Mathematics Standards

Second Grade

B= Beginning D= Developing S= Secure

Problem Solving

Solves problems that arise in math and in other content areas:

• Builds new mathematical knowledge through problem solving  (D)
• Makes, investigates, & applies a variety of strategies to solve problems  (D)
• Monitors and reflects on solutions  (D)
• Develops & evaluates inferences & predictions that are based on data  (D)

Communicates mathematical thinking coherently and clearly:

• Uses mathematical language to express ideas  (D)

• Shows connections among mathematical ideas  (B/D)
• Creates and uses representations to organize, record, and communicate mathematical ideas  (D)

Number and Operations

Understands numbers, ways of showing numbers, relationships among numbers, and number systems:

• Knows & expresses automatically the values of digits in 5-digit numbers  (D)
• Knows and expresses automatically the values of digits in
• 2-, 3-, and 4- digit numbers  (S)
• Identifies place value for ones, tens, and hundreds  (D)
• Completes number sequences; identifies and uses number patterns to solve problems  (D)
• Compares numbers; writes the symbol >, <, or =  (D)
• Finds equivalent names for numbers  (D/S)
• Solves number-grid puzzles  (S)
• Compares fractions  (B/D)
• Understands fractions as names for equal parts of a region or set  (D)
• Understands that the amount represented by a fraction depends
• on the size of the whole (ONE)  (D)
• Shades a specified fractional part of a collection  (D)
• Recognizes equivalent fraction names  (B/D)
• Shades a specified fractional part of a region  (S)
• Gives the fraction name for the shaded part of a region  (S)

Understands meanings of operations and how they relate to one another:

• Solves equal-grouping and equal-sharing division problems  (B/D)
• Models multiplication problems with arrays  (B)
• Knows more difficult subtraction facts  (D)
• Identifies place value in 2-digit and 3-digit numbers  (D/S)
• Knows all addition facts  (D/S)
• Knows easy subtraction facts  (S)
• Completes “What’s My Rule” tables  (S)
• Solves 1-digit multiplication stories (multiples of equal groups)  (D)
• Solves simple division stories (equal sharing and equal grouping)  (D)
• Multiplies numbers with 0 or 1 as a factor  (S)
• Knows “harder” multiplication facts  (B)
• Constructs multiplication /division fact families  (D/S)
• Multiplies numbers with 2, 5, and 10 as a factor  (D/S)
• Solves stories about multiples of equal groups  (B/D)
• Solves addition and subtraction numbers  (S)
• Solves simple subtraction number stories  (D/S)
• Solves simple addition number stories  (S)
• Estimates and solves addition and subtraction number stories with dollar and cents  (D)

Computes fluently and makes reasonable estimates:

• Devises and uses strategies for finding sums of 2-digit numbers  (D)
• Devises and uses strategies for finding differences of 2-digit numbers  (D)
• Adds three 2-digit numbers mentally  (D)
• Estimates totals for “ballpark” check of exact answers  (D)
• Uses the trade-first method to solve 2-digit subtraction problems  (D)
• Makes ballpark estimates of exact answers  (D)
• Adds and subtracts with multiples of 10  (D/S)
• Adds three 1-digit numbers mentally  (S)
• Constructs fact families for addition and subtraction  (S)

Algebra

Understands patterns, relations, and functions:

• Knows complements of 10  (S)
• Counts by 2’s, 5’s,10’s and describe the patterns  (D/S)
• Counts by 2’s, 5”s, and 10’s  (S)

Represents and analyzes mathematical situations and structures using algebraic symbols:

• Uses parentheses in number models  (B)
• Finds missing addends for the next multiple of 10  (S)
• Finds missing addends for any multiple of 10  (D)

Uses mathematical models to show and understand questions:

• Completes simple Frames-and-Arrows diagrams  (S)
• Solves Frames-and-Arrows problems having two rules  (D) 

Geometry

Analyzes characteristics and properties of two-and three-dimensional geometric shapes and develops mathematical arguments about geometric relationships:

• Identifies 3-dimensional shapes such as rectangular prisms, cylinders, pyramids, cones, and spheres  (D)
• Identifies 2-dimensional shapes (polygons)  (D/S)
• Finds common attributes of shapes  (D)

Specifies locations and describes spatial relationships using coordinate geometry and other representational systems:

• Identifies parallel and nonparallel line segments  (D)
• Draws line segments  (D/S)

Applies transformations and uses symmetry to analyze mathematical situations:

• Identifies symmetrical figures  (D)

Measurement

Understands measurable attributes of objects and the units, systems, and processes of measurement:

• Finds values of coin and bill combinations  (D)
• Shows P, N, D, and Q for a given amount  (S)
• Estimates approximate costs and sums  (D)
• Solves money stories involving change  (D)
• Reads and writes money amounts in decimal notation  (S)
• Uses equivalent coins to show money amounts  (D/S)
• Knows exchange of values of U.S. coins  (D/S)
• Uses alternate names for times  (B)
• Tells time to 5-minute intervals  (D/S)
• Demonstrates calendar concepts and skills (S)

Applies appropriate techniques, tools, and formulas to determine

measurements:

• Makes change  (D)

• Measures to the nearest inch  (D/S)
• Measures to the nearest centimeter  (D)
• Identifies equivalencies for mm, cm, dm, and m  (B/D)
• Measures to the nearest 1/2 inch  (D)
• Measures to the nearest 1/2 cm  (D)
• Uses appropriate units for measurement and recognizes sensible measurements  (D)
• Identifies equivalencies for inches, feet, and yards  (D/S)
• Uses a ruler, tape measure, and meter/yardstick correctly  (S)
• Finds area concretely  (B/D)
• Finds perimeter concretely  (B/D)
• Reads degrees F on a thermometer  (S)

Data Analysis and Probability

Formulates questions that can be addressed with data and collects, organizes, and displays relevant data to answer them:

• Plots data on a bar graph  (S)

Selects and uses appropriate statistical methods to analyze data:

• Makes tallies and gives the total  (S)
• Finds the median (middle value) of a data set  (D)
• Makes difference and ratio comparisons  (D)

Develops and evaluates inferences and predictions that are based on data:   

• Determines the mode of a data set  (B)
• Determines the median, maximum, minimum, and range of a data set  (D)
• Compares quantities from a bar graph  (S)