Download Number in Base Ten - Carroll County Public Schools

Second Grade CCSS Progressions
Number and Operations in Base Ten
First Grade CCSS
Second CCSS
1.NBT.2. Understand that
the two digits of a twodigit number represent
amounts of tens and
ones. Understand the
following as special
cases:
2.NBT.1. Understand
that the three digits of a
three-digit number
represent amounts of
hundreds, tens, and
ones; e.g., 706 equals 7
hundreds, 0 tens, and 6
ones. Understand the
following as special
cases:
10 can be thought of as a
bundle of ten ones – called a
“ten”.
The numbers from 11 to 19 are
composed of a ten and one,
two, three, four, five six, seven,
eight, or nine ones.
The numbers 10, 20, 30, 40, 50,
60, 70, 80, 90 refer to one, two
, three, four, five, six, seven,
eight, and nine tens (and 0
ones)
1.NBT.1. Count to 120,
starting at any number
less than 120. In this
range, read and write
numerals and represent
a number of objects with
a written numeral.
1
Progressions
Use number lines, place
value charts and
hundreds charts to
identify the nearest ten
using whole numbers 0 –
99.
Third Grade CCSS
Use number lines and
place value charts to
identify the nearest 100
with whole numbers to
1000.
3.NBT.1. Use place value
understanding to round
whole numbers to the
nearest 10 or 100.
appendix 2
appendix 1
100 can be thought of as a
bundle of ten tens — called a
“hundred.”
The numbers 100, 200, 300,
400, 500, 600, 700, 800, 900
refer to one, two, three, four,
five, six, seven, eight, or nine
hundreds (and 0 tens and 0
ones).
2.NBT.2. Count within
1000; skip-count by 5s,
10s, and 100s.
Count within 1000; skipcount by 2’s, 3’s and 4’s.
Explore counting by 25’s
and make connection
to counting quarters.
Explore arithmetic

patterns in skip counting.
For example, when skip
counting by 5’s all numbers
end in 0 or 5. When
counting by 2’s or 4’s all
numbers are even. How
are these two patterns
related?
3.OA.9. Identify
arithmetic patterns
(including patterns in the
addition table or
multiplication table),
and explain them using
properties of operations.
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama and NCTM, Focus in Grade 2.
Number and Operations in Base Ten

First Grade CCSS
Second CCSS
1.NBT.1. Count to 120,
starting at any number
less than 120. In this
range, read and write
numerals and represent
a number of objects with
a written numeral.
2.NBT.3. Read and write
numbers to 1000 using
base-ten numerals,
number names, and
expanded form.
1.NBT.3. Compare two 
two-digit numbers based
on meanings of tens and
ones digits, recording
the results of
comparisons with the
symbols >, =, <.
2.NBT.4. Compare two
three-digit numbers
based on meanings of
the hundreds, tens, and
ones digits, using >, =,
and < symbols to record
the results of
comparisons.
Progressions
Read and write
numbers to 10,000 using
base-ten numerals,
number names, and
expanded form.
Third Grade CCSS
Read and write
numbers to 100,000
using base-ten
numerals, number
names, and expanded
form.
appendix 3
Compare numbers to
10,000 based on place
value understanding,
using >, =, and < symbols
to record the results of
comparisons.
Compare numbers to 
100,000 based on place
value understanding,
using >, =, and < symbols
to record the results of
comparisons.
appendix 4
appendix 5
# Formative Assessments provided as an evaluation of student achievement toward progression.
2
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama and NCTM, Focus in Grade 2.
Number and Operations in Base Ten
First Grade CCSS
1.OA.3 Apply properties
of operations as
strategies to add and
subtract.
1.OA.6 Add and subtract
within 20, demonstrating
fluency for addition and
subtraction within 10. Use
strategies such as
counting on, making ten
(e.g. 8 + 6 = 8 + 2 + 4,
which leads to 10 + 4 =
14); decomposing a
number leading to a ten
(e.g., 13 – 4 = 13 – 3 – 1,
which leads to 10 – 1 =
9); using the relationship
between addition and
subtraction (e.g.,
knowing that 8 + 4 = 12,
one knows 12 – 8 = 4);
and creating equivalent
but easier or known sums
(e.g., adding 6 + 7 by
creating the known
equivalent 6 + 6 + 1 = 12
+ 1, which equals 13).
3
Second CCSS
2.NBT.5. Fluently add and
subtract within 100 using
strategies based on
place value, properties
of operations, and/or the
relationship between
addition and
subtraction.
Progressions
Third Grade CCSS
Fluently add and
subtract within 100 - 500
using strategies based on
place value, properties
of operations, and/or the
relationship between
addition and
subtraction.
Fluently add and
subtract within 500 - 999
using strategies based on
place value, properties
of operations, and/or the
relationship between
addition and
subtraction.
appendix 6
appendix 7
2.NBT.9. Explain why
addition and subtraction
strategies work, using
place value and the
properties of operations.
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama and NCTM, Focus in Grade 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.
Number and Operations in Base Ten
First Grade CCSS
1.NBT.4 Add within 100,
including adding a two-digit
number and a one-digit
number, and adding a twodigit number and a multiple
of 10, using concrete models
or drawings and strategies
based on place value,

