Standard 1: Number and Computation

The student uses numerical and computational concepts and procedures in a variety of situations.

Second Grade

Benchmark 1
The student demonstrates number sense for whole numbers, fractions, and using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student knows, explains and represents whole numbers from 0 through 1,000 using concrete objects.
  2. The student compares and orders:
    1. whole numbers from 0 through 1,000 using concrete objects;
    2. fractions greater than or equal to zero with like denominators (halves, fourths, thirds, eighths) using concrete objects.
  3. The student uses addition and subtraction to show equivalent representations for whole numbers from 0 through 100.
  4. The student identifies and uses ordinal positions from first (1st) through twentieth (20th).
  5. The student identifies coins, states their values, and determines the total value to $1.00 of a mixed group of coins using pennies, nickels, dimes, quarters, and half-dollars.
  6. The student counts a like combination of currency ($1, $5, $10, $20) to $100.
Application Indicators
  1. The student solves real-world problems using equivalent representations and concrete objects to:
    1. compare and order whole numbers from 0 through 1,000.
    2. add and subtract whole numbers from 0 through 100.
    3. compare and order a mixed group of coins to $1.00.
    4. find equivalent values of coins to $1.00 without mixing coins.
  2. The student determines whether or not numerical values that involve whole numbers from 0 through 1,000 are reasonable.
 Benchmark 2
The student demonstrates an understanding of whole numbers with a special emphasis on place value and recognizes, uses, and explains the concepts of properties as they relate to whole numbers in a variety of situations. Knowledge Base Indicators
  1. The student reads and writes:
    1. whole numbers from 0 through 1,000 in numerical form.
    2. whole numbers from 0 through 100 in words.
    3. whole numbers from 0 through 1,000 in numerical form when presented in word form.
  2. The student represents whole numbers from 0 through 1,000 using various groupings and place value models emphasizing 1s, 10s, and 100s; explains the groups; and states the value of the digit in ones place, tens place, and hundreds place.
  3. The student counts subsets of whole numbers from 0 through 1,000 forwards and backwards.
  4. The student identifies the place value of the digits in whole numbers from 0 through 1,000.
  5. The student identifies any whole number from 0 through 100 as even or odd.
  6. The student uses the concepts of these properties with whole numbers from 0 through 100 and demonstrates their meaning including the use of concrete objects:
    1. commutative property of addition.
    2. zero property of addition (additive identity).
    3. associative property of addition.
    4. symmetric property of equality applied to basic addition and subtraction facts.
Application Indicators
  1. The student solves real-world problems with whole numbers from 0 through 100 using place value models and the concepts of these properties to explain reasoning:
    1. commutative property of addition.
    2. zero property of addition.
  2. The student performs various computational procedures with whole numbers from 0 through 100 using these properties and explains how they were used:
    1. commutative property of addition (5 + 6 = 6 + 5).
    2. zero property of addition (17 + 0 = 0 + 17).
 Benchmark 3
The student uses computational estimation with whole numbers and money in a variety of situations. Knowledge Base Indicators
  1. The student estimates whole number quantities from 0 through 1,000 and monetary amounts through $50 using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.
  2. The student uses various estimation strategies to estimate whole number quantities from 0 through 1,000.
Application Indicators
  1. The student adjusts original whole number estimate of a real-world problem using numbers from 0 through 1,000 based on additional information (a frame of reference).
  2. The student estimates to check whether or not the result of a real-world problem using whole numbers from 0 through 1,000 and monetary amounts through $50 is reasonable and makes predictions based on the information.
  3. The student selects a reasonable magnitude from three given quantities, a one-digit numeral, a two-digit numeral, and a three-digit numeral (5, 50, 500) based on a familiar problem situation and explains the reasonableness of the selection.
 Benchmark 4
The student models, performs, and explains computation with whole numbers and money using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.
  2. N states and uses with efficiency and accuracy basic addition facts with sums from 0 through 20 and corresponding subtraction facts.
  3. The student skip counts by 2s, 5s, and 10s through 100 and skip counts by 3s through 36.
  4. The student uses repeated addition (multiplication) with whole numbers to find the sum when given the number of groups (ten or less) and given the same number of concrete objects in each group (twenty or less).
  5. The student uses repeated subtraction (division) with whole numbers when given the total number of concrete objects in each group to find the number of groups.
  6. The student fair shares/measures out (divides) a total amount through 100 concrete objects into equal groups.
  7. The student performs and explains these computational procedures:
    1. adds and subtracts three-digit whole numbers with and without regrouping including the use of concrete objects,
    2. adds and subtracts monetary amounts through 99¢ using cent notation (25¢ + 52¢) and money models.
  8. The student identifies basic addition and subtraction fact families (facts with sums from 0 through 20 and corresponding subtraction facts).
  9. The student reads and writes horizontally and vertically the same addition or subtraction expression.
Application Indicators
  1. The student solves one-step real-world addition or subtraction problems with various groupings:
    1. two-digit whole numbers with regrouping;
    2. monetary amounts to 99ยข with regrouping.
  2. The student generates a family of basic addition and subtraction facts given one fact/equation.

