(1) Students extend their understanding of the base-ten system. This
includes ideas of counting in fives, tens, and multiples of hundreds,
tens, and ones, as well as number relationships involving these units,
including comparing. Students understand multi-digit numbers (up to
1000) written in base-ten notation, recognizing that the digits in each
place represent amounts of thousands, hundreds, tens, or ones (e.g.,
853 is 8 hundreds + 5 tens + 3 ones).
(2) Students use their understanding of addition to develop fluency
with addition and subtraction within 100. They solve problems within
1000 by applying their understanding of models for addition and
subtraction, and they develop, discuss, and use efficient, accurate,
and generalizable methods to compute sums and differences of whole
numbers in base-ten notation, using their understanding of place value
and the properties of operations. They select and accurately apply
methods that are appropriate for the context and the numbers involved
to mentally calculate sums and differences for numbers with only tens
or only hundreds.
(3) Students recognize the need for standard units of measure
(centimeter and inch) and they use rulers and other measurement tools
with the understanding that linear measure involves an iteration of
units. They recognize that the smaller the unit, the more iterations
they need to cover a given length.
(4) Students describe and analyze shapes by examining their sides and
angles. Students investigate, describe, and reason about decomposing
and combining shapes to make other shapes. Through building, drawing,
and analyzing two- and three-dimensional shapes, students develop a
foundation for understanding area, volume, congruence, similarity,
and symmetry in later grades.
operations and algebraic thinking
Represent and solve problems involving
addition and subtraction.
•2.OA.1. Use addition and subtraction 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.
Add and subtract within 20.
•2.OA.2. Fluently add and subtract within 20 using mental
strategies.2 By end of Grade 2, know from memory all
sums of two one-digit numbers.
Work with equal groups of objects to gain
foundations for multiplication.
•2.OA.3. Determine whether a group of objects (up to 20)
has an odd or even number of members, e.g., by pairing
objects or counting them by 2s; write an equation to
express an even number as a sum of two equal addends.
2.OA.4. Use addition to find the total number of objects
arranged in rectangular arrays with up to 5 rows and
up to 5 columns; write an equation to express the total
as a sum of equal addends.
Base 10 and Place Value
Understand place value.
•2.NBT.1. Understand that the three digits of a threedigit
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:
100 can be thought of as a bundle of ten tens — called a
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
•2.NBT.3. Read and write numbers to 1000 using base-ten
numerals, number names, and expanded form.
•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
Use place value understanding and
properties of operations to add and
•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
•2.NBT.6. Add up to four two-digit numbers using
strategies based on place value and properties of
•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.
•2.NBT.8. Mentally add 10 or 100 to a given number 100–
900, and mentally subtract 10 or 100 from a given
2.NBT.9. Explain why addition and subtraction strategies
work, using place value and the properties of
Measurement and Data
Measure and estimate lengths in standard
•2.MD.1. Measure the length of an object by selecting and
using appropriate tools such as rulers, yardsticks,
meter sticks, and measuring tapes.
•2.MD.2. Measure the length of an object twice, using
length units of different lengths for the two
measurements; describe how the two measurements
relate to the size of the unit chosen.
•2.MD.3. Estimate lengths using units of inches, feet,
centimeters, and meters.
•2.MD.4. Measure to determine how much longer one
object is than another, expressing the length difference
in terms of a standard length unit.
Relate addition and subtraction to length.
•2.MD.5. Use addition and subtraction within 100 to solve
word problems involving lengths that are given in the
same units, e.g., by using drawings (such as drawings
of rulers) and equations with a symbol for the unknown
number to represent the problem.
•2.MD.6. Represent whole numbers as lengths from 0 on a
number line diagram with equally spaced points
corresponding to the numbers 0, 1, 2, ..., and represent
whole-number sums and differences within 100 on a
number line diagram.
Work with time and money.
•2.MD.7. Tell and write time from analog and digital
clocks to the nearest five minutes, using a.m. and p.m.
•2.MD.8. Solve word problems involving dollar bills,
quarters, dimes, nickels, and pennies, using $ and ¢
symbols appropriately. Example: If you have 2 dimes and
3 pennies, how many cents do you have?
Represent and interpret data.
•2.MD.9. Generate measurement data by measuring
lengths of several objects to the nearest whole unit, or
by making repeated measurements of the same object.
Show the measurements by making a line plot, where the
horizontal scale is marked off in whole-number units.
•2.MD.10. Draw a picture graph and a bar graph (with
single-unit scale) to represent a data set with up to
four categories. Solve simple put-together, take-apart,
and compare problems using information presented in a
Reason with shapes and their attributes.
•2.G.1. Recognize and draw shapes having specified
attributes, such as a given number of angles or a given
number of equal faces.1 Identify triangles,
quadrilaterals, pentagons, hexagons, and cubes.
•2.G.2. Partition a rectangle into rows and columns of
same-size squares and count to find the total number
•2.G.3. Partition circles and rectangles into two, three,
or four equal shares, describe the shares using the
words halves, thirds, half of, a third of, etc., and
describe the whole as two halves, three thirds, four
fourths. Recognize that equal shares of identical wholes
need not have the same shape.