Monroe County Middle School
Detailed Pacing Guide
Grade Level: 7th
Unit Title
Content: Pre-Algebra / Mathematics
Key Concepts
Vocabulary
Detailed by Unit
Common
Core
Standards
7.NS.1
7.NS.3
Time
Allotted
Unit #1
The
Number
System
Part 1
ENDURING UNDERSTANDINGS
Rational numbers can be represented in multiple ways
and are useful when examining situations involving
numbers that are not whole.
ESSENTIAL QUESTIONS
In what ways can rational numbers be useful?
KEY IDEAS
 reading/labeling a number line
 adding/subtracting integers
 modeling adding/subtracting integers
 balancing checkbook activity
 integer basketball activity
 using positive/negative chips
 adding/subtracting integers word problems
 modeling open responses
absolute value
additive inverse
integer
negative
opposite
positive
rational number
August
Unit #2
The
Number
System
Part 2
ENDURING UNDERSTANDINGS
Rational numbers can be represented in multiple ways
and are useful when examining situations involving
numbers that are not whole.
ESSENTIAL QUESTIONS
In what ways can rational numbers be useful?
KEY IDEAS
 multiplying integers
 dividing integers
 integer board game
 multiplying/dividing integers word problems
 using long division
 terminating/repeating decimals
 modeling open responses
absolute value
additive inverse
complex fraction
integer
negative
opposite
positive
rational number
repeating decimal
terminating decimal
7.NS.2
7.NS.3
September
Unit #3
Fractions
ENDURING UNDERSTANDINGS
Fractions are an important concept and very useful for
discussions about measurement, probability, and data.
ESSENTIAL QUESTIONS
In what ways can fractions be useful?
KEY IDEAS
 changing improper fractions to mixed numbers
 changing mixed numbers to improper fractions
 adding/subtracting fractions
 adding/subtracting fractions word problems
 multiplying/dividing fractions
 multiplying/dividing fractions word problems
 open responses
equivalent fractions
greatest common
factor
improper fraction
least common multiple
mixed number
rational number
reciprocal
7.NS.3
October
Unit #4
Decimals
and
Conversions
ENDURING UNDERSTANDINGS
Believe it or not, fractions, decimals, and percents are all
related. You will use these basic functions for the rest of
your life.
ESSENTIAL QUESTIONS
In what ways can decimals and conversions be useful?
KEY IDEAS
 adding/subtracting decimals
 adding/subtracting decimals word problems
 multiplying/dividing decimals
 multiplying/dividing decimals word problems
 converting fractions to decimals/percents
 converting decimals to percents/fractions
 converting percents to fractions/decimals
decimals
percent
7.NS.2
7.NS.3
7.RP.3
October &
November
Unit #5
Ratios
and
Proportional
Relationships
ENDURING UNDERSTANDINGS
Ratios and proportional relationships are used to
express how quantities are related and how quantities
change in relation to each other.
ESSENTIAL QUESTIONS
How can ratios and proportional relationships be used to
determine unknown quantities?
KEY IDEAS
 definition of ratio/proportion
 writing a ratio
 setting up proportions
 definition of unit
 unit rate
 unit analysis
 apply knowledge to tables/graphs/similar figures
constant of
proportionality
equivalent ratios
origin
proportional
relationship
rate
ratio
unit rate
7.RP.1
7.RP.2
7.RP.3
November
&
December
Unit #6
Expressions
and
Equations
ENDURING UNDERSTANDINGS
Algebraic expressions and equations are used to model
real-life problems and represent quantitative
relationships, so that the numbers and symbols can be
mindfully manipulated to reach a solution or make sense
of the quantitative relationships.
ESSENTIAL QUESTIONS
How can algebraic expressions and equations be used to
model, analyze, and solve mathematical situations?
