Mathematics Standards & Benchmarks

P.1

Applies properties and concepts of a number

P.1.1  Counts by rote to 10                                                                  P.1.2  Demonstrates "how many" by making sets of 2,3,4, and 5

P.2

Performs computation of a number

P.3

Applies concepts of probability and statisics

P.4

Applies geometric concepts

P.4.1  Identifies circles, square, and triangle                                   P.4.2  Compares and orders objects by size

P.5

Applies algebraic concepts

P.5.1  Sorts objects by color

K.1

Applies properties and concepts of a number

K.1.1  Counts out amount of objects that corresponds to a written number or orally stated number to 20                                                                       K.1.2  Writes numbers 1 to 20                                                                     K.1.3 Counts by 1's to 50                                                                                           K.1.4  Matches a set to a number to 20                                                            K.1.5  Identifies numbers 0 to 20 in random order                                                   K.1.6  Knows the days of the week of the calendar                                              K.1.7  Tells time to tne hour (analog and digital)

K.2

Performs computation of a number

K.2.1  Draws pictures to illustrate simple addition number sentences using sets with a sum of 0 - 10

K.3

Applies concepts of probability and statisics

K.3.1  Recongnizes patterns in a sequence                                              K.3.2  Sorts and classifies objects according to their attributes                                                                                       K.3.3  Understands directional terms (ie: over, under)

K.4

Applies geometric concepts

K.4.1  Recognizes circle, square, rectangle, and triangle

K.5

Applies algebraic concepts

K.5.1  Sorts, classifies, and orders objects by size, number and other properties                                                                              K.5.2  Recognizes, describes, and extends patterns

1.1

Applies properties and concepts of a number

1.1.1  Writes numbers 0 to 100                                                                  1.1.2  Counts by 1's, 5's, and 10's to 100; by 2's to 20                                                                                                                         1.1.3 Understand ordinal numbers 1st to 10th                                                                                           1.1.4  Uses "greater than" and "less than" to compare values of numbers to 99                                                                                 1.1.5  Recognizes the fractional value of one-half, one-third, and one-fourth                                                                                                1.1.6  Tells time to the hour and half-hour  (analog and digital)                                                                                             1.1.7  Measures and makes quantitative estimates of familiar measurements including length, height, weight, capacity using appropriate nonstandard measures (paper clips, connecting cubes, teddy bear counters, water, balance scales)

1.2

Performs computation of a number

1.2.1 Adds and subtracts numbers with sums from 1 to 10                  1.2.2  Names penny, nickel, dime, quarter and their values

1.3

Applies concepts of probability and statisics

1.3.1  Interprets information on pre-constructed pictographs and graphs                                                                                               1.3.2 Uses pictures to solve a problem                                

1.4

Applies geometric concepts

1.4.1 Compares the mass of objects using the terms "heavier than" and "lighter than"                                                                      1.4.2  Recongnizes 3-dimensional shapes (cube, cone, sphere)   1.4.3  Measures length using customary unit

1.5

Applies algebraic concepts

1.5.1  Identifies the missing number in a sequence

2.1

Applies properties and concepts of a number

2.1.1  Identifies place value for 10's and 1's                                                                      2.1.2  Uses <,>, and = to compare numbers up to 99                                                                                                                2.1.3 Catergorizes numbers as even or odd                                                                                          2.1.4  Recognizes mixed numbers and fractional values of halves, fourths, and thirds                                                                           2.1.5  Uses ordinal numbers to twelfth                                                  2.1.6  Tells time by the five minute intervals, using analog and digital clocks.  Using AM and PM                                                          2.1.7  Reads the positive temperature on a thermometer to the the nearest two degrees F.

