Common Core Math Initiative
Common Core Math Quizzes
Practice these Common Core aligned Math quizzes and get better grades in your school exams.
Common Core State Standards Initiative
Common Core State Standards Initiative is an educational initiative from 2010 that details what K–12 students throughout the United States should know in English language arts and mathematics at the conclusion of each school grade. The initiative is sponsored by the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO) and seeks to establish consistent educational standards across the states as well as ensure that students graduating from high school are prepared to enter credit-bearing courses at two- or four-year college programs or to enter the workforce.
In the 1990s, a movement for establishing national standards and accountability began in the United States as states began writing standards (a) outlining what students were expected to know and to be able to do at each grade level, and (b) implementing assessments designed to measure whether students were meeting the standards. As part of this education reform movement, the nation's governors and corporate leaders founded Achieve, Inc. in 1996 as a bipartisan organization to raise academic standards and graduation requirements, improve assessments, and strengthen accountability in all 50 states. The initial motivation for the development of the Common Core State Standards (CCSS) was part of the American Diploma Project (ADP).
A 2004 report, titled Ready or Not: Creating a High School Diploma That Counts, found that employers and colleges are demanding more of high school graduates than in the past. According to Achieve, Inc., "current high-school exit expectations fall well short of employer and college demands." The report explained that the major problem currently facing the American school system is that high school graduates were not provided with the skills and knowledge they needed to succeed in college and careers. Furthermore, "While students and their parents may still believe that the diploma reflects adequate preparation for the intellectual demands of adult life, in reality it falls far short of this common-sense goal." The report also stated that the high school diploma itself lost its value because graduates could not compete successfully beyond high school, and that the solution to this problem is a common set of rigorous standards.
The stated goal of the mathematics standards is to achieve greater focus and coherence in the curriculum. This is largely in response to the criticism that American mathematics curricula are "a mile wide and an inch deep".
The mathematics standards include Standards for Mathematical Practice and Standards for Mathematical Content.
The Standards mandate that eight principles of mathematical practice be taught:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
The practices are adapted from the five process standards of the National Council of Teachers of Mathematics and the five strands of proficiency in the U.S. National Research Council's Adding It Up report. These practices are to be taught in every grade from kindergarten to twelfth grade. Details of how these practices are to be connected to each grade level's mathematics content are left to local implementation of the Standards.
As an example of mathematical practice, here is the full description of the sixth practice:
Attend to precision
- Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
The standards lay out the mathematics content that should be learned at each grade level from kindergarten to Grade 8 (age 13–14), as well as the mathematics to be learned in high school. The standards do not dictate any particular pedagogy or what order topics should be taught within a particular grade level. Mathematical content is organized in a number of domains. At each grade level there are several standards for each domain, organized into clusters of related standards. (See examples below.)
|Counting and Cardinality||X|
|Operations and Algebraic Thinking||X||X||X||X||X||X|
|Number and Operations in Base 10||X||X||X||X||X||X|
|Measurement and Data||X||X||X||X||X||X|
|Number and Operations—Fractions||X||X||X|
|Ratios and Proportional Relationships||X||X|
|The Number System||X||X||X|
|Expressions and Equations||X||X||X|
|Statistics and Probability||X||X||X|
In addition to detailed standards (of which there are 21 to 28 for each grade from kindergarten to eighth grade), the standards present an overview of "critical areas" for each grade. (See examples below.)
In high school (Grades 9 to 12), the standards do not specify which content is to be taught at each grade level, nor does the Common Core prescribe how a particular standard should be taught. Up to Grade 8, the curriculum is integrated; students study four or five different mathematical domains every year. The standards do not dictate whether the curriculum should continue to be integrated in high school with study of several domains each year (as is done in other countries), or whether the curriculum should be separated out into separate year-long algebra and geometry courses (as has been the tradition in most U.S. states). An appendix to the standards describes four possible pathways for covering high school content (two traditional and two integrated), but states are free to organize the content any way they want.
There are six conceptual categories of content to be covered at the high school level:
- Number, and quantity;
- Statistics and probability.
Some topics in each category are indicated only for students intending to take more advanced, optional courses such as calculus, advanced statistics, or discrete mathematics. Even if the traditional sequence is adopted, functions and modeling are to be integrated across the curriculum, not taught as separate courses. Mathematical Modeling is a Standard for Mathematical Practice (see above), and is meant to be integrated across the entire curriculum beginning in kindergarten. The modeling category does not have its own standards; instead, high school standards in other categories which are intended to be considered part of the modeling category are indicated in the standards with a star symbol.
