(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.

• 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.

• 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.

• 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.

• 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

“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.

• 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

comparisons.

• 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.

• 2.NBT.6. Add up to four two-digit numbers using

strategies based on place value and properties of

operations.

• 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

number 100–900.

 2.NBT.9. Explain why addition and subtraction strategies

work, using place value and the properties of

operations.

• 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.

• 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.

• 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?

• 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

bar graph.

• 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

of them.

• 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.