2.2

Performs computation of a number

2.2.1  Counts money amounts to $1.00 by using quarters, nickels, dimes and pennies                                                                         2.2.2  Demonstrates an understanding of addition and subtraction facts 0 - 18                                                                                               2.2.3  Uses renaming/borrowing to compute sums and differences of 2-digit numbers                                                                                 2.2.4  Determines if addition or subtraction is needed to solve a problem                              

2.3

Applies concepts of probability and statisics

2.3.1  Reads information from a pictograph, bar graph, and Venn diagram                                                                                           2.3.2  Drawa and reads a bar graph with a scale of 2                               2.3.3 Writes observations about a graph                                             2.3.4  Uses tally marks to count in place of a number and understands the concept

2.4

Applies geometric concepts

2.4.1  Measures length in inches                                                           2.4.2  Draws and reads a bar graph with a scale of 2                        2.4.3  Recognizes and names sphere, cube, pyramid, rectangular solid, cylinder, and cone

2.5

Applies algebraic concepts

2.5.1  Puts story problems in equation form

3.1

Applies properties and concepts of a number

3.1.1  Understands place value of whole numbers to tenths                                                                                           3.1.2  Converts numbers from word form to standard form up to thousands                                                                                               3.1.3 Counts and compares money amounts to $100.00                                                                                        3.1.4  Rounds numbers to the nearest tens and/or hundreds                                                                      3.1.5 Tells time to 5 minute increments one-minute increments                                                                                    3.1.6  Identifies place value through hundreds                                                    3.1.7  Reads the positive temperature on a thermometer to the the nearest two degrees F.                                                          3.1.8  Categorizes numbers as odd or even

3.2

Performs computation of a number

3.2.1 Adds and subtracts fractions with like denominators        3.2.2  Uses a picture, graph or map to solve a problem                                                                  3.2.3  Chooses addition or subtraction operation to solve problems                                                                                           3.2.4  Add and subtracts 2 digit numbers; three digit numbers                                                                                                                3.2.5  Demonstrates an understanding of the multiplication facts through 10 using concrete models                                                                          3.2.6  Estimates a sum                                                                          3.2.7  Represents and writes fraction halves, fourths, and thirds with pictures, models, and numbers                                                                3.2.8  Mastery of addition facts with addends    0 - 9                

3.3

Applies concepts of probability and statisics

3.3.1  Interprets pictographs, tallies, bar graphs and line graphs                                                                                    

3.4

Applies geometric concepts

3.4.1  Measures with accuracy to the nearest centimeter and 1/2 inch                                                                                                             3.4.2  Identifies attributes of a shape using corners, edges, faces, and/or sides                                                                                     3.4.3  Identifies and names prism, cylinder, cone, pyramid, sphere and cube                                                                                                  3.4.4  Identify and calculate perimeter                                                    3.4.5  Identify line of symmetry

3.5

Applies algebraic concepts

3.5.1  Expresses mathematical relationships with equations                      3.5.2  Identify patterns in numbers and shapes and explain how to extend those patterns

4.1

Applies properties and concepts of a number

4.1.1  Compares fractions with like denominators                                                                                          4.1.2  Understands place value of whole numbers to hundred thousands                                                                                          4.1.3  Understands place value of decimals to hundreths                                                                                       4.1.4  Converts numbers from word form to standard form up to hundred thousands                                                                         4.1.5 Identifies fraction of a group or shaded area                                                                   4.1.6  Compares and order numbers and measurements                                                  4.1.7  Chooses correct operation to solve problems                                                       4.1.8  Rounds whole numbers to nearest ten, hundred, or thousand                                                                                                         4.1.9  Rounds money amounts to nearest dollar                                 4.1.10  Identifies multiples of numbers one to nine                             4.1.11  Tells time to one-minute increments

4.2

Performs computation of a number

4.2.1 Adds and subtracts whole numbers and money amounts to $99.99                                                                                              4.2.2  Master multiplication facts 0 - 9                                             4.2.3 Multiplies using a one digit x 2 digit factor                                                                                            4.2.4  Computes quotient with a one-digit divisor                                                                                4.2.5  Estimates to find a reasonable answer                                     4.2.6  Adds and subtracts fractions with like denominators                         

