Standard 1: Number and Computation

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

Fourth Grade

Benchmark 1
The student demonstrates number sense for whole numbers, fractions (including mixed numbers), decimals, and money including the use of concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student knows, explains, and uses equivalent representations for:
    1. whole numbers from 0 through 100,000;
    2. fractions greater than or equal to zero (halves, fourths, thirds, eights, tenths, twelfths, sixteenths, hundredths) including mixed numbers;
    3. decimals greater than or equal to zero through hundredths place and when used as monetary amounts,
  2. The student compares and orders:
    1. whole numbers from 0 through 100,000;
    2. fractions greater than or equal to zero (halves, fourths, thirds, eighths, tenths, twelfths, sixteenths, hundredths) including mixed numbers with a special emphasis concrete objects;
    3. decimals greater than or equal to zero through hundredths place and when used as monetary amounts.
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 100,000;
    2. add and subtract whole numbers from 0 through 10,000 and decimals when used as monetary amounts,
    3. multiply a one-digit whole number by a two-digit whole number.
  2. The student determines whether or not solutions to real-world problems that involve the following are reasonable:
    1. whole numbers from 0 through 10,000,
    2. fractions greater than or equal to zero (halves, fourths, thirds, eighths, tenths, sixteenths),
    3. decimals greater than or equal to zero when used as monetary amounts,
 Benchmark 2
The student demonstrates an understanding of whole numbers with a special emphasis on place value; recognizes, uses, and explains the concepts of properties as they relate to whole numbers; and extends thses properties to fractions (including mixed numbers), decimals, and money. Knowledge Base Indicators
  1. The student identifies, models reads, and writes numbers using numerals, words, and expanded notation from hundredths place through one-hundred thousands place.
  2. The student classifies various subsets of numbers as whole numbers, fractions (including mixed numbers), or decimals.
  3. The student identifies the place value of various digits from hundredths place through one hundred thousands place.
  4. The student identifies any whole number as even or odd.
  5. The student uses the concepts of these properties with the whole number system and demonstrates their meaning including the use of concrete objects:
    1. commutative properties of addition and multiplication.
    2. zero property of addition (additive identity) and property of one for multiplication (multiplicative identity).
    3. associative properties of addition and multiplication.
    4. symmetric property of equality applied to addition and multiplication.
    5. zero property of multiplication.
    6. distributive property.
Application Indicators
  1. The student solves real-world problems with whole numbers from 0 through 10,000 using place value models; money; and the concepts of these properties to explain reasoning:
    1. commutative properties of addition and multiplication.
    2. zero property of addition.
    3. property of one for multiplication.
    4. associative properties of addition and multiplication.
    5. zero property of multiplication.
  2. The student performs various computational procedures with whole numbers from 0 through 10,000 using the concepts of the following properties; extends the properties to fractions (halves, fourths, thirds, eighths, tenths, sixteenths) including mixed numbers and decimals through hundredths place; and explains how the properties were used:
    1. Commutative property of addition and multiplication.
    2. zero property of multiplication without computing.
    3. associative property of addition.
  3. The student states the reason for using whole numbers, fractions, mixed numbers, or decimals when solving a given real-world problem.
 Benchmark 3
The student uses computational estimation with whole numbers, fractions (including mixed numbers) and money in a variety of situations. Knowledge Base Indicators
  1. The student estimates whole number quantities from 0 through 10,000; fractions (halves, fourths, thirds); and monetary amounts through $1,000 using various computational methods including mental math, paper and pencil, concrete materials, and appropriate technology.
  2. The student uses various estimation strategies and explains how they are used when estimating whole numbers quantities from 0 through 10,000; fractions {(halves, fourths, thirds) including mixed numbers}; and monetary amounts through $1,000.
  3. The student recognizes and explains the difference between an exact and an approximate answer.
  4. The student selects from an appropriate range of estimation strategies and determines if the estimate is an overestimate or underestimate.
Application Indicators
  1. The student adjusts original whole number estimates of a real-world problem using numbers from 0 through 10,000 based on additional information.
  2. The student estimates to check whether or not the result of a real-world problem using whole numbes from 0 through 10,000, fractions (including mixed numbers), and monetary amounts is reasonable and makes predictions based on the information.
  3. The student selects a reasonable magnitude from three given quantities based on a familiar problem situations and explains the reasonableness of selection.
  4. The student determines if a real-world problem calls for an exact or approximate answer and performs the appropriate computation using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technologh.
 Benchmark 4
The student models, performs, and explains computations with whole numbers, fractions, and money including the use of 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 materials, and appropriate technology.
  2. The student states and uses with efficiency and accuracy multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts.
  3. The student performs and explains these computational procedures:
    1. adds and subtracts whole numbers from 0 through 100,000 and when used as monetary amounts;
    2. multiplies through a three-digit whole number by a two-digit whole number;
    3. multiplies whole dollar monetary amounts (through three-digits) by a one-or two-digit whole number;
    4. multiplies monetary amounts less than $100.00 by whole numbers less than ten;
    5. divides through a tow-digit whole number by a one-digit whole number with a one-digit whole number quotient with or without a remainder;
    6. adds and subtracts fractions greater than or equal to zero with like denominators;
    7. figures correct change through $20.00
  4. The student identifies multiplication and division fact families.
  5. The student reads and writes horizontally, vertically, and with different operational symbols the same addition, subtraction, multiplication, or division expression.
    1. addition and subtraction,
    2. addition and multiplication,
    3. multiplication and division,
    4. subtraction and division.
  6. The student finds factors and multiples of whole numbers from 1 through 100.
Application Indicators
  1. The student solves one- and two-step real-world problems with one or two operations using these computational procedures:
    1. adds and subtracts whole numbers from 0 through 10,000 and when used as monetary amounts.
    2. multiplies through a two-digit whole number by a two-digit whole number.
    3. multiplies whole dollar monetary amounts (up through three-digit) by a one- or two-digit whole number.
    4. multiplies monetary amounts less than $100 by whole numbers less than ten.
    5. figures correct change through $20.00.
  2. The student generates a family of multiplication and division facts given one equation/fact.