Standard 2: Algebra

The student uses algebraic concepts and procedures in a variety of situations.

Second Grade

Benchmark 1
The student recognizes, describes, extends, develops, and explains relationships in patterns using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student uses concrete objects, drawings, and other representations to work with types of patterns:
    1. repeating patterns;
    2. growing (extending) patterns.
  2. The student uses the following attributes to generate patterns:
    1. counting numbers related to number theory;
    2. whole numbers that increase or decrease;
    3. geometric shapes;
    4. measurements;
    5. the calendar;
    6. money and time;
    7. things related to daily life;
    8. things related to size, shape, texture, or movement.
  3. The student identifies and continues a pattern presented in various formats including numeric (list or table), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written.
  4. The student generates repeating patterns.
Application Indicators
  1. The student generalizes these patterns using a written description:
    1. whole number patterns;
    2. patterns using geometric shapes;
    3. calendar patterns;
    4. money and time patterns;
    5. patterns using size, shape, color, texture, or movement;
  2. The student recognizes multiple representations of the same pattern.
  3. The student uses concrete objects to model a whole number patterns.
 Benchmark 2
The student uses symbols and whole numbers to solve addition and subtraction equations using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student explains and uses symbols to represent unknown whole number quantities from 0 through 100.
  2. The student finds the sum or difference in one-step equations with:
    1. whole numbers from 0 through 99;
    2. up to two different coins.
  3. The student finds unknown addend or subtrahend using basic addition and subtraction facts (fact family).
  4. The student describes and compares two whole numbers from 0 through 1,000 using the terms: is equal to, is less than, is greater than.
Application Indicators
  1. The student represents real-world problems using symbols and whole numbers from 0 through 30 with one operation (addition, subtraction) and one unknown.
  2. The student generates:
    1. addition or subtraction equations to match a given real-world problem with one operation and one unknown using whole numbers from 0 through 99.
    2. a real-world problem to match a given addition or subtraction equation with one operation using the basic facts.
 Benchmark 3
The student recognizes and describes whole number relationships using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student states mathematical relationships between whole numbers from 0 through 100 using various methods including mental math, paper and pencil, and concrete objects.
  2. The student finds the values and determines the rule that involve addition or subtraction of whole numbers from 0 through 100 using a horizontal or vertical function table (input/output machine, T-table).
  3. The student generalizes numerical patterns using whole numbers from 0 through 100 with one operation (addition, subtraction) by stating the rule using words.
Application Indicators
  1. The student represents and describes mathematical relationships between whole numbers from 0 through 100 using concrete objects, pictures, oral descriptions, and symbols.
  2. The student finds the rule, states the rule, and extends numerical patterns with whole numbers from 0 through 100.
 Benchmark 4
The student uses mathematical models including concrete objects to represent, show, and communicate mathematical relationships in a variety of situations. Knowledge Base Indicators
  1. The student knows, explains, and uses mathematical models to represent mathematical concepts, procedures, and relationships. Mathematical models include:
    1. process models (concrete objects, pictures, diagrams, number lines, unifix cubes, hundred charts, or measurement tools) to model computational procedures and mathematical relationships, to compare and order numerical quantities, and to represent fractional parts;
    2. place value models (place value mats, hundred charts, or base ten blocks) to compare, order, and represent numerical quantities and to model computational procedures;
    3. fraction models (fraction strips or pattern blocks) to compare, order, and represent numerical quantities;
    4. money models (base ten blocks or coins) to compare, order, and represent numerical quantities;
    5. function tables (input/output machines, T-tables) to model numerical relationships;
    6. two-dimensional geometric models (geoboards, dot paper, pattern blocks, tangrams, or attribute blocks) to model perimeter and properties of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and to model attributes of geometric shapes;
    7. two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and process models (concrete objects) to model probability;
    8. graphs using concrete objects, representational objects, or abstract representations, pictographs, frequency tables, horizontal and vertical bar graphs, Venn diagrams or other pictorial displays, and line plots to organize and display data;
    9. Venn diagrams to sort data.
  2. The student creates a mathematical model to show the relationship between two or more things.
Application Indicators
  1. The student recognizes that various mathematical models can be used to represent the same problem situation. Mathematical models include:
    1. process models (concrete objects, pictures, diagrams, number lines, unifix cubes, hundred charts, or measurement tools) to model computational procedures and mathematical relationships to compare and order numerical quantities, and to model problem situations;
    2. place value models (place value mats, hundred charts, or base ten blocks) to compare, order, and represent numerical quantities and to model computational procedures;
    3. money models (base ten blocks or coins) to compare, order, and represent numerical quantities;
    4. two-dimensional geometric models (geoboards, dot paper, pattern blocks, tangrams, or attribute blocks) to model perimeter and properties of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and to model attributes of geometric shapes;
    5. two-dimensional geometric models (spinners), three-dimensional geometric models (number cubes), and process models (concrete objects) to model probability;
    6. graphs using concrete objects, representational objects, or abstract representations, pictographs, horizontal and vertical bar graphs.
  2. The student selects a mathematical model that is more useful than other mathematical models in a given situations.