4.3

Applies concepts of probability and statisics

4.3.1  Interprets pictographs, bar graphs and charts                                                                                    4.3.2  Makes a list to identify the number of choices                                                          4.3.3 Predicts probability of outcomes by performing simple experiments and uses terms, unlikely and likely                                                                                     4.3.4  Applies probability concepts and counting rules

4.4

Applies geometric concepts

4.4.1  Identifies, classifies and compares basic linear figures and geometric shapes                                                                           4.4.2 Chooses an appropriate unit of measure in metric and US customary for length                                                                            4.4.3  Classifies angles as being a right angle or not being a right angle                                                                                                       4.4.4  Uses measurement tools: rulers, meter sticks, yardsticks    4.4.5  Identifies shapes with symmetry                                                 4.4.6  Uses basic tables/graphs to draw conclusions and/or solve problems                                                                                                 4.4.7  Solves problems using elasped time by hour and half hour                                                                                                          4.4.8  Estimates and measures with appropriate precision

4.5

Applies algebraic concepts

4.5.1  Uses a variable as a placeholder when solving for one variable                                                                                                    4.5.2  Uses a number sentence to represent a mathematical situation                                                                                                   4.5.3  Analyzes basic patterns                                                              4.5.4  Solves equations and inequalities

5.1

Applies properties and concepts of a number

5.1.1  Rounds to the nearest tenth                                                                                        5.1.2  Identifies place value of whole numbers to hundred millions                                                                                             5.1.3  Identifies place value of decimals to hundreths                                                                                       5.1.4  Converts numbers from word form to standard form up to hundred millions                                                                              5.1.5 Uses basic properties of multiplicaton to solve problems                                                                                        5.1.6  Lists factors and multiples of a number                                                 5.1.7  Writes an equivalent fraction (reduces to lowest term)                                                               5.1.8 Compares fractions with like denominators                       5.1.9  Compares and orders decimals to the nearest thousandth                                                                                                                                           5.1.10  Uses estimation to check for logical answer      

5.2

Performs computation of a number

5.2.1 Adds and subtracts whole numbers and money amounts to $999.99                                                                                              5.2.2  Multiplies/divides money amounts to $999.99 by a whole number without a remainder                                                          5.2.3 Adds and subtracts decimal amounts                                                                                        5.2.4  Multiplies 4 digit factors by 2 digit factors                                                                               5.2.5  Computes quotient with 4 digit dividend and 2 digit divisor (multiple of 10)                                                                                 5.2.6  Adds and subtracts fractions with like denominators                5.2.7  Chooses correct operation to solve problem                          5.2.8  Counts change with fewest coins                                              5.2.9  Applies fractions to solve problems in everyday situations (i.e. cooking, drafting, construction                                    5.2.10  Identifies percent out of 100

5.3

Applies concepts of probability and statisics

5.3.1  Designs and interprets line graphs                                                                                     5.3.2  Calculates the average of a set of numbers                           5.3.3 Uses tables and graphs to organize information

5.4

Applies geometric concepts

5.4.1 Accurately measures to the 1/4 inch or nearest mm                                                                          5.4.2  Identifies acute, obtuse, and right angle                                                                         5.4.3  Converts within a measurement system (e.g. 10 mm in a cm, 1,000 grams in a kilogram, 12 inches in a foot)                                                                 5.4.4  Identifies horizontal, vertical and oblique                                   5.4.5  Calculates the area of a rectangle                          

5.5

Applies algebraic concepts

5.5.1  Uses inverse operations to check multiplications and division                                                                                             5.5.2 Uses variables to solve equations       

6.1 Applies properties and concepts of a number.

6.1. 1 Applies the properties of addition, subtraction, multiplication, and division. 

