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Math Scope and Sequence Grade 8

Standards
NCTM Curriculum Focal Points

The National Council of Teachers of Mathematics (NCTM) created its Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics (2006) to provide
descriptions of the most significant mathematical concepts and skills at each grade level. These focal points were chosen according to three criteria: they are
mathematically important, both for further study in mathematics and for use in applications in and outside of school; they conform to what is known about learning
mathematics; they connect logically with the mathematics in earlier and later grade levels. According to the NCTM, “these curriculum focal points should be considered
as major instructional goals and desirable learning expectations, not as a list of objectives for students to master.” It is important that none of the focal points be omitted;
it is less important whether they are addressed a year earlier or later, or over a period of two years, compared with the suggested sequence in the document.
On this page, each of the NCTM focal points is followed (in parentheses) by the corresponding New York State performance indicators.

Focal Points
Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations
Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x =
k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a
line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the
output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that
tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in
different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the
same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations
and solve problems. (7.A.7-8, 7.A.10)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle
Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems,
including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a
transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and
distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180
degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean theorem is valid by using a variety of
methods—for example, by decomposing a square in two different ways. They apply the Pythagorean theorem to find distances between points in the Cartesian
coordinate plane to measure lengths and analyze polygons and polyhedra. (5.G.7-8, 7.G.5-9)

Data Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets
Students use descriptive statistics, including mean, median, and range, to summarize and compare data sets, and they organize and display data to pose and answer
questions. They compare the information provided by the mean and the median and investigate the different effects that changes in data values have on these measures
of center. They understand that a measure of center alone does not thoroughly describe a data set because very different data sets can share the same measure of center.
Students select the mean or the median as the appropriate measure of center for a given purpose. (6.S.2, 6.S.4-8, 7.S.1-6)

Connections to the Focal Points

Algebra: Students encounter some nonlinear functions (such as the inverse proportions that they studied in grade 7 as well as basic quadratic and exponential functions)
whose rates of change contrast with the constant rate of change of linear functions. They view arithmetic sequences, including those arising from patterns or problems,
as linear functions whose inputs are counting numbers. They apply ideas about linear functions to solve problems involving rates such as motion at a constant speed.
Geometry: Given a line in a coordinate plane, students understand that all “slope triangles”—triangles created by a vertical “rise” line segment (showing the change in
y), a horizontal “run” line segment (showing the change in x), and a segment of the line itself—are similar. They also understand the relationship of these similar
triangles to the constant slope of a line.
Data Analysis: Building on their work in previous grades to organize and display data to pose and answer questions, students now see numerical data as an aggregate,
which they can often summarize with one or several numbers. In addition to the median, students determine the 25th and 75th percentiles (1st and 3rd quartiles) to obtain
information about the spread of data. They may use box-and-whisker plots to convey this information. Students make scatterplots to display bivariate data, and they
informally estimate lines of best fit to make and test conjectures.
Number and Operations: Students use exponents and scientific notation to describe very large and very small numbers. They use square roots when they apply the
Pythagorean theorem.

Academic Language
Grade 8 Mathematical Language

PreK-8 Glossary of Mathematical Terms

Development of Content Topics and Concepts
For each content strand these documents trace the development year by year of every band (i.e., sub-skill) from elementary school through high school. As such they
provide insight into the foundational work done in previous grades and map the subsequent elaboration of the topics in later courses.
Band Traces:
The chart below depicts the number of performance indicators for the content strands by grade level. The emphasis in grades Pre-Kindergarten-4 is on Number Sense
and Operations. Algebra builds slowly beginning with patterns in the early elementary grades and leads up to relations and functions in grade 8. Geometry builds as well
with a heavy emphasis in the grades 5-8. Measurement increases significantly across the grades with the exception of grade 8. Statistics includes the collection and
display of data in the early elementary grades and probability is introduced in grade 5.

 

Number of Content Performance Indicators by Grade Level
Content Strand Pre-K K TOTAL
Number Sense and
Operations

Algebra

9
 

1

13


2

207
 

56

Geometry

Measurement

2

2

5

3

87

80

Statistics and
Probability

TOTAL

4
 

18

5
 

28

67
 

497

Mathematics Scope and Sequence – Middle School
Grade 8

 

  September-October November-December January- March Post-March
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Operations
8.N.3 Read, write, and identify percents
less than 1% and greater than 100%
8.N.4 Apply percents to: Tax, percent
increase/decrease, simple interest, sale
price, commission, interest rates, and
gratuities

Estimation
8.N.6 Justify the reasonableness of
answers using estimation
Operations
8.N.1 Develop and apply the laws of
exponents for multiplication and
division
8.N.2 Evaluate expressions with integral
exponents

8.N. 3 Read, write, and identify percents
less than 1% and greater than 100%
8.N.4 Apply percents to: Tax, percent
increase/decrease, simple interest, sale
price, commission, interest rates, and
gratuities

