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Second Grade
Mathematics
| Second grade objectives help a student to become a more independent problem solver through concrete and technology supported experiences which explore new problem solving strategies, everyday use of mathematical language, and reasonableness and interrelationships of mathematics. Concepts include place value through thousands, estimation, introduction of properties of mathematics, and measurement that including spatial perception. The West Virginia Standards for 21st Century Learning include the following components: 21st Century Content Standards and Objectives and 21st Century Learning Skills and Technology Tools. All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools and content standards and objectives. |
M.S.2.1
Number and Operations |
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will · demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number systems, · demonstrate meanings of operations and how they relate to one another, and · compute fluently and make reasonable estimates. |
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| M.PD.2.1 |
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| Distinguished |
Above Mastery |
Mastery |
Partial Mastery |
Novice |
| Second grade students at the distinguished level in mathematics:
model, read, compare, order, write (standard and expanded form), identify place value with numbers beyond 1000;
read and compare ordinal numbers to identify position in real world situations;
round three-digit numbers and use rounding to estimate and evaluate sums and differences to solve real world problems;
justify any number as odd or even and create sets with and even and odd set of members;
show quick recall of addition and subtraction facts;
justify number properties and the relationship between addition and subtraction using clear mathematical language;
add and subtract two- and three-digit numbers without and with regrouping and explain the procedures using clear mathematical language;
identify, name, compare and explain fractions without models;
create one and two-step story problems, solve using multiple strategies, present and justify results using clear mathematical language. |
Second grade students at the above mastery level in mathematics:
model, read, compare, order, write (standard and expanded form), identify place value with numbers to 1000;
read and compare ordinal numbers to identify position in real world situations;
round three-digit numbers and use rounding to estimate and evaluate sums and differences;
justify any number as odd or even;
show quick recall of addition and subtraction facts;
justify number properties and the relationship between addition and subtraction;
add and subtract two- and three- digit numbers without and with regrouping;
identify, name, compare and explain fractions using models;
create one and two-step story problems, solve using multiple strategies, present and justify results. |
Second grade students at the mastery level in mathematics:
model, read, compare, order, write (standard and expanded form), identify place value with numbers to 1000;
read and use ordinal numbers to identify position;
round three-digit numbers and use rounding to estimate and evaluate sums and differences;
justify any number as odd or even and determine if a set has an odd or even number;
show quick recall of addition and subtraction facts;
model and justify number properties and the relationship between addition and subtraction;
add and subtract two- and three-digit numbers without regrouping; model addition and subtraction of two- and three-digit numbers with regrouping;
identify, name, and explain fractions using models;
create one and two-step story problems, solve using multiple strategies, present and justify results. |
Second grade students at the partial mastery level in mathematics:
model, read, compare, order, write (standard form), and identify place value with numbers to 1000;
read and use ordinal numbers to identify position, 1st-10th;
round three-digit numbers to the nearest 100 and use rounding to estimate and evaluate sums and differences;
identify numbers as odd or even and determine if a set has an odd or even number;
use strategies to recall of some addition and subtraction facts;
model number properties and the relationship between addition and subtraction;
add and subtract two- and three- digit numbers without regrouping; model addition and subtraction of two-digit numbers with regrouping;
identify and name fractions using models;
solve one and two-step story problems using multiple strategies and present results. |
Second grade students at the novice level in mathematics:
model, read, write (standard form), and identify place value with numbers to 1000;
use ordinal numbers to identify position, 1st-5th;
round three-digit numbers to the nearest 100 to estimate sums and differences;
determine if a set has an odd or even number;
model of addition and subtraction facts;
model the relationship between addition and subtraction;
add and subtract two-digit numbers without regrouping; model addition and subtraction of two-digit numbers without regrouping;
identify fractions using models;
solve one-step story problems and present results. |
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| Number |
Objective |
M.O.2.1.1
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read, write, order, and compare numbers to 1,000 using multiple strategies (e.g. symbols, manipulatives, number line). |
M.O.2.1.2
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justify any number as odd or even and determine if a set has an odd or even number of elements. |
M.O.2.1.3
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count and group concrete manipulatives by ones, tens, and hundreds to 1,000. |
M.O.2.1.4
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model and identify place value of each digit utilizing standard and expanded form through 1000. |
M.O.2.1.5
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identify and read any ordinal number to identify position in a sequence. |
M.O.2.1.6
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round any 3-digit number to both the nearer 10 and 100. |
M.O.2.1.7
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Identify and explain fractions as part of a whole and as part of a set/group using models. |
M.O.2.1.8
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model and justify the relationship between addition and subtraction (e.g., identity element of addition, associative property, commutative property, inverse operations, fact families). |
M.O.2.1.9
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demonstrate quick recall of basic addition facts with sums to 18 and corresponding subtraction facts. |
M.O.2.1.10
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model 2- and 3-digit addition and subtraction with regrouping using multiple strategies. |
M.O.2.1.11
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add and subtract 2- and 3-digit numbers without regrouping. |
M.O.2.1.12
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use rounding to analyze the reasonableness of a sum or a difference. |
M.O.2.1.13
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create story problems that require one or two-step procedures, using a variety of strategies explain the reasoning used , justify the procedures selected and present the results. |
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M.S.2.2
Algebra |
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will - demonstrate understanding of patterns, relations and functions,
- represent and analyze mathematical situations and structures using algebraic symbols,
- use mathematical models to represent and understand quantitative relationships, and
- analyze change in various contexts.
