Sample Core Objectives and Progressions
Excerpt from Whole Numbers:
Multiplication and Division Core Objective and Progression
Core Objectives and Progressions
What are the Core Objectives and Progressions?
To ensure Accelerated Math™ Second Edition content meets today’s highest standards, Renaissance Learning™
has developed a new scope and sequence built upon the set of core objectives and learning progressions
students need to achieve proficiency in mathematics. Core objectives are the most critical objectives for a student
to learn at a grade level. Core objectives and their associated prerequisite skills form the learning progressions.
The Core Objectives and Progressions are presented in an easy-to-use PDF format that provides the information
educators need for making effective decisions, when assigning objectives and differentiating practice for students
at different achievement levels: on grade level, in need of remediation, or ready to advance.
The Core Objectives and Progressions address the National Math Panel’s recommendation that mathematics
courses provide a “focused, coherent progression of mathematics learning, with an emphasis on proficiency with
key topics.”
How can educators use the Core Objectives and Progressions?
Each day, educators face decisions on how to help students increase their proficiency in mathematics skills. What
objectives should I assign next? Are my students prepared for these objectives? What if a student is unsuccessful
with the assigned objectives? What skills is the student missing? What if a student is capable of working ahead?
The Core Objectives and Progressions provide educators with easy-to-read, easy-to-use information to guide them
in answering questions they face each day.
How are the Core Objectives and Progressions organized?
The Core Objectives and progressions are organized into two views. The skill-area view shows the progression
of core objectives from grade to grade in a skill-area, such as the set of Whole Number Addition and Subtraction
skills or the set of Whole Number Multiplication and Division skills. The grade-level view shows the progression of
core objectives within a grade.
What’s in the Core Objectives and Progressions document?
Follow along on the “Sample Core Objective and Progression, Excerpt from Whole Numbers: Multiplication
and Division Core Objective and Progression” to learn about its features:
Core Objective and Progression
Identifies objectives in the Accelerated Math libraries that provide practice for the prerequisite skills that students
need for success with the core objectives. The prerequisite objectives are listed in descending order.
Terminology and Concepts Needed for this Objective
Identifies the terms and concepts your students need for understanding the objective. Before assigning an
objective, ask yourself, “Do my students understand these terms and concepts?”
Skills Needed for this Objective
Identifies the skills your students need for working with the objective. Before assigning an objective, ask yourself,
“Are my students ready to practice these skills?”
Prerequisite Terminology, Concepts, and Skills
Identifies the prerequisite terminology, concepts, and skills your students are expected to know before practicing
this objective. Before assigning an objective, ask yourself, “Are these terms, concepts, and skills already part of
my students’ math foundation?”
Prerequisite Objectives
Identifies objectives for practicing the prerequisite skills. The prerequisite objectives are listed in
descending order.
2
Core Objective
and Progression
Excerpt from Whole Numbers:
Multiplication and Division
Core Objectives and
Progression
Grade 3
Objective 33
Grade 3
Objective 34
Grade 3
Objective 35
Grade 3
Objective 37
Grade 3
Objective 39
Use a multiplication
sentence to represent an
area or an array model
Terminology and
Concepts Needed
for this Objective
Skills Needed for
this Objective
Does your student
understand these
terms and concepts?
Is your student
ready to practice
these skills?
Array, area, multiply,
multiplication sentence,
row, column, total
Use a division sentence to Divide, equal groups,
represent objects divided division symbol,
into equal groups
number sentence
Know basic multiplication
facts to 10 x 10
Know basic division facts
to 100 ÷ 10
WP: Multiply using basic
facts to 10 x 10
Number form, meaning
of multiplication
Number form,
meaning of division
Number form,
multiplication vocabulary
Relate a number
sentence to an array
Relate a number sentence
to objects in a group;
divide objects into equal
groups
Relate multiplication to
repeated addition; add
Divide objects into equal
groups
Know multiplication facts;
write a number sentence
from text
3
Prerequisite
Terminology,
Concepts, and
Skills
Are these terms,
concepts, and skills
already part of
your student’s math
foundation?
