Additional mathematic standards that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics are indicated by a plus symbol (+). The plus symbol indicates that the standard is not required for all students. K-8 Mathematical Domains: Counting and Cardinality – CC Operations and Algebraic Thinking – OA Number and Operations in Base Ten – NBT Measurement and Data – MD Number and Operations – Fractions – NF Geometry – G Ratios and Proportional Relationships – RP The Number System – NS Expressions and Equations – EE Functions – F Statistics and Probability – SP High School Conceptual Categories: Number and Quantity – N Algebra – A Functions – F Modeling – M Geometry – G Statistics and Probability – P The standards for mathematics stress both conceptual understanding and procedural skills to ensure students learn and can apply the critical information needed to succeed at each level. This creates a learning progression where the mathematics learned in elementary school provides the foundation for the study of statistics, probability, ratio and proportion, geometry, and algebra in middle school. This is, in turn, the base upon which the knowledge needed for success in colleges and careers can be developed in high school. The standards organization is not intended to convey the order of instruction nor the length of time to devote to the topics. In the standards, the clusters have been arranged in the grade span to show the continuum between grades. The following table outlines the progression of the content from kindergarten through high school. Standards for Mathematical Content Kindergarten 1 2 3 4 5 6 7 8 High School
Counting and Cardinality Know number names and the count sequence. to tell the number of objects. Compare numbers. Operations and Algebraic Thinking Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Identify and continue patterns. Number and Operations in Base Ten Work with numbers 11–19 to gain foundations for place value. Measurement and Data Describe and compare measurable attributes. Classify objects and count the number of objects in categories. Work with time and money. Geometry Identify and describe shapes. Analyze, compare, create, and compose shapes. Counting and Cardinality Know ordinal names and counting flexibility. Count to tell the number of objects. Compare numbers. Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Understand and apply properties of operations and the relationship between addition and subtraction. Add and subtract up to 20. Work with addition and subtraction equations. Identify and continue patterns. Number and Operations in Base Ten Extend the counting sequence. Understand place value. Use place value understanding and properties of operations to add and subtract. Measurement and Data Measure lengths indirectly and by iterating length units. Work with time and money. Represent and interpret data. Geometry Reason with shapes and their attributes. Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Add and subtract up to 20. Work with groups of objects to gain foundations for multiplication. Identify and continue patterns. Number and Operations in Base Ten Understand place value. Use place value understanding and properties of operations to add and subtract. Measurement and Data Measure and estimate lengths in standard units. Relate addition and subtraction to length. Work with time and money. Represent and interpret data. Geometry Reason with shapes and attributes.
(8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) decomposing a number leading to a ten (13 - 4 = 13 - 3 - 1 = 10 - 1 = 9) the relationship between addition and subtraction, such as fact families, (8 + 4 = 12 and 12 - 8 = 4) creating equivalent but easier or sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Work with addition and subtraction equations. Work with equal groups of objects to gain foundations for multiplication. 1.OA.7. Understand the meaning of the equal sign (e.g., read equal sign as “same as”) and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false?6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2). 1.OA.8. Determine the unknown whole number in an addition or subtraction equation. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 6 + 6 = ?, 5 = ? - 3. 2.OA.3. Determine whether a group of objects (up to 20) is odd or even (e.g., by pairing objects and comparing, counting by 2s). Model an even number as two equal groups of objects and then write an equation as a sum of two equal addends. 2.OA.4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. Write an equation to express the total as repeated addition (e.g., array of 4 by 5 would be 5 + 5 + 5 + 5 = 20). Grade K Grade 1 Grade 2
Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.5 Understand that positive and negative numbers describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explain the meaning of 0 in each situation. 7.NS.3. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) For example, use models, explanations, number lines, real life situations, describing or illustrating the effect of arithmetic operations on rational numbers (fractions, decimals). 6.NS.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. Recognize opposite of numbers as indicating locations on opposite sides of 0 on the number line; Recognize that the opposite of the opposite of a number is the number itself [e.g., –(–3) = 3] and that 0 is its own opposite. b. Understand of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.