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Math Standards of Learning

Kindergarten Through 5th Grade

 

Kindergarten Grade One Grade Two
Grade Three Grade Four Grade Five

 

 

KINDERGARTEN

Number and Number Sense

 

K.1 The student, given two sets containing 10 or fewer concrete items, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.
(No change)

 

K.2    The student, given a set containing 10 or fewer concrete items, will

a)   tell how many are in the set by counting the number of items orally;

b)   select the corresponding numeral from a given set; and

c)   write the numeral to tell how many are in the set.

 

K.3            The student, given an ordered set of three objects and/or pictures, will indicate the ordinal position of each item, first through third, and the ordered position of each item from left-to-right, right-to-left, top-to-bottom, and/or bottom-to-top.  

 

K.4            The student will investigate and recognize patterns from counting by fives and tens to 30, using concrete objects and a calculator.  

 

K.5            The student will count forward to 30 and backward from 10.


Computation and Estimation

 

K.6            The student will add and subtract whole numbers, using up to 10 concrete items.

 

Measurement

 

K.7            The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less.

 

K.8            The student will identify the instruments used to measure length (ruler), weight (scale), time (clock: digital and analog; calendar: day, month, and season), and temperature (thermometer).

 

K.9            The student will tell time to the hour, using an analog or digital clock.

 

K.10          The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, block.

 

Geometry

 

K.11          The student will identify, describe, and draw two-dimensional (plane) geometric figures (circle, triangle, square, and rectangle).

 

K.12          The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane geometric figures (circle, triangle, square, and rectangle) regardless of their position and orientation in space.

 

K.13          The student will compare the size (larger, smaller) and shape of plane geometric figures (circle, triangle, square, and rectangle).

 

Probability and Statistics

 

K.14          The student will gather data relating to familiar experiences by counting and tallying.

K.15          The student will display objects and information, using objects graphs, pictorial graphs, and tables.

K.16          The student will investigate and describe the results of dropping a two-colored counter or using a multicolored spinner.


Patterns, Functions, and Algebra

 

K.17          The student will sort and classify objects according to similar attributes (size, shape, and color).

K.18          The student will identify, describe, and extend a repeating relationship (pattern) found in common objects, sounds, and movements.

 

GRADE ONE

 

Number and Number Sense

 

1.1             The student will count objects in a given set containing between 1 and 100 objects and write the corresponding numeral.

 

1.2             The student will group a collection of up to 100 objects into tens and ones and write the corresponding numeral to develop an understanding of place value.

 

1.3             The student will count forward by ones, fives, and tens to 100, by twos to 20, and backward by ones from 20.

 

1.4             The student will recognize and write numerals 0 through 100.

 

1.5             The student will identify the ordinal positions first through tenth, using an ordered set of objects.

 

1.6             The student will identify and represent the concepts of one-half and one-fourth, using appropriate materials or a drawing.


Computation and Estimation

 

1.7             The student, given a familiar problem situation involving magnitude, will

a)   select a reasonable magnitude from three given quantities: a one-digit numeral, a two-digit numeral, and a three-digit numeral (e.g., 5, 50, and 500); and

b)   explain the reasonableness of his/her choice.

 

1.8             The student will recall basic addition facts — i.e., sums to 10 or less — and the corresponding subtraction facts.

 

1.9             The student will create and solve story and picture problems involving one-step solutions, using basic addition and subtraction facts.

 

Measurement

 

1.10           The student will

a)   identify the number of pennies equivalent to a nickel, a dime, and a quarter;

b)   determine the value of a collection of pennies, nickels, and dimes whose total value is 100 cents or less.

 

1.11           The student will tell time to the half-hour, using an analog or digital clock.

 

1.12           The student will use nonstandard units to measure length and weight.

 

1.13           The student will compare the volumes of two given containers by using concrete materials (e.g., jelly beans, sand, water, rice).

 

1.14           The student will compare the weights of two objects, using a balance scale.

 

Geometry

 

1.15           The student will describe the proximity of objects in space (near, far, close by, below, above, up, down, beside, and next to).

 

1.16           The student will draw, describe, and sort plane geometric figures (triangle, square, rectangle, and circle) according to number of sides, corners, and square corners.

 

1.17           The student will identify and describe objects in his/her environment that depict plane geometric figures (triangle, rectangle, square, and circle).

 

Probability and Statistics

 

1.18           The student will investigate, identify, and describe various forms of data collection in his/her world (e.g., recording daily temperature, lunch count, attendance, and favorite ice cream), using tables, picture graphs, and object graphs.


1.19           The student will interpret information displayed in a picture or object graph, using the vocabulary more, less, fewer, greater than, less than, and equal to.