Estimation

8.N.6 Justify the reasonableness of
answers using estimation
Operations
8.N.4 Apply percents to: Tax, percent
increase/decrease, simple interest, sale
price, commission, interest rates, and
gratuities

Estimation
8.N.5 Estimate a percent of a quantity,
given an application

 

 
   
     
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Variables and Expressions
8.A. 3 Describe a situation involving
relationships that matches a given graph
8.A.4 Create a graph given a description
or an expression for a situation involving
a linear or nonlinear relationship

Patterns, Relations and Functions
8.A.15 Understand that numerical
information can be represented in
multiple ways: arithmetically,
algebraically and graphically
8.A.16 Find sets of ordered pairs to
satisfy an algebraic expression and then
plot the ordered pairs and draw the line

 

 

Variables and Expressions
8.A.5 Use physical models to perform
operations with polynomials (uses area of
rectangles as a way to think about the
distributive property)
8.A.6 Multiply and divide monomials
8.A.7 Add and subtract polynomials
(integer coefficients)
8.A.8 Multiply a binomial by a
monomial or binomial (integer
coefficients)
8.A.9 Divide a polynomial by a
monomial (integer coefficients)

Equations and Inequalities
8.A.12 Apply algebra to determine the
measure of angles formed by or
contained in parallel lines cut by a
transversal and by intersecting lines
Variables and Expressions
8.A.1 Translate verbal sentences into
algebraic inequalities
8.A. 2 Write verbal expressions that
match given mathematical expressions
8.A.3 Describe a situation involving
relationships that matches a given graph
8.A.5 Use physical models to perform
operations with polynomials
8.A.10 Factor algebraic expressions
using the GCF
8.A.11 Factor a trinomial in the form
ax²+bx+c; a=1 and c having no more
than 3 sets of factors

Equations and Inequalities
8.A.13* Solve multi-step inequalities and
graph the solution set on a number line
8.A.14* Solve linear inequalities by
combining like terms, using the
distributive property, or moving variables
to one side of the inequality (include
multiplication or division of inequalities
by a negative number)

Patterns, Relations and Functions
8.A.15 Understand that numerical
information can be represented in
multiple ways: arithmetically,
algebraically and graphically
Patterns, Relations and Functions
8.A.17* Define and use correct
terminology when referring to function
(domain and range)
8.A.18* Determine if a relation is a
function
8.A.19* Interpret multiple
representations using equation, table of
values and graph
 
     
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Geometric Relationships
8.G.1 Identify pairs of vertical angles as
congruent
8.G.2 Identify pairs of supplementary
and complementary angles
8.G.3 Calculate the missing angle in a
supplementary or complementary pair
8.G.4 Determine angle pair relationship
when given two parallel lines cut by a
transversal
8.G.5 Calculate the missing angle
measurements when given two parallel
lines cut by a transversal
8.G.6 Calculate the missing angle
measurements when given two
intersecting lines and an angle

Coordinate Geometry

8.G.13* Determine the slope of a line
from a graph and explain the meaning of
slope as a constant rate of change
8.G.14* Determine the y-intercept of a
line from a graph and be able to explain
the y-intercept
8.G.15* Graph a line using a table of
values
8.G. 16* Determine the equation of a line
given the slope and the y-intercept
8.G.17* Graph a line from an equation in
slope-intercept form (y= mx + b)
  Transformational Geometry
8.G.7 Describe and identify
transformations in the plane, using
proper function notation (rotations,
reflections, translations, and dilations.)
8G.8 Draw the image of a figure under
rotations of 90 and 180 degrees
8.G.9 Draw the image of a figure under a
reflection over a given line
8.G.10 Draw the image of a figure under
a translation
8.G.11 Draw the image of a figure under
a dilation
8.G.12 Identify the properties preserved
and not preserved under a reflection,
rotation, translation, and dilation

Coordinate Geometry
8.G.18* Solve systems of equations
graphically (only linear, integral
solutions, y=mx +b format, no vertical or
horizontal lines)
8.G.19* Graph the solution set of an
inequality on a number line
8.G.20* Distinguish between linear and
nonlinear equations ax²+bx+c; a=1 (only
graphically)
8.G.21* Recognize the characteristics of
quadratics in tables, graphs, equations,
and situations
8.G.0*Construct the following using a
straight edge and compass: Segment
congruent to a segment; angle congruent
to an angle; perpendicular bisector, and
angle bisector

Coordinate Geometry
8.G.20* Distinguish between linear and
nonlinear equations ax²+bx+c; a=1
(only graphically)
8.G.21* Recognize the characteristics of
quadratics in tables, graphs, equations,
and situations
 
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    Units of Measurement
8.M.1 Solve equations/ proportions to
convert to equivalent measurements
within metric and customary
measurement systems.