Standard 2: Algebra

The student recognizes, describes, extends, develops, and explains relationships in patterns using concrete objects in a variety of situations.

Fourth 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 patterns.
  2. uses these attributes to generate patterns:
    1. counting numbers related to number theory;
    2. whole numbers that increase or decrease;
    3. geometric shapes including one or two attributes changes;
    4. measurements;
    5. money and time;
    6. things related to daily life;
    7. things related to size, shape, color, texture, or movement.
  3. The student identifies, states and continues a pattern presented in visual various formats including numeric (list or table), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written.
  4. The student generates:
    1. a pattern (repeating, growing);
    2. a pattern using a function table (input/output machines, T-tables).
Application Indicators
  1. The student generalizes these patterns using a written description:
    1. counting numbers related to number theory,
    2. whole number patterns,
    3. patterns using geometric shapes,
    4. measurement patterns,
    5. money and time patterns,
    6. patterns using size, shape, color, texture, or movement.
  2. The student recognizes multiple representations of the same pattern.
 Benchmark 2
The student uses variables, symbols, and whole numbers to solve equations including the use of concrete objects in a variety of situations. Knowledge base Indicators
  1. The student explains and uses variables and symbols to represent unknown whole number quantities from 0 through 1,000.
  2. The student solves one-step equations using whole numbers with one variable and a whole number solution that:
    1. find the unknown in a multiplication or division equation based on the multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts,
    2. find the unknown in a money equation using multiplication and division based upon the facts and addition and subtraction with values through $10;
    3. find the unknown in a time equation involving whole minutes, hours, days, and weeks with values through 200.
  3. The student compares two whole numbers from 0 through 10,000 using the equality and inequality symbols (=, ≠, <, >) and their corresponding meanings (is equal to, is not equal to, is less than, is greater than).
  4. The student reads and writes whole number equations and inequalities using mathematical vocabulary and notation.
Application Indicators
  1. The student represents real-world problems using variables and symbols with unknown whole number quantities from 0 through 1,000.
  2. The student generates one-step equations to solve real-world problems with one unknown (represented by a variable or symbol) and a whole number solution that:
    1. add or subtract whole numbers from 0 through 1,000.
    2. multiply or divide using the basic facts.
  3. The student generates:
    1. real-world problems with one operation to match a given addition, subtraction, multiplication, or division equation using whole numbers through 99,
    2. number comparison statements using equality and inequality symbols (=, <, >) with whole numbers, measurement, and money.
 Benchmark 3
The student recognizes and describes whole number relationships including the use of concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student states mathematical relationships between whole numbers from 0 through 1,000 using various methods including mental math, paper and pencil, concrete materials, and appropriate technology.
  2. The student finds the values, determines the rule, and states the rule using symbolic notation with one operation of whole numbers from 0 through 200 using a horizontal or vertical function table (input/output machine, T-table).
  3. The student generalizes numerical patterns using whole numbers from 0 through 200 with one operation by stating the rule using words.
  4. The student uses a function table (input/output machine, T-table) to identify, plot, and label the ordered pairs in the first quadrant of a coordinate plane.
Application Indicators
  1. The student represents and describes mathematical relationships between whole numbers from 0 through 1,000 using concrete objects, pictures, written descriptions, symbols, equations, tables, and graphs.
  2. The student finds the rule, states the rule, and extends numerical patterns using real-world applications using whole numbers from 0 through 200.
 Benchmark 4
The student develops and uses mathematical models including the use of concrete objects to represent and explain 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, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate planes/grids) to model computational procedures, mathematical relationships, and equations;
    2. place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures;
    3. fraction and mixed number models (fraction strips or pattern blocks) and decimal models (base ten blocks or coins) 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 and algebraic relationships;
    6. two-dimensional geometric models (geoboards, dot paper, pattern blocks, or tangrams) to model perimeter, area, and properties of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and to model properties of geometric shapes;
    7. two-dimensional geometric models (spinners), three-dimensional models (number cubes), and process models (concrete objects) to model probability;
    8. graphs using concrete objects, pictographs, frequency tables, horizontal and vertical bar graphs, line graphs, circle graphs, Venn diagrams, line plots, charts, and tables to organize and display data;
    9. Venn diagrams to sort data and show relationships.
  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, coordinate planes/grids, hundred charts, measurement tools, multiplication arrays, or division sets) to model computational procedures, mathematical relationships, and problem situations;
    2. place value models (place value mats, hundred charts, base ten blocks, or unfix cubes) to model problem situations;
    3. fraction and mixed number models (fraction strips or pattern blocks) and decimal models (base ten blocks or coins) 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 and algebraic relationships;
    6. two-dimensional geometric models (geoboards, dot paper, pattern blocks, or tangrams) to model perimeter, area, and properties of geometric shapes and three-dimensional geometric models (solids) and real-world objects to compare size and to model properties 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, pictographs, frequency tables, horizontal and vertical bar graphs, line graphs, Venn diagrams, line plots, charts, and tables to organize, display, explain, and interpret data;
    9. Venn diagrams to sort data and show relationships.
  2. The student selects a mathematical model and explains why some mathematical models are more useful than other mathematical models in certain situations.

