squares (specifically, square roots)
•
Write algebraic expressions with up to three
variables
Reason about and solve one-variable equations
and inequalities
•
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
•
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
•
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
•
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
Represent and analyze quantitative relationships
between dependent and independent variables
•
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
Measurement and Data
•
Estimate, compare and convert units of measure
for length, area, weight/mass, and volume in the
U.S. standard system and metric system using
approximate equivalents
•
Understand the Metric System and basic
conversions
•
Estimate the perimeter, circumference, area,
and volume of figures and explain the reasoning
behind the estimation
•
Estimate, measure, and draw angles and
triangles using appropriate tools
Geometry
Solve real-world and mathematical problems
involving area, surface area, and volume
•
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
•
Find the volume of a right rectangular prism
with fractional edge lengths by packing it with
unit cubes of the appropriate unit fraction
edge lengths, and show that the volume is the
same as would be found by multiplying the
edge lengths of the prism; apply the formulas
V = l w h and V = b h to find volumes of
right rectangular prisms with fractional edge
lengths in the context of solving real-world and
mathematical problems
•
Draw polygons in the coordinate plane given
coordinates for the vertices; use coordinates
to find the length of a side joining points with
the same first coordinate or the same second
coordinate; apply these techniques in the
context of solving real-world and mathematical
problems
•
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
•
Describe sizes, positions, and orientations of
shapes under informal transformation
Geometric concepts
•
Identify and define parts of a circle
•
Compare and classify triangles based on sides
(scalene, equilateral, or isosceles) and angles
•
Identify and describe angles as vertical,
adjacent, complementary, or supplementary and
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Sixth Grade
uses these properties to determine unknowns
•
Determine congruence by comparing attributes
•
Use two-dimensional representations of three-
dimensional objects to visualize and solve
problems
Statistics and Probability
Develop understanding of statistical variability
•
Recognize a statistical question as one that
anticipates variability in the data related to the
question and accounts for it in the answers
•
Understand that a set of data collected to
answer a statistical question has a distribution
which can be described by its center, spread,
and overall shape
•
Recognize that a measure of center for a
numerical data set summarizes all of its values
with a single number, while a measure of
variation describes how its values vary with a
single number
Summarize and describe distributions
•
Display numerical data in plots on a number
line, including dot plots, histograms, and box
plots
•
Summarize numerical data sets in relation to
their context
•
Report the number of observations
•
Describe the nature of the attribute under
investigation, including how it was measured
and its units of measurement
•
Give quantitative measures of center and
variability as well as describe any overall pattern
and any striking deviations from the overall
pattern with reference to the context in which
the data were gathered
•
Relate the choice of measures of center and
variability to the shape of the data distribution
and the context in which the data were
gathered
SCIENCE
Processes That Shape the Earth
•
Define the characteristics of the study of Earth
•
Understand the purpose and value of
topography
•
Classify landforms based on observations and
characteristics
•
Classify minerals and rocks based on
properties
•
Describe how minerals are formed
•
Identify the various components of the rock
cycle
•
Analyze the change to the total amount of
material during the rock cycle
•
Compare and contrast properties of the three
different types of rocks
•
Identify the layers of the Earth
•
Recognize and give examples of how natural
catastrophes affect the Earth’s climate
•
Identify evidence of plate tectonics
•
Explain the effect of plate tectonics
•
Define and compare the four types of stresses
•
Define and compare the three types of heat
transfer
•
Create a model that demonstrates the
processes of plate tectonics and how it creates
mountains, valleys, etc.
•
Know that earthquakes often occur along the
boundaries between colliding plates
•
Explain how earthquakes are measured
•
Map the location of volcanoes
•
Describe how volcanoes are formed
•
Identify the physical and chemical properties
of magma
•
Describe the difference between weathering
and erosion
•
Understand how the forces of water contribute
to erosion
The Atmosphere and the Weather
•
Identify gases in atmosphere
•
Investigate the properties of air
•
Label and describe the layers of the
Earth’s atmosphere
•
Research why the East Coast of the U.S.
is affected by hurricanes more than the
West Coast
•
Explain how the transfer of heat energy at the
boundaries results in layers at different
temperatures and densities in the atmosphere
•
Explain how temperatures and densities create
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Nobel Learning Curriculum Reference Guide