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| M.PD.2.2 |
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| Distinguished |
Above Mastery |
Mastery |
Partial Mastery |
Novice |
| Second grade students at the distinguished level in mathematics:
analyze, describe, extend and create growing patterns;
explain how one variable produces a change in another variable (e.g., input/output table)in a real world situation;
describe, complete, extend, and create counting patterns when given the rule; write the rule when given the pattern;
create and analyze equivalent numerical expressions. |
Second grade students at the above mastery level in mathematics:
analyze, describe, extend and create growing patterns;
explain how one variable produces a change in another variable (e.g., input/output table)in a real world situation;
describe, complete, extend, and create counting patterns when given the rule;
create, analyze, and demonstrate equivalent numerical expressions using models or manipulatives. |
Second grade students at the mastery level in mathematics:
analyze, describe, extend and create growing patterns;
explain how one variable produces a change in another variable (e.g., input/output table);
describe, complete, extend counting patterns when given the rule;
create and demonstrate equivalent numerical expressions using models or manipulatives. |
Second grade students at the partial mastery level in mathematics:
analyze, describe, and extend growing patterns;
determine input, output, or rule to show how one variable produces a change in another variable;
extend counting patterns when given the rule;
demonstrate equivalence of numerical expressions using models or manipulatives. |
Second grade students at the novice level in mathematics:
describe and extend growing patterns;
determine output or rule to show how one variable produces a change in another variable;
extend counting patterns when given the rule;
model equivalent numerical expressions using manipulatives. |
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| Number |
Objective |
M.O.2.2.1
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analyze, describe, extend and create a growing pattern using objects or numbers. |
M.O.2.2.2
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explain how one variable produces a change in another variable. |
M.O.2.2.3
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describe, complete and extend a variety of counting patterns, according to a given rule. |
M.O.2.2.4
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create physical models to demonstrate equivalency of two numerical expressions written as a grade-appropriate number sentence. |
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M.S.2.3
Geometry |
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will · analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, · specify locations and describe spatial relationships using coordinate geometry and other representational systems, · apply transformations and use symmetry to analyze mathematical situations, and · solve problems using visualization, spatial reasoning, and geometric modeling. |
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| M.PD.2.3 |
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| Distinguished |
Above Mastery |
Mastery |
Partial Mastery |
Novice |
| Second grade students at the distinguished level in mathematics:
identify, describe, compare, and contrast plane and solid shapes using clear mathematical language;
draw, describe, and combine shapes that show reflections and rotations;
draw or build similar shapes;
model, draw, and describe line segments and angles;
plot and describe the path between locations on a grid. |
Second grade students at the above mastery level in mathematics:
identify, describe, compare, and contrast plane and solid shapes using clear mathematical language;
draw and describe shapes that show reflections and rotations;
draw or build similar shapes;
model, draw, and describe line segments and angles;
plot and describe the path between locations on a grid. |
Second grade students at the mastery level in mathematics:
identify, describe, compare, and contrast plane and solid shapes;
identify and draw shapes that show reflections and rotations;
identify similar shapes;
model and draw line segments and angles;
plot and describe the path between locations on a grid. |
Second grade students at the partial mastery level in mathematics:
identify and describe plane and solid geometric shapes;
identify shapes that have been reflected or rotated;
define similar shapes;
model line segments and angles and draw line segments;
plot locations on a grid. |
Second grade students at the novice level in mathematics:
identify plane and solid geometric shapes;
identify shapes that have been reflected or rotated;
define similar shapes;
model line segments and angles;
identify locations on a grid. |
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| Number |
Objective |
M.O.2.3.1
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identify and describe the following geometric solids according to the number of faces and edges:
- rectangular solid
- cube
- cylinder
- cone
- pyramid
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M.O.2.3.2
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compare and contrast plane and solid geometric shapes. |
M.O.2.3.3
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identify and draw congruent shapes that have been rotated or reflected. |
M.O.2.3.4
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model and draw line segments and angles. |
M.O.2.3.5
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plot and describe the path between locations on a grid. |
M.O.2.3.6
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identify similar shapes. |
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M.S.2.4
Measurement |
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will - demonstrate understanding of measurable attributes of objects and the units, systems, and processes of measurement, and
- apply appropriate techniques, tools and formulas to determine measurements.