Standard 3: Geometry

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

Fourth Grade

Benchmark 1
The student recognizes geometric shapes and investigates their properties including the use of concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student recognizes and investigates properties of plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, hexagons, pentagons) using concrete objects, drawings, and appropriate technology.
  2. The student recognizes, draws, and describes plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, hexagons, pentagons).
  3. The student describes the solids (cubes, rectangular prisms, cylinders, cones, spheres, triangular prisms) using the terms faces, edges, and vertices (corners).
  4. The student recognizes and describes the square, triangle, rhombus, hexagon, parallelogram, and trapezoid from a pattern block set.
  5. The student recognizes:
    1. squares, rectangles, rhombi, parallelograms, trapezoids as special quadrilaterals;
    2. similar and congruent figures;
    3. points, lines (intersecting, parallel, perpendicular), line segments, and rays.
  6. The student determines if geometric shapes and real-world objects contain line(s) of symmetry and draws the line(s) of symmetry if the line(s) exist(s).
Application Indicators
  1. The student solves real-world problems by applying the properties of:
    1. plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, parallelograms, hexagons) and lines of symmetry,
    2. solids (cubes, rectangular prisms, cylinders, cones, spheres),
  2. The student identifies the plane figures (circles, squares, rectangles, triangles, ellipses, rhombi, octagons, hexagons, pentagons, trapezoids) used to form a composite figure.
 Benchmark 2
The student estimates and measures using standard and nonstandard units of measure including the use of concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student uses whole number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure.
  2. The student selects, explains the selection of, and uses measurement tools, units of measure, and degree of accuracy appropriate for a given situation to measure:
    1. length, width, and height to the nearest fourth of an inch or to the nearest centimeter;
    2. volume to the nearest cup, pint, quart, or gallon; to the nearest liter; or to the nearest whole unit of a nonstandard unit;
    3. weight to the nearest ounce or pound or to the nearest whole unit of a nonstandard unit of measure;
    4. temperature to the nearest degree;
    5. time including elapsed time.
  3. The student states:
    1. the number of weeks in a year;
    2. the number of ounces in a pound;
    3. the number of milliliters in a liter, grams in a kilogram, and meters in a kilometer;
    4. the number of items in a dozen.
  4. The student converts:
    1. within the customary system; inches and feet, feet and yards, inches and yards, cups and pints, pints and quarts, quarts and gallons;
    2. within the metric system: centimeters and meters.
  5. The student finds:
    1. the perimeter of two-dimensional figures given the measures of all the sides.
    2. the area of squares and rectangles using concrete objects.
Application Indicators
  1. The student solves real-world problems by applying appropriate measurements:
    1. length to the nearest fourth of an inch,
    2. length to the nearest centimeter,
    3. temperature to the nearest degree,
    4. weight to the nearest whole unit (pounds, grams, nonstandard unit),
    5. time including elapsed time,
    6. months in a year,
    7. minutes in an hour,
    8. perimeter of squares, rectangles, and triangles,
  2. The student estimates to check whether or not measurements and calculations for length, width, weight, volume, temperature, time, and perimeter in real-world problems are reasonable.
  3. The student adjusts original measurement or estimation for length, width, weight, volume, temperature, time, and perimeter in real-world problems based on additional information (a frame of reference).
 Benchmark 3
The student recognizes and performs one transformation on simple shapes or concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student describes a transformation using cardinal points or positional directions.
  2. The student recognizes, performs, and describes one transformation (reflection/flip, rotation/turn, translation/slide) on a two-dimensional figure or concrete object.
  3. the student recognizes three-dimensional figures (rectangular prisms, cylinders) and concrete objects from various perspectives (top, bottom, sides, corners).
Application Indicators
  1. The student recognizes real-world transformations (reflection/flip, rotation/turn, translation/slide).
  2. The student gives and uses cardinal points or positional directions to move from one location to another on a map or grid.
  3. The student describes the properties of geometric shapes or concrete objects that stay the same and the properties that change when a transformation is performed.
 Benchmark 4
The student relates geometric concepts to a number line and the first quadrant of a coordinate plane in a variety of situations. Knowledge Base Indicators
  1. The student uses a number line (horizontal/vertical) to model whole number multiplication facts from 1 x 1 through 12 x 12 and corresponding division facts.
  2. The student uses points in the first quadrant of a coordinate plane (coordinate grid) to identify locations.
  3. The student identifies and plots points as whole number ordered pairs in the first quadrant of a coordinate plane (coordinate grid).
  4. The student organizes whole number data using a T-table and plots the ordered pairs in the first quadrant of a coordinate plane (coordinate grid).
Application Indicators
  1. The student solves real-world problems that involve distance and location using coordinate planes (coordinate grids) and map grids with positive whole number and letter coordinates.
  2. The student solves real-world problems by plotting whole number ordered pairs in the first quadrant of a coordinate plane (coordinate grid).