6.1.2  Compares and orders whole numbers, fractions, and decimals.

6.1.3  Finds the GCF and LCM of a set of numbers.

6.1.4  Recognizes and compares prime and composite numbers using prime factorization and exponents.

6.1.5  Writes, converts, and renames fractions, improper fractions, and mixed numbers.

6.1.6  Solves problems using appropriate strategies.

6.1.7  Recognizes, describes, completes, and extends simple patterns.

6.1.8  Estimates the percent of a number.

6.1.9  Rounds numbers to the nearest tenth, hundredth, and whole number.

6.1.10  Rounds money.

6.2  Performs computation of numbers.

6.2.1  Adds, subtracts, multiplies, and divides up to three-digit whole numbers, fractions, and decimals.

6.2.2  Converts decimals, percents, and fractions from one to the other.

6.2.3  Calculates percent of a number.

6.3  Applies concepts of probability and statistics

6.3.1  Calculates mean, median, mode, and range for a set of whole numbers and represents graphically.

6.3.2  Formulates questions; designs simple studies and collects data.

3.3  Reads and interprets graphs; organizes and displays information in a graph.

6.4  Applies geometric concepts.

6.4.1 Uses metric and customary systems of measurement.

6.4.2  Uses common benchmarks to select appropriate methods to estimate.

6.4.3  Selects and accurately uses technology and tools to measure.

6.4.4  Calculates the perimeter and area of a variety of geometric figures.

6.4.5  Classifies triangles by their sides and angles.

6.4.6.Graphs points using pairs of integer coordinates.

6.4.7  Locates single and multiple lines of symmetry.

6.4.8  Defines and recognizes congruency, similarity, and scale.

6.5  Applies algebraic concepts.

6.5.1  Solves for missing factor "n" in a numerical expression, equation, or word problem.

1.  Applies Properties and Concepts of Numbers.

7.1.1  Converts, orders, and applies whole numbers, exponents, fractions, decimals, percents, ratios, and proportions.

7.1.2  Identifies factors and multiplies using divisibility rules.

7.1.3  Calculates and estimates real numbers using mathematical operations.

7.1.4  Applies various strategies and properties to solve problems.

7.1.5  Identifies place value using exponents.

7.1.6  Finds LCM and GCF.

7.1.7  Expresses fractions in simplest form.

2.  Performs Computations of Numbers

7.2. 1  Converts from one unit of measure to another within the same measurement system.

7.2.2  Adds and subtracts unit of time and measurement.

7.2.3  Multiplies and divides by powers of ten.

7.2.4  Performs the four basic operations with decimal, fractions, and integers.

7.2.5  Converts among decimals, fractions, and percent.

3.  Applies Concepts of Probabilities and Statistics

7.3.1  Understands the basic characteristics of measurements of central tendency (mean, median, mode).

7.3.2  Reads, interprets, and uses charts, graphs, and tables to identify relationships, draw conclusions, identify trends, and make predictions or generalizations.

7.3.3  Collects, organizes, and interprets information in a table or graph to find a pattern to solve problems.

4.  Applies Geometric Concepts

7.4.1  Describes and classifies two and three dimensional geometric figures.

7.4.2  Measures and calculates surface area and volume of geometric figures using appropriate instruments and units of measurement.

7.4.3  Understands the basic concept of the Pythagorean Therom.

7.4.4.  Determines perimeter and area of polygons and circles.

5.  Applies Algebraic Concepts

7.5.1  Creates and evaluates algebraic expressions and equations.

7.5.2  Translates word problems into one step equations.

1  Applies properties and concepts of a number.

8.1.1  Uses and understands scientific notation with both positive and negative exponents.

8.1.2  Use fractions, decimals, and percents to solve problem situations.

8.1.3  Identifies prime numbers and records the prime factorization of composite numbers and uses it to find LCM, GCF, and simplify fractions.

8.1.4.  Uses the distributive property.

8.1.5.  Applies order of operations in the evaluation of equations.

8.1.6.  Estimates appropriately to a given situation including when to estimate and what form to use.

8.1.7.  Reads, writes, simplifies, and evaluates positive and negative exponential expressions.

8.1.8.  Understands and uses the inverse relationships of addition/subtraction, multiplication/division, and squaring/finding square roots to simplify computations and solve problems.

