# New Hampshire State Standards for Mathematics: Grade 2

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NH.M:N&O:2. NECAP - Grade Level Expectation: Number and Operation.

M:N&O:2:1. Demonstrates conceptual understanding of rational numbers with respect to whole numbers from 0 to 199 using place value, by applying the concepts of equivalency in composing or decomposing numbers (e.g., 34 = 17 + 17; 34 = 29 + 5); and in expanded notation (e.g., 141 = 1 hundred + 4 tens + 1 one or 141 = 100 + 40 + 1) using models, explanations, or other representations; and positive fractional numbers (benchmark fractions: a/2, a/3, or a/4, where a is a whole number greater than 0 and less than or equal to the denominator) as a part to whole relationship in area and set models where the denominator is equal to the number of parts in the whole using models, explanations, or other representations. (State)

M:N&O:2:2. Demonstrates understanding of the relative magnitude of numbers from 0 to 199 by ordering whole numbers; by comparing whole numbers to each other or to benchmark whole numbers (10, 25, 50, 75, 100, 125, 150, or 175); by demonstrating an understanding of the relation of inequality when comparing whole numbers by using '1 more', '1 less', '10 more', '10 less', '100 more', or '100 less'; or by connecting number words and numerals to the quantities they represent using models, number lines, or explanations. (State)

M:N&O:2:3. Demonstrates conceptual understanding of mathematical operations involving addition and subtraction of whole numbers by solving problems involving joining actions, separating actions, part-part whole relationships, and comparison situations; and addition of multiple one-digit whole numbers. (State)

M:N&O:2:4. No standard listed at this grade.

M:N&O:2:5. Demonstrates understanding of monetary value by adding coins together to a value no greater than $1.99 and representing the result in dollar notation; making change from $1.00 or less, or recognizing equivalent coin representations of the same value (values up to $1.99). (State)

M:N&O:2:6. Mentally adds and subtracts whole number facts to a sum of 20; names the number that is 10 more or less than the original number, and mentally adds and subtracts two-digit multiplies of ten (e.g., 60 + 80, 90 - 30).

M:N&O:2:7. Makes estimates of the number of objects in a set (up to 50) by selecting an appropriate method of estimation.

M:N&O:2:8. Applies properties of numbers (odd and even) and field properties (commutative for addition, identity for addition, and associative for addition) to solve problems and to simplify computations involving whole numbers.

NH.M:G&M:2. NECAP - Grade Level Expectation: Geometry and Measurement.

M:G&M:2:1. Uses properties, attributes, composition, or decomposition to sort or classify polygons or objects by a combination of two or more non-measurable or measurable attributes. (State)

M:G&M:2:2. No standard listed at this grade.

M:G&M:2:3. No standard listed at this grade.

M:G&M:2:4. Demonstrates conceptual understanding of congruency by composing and decomposing two-dimensional objects using models or explanations (e.g., using triangular pattern blocks to construct a figure congruent to the hexagonal pattern block); and uses line symmetry to demonstrate congruent parts within a shape.

M:G&M:2:5. No standard listed at this grade.

M:G&M:2:6. Demonstrates conceptual understanding of perimeter and area by using models or manipulatives to surround and cover polygons. (State)

M:G&M:2:7. Measures and uses units of measures appropriately and consistently, and makes conversions within systems when solving problems across the content strands. (State)

M:G&M:2:8. No standard listed at this grade.

M:G&M:2:9. Demonstrates understanding of spatial relationships using location and position by using positional language in two- and three- dimensional situations to describe and interpret relative positions (e.g., above the surface of the desk, below the triangle on the paper); and creates and interprets simple maps and names locations on simple coordinate grids.

NH.M:F&A:2. NECAP - Grade Level Expectation: Functions and Algebra.

M:F&A:2:1. M(F&A)-2-1 Identifies and extends to specific cases a variety of patterns (linear and non-numeric) represented in models, tables, or sequences by extending the pattern to the next element, or finding a missing element. (State)

M:F&A:2:2. No standard listed at this grade.

M:F&A:2:3. No standard listed at this grade.

M:F&A:2:4. Demonstrates conceptual understanding of equality by finding the value that will make an open sentence true. (Limited to one operation and limited to use addition or subtraction) (State)

NH.M:DSP:2. NECAP - Grade Level Expectation: Data, Statistics, and Probability.

M:DSP:2:1. Interprets a given representation (pictographs with one-to-one correspondence, line plots, tally charts, or tables) to answer questions related to the data, or to analyze the data to formulate conclusions. (State)

M:DSP:2:2. Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using more, less, or equal. (State)

M:DSP:2:3. No standard listed at this grade.