Prerequisite Objectives
If your student does not have
the needed foundation, which
prerequisite objectives would
provide the appropriate practice?
* Also a Core Objective
Equal; group
Grade 2
Objective 50
Relate a multiplication
sentence to an array
model
Grade 2
Objective 49
Represent repeated
addition as
multiplication
Grade 2
Objective 54
Divide objects into equal
groups using pictures
Grade 2
Objective 53
Recognize the number
of equal groups using
pictures
Grade 2
Objective 51
Know multiplication
tables for 2, 5, and 10
Grade 2
Objective 50
Relate a multiplication
sentence to an array
model
Grade 2
Objective 49
Represent repeated
addition as
multiplication
Grade 2
Objective 48
Use a multiplication
sentence to
represent the sum
of equal groups
Grade 2
Objective 54
Divide objects into equal
groups using pictures
Grade 2
Objective 53
Recognize the number
of equal groups using
pictures
Grade 3
Objective 63
WP: Determine a
multiplication or
division sentence for
a given situation*
Divide; repeated
subtraction
Add; skip count; repeated
addition; array
Equal groups
Add; multiply; repeated
addition; multiplication
terminology
Core Objective
and Progression
Excerpt from Whole Numbers:
Multiplication and Division
Core Objectives and
Progression
Grade 3
Objective 40
Grade 4
Objective 20
WP: Divide using basic
facts to 100 ÷ 10
Multiply a 1- or 2-digit
whole number by a
multiple of 10, 100,
or 1,000
Terminology and
Concepts Needed
for this Objective
Skills Needed for
this Objective
Does your student
understand these
terms and concepts?
Is your student
ready to practice
these skills?
Number form, division
vocabulary
Multiple of a number,
multiply
Know division facts;
write a number sentence
from text
Know multiplication facts;
multiply by 10, 100, or
1,000
4
Prerequisite
Terminology,
Concepts, and
Skills
Are these terms,
concepts, and skills
already part of
your student’s math
foundation?
Prerequisite Objectives
If your student does not have
the needed foundation, which
prerequisite objectives would
provide the appropriate practice?
* Also a Core Objective
Grade 3
Objective 35
Know basic
multiplication facts
to 10 x 10*
Grade 3
Objective 33
Use a multiplication
sentence to represent an
area or an array model*
Grade 2
Objective 74
Extend a pattern given a
table of related
number pairs
Grade 2
Objective 51
Know multiplication
tables for 2, 5, and 10
Grade 2
Objective 50
Relate a multiplication
sentence to an array
model
Grade 2
Objective 49
Represent repeated
addition as multiplication
Grade 2
Objective 48
Use a multiplication
sentence to represent the
sum of equal groups
Grade 3
Objective 63
WP: Determine a
multiplication or
division sentence for
a given situation*
Grade 3
Objective 37
Know basic division facts
to 100 ÷ 10*
Grade 3
Objective 34
Use a division sentence to
represent objects divided
into equal groups*
Grade 2
Objective 54
Divide objects into equal
groups using pictures
Grade 2
Objective 53
Recognize the number
of equal groups using
pictures
Grade 3
Objective 43
Multiply a 2-digit whole
number by a 1-digit
number
Grade 3
Objective 42
Multiply a 1-digit whole
number by a multiple of
10 to 100
Equal groups; division
terminology
Multiplication facts;
multiply 1-digit number
by a multiple of 10
Core Objective
and Progression
Excerpt from Whole Numbers:
Multiplication and Division
Core Objectives and
Progression
Grade 4
Objective 22
Grade 4
Objective 23
Grade 4
Objective 24
Grade 4
Objective 27
Apply the distributive
property to multiply a
multi-digit number by a
1-digit number
Multiply a 3- or 4-digit
whole number by a
1-digit whole number
Multiply a 2-digit whole
number by a 2-digit
whole number
WP: Multiply a
multi-digit whole
number by a 1-digit
whole number
Terminology and
Concepts Needed
for this Objective
Skills Needed for
this Objective
Does your student
understand these
terms and concepts?
Is your student
ready to practice
these skills?