Standard 4: Data

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

Fourth Grade

Benchmark 1
The student applies the concepts of probability to draw conclusions and to make predictions and decisions including the use of concrete objects in a variety of situations. Knowledge Base Indicators
  1. The student recognizes that the probability of an impossible event is zero and that the probability of a certain event is one.
  2. The student lists all possible outcomes of a simple event in an experiment or simulation including the use of concrete objects.
  3. The student recognizes and states the probability of a simple event in an experiment or simulation.
Application Indicators
  1. The student makes predictions about a simple event in an experiment or simulation; conducts an experiment or simulation including the use of concrete objects; records the results in a chart, table, or graph; and uses the results to draw conclusions about the event.
  2. The student uses the results from a completed experiment or simulation of a simple event to make predictions in a variety of real-world problems.
  3. The student compares what should happen (theoretical probability/expected results) with what did happen (empirical probability/experimental results) in an experiment or simulation with a simple event.
 Benchmark 2
The student collects, organizes, displays, explains, and interprets 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, (for testing, does not have to use concrete objects in items);
    2. pictographs with a symbol or picture representing one, two, five, ten, twenty-five, or one-hundred including partial symbols when the symbol represents an even amount;
    3. frequency tables (tally marks);
    4. horizontal and vertical bar graphs:
    5. Venn diagrams or other pictorial displays,
    6. line plots;
    7. charts and tables;
    8. line graphs;
    9. circle graphs;
  2. The student collects data using different techniques (observations, polls, surveys, interviews, or random sampling) and explains the results.
  3. The student identifies, explains, and calculates or finds these statistical measures of a data set with less than ten whole number data points using whole numbers from 0 through 1,000;
    1. minimum and maximum values,
    2. range,
    3. mode,
    4. median when data set has an odd number of data points,
    5. mean when data set has a whole number mean.
Application Indicators
  1. The student interprets and uses data to make reasonable inferences and predictions, answer questions, and make decisions from these data displays:
    1. graphs using concrete objects;
    2. pictographs with a symbol or picture representing one, two, five, ten, twenty-five, or one-hundred including partial symbols when the symbol represents an even amount;
    3. frequency tables (tally marks);
    4. horizontal and vertical bar graphs;
    5. Venn diagrams or other pictorial displays;
    6. line plots;
    7. charts and tables;
    8. line graphs.
  2. The student uses these statistical measures of a data set using whole numbers from 0 through 1,000 with less than ten whole number data points to make reasonable inferences and predictions, answer questions, and make decisions:
    1. minimum and maximum values,
    2. range,
    3. mode,
    4. median when the data set has an odd number of data points,
    5. mean when the data set has a whole number mean.
  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 and explains the effects of scale and interval changes on graphs of whole number sets.