# New Hampshire State Standards for Mathematics: Grade 3

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NH.M:N&O:3. NECAP - Grade Level Expectation: Number and Operation.

M:N&O:3:1. Demonstrates conceptual understanding of rational numbers with respect to whole numbers from 0 to 999 through equivalency, composition, decomposition, or place value using models, explanations, or other representations; and positive fractional numbers (benchmark fractions: a/2, a/3, a/4, a/6, or a/8, 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 number of parts in the whole is equal to the denominator; and decimals (within a context of money) as a part of 100 using models, explanations, or other representations. (State)

M:N&O:3:2. Demonstrates understanding of the relative magnitude of numbers from 0 to 999 by ordering whole numbers; by comparing whole numbers to benchmark whole numbers (100, 250, 500, 750); or by comparing whole numbers to each other; and comparing or identifying equivalent positive fractional numbers (a/2, a/3, a/4 where a is a whole number greater than 0 and less than or equal to the denominator) using models, number lines, or explanations. (State)

M:N&O:3:3. Demonstrates conceptual understanding of mathematical operations by describing or illustrating the inverse relationship between addition and subtraction of whole numbers; and the relationship between repeated addition and multiplication using models, number lines, or explanations. (State)

M:N&O:3:4. Accurately solves problems involving addition and subtraction with regrouping; the concept of multiplication; and addition or subtraction of decimals (in the context of money). (State)

M:N&O:3:5. No standard listed at this grade.

M:N&O:3:6. Mentally adds and subtracts whole number facts through 20; adds two-digit and one-digit whole numbers; adds combinations of two-digit and three-digit whole numbers that are multiples of ten (e.g., 60 + 50, 300 + 400, 320 + 90); subtracts a one-digit whole number from a two-digit whole number (e.g., 37 - 5); and subtracts two-digit whole numbers that are multiples of ten and three-digit whole numbers that are multiples one hundred (e.g., 50 - 20, 500 - 200).

M:N&O:3:7. Makes estimates in a given situation by identifying when estimation is appropriate, selecting the appropriate method of estimation, and evaluating the reasonableness of solutions appropriate to grade level GLEs across content strands.

M:N&O:3:8. Applies properties of numbers (odd, even, and multiplicative property of zero for single-digit whole numbers [6 x 0 = 0]) and field properties (commutative for addition, associative for addition, identity for multiplication, and commutative for multiplication for single-digit whole numbers [e.g., 3 x 4 = 4 x 3]) to solve problems and to simplify computations involving whole numbers.

NH.M:G&M:3. NECAP - Grade Level Expectation: Geometry and Measurement.

M:G&M:3:1. Uses properties or attributes of angles (number of angles) or sides (number of sides or length of sides) or composition or decomposition of shapes to identify, describe, or distinguish among triangles, squares, rectangles, rhombi, trapezoids, hexagons, or circles. (State)

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

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

M:G&M:3:4. Demonstrates conceptual understanding of congruency by matching congruent figures using reflections, translations, and rotations (flips, slides, and turns) (e.g., recognizing when pentominoes are reflections, translations and rotations of each other); composing and decomposing two- and three-dimensional objects using models or explanations (e.g., Given a cube, students use blocks to construct a congruent cube.); and by using line symmetry to demonstrate congruent parts within a shape.

M:G&M:3:5. Demonstrates conceptual understanding of similarity by identifying similar shapes.

M:G&M:3:6. Demonstrates conceptual understanding of perimeter of polygons, and the area of rectangles on grids using a variety of models or manipulatives. Expresses all measures using appropriate units. (State)

M:G&M:3:7. 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:3:8. No standard listed at this grade.

M:G&M:3:9. Demonstrates understanding of spatial relationships using location and position by interpreting and giving directions from one location to another (e.g., classroom to the gym, from school to home) using positional words; and between locations on a map or coordinate grid (first quadrant) using positional words or compass directions.

M:G&M:3:10. Demonstrates conceptual understanding of spatial reasoning and visualization by copying, comparing, and drawing models of triangles, squares, rectangles, rhombi, trapezoids, hexagons, and circles; and builds models of rectangular prisms from three-dimensional representations.

NH.M:F&A:3. NECAP - Grade Level Expectation: Functions and Algebra.