 

Patterns, Functions, and Algebra

 

1.20           The student will sort and classify concrete objects according to one or more attributes, including color, size, shape, and thickness.

 

1.21           The student will recognize, describe, extend, and create a wide variety of patterns, including rhythmic, color, shape, and numerical. Patterns will include both growing and repeating patterns. Concrete materials and calculators will be used by students.

 

GRADE TWO

 

Number and Number Sense

 

2.1             The student will

a)   read, write, and identify the place value of each digit in a three-digit numeral, using numeration models; and

b)   round two-digit numbers to the nearest ten.

 

2.2             The student will compare two whole numbers between 0 and 999, using symbols (>, <, or =) and words (greater than, less than, or equal to).

 

2.3             The student will identify the ordinal positions first through twentieth, using an ordered set of objects.

 

2.4             The student will identify the part of a set and/or region that represents fractions for one-half, one-third, one-fourth, one-eighth, and one-tenth and write the corresponding fraction.


2.5       The student will

a)   count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5, or 10, using mental mathematics, paper and pencil, hundred chart, calculators, and/or concrete objects, as appropriate;

b)   count backward by tens from 100;

c)   group objects by threes and fours; and

d)   recognize even and odd numbers, using objects.

 

Computation and Estimation

 

2.6             The student will recall basic addition facts — ­i.e., sums to 18 or less — and the corresponding subtraction facts.

 

2.7             The student, given two whole numbers whose sum is 99 or less, will

a)   estimate the sum; and

b)   find the sum, using various methods of calculation (mental computation, concrete materials, and paper and pencil).

 

2.8             The student, given two whole numbers, each of which is 99 or less, will

a)   estimate the difference; and

b)   find the difference, using various methods of calculation (mental computation, concrete materials, and paper and pencil).

 

2.9             The student will create and solve one-step addition and subtraction problems using data from simple tables, picture graphs, bar graphs, and practical situations.

 

2.10           The student, given a simple addition or subtraction fact, will recognize and describe the related facts which represent and describe the inverse relationship between addition and subtraction (e.g., 3 + __ = 7, ___ + 3 = 7; 7 – 3 = __, and 7 – __ = 3).

 

Measurement

 

2.11           The student will

a)   count and compare a collection of pennies, nickels, dimes, and quarters whose total value is $2.00 or less; and

b)   identify the correct usage of the cent symbol (’), dollar symbol ($), and decimal

point (.).

 

2.12           The student will estimate and then use a ruler to make linear measurements to the nearest centimeter and inch, including measuring the distance around a polygon in order to determine perimeter.

 

2.13           The student, given grid paper, will estimate and then count the number of square units needed to cover a given surface in order to determine area.


2.14           The student will estimate and then count the number of cubes in a rectangular box in order to determine volume.

 

2.15           The student will estimate and then determine weight/mass of familiar objects in pounds and/or kilograms, using a scale.

 

2.16           The student will tell and write time to the quarter hour, using analog and digital clocks.

 

2.17           The student will use actual measuring devices to compare metric and U.S. Customary units (cups, pints, quarts, gallons, and liters) for measuring liquid volume, using the concepts of more, less, and equivalent.

 

2.18           The student will

a)   use calendar language appropriately (e.g., months, today, yesterday, next week, last week);

b)   determine past and future days of the week; and

c)   identify specific dates on a given calendar.

 

2.19           The student will read the temperature on a Celsius and/or Fahrenheit thermometer to the nearest 10 degrees.

 

Geometry

 

2.20           The student will identify, describe, and sort three-dimensional (solid) concrete figures, including a cube, rectangular solid (prism), square pyramid, sphere, cylinder, and cone, according to the number and shape of the solid’s faces, edges, and corners.

 

2.21           The student will identify and create figures, symmetric along a line, using various concrete materials.

 

2.22           The student will compare and contrast plane and solid geometric shapes (circle/sphere, square/cube, and rectangle/rectangular solid).

 

Probability and Statistics

 

2.23           The student will read, construct, and interpret a simple picture and bar graph.

 

2.24           The student will record data from experiments, using spinners and colored tiles/cubes, and use the data to predict which of two events is more likely to occur if the experiment is repeated.


Patterns, Functions, and Algebra

 

2.25           The student will identify, create, and extend a wide variety of patterns, using numbers concrete objects and pictures.

 

2.26           The student will solve problems by completing a numerical sentence involving the basic facts for addition and subtraction. Examples include: 3 + __ = 7, or 9 – __ = 2. Students will create story problems, using the numerical sentences.

