inequalities with variables, and a proposed solution, students will use substitution to correctly determine whether the given
number makes the equation or inequality true.

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. (MA10-GR.6-S.2-GLE.2-EO.d)

Solve real-world problems by solving equations with variables, especially of the form x + p = q and px = q (for cases in which p, q, and x are all
non-negative rational numbers)

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem and recognize that inequalities of the form x > c
or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. (MA10-GR.6-S.2-GLE.2-EO.e, f)
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Recognize that a variable can represent an unknown number or any number in a specified set

Distinguish between dependent and independent variables
Use variables to represent two quantities in a real-world problem that change in relationship to one another
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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. (MA10-GR.6-S.2-GLE.2-EO.g, g.i, g.ii)
Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (MA10-GR.6-S.2-GLE.2-EO.g.iii)
Authors of the Sample: Sara Gust (Sangre De Cristo RE-22J); Shirley Martinson (Thompson R-2J), Crystal Schmidt (Otis R3)
Complete Sample Curriculum – Posted: February 15, 2013
6th Grade, Mathematics
Page 17 of 20
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Curriculum Development Overview
th
Unit Planning for 6 Grade Mathematics
Identify dependent and independent variables in real-world situations
Describe the relationship between such variables in an equation
Use graphs and tables to show the relationship between the dependent and independent variables
Critical Language: includes the Academic and Technical vocabulary, semantics, and discourse which are particular to and necessary for accessing a given discipline.
EXAMPLE: A student in Language Arts can demonstrate the ability to apply and comprehend critical language through the following statement: “Mark Twain exposes the
hypocrisy of slavery through the use of satire.”
A student in
can demonstrate the
ability to apply and comprehend critical language
through the following statement(s):
Algebraic inequalities have infinitely many solutions because there are infinitely many values on a number line
between any two points.
Academic Vocabulary:
Multiplication, characteristics, identify, apply, solve, represent
Technical Vocabulary:
Exponents, base, substitution, variable, inequalities, equations, solutions, order of operations, commutative, associate, distributive, numeric
expressions, algebraic expressions, term, coefficient, sum, factor, quotient, product, constraint, condition, infinite, number line diagram, values,
equivalent, evaluate, independent, dependent
Authors of the Sample: Sara Gust (Sangre De Cristo RE-22J); Shirley Martinson (Thompson R-2J), Crystal Schmidt (Otis R3)
Complete Sample Curriculum – Posted: February 15, 2013
6th Grade, Mathematics
Page 18 of 20