# Courses of Study : Mathematics (Grade 2)

Operations and Algebraic Thinking
Represent and solve problems involving addition and subtraction.
 Mathematics (2016) Grade(s): 2 All Resources: 0
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. (See Appendix A, Table 1.) [2-OA1]

NAEP Framework
NAEP Statement::
• Whole numbers, or
• Fractions with like denominators, or
• Decimals through hundredths.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.1- Represent addition and subtraction by using objects, pictures, fingers, or sounds (within 30).

 Mathematics (2016) Grade(s): 2 All Resources: 0
2 ) Fluently add and subtract within 20 using mental strategies. (See standard 6, Grade 1, for a list of mental strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers. [2-OA2]

NAEP Framework
NAEP Statement::
• Whole numbers, or
• Fractions with like denominators, or
• Decimals through hundredths.

NAEP Statement::
4NPO3f: Solve application problems involving numbers and operations.

Work with equal groups of objects to gain foundations for multiplication.
 Mathematics (2016) Grade(s): 2 All Resources: 0
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-OA3]

NAEP Framework
NAEP Statement::
4NPO5a: Identify odd and even numbers.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.3- Separate even numbers of objects into two groups (limited to twenty total objects).

 Mathematics (2016) Grade(s): 2 All Resources: 0
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-OA4]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.4- Find the total number of objects in two equal groups (limit of twenty total objects).

Number and Operations in Base Ten
Understand place value.
 Mathematics (2016) Grade(s): 2 All Resources: 0
5 ) 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: [2-NBT1]

a. 100 can be thought of as a bundle of ten tens, called a "hundred." [2-NBT1a]

b. 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-NBT1b]

NAEP Framework
NAEP Statement::
4NPO1a: Identify place value and actual value of digits in whole numbers.

NAEP Statement::
4NPO1c: Compose or decompose whole quantities by place value (e.g., write whole numbers in expanded notation using place value: 342 = 300 + 40 + 2).

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.5- Recognize and represent numbers up to 30 with sets of tens and ones (objects, columns, arrays).

 Mathematics (2016) Grade(s): 2 All Resources: 0
6 ) Count within 1000; skip-count by 5s, 10s, and 100s. [2-NBT2]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.6- Count to 50 by ones. When given a numeral 0 to 25, name the next number in a three-item sequence.

 Mathematics (2016) Grade(s): 2 All Resources: 0
7 ) Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. [2-NBT3]

NAEP Framework
NAEP Statement::
4NPO1d: Write or rename whole numbers (e.g., 10: 5 + 5, 12 - 2, 2 × 5).

NAEP Statement::
4NPO1e: Connect model, number word, or number using various models and representations for whole numbers, fractions, and decimals.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.7- Recognize numerals 0 through 30 as written. When given a numeral 0 to 30, represent the numeral with objects. Match a numeral 1 to 30 to a quantity.

 Mathematics (2016) Grade(s): 2 All Resources: 0
8 ) 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-NBT4]

NAEP Framework
NAEP Statement::
4NPO1i: Order or compare whole numbers, decimals, or fractions.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.8- Compare sets of objects and numbers using appropriate vocabulary (greater than, less than, equal to; limited to thirty objects in a group).

Use place value understanding and properties of operations to add and subtract.
 Mathematics (2016) Grade(s): 2 All Resources: 0
9 ) Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. [2-NBT5]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.9- Identify the meaning of the + sign (add, plus, put together) and the - sign (subtract, take away, take from) and the = sign (equal, the same as); compose and decompose numbers up to 30 using objects, pictures, drawings, or numbers.

 Mathematics (2016) Grade(s): 2 All Resources: 0
10 ) Add up to four two-digit numbers using strategies based on place value and properties of operations. [2-NBT6]

NAEP Framework
NAEP Statement::
• Whole numbers, or
• Fractions with like denominators, or
• Decimals through hundredths.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.10- Add and subtract numbers 0 to 30 using objects, pictures, and numbers.

 Mathematics (2016) Grade(s): 2 All Resources: 0
11 ) 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-NBT7]

NAEP Framework
NAEP Statement::
• Whole numbers, or
• Fractions with like denominators, or
• Decimals through hundredths.

 Mathematics (2016) Grade(s): 2 All Resources: 0
12 ) Mentally add 10 or 100 to a given number 100 - 900, and mentally subtract 10 or 100 from a given number 100 - 900. [2-NBT8]

 Mathematics (2016) Grade(s): 2 All Resources: 0
13 ) Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.) [2-NBT9]

NAEP Framework
NAEP Statement::
4NPO6a: Explain or justify a mathematical concept or relationship (e.g., explain why 15 is an odd number or why 7-3 is not the same as 3-7).

Measurement and Data
Measure and estimate lengths in standard units.
 Mathematics (2016) Grade(s): 2 All Resources: 0
14 ) Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. [2-MD1]

NAEP Framework
NAEP Statement::
4M1e: Select or use appropriate measurement instruments such as ruler, meter stick, clock, thermometer, or other scaled instruments.

