K–3 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,
In conjunction with the Massachusetts
Curriculum Frameworks, the CCOs were used
by a team of WestEd evaluators to ensure
content alignment in the identification and
evaluation of example assessments suitable
for use as District-Determined Measures
(DDMs). Districts can utilize the CCOs
themselves or the process of developing
CCOs in their own work when selecting
DDMs.
At each meeting, educators developed highquality CCOs that met the following criteria:


essential content (knowledge, skills,
or abilities);
are pulled, created, or synthesized
from a larger set of curriculum
standards; and
clarify key knowledge, skills, and
abilities that many educators and
other content experts working
together agree are most critical in
that content area, grade, or course.
Each CCO should be high-level and
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 mathematics grades K-2. Initial CCO development
was focused on high- priority “non-tested” grades and subjects. Because grade 3 is a
tested grade in Massachusetts, it was not included among those grades and subjects
targeted for development in summer 2013.
1
Massachusetts District-Determined Measures
Core Course Objectives (CCOs)
Mathematics – Grade: K
#
Objective
1
Students count forward from a given number within the known sequence, instead of
beginning at one, and continue as far as 100.
2
Students count orally by tens to 100.
3
Students write and recognize numbers from 0 to 20 and represent a number of objects
with a written numeral 0 to 20.
4
Students say the number names in standard order, pairing each object with one and only
one number and each number with one and only one object (1 to 1).
5
Students count to answer “how many?” questions about as many as 20 things arranged in
a line, a rectangular array, or a circle, or as many as ten things in a scattered
configuration; and given a number from 1 to 20, count out that many objects.
6
Students compare two sets of objects and/or two written numerals and identify whether
the number of objects in one group is greater than, less than, or equal to the number of
objects in another group. (Include groups with up to ten objects.)
7
Students solve addition and subtraction situations within ten with objects, fingers, mental
images, drawings, sounds, acting out situations, verbal explanations, expressions, or
equations (number stories, word problems).
8
Students decompose numbers less than or equal to ten into pairs in more than one way
by using objects or drawings, and record each decomposition by drawing or equation.
9
Students name, describe, construct, and/or manipulate both two-dimensional and
three-dimensional shapes in their environment using mathematical vocabulary and spatial
reasoning.
10
Students analyze and compare two-dimensional and three-dimensional shapes, in
different sizes and orientations, using informal language to describe similarities,
differences, parts (number of sides, vertices, “corners”), and other attributes (e.g., having
sides of equal length).
11
Students directly compare two objects with a measurable attribute by describing the
measurable attribute and determining which object has more or less of that attribute.
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).
2
Massachusetts District-Determined Measures
Core Course Objectives (CCOs)
Mathematics – Grade: 1
#
Objective
1
Students illustrate or show that the two digits of a two-digit number represent amounts of
tens and ones using models such as drawings, base-ten blocks, ten frames, or hundreds
charts; or given a model students will write the two-digit number.
2
Students compare two two-digit numbers and record the results of comparisons using the
symbols >, =, and <.
3
Students add and subtract within 100 using concrete models or drawings and strategies
based on place value, properties of operations, and/or the relationship between addition
and subtraction.
4
Students subtract multiples of ten using concrete models or drawings and strategies
based on place value, properties of operations, and/or the relationship between addition
and subtraction.
5
Students solve addition and subtraction within 20 to solve word problems involving
situations of adding to, taking from, putting together, taking apart, and comparing, with
unknowns in all positions, by using objects, drawings, and equations, with a box or
pictorial representation for the unknown number to represent the problem.
6
Students add and subtract within 20, demonstrating fluency for addition and subtraction
within ten, using mental strategies such as:
 counting on/back;
 making ten;
 decomposing a number leading to a ten;
 using the relationship between addition and subtraction; and
 creating equivalent but easier or known sums (e.g., adding six plus seven by
creating the known equivalent).
7
Students write and solve number sentences from problem situations, demonstrating
understanding of the equal sign.
8
Students express the length of an object as a whole number of length units, by laying
multiple copies of a shorter object end to end with no gaps or overlaps, using standard
units of length.
9
Students sequence three objects by length and compare the lengths of three objects
indirectly by using a third object.
10
Students identify values and use the values of all U.S. coins in the solution of problems,
using appropriate notation.
11
Students distinguish between defining attributes of shapes versus non-defining attributes
and draw shapes to possess defining attributes.
3
Massachusetts District-Determined Measures
Core Course Objectives (CCOs)
#
12
Objective
Students compose two-dimensional shapes or three-dimensional shapes (e.g., cubes,
rectangular prisms, circular cones, and circular cylinders) to create a composite shape (an
object composed of a combination of two or more basic shapes), and compose new
shapes from the composite shape.
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).
4
Massachusetts District-Determined Measures
Core Course Objectives (CCOs)
Mathematics – Grade: 2
#
Objective
1
Students explain that the three digits of a three-digit number represent amounts of
hundreds, tens, and ones and compare three-digit numbers based on meanings of the
hundreds, tens, and ones digits using words and symbols for more than, less than, and/or
equal to.
2
Students fluently add and subtract within 100 using strategies based on place value,
properties of operations, and/or the relationship between addition and subtraction.
 Mentally add ten to a given number, and mentally subtract ten from a given
number.
 Explain why addition and subtraction strategies work, using place value and the
properties of operations.
3
Students add and subtract within 1,000, using concrete models or drawings and strategies
based on place value, properties of operations, and/or the relationship between addition
and subtraction and relate the strategy to a written method.
 Mentally add ten or 100 to a given number 100–900, and mentally subtract ten or
100 from a given number 100–900.
4
Students add and subtract within 100 to solve one- and two-step word problems involving
situations of adding to, taking from, putting together, taking apart, and comparing, with
unknowns in all positions (e.g., by using drawings and equations with a symbol for the
unknown number) to represent the problem.
 Most work with two-step problems should involve single-digit addends.
 Word problems about length and about money can be included.
5
Students fluently add and subtract within 20 using mental strategies.
 By end of grade 2, know from memory all sums of two one-digit numbers.
 By the end of grade 2, know from memory related subtraction facts of sums of two
one-digit numbers.
6
Students recognize and draw shapes having specified attributes.
 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
7
Students measure the length of an object in units of inches, feet, centimeters, and/or
meters, by selecting and using appropriate tools such as rulers, yardsticks, meter sticks,
and measuring tapes. (Units of measure were identified to correlate to the appropriate
measuring tool.)
8
Students tell and write time from analog and digital clocks to the nearest five minutes,
using a.m. and p.m.
9
Students draw a picture graph and a bar graph (with single-unit scale) to represent a data
set with up to four categories and solve simple put-together, take-apart, and compare
problems, using information presented in a bar graph.
5
Massachusetts District-Determined Measures
Core Course Objectives (CCOs)
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).
6