# New Hampshire State Standards for Mathematics: Grade 4

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NH.M:N&O:4. NECAP - Grade Level Expectation: Number and Operation.

M:N&O:4:1. Demonstrates conceptual understanding of rational numbers with respect to whole numbers from 0 to 999,999 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/5, a/6, a/8, or a/10, 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, set, or linear models where the number of parts in the whole are equal to, and a multiple or factor of the denominator; and decimals as hundredths within the context of money, or tenths within the context of metric measurements (e.g., 2.3 cm) using models, explanations, or other representations. (State)

M:N&O:4:2. Demonstrates understanding of the relative magnitude of numbers from 0 to 999,999 by ordering or comparing whole numbers; and ordering, comparing, or identifying equivalent proper positive fractional numbers; or decimals using models, number lines, or explanations. (State)

M:N&O:4:3. Demonstrates conceptual understanding of mathematical operations by describing or illustrating the relationship between repeated subtraction and division (no remainders); the inverse relationship between multiplication and division of whole numbers; or the addition or subtraction of positive fractional numbers with like denominators using models, number lines, or explanations. (State)

M:N&O:4:4. Accurately solves problems involving multiple operations on whole numbers or the use of the properties of factors and multiples; and addition or subtraction of decimals and positive proper fractions with like denominators. (Multiplication limited to 2 digits by 2 digits, and division limited to 1-digit divisors.) (State)

M:N&O:4:5. No standard listed at this grade.

M:N&O:4:6. Mentally adds and subtracts whole number facts through 20; multiplies whole number facts to a product of 100, and calculates related division facts; adds two-digit whole numbers, combinations of two-digit and 3-digit whole numbers that are multiples of ten, and 4-digit whole numbers that are multiples of 100 (limited to two addends) (e.g., 67 + 24; 320 + 430; 320 + 90; 1,300 + 1,400); and subtracts a one-digit whole number from a two-digit whole number (e.g., 67 - 9); and subtracts combinations of two-digit and three-digit whole numbers that are multiples of ten (e.g., 50 - 20, 230 - 80, 520 - 200).

M:N&O:4:7. 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:4:8. Applies properties of numbers (odd, even, multiplicative property of zero, and remainders) and field properties (commutative, associative, and identity) to solve problems and to simplify computations.

NH.M:G&M:4. NECAP - Grade Level Expectation: Geometry and Measurement.

M:G&M:4:1. Uses properties or attributes of angles (number of angles) or sides (number of sides, length of sides, parallelism, or perpendicularity) to identify, describe, or distinguish among triangles, squares, rectangles, rhombi, trapezoids, hexagons, or octagons; or classify angles relative to 90 degrees as more than, less than, or equal to. (State)

M:G&M:4:2. No standard at this grade

M:G&M:4:3. Uses properties or attributes (shape of bases or number of lateral faces) to identify, compare, or describe three-dimensional shapes (rectangular prisms, triangular prisms, cylinders, or spheres). (State)

M:G&M:4:4. Demonstrates conceptual understanding of congruency by matching congruent figures using reflections, translations, or rotations (flips, slides, or turns), or as the result of composing or decomposing shapes using models or explanations. (State)

M:G&M:4:5. Demonstrates conceptual understanding of similarity by applying scales on maps, or applying characteristics of similar figures (same shape but not necessarily the same size) to identify similar figures, or to solve problems involving similar figures. Describes relationships using models or explanations. (State)

M:G&M:4:6. Demonstrates conceptual understanding of perimeter of polygons, and the area of rectangles, polygons or irregular shapes on grids using a variety of models, manipulatives, or formulas. Expresses all measures using appropriate units. (State)

M:G&M:4:7. 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:4:8. No standard listed at this grade.

M:G&M:4:9. Demonstrates understanding of spatial relationships using location and position by interpreting and giving directions between locations on a map or coordinate grid (first quadrant); plotting points in the first quadrant in context (e.g., games, mapping); and finding the horizontal and vertical distances between points on a coordinate grid in the first quadrant.

M:G&M:4:10. Demonstrates conceptual understanding of spatial reasoning and visualization by copying, comparing, and drawing models of triangles, squares, rectangles, rhombi, trapezoids, hexagons, octagons, and circles; and builds models of rectangular prisms from two- or three-dimensional representations.

NH.M:F&A:4. NECAP - Grade Level Expectation: Functions and Algebra.

M:F&A:4:1. Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables or sequences; and writes a rule in words or symbols to find the next case. (State)

M:F&A:4:2. Demonstrates conceptual understanding of linear relationships (y = kx) as a constant rate of change by identifying, describing, or comparing situations that represent constant rates of change.

M:F&A:4:3. Demonstrates conceptual understanding of algebraic expressions by using letters or symbols to represent unknown quantities to write simple linear algebraic expressions involving any one of the four operations; or by evaluating simple linear algebraic expressions using whole numbers. (State)

M:F&A:4:4. Demonstrates conceptual understanding of equality by showing equivalence between two expressions using models or different representations of the expressions, by simplifying numerical expressions where left to right computations may be modified only by the use of parentheses [e.g., 14 - (2 x 5)] (expressions consistent with the parameters of M(F&A)-4-3), and by solving one-step linear equations of the form ax = c, x +/- b = c, where a, b, and c are whole numbers with a not equal to 0. (State)

NH.M:DSP:4. NECAP - Grade Level Expectation: Data, Statistics, and Probability.

M:DSP:4:1. Interprets a given representation (line plots, tables, bar graphs, pictographs, or circle graphs) to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. (State)

M:DSP:4:2. Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (median or mode), or range. (State)

M:DSP:4:3. Organizes and displays data using tables, line plots, bar graphs, and pictographs to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems.

M:DSP:4:4. Uses counting techniques to solve problems in context involving combinations or simple permutations (e.g., Given a map - Determine the number of paths from point A to point B.) using a variety of strategies (e.g., organized lists, tables, tree diagrams, or others). (State)

M:DSP:4:5. For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the likelihood of an event as a part to whole relationship (e.g., two out of five, zero out of five, five out of five) and tests the prediction through experiments; and determines if a game is fair.

M:DSP:4:6. 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; and asks new questions and makes connections to real world situations.

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).