NAEP Statement::
4M2a: Select or use an appropriate type of unit for the attribute being measured such as length, time, or temperature.

NAEP Statement::
8M1e: Select or use appropriate measurement instrument to determine or create a given length, area, volume, angle, weight, or mass.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.14- Identify standard tools associated with measurement (clock, ruler, scale, measuring cup); measure the lengths of objects using nonstandard units (e.g., hands, paper clips).

 Mathematics (2016) Grade(s): 2 All Resources: 0
15 ) 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-MD2]

NAEP Framework
NAEP Statement::
4M1b: Compare objects with respect to a given attribute, such as length, area, volume, time, or temperature.

NAEP Statement::
4M1c: Estimate the size of an object with respect to a given measurement attribute (e.g., length, perimeter, or area using a grid).

 Mathematics (2016) Grade(s): 2 All Resources: 0
16 ) Estimate lengths using units of inches, feet, centimeters, and meters. [2-MD3]

NAEP Framework
NAEP Statement::
4M1c: Estimate the size of an object with respect to a given measurement attribute (e.g., length, perimeter, or area using a grid).

NAEP Statement::
4NPO2b: Make estimates appropriate to a given situation with whole numbers, fractions, or decimals by:
• Knowing when to estimate,
• Selecting the appropriate type of estimate, including overestimate, underestimate, and range of estimate, or
• Selecting the appropriate method of estimation (e.g., rounding).

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.16- Order three objects by length (long/longer/longest; short/shorter/shortest).

 Mathematics (2016) Grade(s): 2 All Resources: 0
17 ) Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. [2-MD4]

NAEP Framework
NAEP Statement::
4M1b: Compare objects with respect to a given attribute, such as length, area, volume, time, or temperature.

NAEP Statement::
8M1b: Compare objects with respect to length, area, volume, angle measurement, weight, or mass.

Relate addition and subtraction to length.
 Mathematics (2016) Grade(s): 2 All Resources: 0
18 ) 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-MD5]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.18- Increase or decrease length by adding or subtracting nonstandard unit(s).

 Mathematics (2016) Grade(s): 2 All Resources: 0
19 ) 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-MD6]

NAEP Framework
NAEP Statement::
4NPO1b: Represent numbers using models such as base 10 representations, number lines, and two-dimensional models.

NAEP Statement::
4NPO1e: Connect model, number word, or number using various models and representations for whole numbers, fractions, and decimals.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.19- Represent whole-number sums within 20 using a number line.

Work with time and money.
 Mathematics (2016) Grade(s): 2 All Resources: 0
20 ) Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. [2-MD7]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.20- Identify the time that matches a routine activity using a clock (limited to hour).

 Mathematics (2016) Grade(s): 2 All Resources: 0
21 ) Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately. [2-MD8]

Example: If you have 2 dimes and 3 pennies, how many cents do you have'

NAEP Framework
NAEP Statement::
4NPO3f: Solve application problems involving numbers and operations.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.21- Demonstrate knowledge that money has value; identify coins (penny, nickel, dime).

Represent and interpret data.
 Mathematics (2016) Grade(s): 2 All Resources: 0
22 ) 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-MD9]

 Mathematics (2016) Grade(s): 2 All Resources: 0
23 ) 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. (See Appendix A, Table 1.) [2-MD10]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.23- Use a pictograph, limited to 2 categories, to answer more/less, most/least, or equal to questions (limited to two categories and a combined total of no more than 30 objects/pictures shown for the 2 categories).

Geometry
Reason with shapes and their attributes.
 Mathematics (2016) Grade(s): 2 All Resources: 0
24 ) Recognize and draw shapes having specified attributes such as a given number of angles or a given number of equal faces. (Sizes are compared directly or visually, not compared by measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. [2-G1]

NAEP Framework
NAEP Statement::
4G1b: Identify or describe (informally) real-world objects using simple plane figures (e.g., triangles, rectangles, squares, and circles) and simple solid figures (e.g., cubes, spheres, and cylinders).

NAEP Statement::
4G3f: Describe and compare properties of simple and compound figures composed of triangles, squares, and rectangles.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.24- Identify two-dimensional shapes (limited to square, circle, triangle, and rectangle).

 Mathematics (2016) Grade(s): 2 All Resources: 0
25 ) Partition a rectangle into rows and columns of same-size squares, and count to find the total number of them. [2-G2]

NAEP Framework
NAEP Statement::
4NPO1e: Connect model, number word, or number using various models and representations for whole numbers, fractions, and decimals.

 Mathematics (2016) Grade(s): 2 All Resources: 0
26 ) 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, or four fourths. Recognize that equal shares of identical wholes need not have the same shape. [2-G3]

NAEP Framework
NAEP Statement::
4NPO1e: Connect model, number word, or number using various models and representations for whole numbers, fractions, and decimals.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.26- Identify half as being two equal parts of a shape (limited to circle, square, rectangle, and triangle).