5–8 Mathematics
Core Course Objectives
The Massachusetts Department of Elementary and Secondary Education (ESE)
partnered with WestEd to convene panels of
expert educators to review and develop
statements of essential curriculum content,
Core Course Objectives
Core Course Objectives (CCOs), for
(CCOs)
are statements that:
approximately 100 different grades/subjects
and courses.
 describe different elements of core,
essential content (knowledge, skills,
In conjunction with the Massachusetts
or abilities);
Curriculum Frameworks, the CCOs were used
 are pulled, created, or synthesized
by a team of WestEd evaluators to ensure
from a larger set of curriculum
content alignment in the identification and
standards; and
evaluation of example assessments suitable
 clarify key knowledge, skills, and
for use as District-Determined Measures
abilities that many educators and
other content experts working
(DDMs). Districts can utilize the CCOs
together agree are most critical in
themselves or the process of developing
that content area, grade, or course.
CCOs in their own work when selecting
DDMs.
Each CCO should be high-level and
At each meeting, educators developed highquality CCOs that met the following criteria:
represent broad enough learning goals
to be taught using a wide variety of
instructional tools or methods (scope),
while also focused enough that
students’ growth in learning that
knowledge or skill can be measured by
an assessment (assess-ability).

Scope: The CCO describes an
overarching learning goal.

Assess-ability: The CCO describes
knowledge, skills, or abilities that are
readily able to be measured.

Centrality: The CCO describes a critically important concept, skill, or ability that
is central to the subject/grade or course.

Relevance: The CCO represents knowledge, skills, and abilities that are
consistent with Massachusetts’s values and goals.
After public review, WestEd’s content specialists reviewed the comments submitted by
educators and other stakeholders. The CCOs that emerged from this process are
presented below.
Note: Listed below are the CCOs for Pre-Algebra. Initial CCO development was
focused on high- priority “non-tested” grades and subjects. Because grades 5-8 are
tested grades in Massachusetts, other grade-specific middle school courses (e.g., grade
7 mathematics) were not included among those grades and subjects targeted for
development in summer 2013.
1
Massachusetts District-Determined Measures
Core Course Objectives (CCOs)
Mathematics/Pre-Algebra – Grade: 8
#
Objective
1
Students solve problems involving scale factors, rates, and derived measures (e.g.,
density).
2
Students represent and compute unit rates by modeling, solving, and explaining real-world
problems.
3
Students model rational numbers, distinguish rational numbers from irrational numbers,
represent each on the number line, and recognize that together the rational numbers and
the irrational numbers form the real number system.
4
Students solve real-world problems involving the four operations with rational numbers.
5
Students write and interpret mathematical expressions, equations, and inequalities in
context.
6
Students evaluate expressions and use expressions, linear equations (including pairs of
simultaneous linear equations), and inequalities to solve problems.
7
Students recognize that a function is a rule that assigns to each input exactly one output.
8
Students determine the slope and y-intercept of a linear function described by a symbolic
expression, table, or graph, and interpret the slope and y-intercept of the graph of a linear
function representing a contextual situation.
9
Students represent and explain the effect of one or more translations, rotations,
reflections, or dilations (centered at the origin) of a geometric figure on the coordinate
plane.
10
Students apply the Pythagorean Theorem to determine measures in context.
11
Students explore and explain angle relationships; identify pairs of angles as
complementary, supplementary, adjacent, or vertical, and determine missing angle
measures using these relationships; and use informal arguments to establish facts about
angles.
12
Students solve real-world area, surface area, and volume problems using different
strategies (formulas and decomposing figures.)
2
Massachusetts District-Determined Measures
Core Course Objectives (CCOs)
#
Objective
13
Students describe data sets using measures of center and variability; and they summarize
and compare two unequal distributions of data using number of data points, measures of
center, shape, and variability (numerical data), and two-way tables (categorical variables).
14
Students identify, design, and conduct multi-stage (compound) probability experiments
(independent events) and compare the results with theoretical probabilities.
Note: These Core Course Objectives were developed by Massachusetts educators in summer
2013. They are intended to provide districts with information about the content taught in this
course. Source documents used are as follows: Massachusetts Mathematics Curriculum
Framework (2011); Learning Progressions Frameworks Designed for Use with The Common
Core State Standards in Mathematics K–12 (NCIEA) (2011); Pre-Algebra Power Standards,
Auburn School District #408 (Washington 2011).
3