Distributive property,
expanded form, place
value
Multiply, regrouping
Multiply, regrouping
Multiply, regrouping,
number sentence
Identify the value of a
digit in a number; write a
number in expanded form
Multiply a 2-digit number
by a 1-digit number
regrouping; know
multiplication facts
Multiply a 2-digit number
by a 1-digit number
regrouping; know
multiplication facts
Write a number sentence
from text; multiply a
multi-digit number by a
1-digit number; regroup;
know multiplication facts
5
Prerequisite
Terminology,
Concepts, and
Skills
Are these terms,
concepts, and skills
already part of
your student’s math
foundation?
Prerequisite Objectives
If your student does not have
the needed foundation, which
prerequisite objectives would
provide the appropriate practice?
* Also a Core Objective
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 4
Objective 20
Multiply a 1- or 2-digit
whole number by a
multiple of 10, 100, or
1,000*
Grade 3
Objective 7
Represent a 4- or
5-digit whole number in
expanded form*
Grade 3
Objective 5
Represent a 4-digit whole
number as thousands,
hundreds, tens, and
ones*
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 3
Objective 43
Multiply a 2-digit whole
number by a 1-digit
number
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 3
Objective 43
Multiply a 2-digit whole
number by a 1-digit
number
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 3
Objective 63
WP: Determine a
multiplication or
division sentence for
a given situation*
Expanded form; place
value; multiply by 10,
100, or 1,000;
multiplication facts
Multiply a 2-digit number
by a 1-digit number;
multiplication facts
Multiply a 2-digit number
by a 1-digit number;
multiplication facts
Multiply a 2-digit number
by a 1-digit number;
multiplication facts; write
a number sentence from
text; multiplication
terminology
Core Objective
and Progression
Excerpt from Whole Numbers:
Multiplication and Division
Core Objectives and
Progression
Grade 4
Objective 28
Grade 4
Objective 31
Grade 4
Objective 32
WP: Multiply a 2-digit
whole number by a
2-digit whole number
Estimate a product of
whole numbers using
any method
WP: Estimate a product of
two whole numbers using
any method
Terminology and
Concepts Needed
for this Objective
Skills Needed for
this Objective
Does your student
understand these
terms and concepts?
Is your student
ready to practice
these skills?
Multiply, regrouping,
number sentence
Product, estimate,
multiply, rounding
Product, estimate,
multiply
Write a number sentence
from text; multiply a
multi-digit number by
a 1-digit number
regrouping; know
multiplication facts
Round a number; know
multiplication facts;
multiply by a
multiple of 10
Write a number
sentence from text;
round a number; know
multiplication facts;
multiply by a multiple
of 10
6
Prerequisite
Terminology,
Concepts, and
Skills
Are these terms,
concepts, and skills
already part of
your student’s math
foundation?
Prerequisite Objectives
If your student does not have
the needed foundation, which
prerequisite objectives would
provide the appropriate practice?
* Also a Core Objective
Grade 3
Objective 43
Multiply a 2-digit whole
number by a 1-digit
number
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 3
Objective 63
WP: Determine a
multiplication or
division sentence for
a given situation*
Grade 3
Objective 43
Multiply a 2-digit whole
number by a 1-digit
number
Grade 3
Objective 39
WP: Multiply using basic
facts to 10 x 10*
Grade 4
Objective 30
Estimate a product
of whole numbers by
rounding
Grade 4
Objective 20
Multiply a 1- or 2-digit
whole number by a
multiple of 10, 100,
or 1,000*
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 3
Objective 63
WP: Determine a
multiplication or
division sentence for
a given situation*
Grade 3
Objective 37
Know basic division facts
to 100 ÷ 10*
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Multiply with no
regrouping; multiplication
facts; write a number
sentence from text;
multiplication
terminology
Multiply by 10, 100, or
1,000; multiplication
facts; rounding
Write a number sentence
from text; multiply by
10, 100, or 1,000;
multiplication facts;
rounding; multiplication
terminology
Core Objective
and Progression
Excerpt from Whole Numbers:
Multiplication and Division
Core Objectives and
Progression
Grade 4
Objective 37
Grade 4
Objective 39
Grade 4
Objective 41
Divide a 3-digit whole
number by a 1-digit
whole number with a
remainder in the quotient
WP: Divide a 3-digit
whole number by a
1-digit whole number
with no remainder in the
quotient
WP: Divide a 3-digit
whole number by a
1-digit whole number
with a remainder in the
quotient
Terminology and
Concepts Needed
for this Objective
Skills Needed for
this Objective
Does your student
understand these
terms and concepts?