 

GRADE THREE

 

Number and Number Sense

 

3.1             The student will read and write six-digit numerals and identify the place value for each digit.

 

3.2             The student will round a whole number, 9,999 or less, to the nearest ten, hundred, and thousand.

 

3.3             The student will compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).

 

3.4             The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. Students will use these relationships to solve problems such as 5 + 3 = 8 and 8 – 3 = ____.

 

3.5             The student will

a)   divide regions and sets to represent a fraction; and

b)   name and write the fractions represented by a given model (area/region,

      length/measurement, and set). Fractions (including mixed numbers) will include halves, thirds, fourths, eighths, and tenths.


3.6             The student will compare the numerical value of two fractions having like and unlike denominators, using concrete or pictorial models involving areas/regions, lengths/measurements, and sets.

 

3.7             The student will read and write decimals expressed as tenths and hundredths, using concrete materials and models.

 

Computation and Estimation

 

3.8             The student will solve problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping, using various computational methods, including calculators, paper and pencil, mental computation, and estimation.

 

3.9             The student will recall the multiplication and division facts through the nines table.

 

3.10           The student will represent multiplication and division, using area and set models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.

 

3.11           The student will add and subtract with proper fractions having like denominators of 10 or less, using concrete materials and pictorial models representing areas/regions, lengths/measurements, and sets.

 

3.12           The student will add and subtract with decimals expressed as tenths, using concrete materials, pictorial representations, and paper and pencil.

 

Measurement

 

3.13           The student will determine by counting the value of a collection of bills and coins whose total value is $5.00 or less, compare the value of the coins or bills, and make change.

 

3.14           The student will estimate and then use actual measuring devices with metric and U.S. Customary units to measure

a)   length — inches, feet, yards, centimeters, and meters;

b)   liquid volume — cups, pints, quarts, gallons, and liters; and

c)   weight/mass — ounces, pounds, grams, and kilograms.

 

3.15           The student will tell time to the nearest five-minute interval and to the nearest minute, using analog and digital clocks.

 

3.16           The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours.


3.17           The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used.

 

Geometry

 

3.18           The student will analyze two-dimensional (plane) and three-dimensional (solid) geometric figures (circle, square, rectangle, triangle, cube, rectangular solid [prism], square pyramid, sphere, cone, and cylinder) and identify relevant properties, including the number of corners, square corners, edges, and the number and shape of faces, using concrete models.

 

3.19           The student will identify and draw representations of line segments and angles, using a ruler or straightedge.

 

3.20           The student, given appropriate drawings or models, will identify and describe congruent and symmetrical, two-dimensional (plane) figures, using tracing procedures.

 

Probability and Statistics

 

3.21           The student, given grid paper, will

a)   collect and organize data on a given topic of his/her choice, using observations, measurements, surveys, or experiments; and

b)   construct a line plot, a picture graph, or a bar graph to represent the results. Each graph will include an appropriate title and key.

 

3.22           The student will read and interpret data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the data.

 

3.23           The student will investigate and describe the concept of probability as chance and list possible results of a given situation.

 

Patterns, Functions, and Algebra

 

3.24           The student will recognize and describe a variety of patterns formed using concrete objects, numbers, tables, and pictures, and extend the pattern, using the same or different forms (concrete objects, numbers, tables, and pictures).

 

3.25           The student will

a)   investigate and create patterns involving numbers, operations (addition and multiplication), and relations that model the identity and commutative properties for addition and multiplication; and

b)   demonstrate an understanding of equality by recognizing that the equal sign (=) links equivalent quantities, such as 4 • 3 = 2 • 6.

 

GRADE FOUR

 

Number and Number Sense

 

4.1             The student will

a)   identify (orally and in writing) the place value for each digit in a whole number expressed through millions;

b)   compare two whole numbers expressed through millions, using symbols ( >, <,

      or = ); and

c)   round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand.

 

4.2             The student will

a)   identify, model, and compare rational numbers (fractions and mixed numbers), using concrete objects and pictures;

b)   represent equivalent fractions; and

c)   relate fractions to decimals, using concrete objects.


4.3             The student will compare the numerical value of fractions (with like and unlike denominators) having denominators of 12 or less, using concrete materials.

 

4.4             The student will

a)   read, write, represent, and identify decimals expressed through thousandths;

b)   round to the nearest whole number, tenth, and hundredth; and

c)   compare the value of two decimals, using symbols (<, >, or =), concrete materials, drawings, and calculators.

 

Computation and Estimation

 

4.5             The student will estimate whole-number sums and differences and describe the method of estimation. Students will refine estimates, using terms such as closer to, between, and a little more than.

 

4.6             The student will add and subtract whole numbers written in vertical and horizontal form, choosing appropriately between paper and pencil methods and calculators.

