Cheryle Verish
CCLM^2 Project
Summer 2012
DRAFT DOCUMENT. This material was developed as part of the Leadership for the Common Core in Mathematics project at the University of Wisconsin-Milwaukee.
CCSSM Analysis of 3.NBT.2 Part 1: Standard: 3.NBT.2
Grade: 3rd Grade
Domain: Numbers & Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic.
Standard 2: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or
the relationship between addition and subtraction.
Part 2: Explanations and Examples of the Standard
Standard
3.NBT.2
Fluently add and
subtract within
1000 using
strategies and
algorithms based
on place value,
properties of
operations,
and/or the
relationship
between addition
and subtraction.
Explanation
Students are expected to be able to solve addition and
subtractions with totals of 1,000 or less
They are using a variety of strategies and
beginning to use algorithms
They are applying place value knowledge when
using the strategies and algorithms to solve problems
within 1,000
They should be able to explain and show the
relationship between addition and subtraction, so
they can use addition to subtract, and show how one
can check subtraction by using the related addition
facts
They are able to use their knowledge about
decomposing numbers & properties of operations
so they can apply the strategies and algorithms, e.g.,
using the Associative Property to solve 698 + 6 by
breaking up the 6 into a 2 and 4 because 698 + 2 =
700, so then we can add the 4 to 700 to get 704.
What It Looks Like in the Classroom/Examples
Using representations and tools to show thinking to addition and
subtraction problems within 1,000, e.g., place value blocks, place
value drawings and tying them to the equations
Using special strategies and general methods, and algorithms to
add and subtract within 1,000 (students & teachers are sharing,
discussing, and questioning each other to understand and acquire
new approaches
Students and teachers use vocabulary when discussing or writing
about these types of problems, e.g. use words such as ones, tens,
hundreds, thousands, digits vs. number, strategy, value
Using trade books to provide context, e.g., Shark Swimathon by
Stuart Murphy, Mission Addition by Loreen Leedy, & One
Hundred Angry Ants by Elinor Pinczes
Create anchor charts with students to capture their discoveries
of special strategies & general methods: Partial Sums, Adjusting
and Compensating strategies (manipulate numbers to make
multiples of tens or hundreds to make solving it easier)
Tying equations to representational drawings; focusing on
labeling each part of equations, e.g, using labels for items, groups,
and total as well as group size & # of groups for Equal Groups
problems
Solving problems within context
Working on deciding which tools and strategies are most helpful
Small group explorations, Math Stations, Whole Group summaries
to lock in learning, Small Groups for Guided Math to help students
move forward involving activities described above
Math Wall with a) vocabulary such as: ones, tens, hundreds,
thousands, digits vs. number, strategy, value b) anchor charts on
math wall and around room that capture discoveries such as those
described above
Newsletters home to families with math section, including
pictures of anchor charts, description, & websites that include
activities supporting the standard, e.g., Thinkcentral.com:
Expressions Intervention Skill 46: Drawing a Picture, Intervention
Skill 66: Choose the Operation
Parents invited to classroom to participate in math activities &
games that further this thinking (card or board game with story
problem types)
Math Practices discussed by teacher and among students,
modeled by teacher & students, & utilized by students during
lessons
Part 3: School Textbook – Scott Foresman Mathematics
a) Textbook Development
Grade
How Standard is Introduced & Developed
Level
Ways the Textbook Addresses the Standards
nd
The textbook begins with problems that are expected of 1st
2 Grade
graders – an entire chapter is spent on it
The second chapter deals with strategies such as making tens
and using doubles, which help students with 2.OA.2 and
make 3.NBT.2 easier.
2.NBT.7*
Students then work on place value within 100
Add and subtract
Students use counters, place value charts, workmats so
within 1000, using
students can sort ones, tens, hundreds, work with money to
concrete models or
see the place value connection
drawings and
Mental math is explored and modeled, such as adding the
strategies based on
place value,
tens, then the ones. Students can use counters, but it’s
properties of
encouraged for them to try it without too. This is also done
operations, and/or
with subtraction.
the relationship
Place value explored within 1,000
between addition
Adding and Subtracting within 1,000 near end of book,
and subtraction;
relate the strategy
focuses on the mental math strategies of counting by
to a written
hundreds, tens, then ones, but doesn’t deal with properties of
method.
operations; includes using place value blocks, drawing of
Understand that in
place value blocks, & place value workmats are used.
adding or
A lesson on part, part, whole diagram meant to relate
subtracting threedigit numbers, one
addition to subtraction, but then the text jumps shortly
adds or subtracts
afterward to the standard algorithm.
hundreds and
Addition and subtraction within 100 and 1,000 is addressed
hundreds, tens and
primarily through counting on by hundreds, tens, and then
tens, ones and ones;
ones & the standard algorithms paired with place value
and sometimes it is
necessary to
representations. The practice pages often don’t lend
compose or
themselves well to other strategies – either no room is left for
decompose tens or
students to show work or a diagram is drawn and they have
hundreds.
to fill in missing parts. The examples are also focused on the
mental math counting on or standard algorithm.
rd
3 Grade The text book begins by focusing on important skills such as
Properties of Operations, e.g., Commutative & Associative
(grade of the
Relating Addition and Subtraction
standard)
(Foundation
leading to
standard)
What’s Missing/Concerns
Location
There isn’t an adequate amount of
time looking at using the properties
of operation for addition and
subtraction with larger numbers, e.g.
associative property isn’t touched
upon with adding within 100 or
1,000
There aren’t a wide enough variety
of strategies explored well enough,
teacher will need to supplement
Textbook is using the standard
algorithm with place value blocks or
drawings of place value blocks for
addition and subtraction of 2-digit
numbers, instead of using strategies
and general methods
Not enough time spent working on
adding and subtracting within 1,000
(at very end of book with a few
lessons)
Much of the standards in 2nd grade
are focused on a variety of NBT
standards, which lay the foundation
for 3.NBT.2. Since the textbook is
missing key skills, it will be
important that 2nd grade teachers are
aware of what’s missing and
addressing those areas with their
students.