properties of operations,
and/or the relationship
between addition and

subtraction; relate the
strategy to a written method
and explain the reasoning
used. Understand that in
adding two-digit numbers,
one adds tens and tens, ones
and ones, and sometimes it is
necessary to compose a ten.
1.NBT.6 Subtract multiples of
10 in the range of 10-90 from
multiples of 10 in the range of
10-90 (positive or zero
differences), using concrete
models or drawings and
strategies based on place
value, properties of
operations, and/or the
relationship between
addition and subtraction;
relate the strategy to a
written method and explain
the reasoning used.
4
Second CCSS
2.NBT.6. Add up to four
two-digit numbers using
strategies based on
place value and
properties of
operations.
Progressions
Third Grade CCSS
Apply strategies based on place value, properties of
operations, and/or the relationship between
addition and subtraction developed for adding two
digit numbers to adding three digit numbers within
1000.
appendix 8
2.NBT.7. Add and
subtract within 1000,
using concrete models
or drawings and
strategies based on
place value, properties
of operations, and/or
the relationship
between addition and
subtraction; relate the
strategy to a written
method. Understand
that in adding or
subtracting three-digit
numbers, one adds or
subtracts hundreds and
hundreds, tens and
tens, ones and ones;
and sometimes it is
necessary to compose
or decompose tens or
hundreds.
Apply strategies based
on place value,
properties of operations,
and/or the relationship
between addition and
subtraction developed
for adding within 1000
and relate the strategy
to a written method.
appendix 9
Apply strategies based 
on place value,
properties of operations,
and/or the relationship
between addition and
subtraction developed
for subtracting within
1000 and relate the
strategy to a written
method.
appendix 10
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama and NCTM, Focus in Grade 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.
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.
Number and Operations in Base Ten
First Grade CCSS
Second CCSS
1.NBT.5 Given a two-digit
number, mentally find 10
more or 10 less than the
number, without having
to count; explain the
reasoning used.
2.NBT.8. Mentally add 10
or 100 to a given
number 100–900, and
mentally subtract 10 or
100 from a given
number 100–900.
5
Progressions
Third Grade CCSS
Develop strategies
based on place value,
properties of operations,
and/or the relationship
between addition and
subtraction for adding
10 or 100 to a given
number and for
subtracting 10 or 100
from a given number.
Apply strategies
developed for adding
and subtracting 10 or
100 to a number to
adding and subtracting
any numbers within
1000.
appendix 11
appendix 12
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.
Progression based on Learning and Teaching Early Math by Douglas H. Clements and Julie Sarama and NCTM, Focus in Grade 2.
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression- 2.NBT.1 Use number lines, place value charts and hundreds charts to identify the
nearest ten using whole numbers 0 – 99.
Which of these numbers are nearest to 30?
Show your thinking.
34
31
29
38
37
22
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
Name- ___________________________________________ Date- ______________________ appendix 1
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.1 Use number lines and place value charts to identify the nearest 100 with
whole numbers to 1000.
Place an “x” on the number line to show where
120 would be.
Is this number closest to 100 or 200?
Explain your thinking in words or pictures.


