# New Hampshire State Standards for Mathematics: Grade 1

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NH.M:N&O:1. NECAP - Grade Level Expectation: Number and Operation.

M:N&O:1:1. Demonstrates conceptual understanding of rational numbers with respect to whole numbers from 0 to 100 using place value, by applying the concepts of equivalency in composing or decomposing numbers; and in expanded notation 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 models where the denominator is equal to the number of parts in the whole using models, explanations, or other representations.

M:N&O:1:2. Demonstrates understanding of the relative magnitude of numbers from 0 to 100 by ordering whole numbers; by comparing whole numbers to each other or to benchmark whole numbers (5, 10, 25, 50, 75, 100); by demonstrating an understanding of the relation of inequality when comparing whole numbers by using '1 more', '1 less', '5 more', '5 less', '10 more', '10 less'; and by connecting number words (from 0 to 20) and numerals (from 0 to 100) to the quantities and positions that they represent using investigations, models, representations, or number lines.

M:N&O:1:3. Demonstrates conceptual understanding of mathematical operations involving addition and subtraction of whole numbers (from 0 to 30) by solving problems involving joining actions, separating actions, part-part whole relationships, and comparison situations; and addition of multiple one-digit whole numbers.

M:N&O:1:4. No standard listed at this grade.

M:N&O:1:5. Demonstrates understanding of monetary value by knowing the names and values for coins (penny, nickel, dime, and quarter) and by adding collections of like coins together to a sum no greater than $1.00.

M:N&O:1:6. Mentally adds and subtracts whole numbers by naming the number that is one or two more or less than the original number; and adds and subtracts whole number facts to ten (e.g., 5 + 3 = 8; 8 - 5 = 3).

M:N&O:1:7. Makes estimates of the number of objects in a set (up to 30 ) and revises estimates as objects are counted (e.g., A student estimates the number of pennies in a jar as 28. Then the student counts the first 10 and makes another estimate based on those that have been counted and those that remain in the jar.).

M:N&O:1:8. Applies properties of numbers (odd, even, composition, and decomposition) and field properties (commutative and identity for addition) to solve problems and to simplify computations involving whole numbers.

NH.M:G&M:1. NECAP - Grade Level Expectation: Geometry and Measurement.

M:G&M:1:1. Uses properties, attributes, composition, or decomposition to sort or classify polygons (triangles, squares, rectangles, rhombi, trapezoids, and hexagons) or objects by a combination of two non-measurable or measurable attributes; and recognizes, names, builds, and draws polygons and circles in the environment.

M:G&M:1:2. No standard listed at this grade.

M:G&M:1:3. Given an example of a three-dimensional geometric shape (rectangular prisms, cylinders, or spheres) finds examples of objects in the environment that are of the same geometric shape (e.g., show a wooden cylinder and students identify common objects of the same shape).

M:G&M:1:4. Demonstrates conceptual understanding of congruency by making mirror images and creating shapes that have line symmetry.

M:G&M:1:5. No standard listed at this grade.

M:G&M:1:6. Demonstrates conceptual understanding of the length/height of a two-dimensional object using non-standard units (e.g. comparing objects to trains of small cubes, using iterations of a small unit to measure an object).

M:G&M:1:7. Demonstrates conceptual understanding of measurable attributes using comparative language to describe and compare attributes of objects (length [longer, shorter], height [taller, shorter], weight [heavier, lighter], temperature [warmer, cooler], and capacity [more, less]); compares objects visually, with direct comparison, and using non-standard units.

M:G&M:1:8. Determines elapsed and accrued time as it relates to calendar patterns (days of the week, months of the year), the sequence of events in a day; and recognizes an hour and 'on the 1/2 hour'.

M:G&M:1:9. Demonstrates understanding of spatial relationships using location and position by using positional words (e.g., close by, on the right, underneath, above, beyond) to describe one location in reference to another on a map, in a diagram, and in the environment.

NH.M:F&A:1. NECAP - Grade Level Expectation: Functions and Algebra.

M:F&A:1:1. Identifies and extends to specific cases a variety of patterns (repeating and growing [numeric and non-numeric]) represented in models, tables, or sequences by extending the pattern to the next one, two, or three elements, by finding a missing element, or by translating repeating patterns across formats (e.g., an abb pattern can be represented as snap, clap, clap; or red, yellow, yellow; or 1,2,2).

M:F&A:1:2. No standard listed at this grade.

M:F&A:1:3. No standard listed at this grade.

M:F&A:1:4. Demonstrates conceptual understanding of equality by finding the value that will make an open sentence true using models, verbal explanations, or written equations. (Limited to one operation and limited to use addition or subtraction)

NH.M:DSP:1. NECAP - Grade Level Expectation: Data, Statistics, and Probability.

M:DSP:1:1. Interprets a given representation created by the class (models, tally charts, pictographs with one-to-one correspondence, and tables) to answer questions related to the data, or to analyze the data to formulate conclusions using words, diagrams, or verbal/scribed responses to express answers.

M:DSP:1:2. Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using more, less, or equal.

M:DSP:1:3. No standard listed at this grade.

M:DSP:1:4. No standard listed at this grade.

M:DSP:1:5. For a probability event in which the sample space may or may not contain equally likely outcomes, groups use experiments to describe the likelihood or chance of an event (using 'more likely,' 'less likely', or 'equally likely').

M:DSP:1:6. No standard listed at this grade.

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).