Standard 3: Geometry

The student uses geometric concepts and procedures in a variety of situations.

Second Grade

Benchmark 1
The student recognizes geometric shapes and describes their properties using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student recognizes and investigates properties of circles, squares, rectangles, triangles, and ellipses (ovals), (plane figures/two dimensional shapes) using concrete objects, drawings, and appropriate technology.
  2. The student recognizes, draws, and describes circles, squares, rectangles, triangles, ellipses (ovals), (plane figures).
  3. The student recognizes cubes, rectangular prisms, cylinders, cones, and spheres (solids/three-dimensional figures).
  4. The student recognizes the square, triangles, rhombus, hexagon, parallelogram, and trapezoid from a pattern block set.
  5. The student compares geometric shapes (circles, squares, rectangles, triangles, ellipses) to one another.
  6. The student recognizes whether a shape has a line of symmetry.
Application Indicators
  1. The student solves real-world problems by applying the properties of plane figures (circles, squares, rectangles, triangles, ellipses).
  2. The student demonstrates how:
    1. plane figures (circles, squares, rectangles, triangles, ellipses) can be combined or separated to make a new shape;
    2. solids (cubes, rectangular solids, cylinders, cones, spheres) can be combined or separated to make a new shape.
  3. The student identifies the plane figures (circles, squares, rectangles, triangles, ellipses) used to form a composite figure.
 Benchmark 2
The student estimates and measures using standard and nonstandard units of measure with concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student uses whole number approximations (estimations) for length, weight, and volume using standard and nonstandard units of measure.
  2. The student reads and tells time by five-minute intervals using analog and digital clocks.
  3. The student selects and uses appropriate measurement tools and units of measure for length, weight, volume, and temperature for a given situation.
  4. The student measures:
    1. length to the nearest inch or foot and to the nearest whole unit of a nonstandard unit;
    2. weight to the nearest nonstandard unit;
    3. volume to the nearest cup, pint, quart, or gallon;
    4. temperature to the nearest degree.
  5. The student states:
    1. the number of minutes in an hour,
    2. the number of days in each month.
Application Indicators
  1. The student compares the weights of more than two concrete objects using a balance.
  2. The student solves real-world problems by applying appropriate measurements:
    1. length to the nearest inch or foot.
    2. length to the nearest whole unit of a nonstandard unit.
  3. The student estimates to check whether or not measurements or calculations for length in real-world problems are reasonable.
  4. The student adjusts original measurement or estimation for length and weight in real-world problems based on additional information (a frame of reference).
 Benchmark 3
Transformational Geometry - The student recognizes and shows one transformation on simple shapes and concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student knows and uses the cardinal points (north, south, east, west)
  2. The student recognizes that changing an object's position or orientation including whether the object is nearer or farther away does not change the name, size, or shape of the object.
  3. The student recognizes when a shape has undergone one transformation (flip/reflection, turn/rotation, slide/translation).