Much of Chapters
1-6 & 10-11
The teacher will need to make sure
students are exposed and continue to
be exposed to special strategies and
1.13
2.1
2.2
3.NBT.2
Fluently add and
subtract within
1000 using
strategies and
algorithms based
on place value,
properties of
operations, and/or
the relationship
between addition
and subtraction.
4th Grade
(Extension of
standard & how
it’s foundational
for later skills
related to the
standard)
4.NBT.4.
Fluently add and
subtract multidigit whole
numbers using
the standard
algorithm.
Dealing with strategies built upon the properties of
operations and place value, e.g., breaking up numbers by
place value and breaking up based on making tens
Using tens to add and subtract mentally and estimating to
help students consider if their answers are reasonable
Using place value blocks & tape diagrams to add and
subtract 3-digit numbers
Students are adding horizontally and with general methods
such as recording hundreds, tens, and ones on special lines
In one of the first lessons on the chapter on adding and
subtracting 3-digit numbers, students are using the standard
algorithm (lesson 3-3) paired with place value blocks or
drawings. While the margin of the TE says other ways can
be done, they aren’t shown.
The standards for 4th grade progress into students adding and
subtracting multi-digit numbers with the standard algorithm.
During earlier grades, students should have acquired the place
value knowledge, understanding, and capability of using the
properties of operations to use strategies and general methods
that prepare them for using the standard algorithm in 4th grade so
that they understand what it means when they are using it.
There is one chapter on multi-digit addition and subtraction
in the 4th grade Scott Foresman textbook.
Book discusses and models commutative and associative
properties. It also shows adjusting/compensating strategies
so students can add or subtract a multiple of 10.
Students work on using the standard algorithm while
referring to part, part whole diagrams and estimating their
answer to make sure it’s reasonable
Written responses about whether or not their answer is
reasonable are modeled in a couple lessons, but not expected
by the students during their own work
The book includes a variety of lessons within each lesson to
help students who aren’t able to do the standard algorithm
within a clear understanding of place value knowledge
general methods since the book
jumps into the standard algorithm
for both addition and subtraction and
focuses on it pretty strongly (it does
connect it to place value blocks, but
the special strategies and general
methods aren’t addressed as much.
When special strategies and general
methods are addressed, they are
frequently under the umbrella of
mental math, so they aren’t explored
as much
When students work on special
strategies, properties of operations,
general methods it’s usually within
the context of adding within 100, so
students might stop applying these
within 1,000.
The book does go back and briefly
address the properties of operations
and place value to help students
understand the standard algorithms
My main concerns lie with the face
that the Scott Foresman text in
previous grade levels does not lay a
foundation whereby students were
getting a solid understanding of the
properties of operations, special
strategies, or general methods.
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.12
2.13
3.1
3.2
3.3
3.4
3.6
3.7
2.1 Mental Math:
Adding
2.2 Mental Math:
Subtracting
2.3 Estimating
Sums &
Differences
2.4 Overestimates
& Underestimate
2.5 Adding Whole
#s & Money
2.6 Column
Addition
2.7 Subtracting
Whole Numbers &
Money
2.8 Using a
Computation
Method
*The Scott-Foresman math textbooks for elementary aged students has the following daily format:
1) Getting Started (Review), 2) Investigating the Concept, 3) Reaching All Learners (4 mini-lessons teachers may choose from:
an ELL lesson, Reteaching lesson, cross-curricular lesson/s, and sometimes an Advanced Learners mini-lesson) , 4) Warm-Up to
main lesson, 5) Main Lesson (under heading, Teach), 6) Practice, & 7) Assess
b) Conclusions & Suggestions:
While the text focuses a great deal on number and base ten ideas, there are significant gaps in how standards expect these ideas to
be addressed. As such, the teacher will need to do a fair amount of supplementing. This is especially evident in the properties of
operations, since the Associative Property, a key property, is rarely dealt with. Special strategies and general methods, as outlined
in the Progressions document are not adequately dealt with either. Instead this text focuses almost exclusively on 2 ways to
approach multi-digit addition and subtraction: mental math by way of adding hundreds, then tens, then ones (a fine way of
approaching it) and using the standard algorithm with place value representations. What’s missing is other strategies. They aren’t
modeled much in the textbook, and they are basically non-existent as the numbers become larger. Unfortunately, many students
will likely lose those strategies when dealing with larger numbers if the teacher doesn’t heartily supplement the book for this
standard. Anchor charts will be particularly important since they will be one of the few things students can access throughout the
year.
It is important that the teacher develop a strong understanding of each standard to fill the gaps in the curriculum materials provided
by the school. Using the Expressions curriculum materials on Thinkcentral.com is one way the Milwaukee Public Schools
District will have teachers who have the Scott Foresman books access resources that are better aligned to the CCSS for Math. The
teacher should also utilize trade books. Beyond that, there are resources on the internet that include lessons based on the new
CCSS for Math, e.g. The Tennessee Early Grades Math Toolkit has a variety of resources organized by the standard* at the
address: http://www.readtennessee.org/math/teachers/k3_common_core_math_standards/third_grade/number_operations_in_base_ten/3nbt2.aspx These include lesson plans, media, activities, assessments, and more.
Teachers will need to adapt, create, or locate assessments that properly reflect the standards, instead of relying on the
assessments within the textbook since they do not properly reflect the standards (as discussed above).’’’ *Teachers should still compare the resources to the CCSS for Math to ensure they do indeed represent the standards.