Math Standards Pre-K through 8
Pre-K Kindergarten 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th Grade 8th Grade
Counting and Cardinality Demonstrates an increasing ability to count in sequence to 10 and beyond. Counts to 100 by ones and tens. Counts forward beginning from a given number within the known sequence. Writes numbers from 0 to 20. Represents number of object with a written numeral 0-20.                
Numbers and Operations -Base Ten   Work with numbers 11-19 to gain foundations for place value. Reads, writes, and counts to 120, starting from any number. Represents 10s and 1s in any 2-digit number. Compares two 2-digit numbers using symbols. Adds within 100 using place value. Mentally adds and subtracts 10 to 2-digit numbers. Reads, writes, counts to 1,000 in different ways. Represents 100s, 10s, 1s in any 3-digit number. Compares two 3-digit numbers using symbols. Adds 2-digit numbers using symbols. Adds 2-digit whole numbers fluently. Subtracts 2-digit numbers fluently. Mentally adds and subtracts 10 or 100 to 3-digit numbers. Adds within 1,000 using place value. Demonstates understnading of place value. Adds 3-digit whole numbers fluently. Subtract 3-digit whole numbers fluently. Rounds multi-digit whole numbers to any place. Multiplies two 2-digit whole numbers. Divides whole numbers within 1,000, with remainders. Explains patterns in the placement of the decimal point when a decimal is multiplied or divided by a multiple of 10. Uses whole number exponents to denote powers of 10. Reads, writes, rounds and compares decimals to thousandths. Fluently multiplies multi-digit whole numbers. Adds, subtracts, multiplies, divides decimals to hundrths.      
Numbers and Operations -Fractions         Shows and understands fractions represent equal parts of a whole. Compares fractions by reasoning about their size. Adds and subtracts fractions with unlike denominators. Multiplies a fraction by a whole number. Writes fractions and decimals to hundreths. Adds and subtracts fractions and mixed numbers with unlike denominators. Solves word problems involving addition and subtraction of fractions. Rewrites a fraction as a division problem.      
Operations and Algebraic Thinking Builds increasing undertanding of directionality, order and position of objects and words such as up, down, inside, utside, next to, in front, behnind, on top of, under. Recognizes some basic concepts of time and sequence, e.g. morning, afternoon, yesterday, today, tomrrow, before, after. I can solve addition and subtraction pronlems within 10, using objects or drawings to represent the problem. Solves word problems using addition and subtraction within 20. Solves turn-around facts. Combines and breaks apart numbers to solve addition and subtraction problems. Adds and subtracts fluently within 20. Solves word problems using addition and subtraction within 100, adds and subtracts fluently withiin 20. Solves problems using repeated addition, and to understand addition. Multiplies from memory all products of two 1-digt numbers. Divides whole numbers within 100, without remainders. Solves one-step word problems. Uses equations to solve one-step word problems. Solves two step word problems. Uses equations to solve two-step problems Solves multi-step word problems . Finds factors and multiples in the range of 1-100. Use the four operations with whole numbers to solve problems. Uses the order of operations correctly to evaluate numerical expressions. Analyzes patterns and relationships.      
Measurement and Data Mathematical Decision Making: Responds to questions that can be answered with information gained through data analysis. Describes and compares objects with measurable attributes. Classifies objects and counts the number of objects in each category. Orders, compares, and measures objects. Tells and writes time in hours and half hours. Represents and interprets data. Measures and Explains lengths in standard units. Tells and writes times to the nearest 5 miinutes, using a.m. and p.m. Solves problems using money and symbols correctly. Draws and interprets graphs. Tells and writes time to the nearest minute. Measures liquid volumes and masses of objects. Creates scaled graphs to represent data. Measures length to the nearest 1/4 inch. Measures the area and perimeter of plane figures. Solve problems involving measurement and estimation. Converts relative sizes of measurement within a sytem. Applies the area and perimeter formulas for rectangles. Understands and measures angles. Collects, represents, and interprets data. Converts relative sizes of measurement within a system. Makes a line plot to display a data set of measurement in fractions of a unit. Calcualtes the volume of a rectangular prism using unit cubes and a formula.      
Geometry Patterns: Matches and sorts objects. Begins to recognize, copy, extend, and create simple patterns. Correctly names shapes. Describes objects' positions using terms such as above, below, beside, in front of, behind, and next to. I can describe, compare, and create shapes. Sorts and identifies shapes using attributes. Breaks shapes into halves and quarters. Identifies and draws shapes based on attributes. Breaks shapes into halves, thirds, and quarters. Categorizes shapes and their attributes. Draws and identifies lines and angles, and classifies shapes. Graphs points on the coordinate plane. Classifies two-dimensional figures into categories based on their properties. Finds the area of polygons, using triangles. Uses the formula for volume of right rectangular prisms. Finds the surface area of 3D objects. Solve real-world and mathematical problems involving area, surface area, and volume. Draws, constructs, and uses scale drawings to describe geometrical figures and their relationships. Solves word problems involving area, surface area, and volume. Uses congruence and similarity to solve geometrical problems. Applies the Pythagoren Theorem to solve mathematical problems. Uses formulas to find the volumes of cylinders, cones, and spheres.
Statistics and Probability               Describes a set of data collected to answer a statistical question. Can contruct dat into plots on a number line and summarize statistical landmarks and overall patterns. Develop understanding of statistical variability. Uses random sampling to draw inferences about a population. Calculates probablilty of simple and compound events. Draw informal comparative inferences about two populations. Models a scatter plot with a linear equation. Constructs a scatter plot and determines trends with bivariate data.
Ratios and Proportional Relationships               Describes a ratio as a relationship between two quantities. Finds a rate when given a specific ratio. Finds a percentage of a quantity. Simplifies complex fractions. Identifies, represents and explains proportional relationships using tables, graphs, and equations. Functions: Define, evaluate, and compare functions. Use functions to model relationships between quantities.
The Number System           Divides fractions by fractions. Fluently divides multi-digit numbers. Fluently adds, subtracts, multiplies, divides with decimals. Finds the Greatest Common Factor and Least Common Multiple. Recognizes opposite signs of numbers as showing places on opposite of 0 or coordinate on an axis. Orders rational numbers and expresses two numbers in an equality statement. Shows the absolute value as its distance from zero. Graphs and analyzes points on the coordinate plane. Adds and subtracts rational numbers. Multiplies and divides rational numbers. Solves word problems using the four operations with rational numbers. Apply and extend previous understandings of operations with fractions. Uses funtions to model relationships between quantities. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. Know that there are numbers that are not rational, and approximate them by rational numbers.
Expressions and Equations               Writes and Evalutates numerical expressions with exponents and one-variable (including inequalitites. Identifies parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient) Apply and extend previous understandings of arithmetic to algebraic expression. Factors, expands, and simplifies expressions with rational coefficients (fractions and decimals) Solves multi-step problems posed with positive and negative rational numbers. Uses variables to write equations to solve word problems. Uses variables to write inequalitites to solve word problems. Uses properties of exponents to simplify an expression. Performs operations with numbers expressed in scientific notation. Uses cslope and the y-intercept to write equation of a line. Solves pairs of simultaneous linear equations. Uses pairs of simultaneous linear equations to solve word problems.