 

4.7             The student will find the product of two whole numbers when one factor has two digits or fewer and the other factor has three digits or fewer, using estimation and paper and pencil. For larger products (a two-digit numeral times a three-digit numeral), estimation and calculators will be used.

 

4.8             The student will estimate and find the quotient of two whole numbers, given a one-digit divisor.

 

4.9             The student will

a)   add and subtract with fractions having like and unlike denominators of 12 or less, using concrete materials, pictorial representations, and paper and pencil;

b)   add and subtract with decimals through thousandths, using concrete materials, pictorial representations, and paper and pencil; and

c)   solve problems involving addition and subtraction with fractions having like and unlike denominators of 12 or less and with decimals expressed through thousandths, using various computational methods, including calculators, paper and pencil, mental computation, and estimation.


Measurement

 

4.10           The student will

a)   estimate and measure weight/mass, using actual measuring devices, and describe the results in U.S. Customary/metric units as appropriate, including ounces, pounds, grams, and kilograms;

b)   identify equivalent measurements between units within the U.S. Customary system (ounces and pounds) and between units within the metric system (grams and kilograms); and

c)   estimate the conversion of ounces and grams and pounds and kilograms, using approximate comparisons (1 ounce is about 28 grams, or 1 gram is about the weight of a paper clip; 1 kilogram is a little more than 2 pounds). *

 

* The intent of this standard is for students to make ballpark comparisons and not to memorize conversion factors between U.S. Customary and metric units.

 

4.11           The student will

a)   estimate and measure length, using actual measuring devices, and describe the results in both metric and U.S. Customary units, including part of an inch (1/2, 1/4, and 1/8), inches, feet, yards, millimeters, centimeters, and meters;

b)   identify equivalent measurements between units within the U.S. Customary system (inches and feet; feet and yards; inches and yards) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters); and

c)   estimate the conversion of inches and centimeters, yards and meters, and miles and kilometers, using approximate comparisons (1 inch is about 2.5 centimeters, 1 meter is a little longer than 1 yard, 1 mile is slightly farther than 1.5 kilometers, or 1 kilometer is slightly farther than half a mile). *

 

* The intent of this standard is for students to make ballpark comparisons and not to memorize conversion factors between U.S. Customary and metric units.

 

4.12           The student will

a)   estimate and measure liquid volume, using actual measuring devices and using metric and U.S. Customary units, including cups, pints, quarts, gallons, milliliters, and liters;

b)   identify equivalent measurements between units within the U.S. Customary system (cups, pints, quarts, and gallons) and between units within the metric system (milliliters and liters); and

c)   estimate the conversion of quarts and liters, using approximate comparisons (1 quart is a little less than 1 liter, 1 liter is a little more than 1 quart).*

 

* The intent of this standard is for students to make ballpark comparisons and not to memorize conversion factors between U. S. Customary and metric units.


4.13           The student will

a)   identify and describe situations representing the use of perimeter and area; and

b)   use measuring devices to find perimeter in both standard and nonstandard units of measure.

 

Geometry

 

4.14           The student will investigate and describe the relationships between and among points, lines, line segments, and rays.

 

4.15           The student will

a)   identify and draw representations of points, lines, line segments, rays, and angles, using a straightedge or ruler; and

b)   describe the path of shortest distance between two points on a flat surface.

 

4.16           The student will identify and draw representations of lines that illustrate intersection, parallelism, and perpendicularity.

 

4.17           The student will

a)   analyze and compare the properties of two-dimensional (plane) geometric figures (circle, square, rectangle, triangle, parallelogram, and rhombus) and three-dimensional (solid) geometric figures (sphere, cube, and rectangular solid [prism]);

b)   identify congruent and noncongruent shapes; and

c)   investigate congruence of plane figures after geometric transformations such as reflection (flip), translation (slide) and rotation (turn), using mirrors, paper folding, and tracing.

 

4.18           The student will identify the ordered pair for a point and locate the point for an ordered pair in the first quadrant of a coordinate plane.

 

Probability and Statistics

 

4.19           The student will

a)   predict the likelihood of outcomes of a simple event, using the terms certain, likely, unlikely, impossible; and

b)   determine the probability of a given simple event, using concrete materials.

 

4.20           The student will collect, organize, and display data in line and bar graphs with scale increments of one or greater than one and use the display to interpret the results, draw conclusions, and make predictions.


Patterns, Functions, and Algebra

 

4.21           The student will recognize, create, and extend numerical and geometric patterns, using concrete materials, number lines, symbols, tables, and words.