M:F&A:3:1. 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 one, two, or three elements, or finding missing elements. (State)

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

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

M:F&A:3:4. Demonstrates conceptual understanding of equality by showing equivalence between two expressions using models or different representations of the expressions; or by finding the value that will make an open sentence true. (Limited to one operation and limited to use addition, subtraction, or multiplication) (State)

NH.M:DSP:3. NECAP - Grade Level Expectation: Data, Statistics, and Probability.

M:DSP:3:1. Interprets a given representation (line plots, tally charts, tables, or bar graphs) to answer questions related to the data, to analyze the data to formulate conclusions, or to make predictions. (State)

M:DSP:3:2. Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using most frequent (mode), least frequent, largest, or smallest. (State)

M:DSP:3:3. Organizes and displays data using tables, tally charts, and bar graphs, to answer questions related to the data, to analyze the data to formulate conclusions, to make predictions, or to solve problems.

M:DSP:3:4. Uses counting techniques to solve problems involving combinations and simple permutations using a variety of strategies (e.g., student diagrams, organized lists, tables, tree diagrams, or others).

M:DSP:3:5. For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the likelihood of an event using 'more likely,' 'less likely,' 'equally likely,' certain, or impossible and tests the prediction through experiments; and determines if a game is fair.

M:DSP:3:6. 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:5. NECAP - Grade Level Expectation: Problem Solving, Reasoning, and Proof

M:PRP:5:1. Students will use problem-solving strategies to investigate and understand increasingly complex mathematical content and be able to:

M:PRP:5:1.1. Determine the reasonableness of solutions to real-world problems.

M:PRP:5:1.2. Generalize solutions and apply strategies to new problem situations.

M:PRP:5:1.3. Add to the repertoire of problem-solving strategies (e.g., looking for similar problems) and use those strategies in more sophisticated ways.

M:PRP:5:1.4. Solve problems with multiple solutions, recognize when a problem has no solution, and recognize problems where more information is needed.

M:PRP:5:1.5. Translate results of a computation into solutions that fit the real-world problem (e.g., when a computation shows that one needs 3.2 gallons of paint to paint a room, how much paint do you buy?).

M:PRP:5:2. Students will use mathematical reasoning and proof and be able to:

M:PRP:5:2.1. Draw conclusions and solve problems using elementary deductive reasoning and reasoning by analogy.

M:PRP:5:2.2. Make and defend conjectures and generalizations.

M:PRP:5:2.3. Use models, known facts, properties, and relationships to explain thinking and to justify answers and solution processes.

M:PRP:5:2.4. Recognize the pervasive use and power of reasoning as a part of mathematics.

NH.M:CCR:5. NECAP - Grade Level Expectation: Communication, Connections, and Representations.

M:CCR:5:1. Students will communicate their understanding of mathematics and be able to:

M:CCR:5:1.1. Discuss mathematical ideas and write convincing arguments.

M:CCR:5:1.2. Understand, explain, analyze, and evaluate mathematical arguments and conclusions presented by others.

M:CCR:5:1.3. Ask clarifying and extending questions related to mathematics they have heard or read about.

M:CCR:5:1.4. Understand and appreciate the economy and power of mathematical symbolism and its role in the development of mathematics.

M:CCR:5:1.5. Demonstrate an understanding of mathematical concepts and relationships through a variety of methods (e.g., writing, graphing, charts, diagrams, number sentences, or symbols).

M:CCR:5:1.6. Use a variety of technologies (e.g., computers, calculators, video, probes) to represent and communicate mathematical ideas.

M:CCR:5:2. Students will create and use representations to communicate mathematical ideas and to solve problems and be able to:

M:CCR:5:2.1. Use physical models and diagrams to represent important mathematical ideas (e.g., multiplication).

M:CCR:5:2.2. Use appropriate representations to solve problems or to portray, clarify, or extend a mathematical idea.

M:CCR:5:2.3. Recognize equivalent representations of concepts and procedures and translate among them as appropriate (for example, understand how the addition of whole numbers, fractions, and decimals are related).

M:CCR:5:3. Students will recognize, explore, and develop mathematical connections and be able to:

M:CCR:5:3.1. See mathematics as an integrated whole.

M:CCR:5:3.2. Recognize relationships among different topics in mathematics.

M:CCR:5:3.3. Recognize and use mathematics in other curriculum areas and in their daily lives.

M:CCR:5:3.4. Link concepts and procedures.

M:CCR:5:3.5. Use mathematical skills, concepts, and applications in other disciplines (e.g., graphs in social studies, patterns in art, or music and geometry in technology education).