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Tennessee
Mathematics Standards:
Grade Seven Mathematics
Standard 1 – Mathematical Processes
Grade
Level Expectations:
GLE 0706.1.1 Use mathematical language, symbols, and definitions
while developing mathematical reasoning.
GLE 0706.1.2 Apply and adapt a variety of appropriate strategies
to problem solving, including estimation, and reasonableness of
the solution.
GLE 0706.1.3 Develop independent reasoning to communicate
mathematical ideas and derive algorithms and/or formulas.
GLE 0706.1.4 Move flexibly between concrete and abstract
representations of mathematical ideas in order to solve
problems, model mathematical ideas, and communicate solution
strategies.
GLE 0706.1.5 Use mathematical ideas and processes in different
settings to formulate patterns, analyze graphs, set up and solve
problems and interpret solutions.
GLE 0706.1.6 Read and interpret the language of mathematics and
use written/oral communication to express mathematical ideas
precisely.
GLE 0706.1.7 Recognize the historical development of
mathematics, mathematics in context, and the connections between
mathematics and the real world.
GLE 0706.1.8 Use technologies/manipulatives appropriately to
develop understanding of mathematical algorithms, to facilitate
problem solving, and to create accurate and reliable models of
mathematical concepts.
Check for Understanding (Formative/Summative Assessment):
0706.1.1
Recognize common abbreviations (such as gcd/gcf and lcm).
0706.1.2
Recognize round-off error and the inaccuracies it introduces.
0706.1.3
Check answers both by estimation and by appropriate independent
calculations, using calculators or computers judiciously.
0706.1.4
Recognize quantities that are inversely proportional (such as
the relationship between the lengths of the base and the side of
a rectangle with fixed area).
0706.1.5
Understand that a linear function in which f(0) = 0 is called a
directly proportional relationship.
0706.1.6
Develop meaning of intercept and rate of change in contextual
problems.
0706.1.7
Explain and demonstrate how scale in maps and drawings shows
relative size and distance.
0706.1.8
Recognize the applications of scale factor by exploring
blueprints, shadow measuring, and scale models.
0706.1.9
Use age-appropriate books, stories, and videos to convey ideas
of mathematics.
0706.1.10
Model algebraic equations with manipulatives, technology, and
pencil and paper.
0706.1.11
Translate from calculator notation to scientific/standard
notation.
0706.1.12
Use dynamic geometry software to explore scale factor and
similarity.
State Performance Indicators:
SPI 0706.1.1 Use proportional reasoning to solve
mixture/concentration problems.
SPI 0706.1.2 Generalize a variety of patterns to a symbolic rule
from tables, graphs, or words.
SPI 0706.1.3 Recognize whether information given in a table,
graph, or formula suggests a directly proportional, linear,
inversely proportional, or other nonlinear relationship.
SPI 0706.1.4 Use scales to read maps.
Standard 2 – Number & Operations
Grade Level Expectations:
GLE 0706.2.1 Extend understandings of addition, subtraction,
multiplication and division to integers.
GLE 0706.2.2 Understand and work with the properties of and
operations on the system of rational numbers.
GLE 0706.2.3 Develop an understanding of and apply
proportionality.
GLE 0706.2.4 Use ratios, rates and percents to solve single- and
multi-step problems in various contexts.
GLE 0706.2.5 Understand and work with squares, cubes, square
roots and cube roots.
GLE 0706.2.6 Introduce the concept of negative exponents.
GLE 0706.2.7 Understand and use scientific notation.
Check for Understanding (Formative/Summative Assessment):
0706.2.1
Understand that the set of rational numbers includes any number
that can be written as a ratio of two integers in which the
denominator is not zero.
0706.2.2
Develop and analyze algorithms and compute efficiently with
integers and rational numbers.
0706.2.3
Recognize that rational numbers satisfy the commutative and
associative laws of addition and multiplication and the
distributive law.
0706.2.4
Understand that a and –a are additive inverses and are located
the same distance from zero on the number line; relate distance
from zero to absolute value.
0706.2.5
Understand that –(–a) = a for any number a.
0706.2.6
Use the number line to demonstrate addition and subtraction with
integers.
0706.2.7
Write number sentences to solve contextual problems involving
ratio and percent.
0706.2.8
Apply ratios, rates, proportions and percents (such as
discounts, interest, taxes, tips, distance/rate/time, and
percent increase or decrease).
0706.2.9
Efficiently compare and order rational numbers and roots of
perfect squares/cubes; determine their approximate locations on
a number line.
0706.2.10
Recognize that when a whole number is not a perfect square, then
its square root is not rational and cannot be written as the
ratio of two integers.
0706.2.11
Estimate square/cube roots and use calculators to find
approximations.
0706.2.12
Recognize  and 
0706.2.13
Use the meaning of negative exponents to represent small
numbers; translate between scientific and standard notation.
0706.2.14
Express numbers in scientific notation and recognize its
importance in representing the magnitude of a number.
0706.2.15
Report results of calculations appropriately in a given context
(i.e. using rules of rounding, degree of accuracy, and/or
significant digits).
State Performance Indicators:
SPI 0706.2.1 Simplify numerical expressions involving rational
numbers.
SPI
0706.2.2 Compare rational numbers using appropriate inequality
symbols.
SPI 0706.2.3 Use rational numbers and roots of perfect
squares/cubes to solve contextual problems.
SPI 0706.2.4 Determine the approximate location of square/cube
roots on a number line.
SPI
0706.2.5 Solve contextual problems that involve operations with
integers.