100
200
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
Name- ___________________________________________ Date- ______________________
 Look for and express regularity in
repeated reasoning.
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.3 Read and write numbers to 100,000 using base-ten numerals, number
names, and expanded form.
Fill in the missing numbers to complete the
equations.
20,000 + 1,000 +
___ + 50 + 3 = 21,453
30,000 + ______ + 600 + ______ + 9 = 37,619
_______ + 5000 + ______ + 30 + 8 = 45, 338
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
Name- ___________________________________________ Date- ______________________ appendix 3
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.4 Compare numbers to 10,000 based on place value understanding, using >, =,
and < symbols to record the results of comparisons.
Look at the two number sentences below.
Circle the number sentence that is true.
Explain your thinking.
5, 000 + 30 + 9 > 5, 000 + 300 + 9
3, 000 + 700 + 8 > 3,000 + 80 + 9
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
Name- ___________________________________________ Date- ______________________
appendix 4
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.4 Compare numbers to 10,000 based on place value understanding, using >, =,
and < symbols to record the results of comparisons.
John and Andy have candy grouped into bags of thousands,
hundreds, tens and some ones.
Who has more candy, John or Andy? Explain your thinking
Complete the number sentence to compare the two amounts.
_________ > _________
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
Name- ___________________________________________ Date- ______________________
appendix 5
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.5 Fluently add and subtract within 100 - 500 using strategies based on place
value, properties of operations, and/or the relationship between addition and subtraction.
Jill wants to add 176 + 145 but she is unsure of how to do this.
Solve this problem and explain how you solved it.
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
Name- ___________________________________________ Date- ______________________
appendix 6
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.5 Fluently add and subtract within 500 - 999 using strategies based on
place value, properties of operations, and/or the relationship between addition and subtraction.
Kyle needs to subtract 952 – 727 but he is unsure of how to do
this. Solve this problem and explain how you solved it.
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
Name- ___________________________________________ Date- ______________________
appendix 7
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.6 Apply strategies based on place value, properties of operations, and/or
the relationship between addition and subtraction developed for adding two digit numbers to
adding three digit numbers within 1000.
Ben needs to know how to solve 164 + 237 + 126. Explain how
you would solve it.
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
appendix 8
Name- ___________________________________________ Date- ______________________
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.7 Apply strategies based on place value, properties of operations, and/or
the relationship between addition and subtraction developed for adding within 1000 and relate
the strategy to a written method.
Solve 629 + 287 using a written method.
Show your written work below.
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
appendix 9
Name- ___________________________________________ Date- ______________________
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.7. Apply strategies based on place value, properties of operations, and/or
the relationship between addition and subtraction developed for subtracting within 1000 and
relate the strategy to a written method.
Solve 800 - 578 using a written method.
Show your written work below.
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
appendix 10
Name- ___________________________________________ Date- ______________________
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.8 - Develop strategies based on place value, properties of operations, and/or
the relationship between addition and subtraction for adding 10 or 100 to a given number and
for subtracting 10 or 100 from a given number.
Explain how you would find:
100 more than 349
10 more than 692
100 less than 319
10 less than 405
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
Name- ___________________________________________ Date- ______________________
appendix 11
Carroll County Public Schools
Mathematics Formative Assessment Task
Grade 2 Progressions
Progression: 2.NBT.8. Apply strategies developed for adding and subtracting 10 or 100 to a
number to adding and subtracting any numbers within 1000.
Explain how you would find:
250 more than 549
320 less than 845
38 more than 162
75 less than 325
Mathematical Practices
 Make sense of problems and persevere in
solving them.
 Reason abstractly and quantitatively.
 Construct viable arguments and critique
the reasoning of others.
 Model with mathematics.
 Use appropriate tools strategically.
 Attend to precision.
 Look for and make use of structure.
 Look for and express regularity in
repeated reasoning.
Name- ___________________________________________ Date- ______________________
appendix 12