Is your student
ready to practice
these skills?
Divide, remainder,
multiply, subtract
Divide, multiply, subtract
Divide, remainder,
multiply, subtract
Perform long division;
know division facts; know
multiplication facts;
know subtraction facts
Write a number sentence
from text; perform long
division; know division
facts; know multiplication
facts; know
subtraction facts
Write a number sentence
from text; perform
long division; perform
multiplication; perform
subtraction
7
Prerequisite
Terminology,
Concepts, and
Skills
Are these terms,
concepts, and skills
already part of
your student’s math
foundation?
Prerequisite Objectives
If your student does not have
the needed foundation, which
prerequisite objectives would
provide the appropriate practice?
* Also a Core Objective
Divide with no remainder;
divide; multiply; subtract
Grade 4
Objective 35
Divide a 3-digit whole
number by a 1-digit
whole number with no
remainder in the quotient
Grade 3
Objective 37
Know basic division facts
to 100 ÷ 10*
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 2
Objective 38
Subtract a 1- or 2-digit
number from a 2-digit
number with one
regrouping*
Grade 1
Objective 43
Know basic subtraction
facts to 20 minus 10*
Grade 3
Objective 63
WP: Determine a
multiplication or
division sentence for
a given situation*
Grade 3
Objective 37
Know basic division facts
to 100 ÷ 10*
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 2
Objective 38
Subtract a 1- or 2-digit
number from a 2-digit
number with one
regrouping*
Grade 1
Objective 43
Know basic
subtraction facts to
20 minus 10*
Grade 4
Objective 34
Divide a 2-digit whole
number by a 1-digit
whole number with no
remainder in the quotient
Write a number sentence
from text; division facts;
division terminology;
divide; multiply; subtract
Write a number sentence
from text; division facts;
division terminology;
divide with no remainder;
divide; multiply; subtract
Core Objective
and Progression
Excerpt from Whole Numbers:
Multiplication and Division
Core Objectives and
Progression
Grade 5
Objective 21
Divide a multi-digit whole
number by a 2-digit
whole number, with a
remainder and at least
one zero in the quotient
Terminology and
Concepts Needed
for this Objective
Skills Needed for
this Objective
Does your student
understand these
terms and concepts?
Is your student
ready to practice
these skills?
Divide, remainder,
multiply, subtract,
place value
Perform long division;
perform division; perform
multiplication; perform
subtraction; write a
number with zero as
a digit in expanded form;
estimate a product
8
Prerequisite
Terminology,
Concepts, and
Skills
Are these terms,
concepts, and skills
already part of
your student’s math
foundation?
Prerequisite Objectives
If your student does not have
the needed foundation, which
prerequisite objectives would
provide the appropriate practice?
* Also a Core Objective
Grade 3
Objective 63
WP: Determine a
multiplication or
division sentence for
a given situation*
Grade 3
Objective 37
Know basic division facts
to 100 ÷ 10*
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 1
Objective 43
Know basic subtraction
facts to 20 minus 10*
Grade 5
Objective 14
Divide a multi-digit whole
number by a 1-digit
number with no
remainder and at least
one zero in the quotient
Grade 4
Objective 30
Estimate a product
of whole numbers
by rounding
Grade 3
Objective 37
Know basic division
facts to 100 ÷ 10*
Grade 3
Objective 35
Know basic multiplication
facts to 10 x 10*
Grade 3
Objective 8
Determine the 4- or
5-digit whole number
represented in
expanded form*
Grade 2
Objective 38
Subtract a 1- or 2-digit
number from a 2-digit
number with one
regrouping*
Grade1
Objective 43
Know basic subtraction
facts to 20 minus 10*
Know zero as a place
holder; divide;
multiply; subtract
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