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| M.PD.2.4 |
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| Distinguished |
Above Mastery |
Mastery |
Partial Mastery |
Novice |
| Second grade students at the distinguished level in mathematics:
design a project to measure length, weight, or temperature; make and test a hypothesis; collect, organize, and analyze data; and present the results;
estimate and measure to determine perimeter and find area by counting square units of regular and irregular shapes;
order events, tell time to the nearest five minutes;
use a calendar to find past and future dates of specific events;
show multiple solutions to model given values and to make change to the next dollar. |
Second grade students at the above mastery level in mathematics:
design a project to measure length, weight, or temperature; make and test a hypothesis; collect, organize, and analyze data; and present the results;
estimate and measure to determine perimeter and find area by counting square units;
order events and tell time to the nearest five minutes;
use a calendar to find past and future dates;
use coins to model given values and to make change up to the next dollar. |
Second grade students at the above mastery level in mathematics:
design a project to measure length, weight, or temperature; make and test a hypothesis; collect, organize, and analyze data; and present the results;
estimate and measure to determine perimeter and find area by counting square units;
order events and tell time to the nearest five minutes;
use a calendar to find past and future dates;
use coins to model given values and to make change up to the next dollar. |
Second grade students at the partial mastery level in mathematics:
carry out a project using tools to measure length, weight, temperature; test a hypothesis; collect, organize, and analyze data; and present the results;
find perimeter and count square units to determine area;
order events and tell time to the nearest half hour;
use a calendar to find today’s date and future dates;
use coins to model given values and to make change up to a quarter. |
Second grade students at the novice level in mathematics:
carry out a project to measure length, weight, or temperature; collect, organize, and analyze data; and present the results;
add to find perimeter and count square units to determine area;
order events and tell time to the nearest hour;
use a calendar to find today’s date;
use coins to model given values. |
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| Number |
Objective |
M.O.2.4.1
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identify a real life situation to use appropriate measurement tools; over time make a hypothesis as to the change overtime using whole units:
- length in centimeters and inches,
- temperature in Celsius and Fahrenheit,
- weight/mass in pounds and kilograms, and design and implement a method to collect, organize, and analyze data; analyze the results to make a conclusion evaluate the validity of the hypothesis based upon collected data; design a mode of presentation (with and without technology).
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M.O.2.4.2
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estimate and determine the perimeter of squares, rectangles and triangles. |
M.O.2.4.3
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estimate and count the number of square units needed to cover a given area using manipulatives. |
M.O.2.4.4
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order events in relation to time. |
M.O.2.4.5
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determine past and future days of the week and identify specific dates, given a calendar. |
M.O.2.4.6
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read time to the quarter hour using an analog and digital clock. |
M.O.2.4.7
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identify, count and organize coins and bills to display a variety of price values from real-life examples with a total value of one dollar or less and model making change using manipulatives. |
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M.S.2.5
Data Analysis and Probability |
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will - formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them,
- select and use appropriate statistical methods to analyze data,
- develop and evaluate inferences and predictions that are based on models, and
- apply and demonstrate an understanding of basic concepts of probability.
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| M.PD.2.5 |
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| Distinguished |
Above Mastery |
Mastery |
Partial Mastery |
Novice |
| Second grade students at the distinguished level in mathematics:
create, read, and interpret pictographs with each picture representing greater than a single unit and present their findings;
formulate questions, collect, organize, and display data as a chart, table, or bar graph and present their findings; analyze data represented on a graph and formulate questions that can be answered by the graph;
conduct experiments with more than two outcomes, organize, display, and present the data, and use the data to predict outcomes if the experiment is repeated. |
Second grade students at the above mastery level in mathematics:
create, read, and interpret pictographs with each picture representing greater than or equal to a single unit;
formulate questions, collect, organize, and display data as a chart, table, or bar graph; analyze data represented on a graph and formulate questions that can be answered by the graph;
conduct experiments with more than two outcomes, organize, display, and use the data to predict outcomes if the experiment is repeated. |
Second grade students at the mastery level in mathematics:
create, read, and interpret pictographs with each picture representing greater than or equal to a single unit;
formulate questions, collect, organize, and display data as a chart, table, or bar graph and analyze data represented on a graph;
conduct simple probability experiments with two or more outcomes and use the data to predict outcomes if the experiment is repeated. |
Second grade students at the partial mastery level in mathematics:
create, read, and interpret pictographs with each picture representing a single unit;
organize and display data as a chart, table, or bar graph and analyze data represented on a graph;
conduct simple probability experiments with two or more outcomes and record the data. |
Second grade students at the novice level in mathematics:
read and interpret pictographs with each picture representing a single unit;
display data as a chart, table, or bar graph and analyze data represented on a graph;
conduct simple probability experiments with two outcomes and record the data. |
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| Number |
Objective |
M.O.2.5.1
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create, read, and interpret a pictograph with each picture representing greater than or equal to a single unit. |
M.O.2.5.2
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conduct simple experiments with more than two outcomes and use the data to predict which event is more, less, or equally likely to occur if the experiment is repeated. |
M.O.2.5.3
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analyze data represented on a graph using grade-appropriate questions. |
M.O.2.5.4
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formulate questions, collect data, organize and display as a chart, table or bar graph. |
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