KEY IDEAS
 variables
 coefficients
 constants
 difference between equations/expressions
 writing expressions verbally/algebraically
 writing equations verbally/algebraically
 solving for the variable
 using scales to model algebraic equations
 solving for the variable: one-step equations
 solving for the variable: two-step equations
coefficient
equation
expression
inequality
like terms
linear expression
rational number
variable
7.EE.1
7.EE.2
7.EE.3
7.EE.4
January &
February




working with inequalities
graphing inequalities on a number line
solving one-step inequalities
solving two-step inequalities
Unit #7
Using
Probability
ENDURING UNDERSTANDINGS
The rules of probability can lead to more valid and
reliable predictions about the likelihood of an event
occurring.
ESSENTIAL QUESTIONS
How is probability used to make informed decisions
about uncertain events?
KEY IDEAS
 finding probability
 “certain” events
 “impossible” events
 different between probability/chance
 event/complement
 theoretical probability
 experimental probability
 coin activity
 sample space
 counting principle
 compound events
 dependent/independent events
 permutations/combinations
chance
combination
complement
compound event
counting principle
dependent events
event
experimental
probability
factorial
independent events
likely
outcome
permutation
sample space
theoretical probability
tree diagram
unlikely
7.SP.5
7.SP.6
7.SP.7
7.SP.8
February &
March
Unit #8
Geometry
Part 1
ENDURING UNDERSTANDINGS
Geometric attributes (such as shapes, lines, angles,
figures, and planes) provide descriptive information
about an object’s properties and position in space and
support visualization and problem solving.
ESSENTIAL QUESTIONS
How does geometry better describe objects?
KEY IDEAS
 identifying rays/segments/lines
 right/acute/obtuse angles
 angles that are complementary/supplementary
 adjacent/vertical/congruent angles
 scalene/isosceles/equilateral triangles
 right/acute/obtuse triangles
 classifying polygons
 regular/irregular polygons
 special quadrilaterals
 difference between square/rectangle
 trapezoid/parallelogram/rhombus
 congruent polygons
 identifying parts of a circle
 constructing circle graphs
 constructing perpendicular lines
 finding bisector/section bisector/midpoint
acute triangle
circle graph
complementary
equilateral triangle
isosceles triangle
obtuse triangle
parallel lines
parallelogram
rectangle
regular polygon
rhombus
right triangle
scalene triangle
square
supplementary
trapezoid
7.G.1
7.G.2
7.G.3
7.G.5
March

compass activity
Unit #9
Part 2
ENDURING UNDERSTANDINGS
Geometric attributes (such as shapes, lines, angles,
figures, and planes) provide descriptive information
about an object’s properties and position in space and
support visualization and problem solving.
ESSENTIAL QUESTIONS
How does geometry better describe objects?
KEY IDEAS
 estimating perimeter area
 finding height/base of parallelograms
 finding perimeter/area of parallelograms
 finding perimeter/area of triangles
 finding area of trapezoids
 finding area of irregular shapes
 finding circumference/area of circles
 perfect square/square root
 the Pythagorean Theorem
 classifying 3-dimensional figures
 drawing 3-dimensional figures
 finding surface area/volume of prisms
 finding surface area/volume of cylinders
 using nets activity
 finding geometry in the real world activity
area
circumference
cone
cylinder
hypotenuse
irrational number
net
perimeter
prism
pyramid
Pythagorean Theorem
sphere
square root
surface area
three-dimensional
figure
volume
7.G.1
7.G.3
7.G.4
7.G.6
March &
April
Unit #10
Displaying
and
Analyzing
Data
ENDURING UNDERSTANDINGS
The rules of probability can lead to more valid and
reliable predictions about the likelihood of an event
occurring.
ESSENTIAL QUESTIONS
How is probability used to make informed decisions
about uncertain events?
KEY IDEAS
 displaying data
 using frequency tables/line plots/histograms
 interpreting data
 using spreadsheets
 using double bar graphs/double line graphs
 working with stem-and-leaf plots
 identifying random samples
 writing survey questions
 survey activity
 identifying populations
 identifying misleading graphs/statistics
 drawing/interpreting scatter plots
biased question
cell
double bar graph
double line graph
frequency table
histogram
legend
line plot
negative trend
no trend
population
positive trend
random sample
sample
scatter plot
spreadsheet
stem-and-leaf plot
7.SP.1
7.SP.2
7.SP.3
7.SP.4
April &
May