 

4.22           The student will recognize and demonstrate the meaning of equality, using symbols representing numbers, operations, and relations [e.g., 3 + 5 = 5 + 3 and

15 + (35 + 16) = (15 + 35) + 16].

 

GRADE FIVE

 

Number and Number Sense SOL STATEMENT

 

5.1             The student will

a)   read, write, and identify the place values of decimals through thousandths;

b)   round decimal numbers to the nearest tenth or hundredth; and

c)   compare the values of two decimals through thousandths, using the symbols >, <,

or =.

 

5.2             The student will

a)   recognize and name commonly used fractions (halves, fourths, fifths, eighths, and tenths) in their equivalent decimal form and vice versa; and

b)   order a given set of fractions and decimals from least to greatest. Fractions will include like and unlike denominators limited to 12 or less, and mixed numbers.

 

Computation and Estimation

 

5.3             The student will create and solve problems involving addition, subtraction, multiplication, and division of whole numbers, using paper and pencil, estimation, mental computation, and calculators.


5.4             The student will find the sum, difference, and product of two numbers expressed as decimals through thousandths, using an appropriate method of calculation, including paper and pencil, estimation, mental computation, and calculators.

 

5.5             The student, given a dividend of four digits or fewer and a divisor of two digits or fewer, will find the quotient and remainder.

 

5.6             The student, given a dividend expressed as a decimal through thousandths and a single-digit divisor, will find the quotient.

 

5.7             The student will add and subtract with fractions and mixed numbers, with and without regrouping, and express answers in simplest form. Problems will include like and unlike denominators limited to 12 or less.

 

Measurement

 

5.8             The student will describe and determine the perimeter of a polygon and the area of a square, rectangle, and right triangle, given the appropriate measures.

 

5.9             The student will identify and describe the diameter, radius, chord, and circumference of a circle.

 

5.10           The student will differentiate between perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation.

 

5.11           The student will choose an appropriate measuring device and unit of measure to solve problems involving measurement of

a)   length — part of an inch (1/2, 1/4, and 1/8), inches, feet, yards, miles, millimeters, centimeters, meters, and kilometers;

b)   weight/mass — ounces, pounds, tons, grams, and kilograms;

c)   liquid volume — cups, pints, quarts, gallons, milliliters, and liters;

d)   area — square units; and

e)   temperature — Celsius and Fahrenheit units.

Problems also will include estimating the conversion of Celsius and Fahrenheit units relative to familiar situations (water freezes at 0°C and 32°F, water boils at 100°C and 212°F, normal body temperature is about 37°C and 98.6°F).

 

5.12           The student will determine an amount of elapsed time in hours and minutes within a 24-hour period.

 

5.13           The student will measure and draw right, acute, and obtuse angles and triangles, using appropriate tools.


Geometry

 

5.14           The student will classify angles and triangles as right, acute, or obtuse.

 

5.15           The student, using two-dimensional (plane) figures (square, rectangle, triangle, parallelogram, rhombus, kite, and trapezoid) will

a)   recognize, identify, describe, and analyze their properties in order to develop definitions of these figures;

b)   identify and explore congruent, noncongruent, and similar figures;

c)   investigate and describe the results of combining and subdividing shapes;

d)   identify and describe a line of symmetry; and

e)   recognize the images of figures resulting from geometric transformations such as translation (slide), reflection (flip), or rotation (turn).

 

5.16           The student will identify, compare, and analyze properties of three-dimensional (solid) geometric shapes (cylinder, cone, cube, square pyramid, and rectangular prism).

 

Probability and Statistics

 

5.17           The student will

a)   solve problems involving the probability of a single event by using tree diagrams or by constructing a sample space representing all possible results;

b)   predict the probability of outcomes of simple experiments, representing it with fractions or decimals from 0 to 1, and test the prediction; and

c)   create a problem statement involving probability and based on information from a given problem situation. Students will not be required to solve the created problem statement.

 

5.18           The student will, given a problem situation, collect, organize, and display a set of numerical data in a variety of forms, using bar graphs, stem-and-leaf plots, and line graphs, to draw conclusions and make predictions.

 

5.19           The student will find the mean, median, mode, and range of a set of data.

 

Patterns, Functions, and Algebra

 

5.20           The student will analyze the structure of numerical and geometric patterns (how they change or grow) and express the relationship, using words, tables, graphs, or a mathematical sentence. Concrete materials and calculators will be used.


5.21           The student will

a)   investigate and describe the concept of variable;

b)   use a variable expression to represent a given verbal quantitative expression involving one operation ; and

c)   write an open sentence to represent a given mathematical relationship, using a variable.

 

5.22           The student will create a problem situation based on a given open sentence using a single variable.