8.1.9.  Demonstrates the ability to read, write, rename, and compare real numbers.

8.1.10.  Identify repeating and non-repeating decimals and percents by being able to express each in the other form.

2  Performs computation of numbers.

8.2.1.  Calculates base, percent, and percentage.

8.2.2.  Multiplies and divides numbers in scientific notation.

3  Uses concepts of probability and statistics.

8.3.1.  Identifies upper/lower quartiles of a set of numbers.

8.3.2.  Reads, interprets, and makes predictions using tables and graphs.

8.3.3.  Organizes and displays data and makes inferences using tables and graphs.

8.3.4.  Calculates probabilities and odds in a situation with equally likely outcomes and mutually exclusive events.

4  Applies geometric concepts.

8.4.1.  Understands geometric transformations of figures (e.g. rotations, translations, dilations).

8.4.2.  Understands the relationships between two - and three-dimensional representations of a figure ( e.g. scale drawings, blueprints).

8.4.3.  Understands the concepts of precision and significant digits as they relate to measurement (e.g. how units indicate precision).

8.4.4.  Visualizes, draws, and constructs two dimensional geometric figures to solve problems.

8.4.5.  Measures and calculates surface area and volume of geometric figures using appropriate instruments and units of measurement. 

5  Applies algebraic concepts

8.5.1.  Understands basic operation (e.g. combining like terms, substituting for unknowns) on algebraic expressions.

8.5.2.  Solves linear equations and inequalities.

8.5.3.  Recognizes and extends a wide variety of patterns and functional relationships within a set of data.

8.5.4.  Represents functional and nonfunctional data by the following:  number sentences, verbal statements, models, table graphs, variables, algebraic expressions, and equations, and translates between these modes.

8.5.5.  Solves systems of equations and inequalities algebraically and graphically.

9.1  Uses properties and concepts of a number.

1.1  Applies properties of equality.

1.2  Uses scientific notation.

1.3.  Represents relations in a variety of methods.

1.4 Determine if a relation is a function.

9.2  Performs computation of numbers

2.1  Uses exponents to simplify mathematical expressions involving identical factors.

2.2  Uses substitution to solve problems involving formulas.

2.3  Performs the four basic operations using rational numbers.

2.4  Compares numbers using equalities.

2.5  Compares numbers using inequalities.

2.6  Represents equalities and inequalities on a numberline.

2.7  Solves equalities and inequalities using multiple operations.

2.8  Finds the prime factorization of a monomial.

2.9  Factors by using the Greatest Common Factor.

2.10 A  Finds the slope of a line given two points on the line.

9.3  Uses concepts of probability and statistics.

3.1  Identifies the mean, median, mode, range, and upper and lower quartiles of a set of numbers.

3.2 A  Identifies and uses various types of graphs used in statistics.

3.3  Identifies the concepts of independent and dependent probability.

9.4  Applies geometric concepts

4.1  Represents numbers graphically using a number line.

4.2  Graphs ordered pairs on a number plane.

4.3  Graphs linear equations and inequalities.

4.4  Solves problems involving circumference, area, and volume of various geometric shapes.

4.5  Solves problems involving angles and the use of tools to bisect line segments and angles.

4.6 Translates verbal expressions into Geometric expressions.

9.5  Applies algebraic concepts

5.1 Translates verbal expressions into mathematical expressions or equations.

5.2  Evaluates expressions using order of operations.

5.3  Solves verbal problems.

5.4  Solves open sentences involving one basic operation.

5.5  Solves open sentences using multiple operations.

5.6  Solves open sentences involving ratio and proportion.

5.7  Solve problems involving percent.

5.8  Simplifies expressions involving powers and quotient of monomials.

5.9 A  Determines if an expression is a monomial or a polynomial.

5.10 Solve problems involving variation

5.11  Determine the degree of a polynomial

5.12 Add, subtract, multiply and divide polynomials

5.13  Solve problems involving variation

5.14  Factor polynomials using a variety of methods

5.15 Solve equations by factoring

5.16  Solves linear equations for a specific variable.

5.20 Writes linear equations in standard or slope-intercept form.

5.21  Determine x-y- intercepts of a linear equation.