Application Indicators
  1. The student shows two concrete objects or shapes are congruent by physically fitting one shape or object on top of the other.
  2. The student follows directions to move objects from one location to another using appropriate vocabulary and the cardinal points (north, south, east, west).
 Benchmark 4
The student identifies one or more points on a number line in a variety of situations. Knowledge Base Indicators
  1. The student locates and plots whole numbers from 0 through 1,000 on a segment of a number line (horizontal/vertical).
  2. The student represents the distance between two whole numbers from 0 through 1,000 on a segment of a number line.
  3. The student uses a segment of a number line to model addition and subtraction using whole numbers from 0 through 1,000.
Application Indicators
  1. The student solves real-world problems involving counting, adding, and subtracting whole numbers from 0 through 1,000 using a segment of a number line.

Standard 4: Data

The student uses concepts and procedures of data analysis in a variety of situations.

Second Grade

Benchmark 1
The student applies the concepts of probability using concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student recognizes any outcome of a simple event in an experiment or simulation as impossible, possible, certain, likely, or unlikely.
  2. The student lists some of the possible outcomes of a simple event in an experiment or simulation including the use of concrete objects.
Application Indicators
  1. The student makes a prediction about a simple event in an experiment or simulation; conducts the experiment or simulation including the use of concrete objects; records the results in a chart, table, or graph; and makes an accurate statement about the results.
 Benchmark 2
The student collects, organizes, displays, and explains numerical (whole numbers) and non-numerical data sets including the use of concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student organizes, displays, and reads numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate manner including a title, labels, categories, and whole number intervals using these data displays:
    1. graphs using concrete objects;
    2. pictographs with a whole symbol or picture representing one, two, or ten (no partial symbols or pictures);
    3. frequency tables (tally marks);
    4. horizontal and vertical bar graphs;
    5. Venn diagrams or other pictorial displays, e.g., glyphs;
    6. line plots.
  2. The student collects data using different techniques (observations, interviews, or surveys) and explains the results.
  3. The student identifies the minimum (lowest) and maximum (highest) values in a whole number data set.
  4. The student finds the range for a data set using two-digit whole numbers.
  5. The student finds the mode (most) for a data set using concrete objects that include:
    1. quantitative/numerical data (whole numbers through 100);
    2. qualitative/non-numerical data (category that occurs most often).
Application Indicators
  1. The student communicates the results of data collection and answers questions based on information from:
    1. graphs using concrete objects,
    2. pictographs with a whole symbol or picture representing one (no partial symbols or pictures),
    3. horizontal and vertical bar graphs.
  2. The student determines categories from which data could be gathered.
  3. The student recognizes that the same data set can be displayed in various formats including the use of concrete objects.
  4. The student recognizes appropriate conclusions from data collected.