M:DSP:2:4. Uses counting techniques to solve problems involving combinations using a variety of strategies (e.g., student diagrams, organized lists, tables, tree diagrams, or others); (e.g., How many ways can you make 50 cents using nickels, dimes, and quarters?) (State)

M:DSP:2:5. For a probability event in which the sample space may or may not contain equally likely outcomes, uses experiments to describe the likelihood or chance of an event using 'more likely,' 'less likely,' 'equally likely,' certain or impossible.

M:DSP:2:6. In response to a teacher or student generated question or hypothesis, groups decide the most effective method (e.g., survey, observation, experimentation) to collect the data (numerical or categorical) necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the question or hypothesis being tested, and when appropriate makes predictions.

NH.M:PRP:2. NECAP - Grade Level Expectation: Problem Solving, Reasoning, and Proof.

M:PRP:2:1. Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to:

M:PRP:2:1.1. Formulate and solve multi-step problems from everyday and mathematical situations.

M:PRP:2:1.2. Solve problems using a variety of strategies (e.g., working backwards, looking for patterns and relationships; guess and check; making tables, charts, or organized lists; solving a simpler version of a problem, drawing a diagram; or creating a model)

M:PRP:2:1.3. Verify and interpret results with respect to the original problem.

M:PRP:2:1.4. Determine if the solution of a problem is reasonable.

M:PRP:2:1.5. Solve problems using manipulatives, graphs, charts, diagrams, and calculators.

M:PRP:2:1.6. Demonstrate that a problem may be solved in more than one way.

M:PRP:2:1.7. Exhibit confidence in their ability to solve problems independently and in groups.

M:PRP:2:1.8. Display increasing perseverance, and persistence in problem solving.

M:PRP:2:2. Students will use mathematical reasoning and proof and be able to:

M:PRP:2:2.1. Use models, known facts, properties, and relationships to explain their thinking.

M:PRP:2:2.2. Justify solution processes and answers (e.g., 'I chose this method to solve the problem because...').

M:PRP:2:2.3. Draw conclusions using inductive reasoning.

M:PRP:2:2.4. Identify the missing information needed to find a solution to a given story problem.

M:PRP:2:2.5. Use patterns and relationships to analyze mathematical situations (e.g., count by fives).

M:CCR:2:1. Students will communicate their understanding of mathematics and be able to:

M:CCR:2:1.2. Discuss relationships between everyday language and mathematical language and symbols (e.g., words that mean something different in mathematics and in everyday life).

M:CCR:2:1.3. Explain conclusions, thought processes, and strategies in problem-solving situations.

M:CCR:2:1.5. Draw pictures and use objects to illustrate mathematical concepts.

M:CCR:2:2. Students will create and use representations to communicate mathematical ideas and to solve problems and be able to:

M:CCR:2:2.2. Select, apply, and translate among mathematical representations to solve problems (e.g., representing fractions with circles, with geoboards, and with pattern blocks).

M:CCR:2:2.3. Link different representations.

M:CCR:2:2.5. Use conventional and self-generated (invented) representations and connect them.

M:CCR:2:2.6. Realize that any representation is subject to multiple interpretations (e.g., drawings and graphs can be read in a different way).

M:CCR:2:3. Students will recognize, explore, and develop mathematical connections and be able to:

M:CCR:2:3.1. Link conceptual and procedural knowledge (e.g., they will know that when they 'regroup,' they are simply changing the representation of the minuend, but not its value).

M:CCR:2:3.2. Recognize and use mathematics in other curriculum areas (e.g., science, social studies).

M:CCR:2:3.4. Identify mathematical situations occurring in literature for children.

M:CCR:2:3.5. Identify examples of geometry in nature, art, and architecture.

NH.M:CCR:2. NECAP - Grade Level Expectation: Communication, Connections, and Representations.

M:CCR:2:1.1. Demonstrate mathematical communication through discussion, reading, writing, listening, and responding, individually and in groups.

M:CCR:2:1.4. Discuss, illustrate, and write about mathematical concepts and relationships.

M:CCR:2:2.1. Create and use age level appropriate representations to organize, record, and communicate mathematical ideas (e.g., students should recognize the relationship among seven counters, seven tally marks, and the symbol 7).

M:CCR:2:2.4. Use representations to model and interpret physical, social, and mathematical phenomena.

M:CCR:2:3.3. Recognize and use mathematics in their daily lives (e.g., graphs, tables, or maps).