By the end of 2nd grade, students understand place value and number relationships in addition and subtraction, and they use simple concepts of multiplication. They measure quantities with appropriate units. They classify shapes and see relationships among them by paying attention to their geometric attributes. They collect and analyze data and verify the answers.

Number sense
1) Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000
2) Count, read, and write whole numbers to 1,000 and identify the place value for each digit.
3) Use words, models, and expanded forms
(Example: 45 = 4 tens + 5 = 4 x 10 + 5 = 40 + 5) to represent numbers (to 1,000).
4) Order and compare whole numbers to 1,000 by using less than (<), equal to (=), greater than ( >).
5) Students estimate, calculate, and solve problems involving addition and subtraction of two-and three-digit numbers:
6) Understand and use the inverse relationship between addition and subtraction (Example: an opposite number sentence for 8 + 6 = 14 is 14 - 6 = 8) to solve problems and check solutions.
7) Find the sum or difference of two whole numbers up to three digits long. 8) Use mental arithmetic to find the sum or difference of two two-digit numbers. 9) Students model and solve simple problems involving multiplication and division(for US and UK students).
10) Use repeated addition, arrays, and counting by multiples to do multiplication. (for US and UK students).
11) Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division.
12) Know the multiplication tables of 2s, 5s, and 10s (to "times 10") and commit them to memory. Tables
13) Students understand that fractions and decimals may refer to parts of a set and parts of a whole Fractions Decimals
14) Recognize, name, and compare unit fractions from 1/12 to 1/2. (2nd grade)
15) Recognize fractions of a whole and parts of a group
(Example: one-fourth of a pie) Fractions of a whole
16) Know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one.
17) Students model and solve problems by representing, adding, and subtracting amounts of money:
18) Solve problems using combinations of coins and bills.
19) Know and use the decimal notation and the dollar and cent symbols for money. Decimal notation
20) Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places. Rounding
21) Recognize when an estimate is reasonable in measurements (Example: closest inch).

Algebra and Functions ( For US and UK)
22) Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction.
23) Use the commutative and associative rules to simplify mental calculations and to check results. Commutative Property Associative Property (2nd grade)
24) Relate problem situations to number sentences involving addition and subtraction.
25) Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences.

Measurement and Geometry (For US and UK)
26) Students understand that measurement is accomplished by identifying a unit of measure, iterating (repeating) that unit, and comparing it to the item to be measured.
27) Measure the length of objects by iterating (repeating) a nonstandard or standard unit.
28) Use different units to measure the same object and predict whether the measure will be greater or smaller when a different unit is used.
29) Measure the length of an object to the nearest inch and/ or centimeter.
30) Tell time to the nearest quarter hour and know relationships of time (Example: minutes in an hour, days in a month, weeks in a year).
31) Determine the duration of intervals of time in hours
(Example: 10:00 a.m. to 3:00 p.m.).
32) Students identify and describe the attributes of common figures in the plane and of common objects in space.
33) Describe and classify plane and solid geometric shapes
(Example: circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) according to the number and shape of faces, edges, and vertices. Geometric Shapes

Statistics, Data Analysis, and Probability (2nd grade)
34) Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations.
35) Record numerical data in systematic ways, keeping track of what has been counted.
36) Represent the same data set in more than one way
(Example: bar graphs and charts with tallies)
37) Identify features of data sets (range and mode). Mean,Mode and Median
38) Patterns

Mathematical Reasoning (For US )
39) Students make decisions about how to set up a problem.
40) Determine the approach, materials, and strategies to be used.(2nd grade)
41) Use tools, such as manipulatives or sketches, to model problems.
42) Students solve problems and justify their reasoning.
43) Defend the reasoning used and justify the procedures selected.
44) Make precise calculations and check the validity of the results in the context of the problem.