SPI 0706.2.6 Express the ratio between two quantities as a
percent, and a percent as a ratio or fraction.
SPI 0706.2.7 Use ratios and proportions to solve problems.
Standard 3 – Algebra
Grade Level Expectations:
GLE 0706.3.1 Recognize and generate equivalent forms for simple
algebraic expressions.
GLE 0706.3.2 Understand and compare various representations of
relations and functions.
GLE 0706.3.3 Understand the concept of function as a rule that
assigns to a given input one and only one number (the output).
GLE 0706.3.4 Use function notation where f(x)
represents the output that the function f assigns to the
input x.
GLE 0706.3.5 Understand and graph proportional relationships.
GLE 0706.3.6 Conceptualize the meanings of slope using various
interpretations, representations, and contexts.
GLE 0706.3.7 Use mathematical models involving linear equations
to analyze real-world phenomena.
GLE 0706.3.8 Use a variety of strategies to efficiently solve
linear equations and inequalities.
Check for Understanding (Formative/Summative Assessment):
0706.3.1
Perform basic operations on linear expressions (including
grouping, order of operations, exponents, simplifying and
expanding).
0706.3.2
Represent and analyze mathematical situations using algebraic
symbols.
0706.3.3
Identify a function from a written description, table, graph,
rule, set of ordered pairs, and/or mapping.
0706.3.4
Make tables of inputs x and outputs f(x) for a
variety of rules that include rational numbers (including
negative numbers) as inputs.
0706.3.5
Plot points to represent tables of linear function values.
0706.3.6
Understand that the graph of a linear function f is the
set of points on a line representing the ordered pairs (x, f(x)).
0706.3.7
Distinguish proportional relationships (y/x = k, or y = kx) from
other relationships, including inverse proportionality (xy = k,
or y = k/x).
0706.3.8
Understand slope as the ratio of vertical change to horizontal
change.
0706.3.9
Identify a function exhibiting a constant rate of change as a
linear function and identify the slope as a unit rate.
0706.3.10
Solve problems involving unit rates (e.g., miles per hour, words
per minute).
0706.3.11
Relate the features of a linear equation to a table and/or graph
of the equation.
0706.3.12
Use linear equations to solve problems and interpret the meaning
of slope, m, and the y-intercept, b, in f(x)= mx +
b in terms of the context.
0706.3.13
Given a graph that exhibits the intersection of a line and the
y-axis, write a linear function in slope-intercept form: y = mx
+ b.
0706.3.14
Understand that when solving linear inequalities, multiplication
or division by a negative reverses the inequality symbol.
State Performance Indicators:
SPI 0706.3.1 Evaluate algebraic expressions involving rational
values for coefficients and/or variables.
SPI 0706.3.2 Determine whether a relation (represented in
various ways) is a function.
SPI 0706.3.3 Given a table of inputs x and outputs f(x),
identify the function rule and continue the pattern.
SPI 0706.3.4 Interpret the slope of a line as a unit rate given
the graph of a proportional relationship.
SPI 0706.3.5 Represent proportional relationships with
equations, tables and graphs.
SPI 0706.3.6 Solve linear equations with rational coefficients
symbolically or graphically.
SPI 0706.3.7 Translate between verbal and symbolic
representations of real-world phenomena involving linear
equations.
SPI 0706.3.8 Solve contextual problems involving two-step linear
equations.
SPI 0706.3.9 Solve linear inequalities in one variable with
rational coefficients symbolically or graphically.
Standard 4 – Geometry & Measurement
Grade Level Expectations:
GLE 0706.4.1 Understand the application of proportionality with
similar triangles.
GLE 0706.4.2 Apply proportionality to converting among different
units of measurements to solve problems involving rates such as
motion at a constant speed.
GLE 0706.4.3 Understand and use scale factor to describe the
relationships between length, area, and volume.
GLE 0706.4.4 Understand and use ratios, derived quantities, and
indirect measurements.
Check for Understanding (Formative/Summative Assessment):
0706.4.1
Solve problems involving indirect measurement such as finding
the height of a building by comparing its shadow with the height
and shadow of a known object.
0706.4.2
Use similar triangles and proportionality to find the lengths of
unknown line segments in a triangle.
0706.4.3
Understand that if a scale factor describes how corresponding
lengths in two similar objects are related, then the square of
the scale factor describes how corresponding areas are related,
and the cube of the scale factor describes how corresponding
volumes are related.
0706.4.4
Compare angles, side lengths, perimeters and areas of similar
shapes.
0706.4.5
Solve problems using ratio quantities: velocity (measured in
units such as miles per hour), density (measured in units such
as kilograms per liter), pressure (measured in units such as
pounds per square foot), and population density (measured in
units such as persons per square mile).
State Performance Indicators:
SPI 0706.4.1 Solve contextual problems involving similar
triangles.
SPI 0706.4.2 Use SSS, SAS, and AA to determine if two triangles
are similar.
SPI 0706.4.3 Apply scale factor to solve problems involving area
and volume.
Standard 5 – Data Analysis, Statistics, & Probability
State
Performance Indicators:
SPI 0706.5.1 Interpret and employ various graphs and charts to
represent data.
SPI 0706.5.2 Select suitable graph types (such as bar graphs,
histograms, line graphs, circle graphs, box-and-whisker plots,
and stem-and-leaf plots) and use them to create accurate
representations of given data.
SPI 0706.5.3 Calculate and interpret the mean, median,
upper-quartile, lower-quartile, and interquartile range of a set
of data.
SPI 0706.5.4 Use theoretical probability to make predictions.
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