Each of the six high school categories includes a number of domains. For example, the "number and quantity" category contains four domains: the real number system; quantities; the complex number system; and vector and matrix quantities. The "vector and matrix quantities" domain is reserved for advanced students, as are some of the standards in "the complex number system".
Examples of mathematical content
Second grade example: In the second grade there are 26 standards in four domains. The four critical areas of focus for second grade are (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes. Below are the second grade standards for the domain of "operations and algebraic thinking" (Domain 2.OA). This second grade domain contains four standards, organized into three clusters:
- Represent and solve problems involving addition and subtraction.
- 1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
- Add and subtract within 20.
- 2. Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.
- Work with equal groups of objects to gain foundations for multiplication.
- 3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
- 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 a sum of equal addends.
Domain example: As an example of the development of a domain across several grades, here are the clusters for learning fractions (Domain NF, which stands for "Number and Operations—Fractions") in Grades 3 through 6. Each cluster contains several standards (not listed here):
- Grade 3:
- Develop an understanding of fractions as numbers.
- Grade 4:
- Extend understanding of fraction equivalence and ordering.
- Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
- Understand decimal notation for fractions, and compare decimal fractions.
- Grade 5:
- Use equivalent fractions as a strategy to add and subtract fractions.
- Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
- In Grade 6, there is no longer a "number and operations—fractions" domain, but students learn to divide fractions by fractions in the number system domain.
High school example: As an example of a high school category, here are the domains and clusters for algebra. There are four algebra domains (in bold below), each of which is broken down into as many as four clusters (bullet points below). Each cluster contains one to five detailed standards (not listed here). Starred standards, such as the Creating Equations domain (A-CED), are also intended to be part of the modeling category.
- Seeing Structure in Expressions (A-SSE)
- Interpret the structure of expressions
- Write expressions in equivalent forms to solve problems
- Arithmetic with Polynomials and Rational Functions (A-APR)
- Perform arithmetic operations on polynomials
- Understand the relationship between zeros and factors of polynomials
- Use polynomial identities to solve problems
- Rewrite rational expressions
- Creating Equations.★ (A-CED)
- Create equations that describe numbers or relationships
- Reasoning with Equations and Inequalities (A-REI)
- Understand solving equations as a process of reasoning and explain the reasoning
- Solve equations and inequalities in one variable
- Solve systems of equations
- Represent and solve equations and inequalities graphically
As an example of detailed high school standards, the first cluster above is broken down into two standards as follows:
- Interpret the structure of expressions
- 1. Interpret expressions that represent a quantity in terms of its context.★
- a. Interpret parts of an expression, such as terms, factors, and coefficients.
- b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
- 2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as(x2 – y2)(x2 + y2).
According to the Common Core State Standards Initiative website, formal assessment is expected to take place in the 2014–2015 school year, which coincides with the projected implementation year for most states. The assessment is being created by two consortia with different approaches. The final decision of which assessment to use will be determined by individual state education agencies. Both of these leading consortiums are proposing computer-based exams that include fewer selected and constructed response test items, unlike the Standardized Test that has been more common.
- The PARCC RttT Assessment Consortium comprises the 19 jurisdictions of Arizona, Arkansas, Colorado, District of Columbia, Florida, Illinois, Indiana, Kentucky, Louisiana, Maryland, Massachusetts, Mississippi, New Jersey, New Mexico, New York, Ohio, Pennsylvania, Rhode Island, and Tennessee. Their approach focuses on computer-based "through-course assessments" in each grade together with streamlined end-of-year tests. (PARCC refers to "Partnership for Assessment of Readiness for College and Careers" and RttT refers to the Race to the Top.)
- The second consortium, called the Smarter Balanced Assessment Consortium, comprised 31 states and territories (as of January 2014) focusing on creating "adaptive online exams". Member states include Alaska, California, Connecticut, Delaware, Hawaii, Idaho, Iowa, Maine, Michigan, Missouri, Montana, Nevada, New Hampshire, North Carolina, North Dakota, Oregon, Pennsylvania, South Carolina, South Dakota, U.S. Virgin Islands, Vermont, Washington, West Virginia, Wisconsin, and Wyoming.
As of October 2015, SBAC membership was reduced to 20 members: California, Connecticut, Delaware, Hawaii, Idaho, Iowa, Maine, Michigan, Montana, New Hampshire, North Carolina, North Dakota, Oregon, South Dakota, U.S. Virgin Islands, The Bureau of Indian Education, Vermont, Washington, West Virginia, Wyoming.
While some states are working together to create a common, universal assessment based on the Common Core State Standards, other states are choosing to work independently or through these two consortiums to develop the assessment. Florida Governor Rick Scott directed his state education board to withdraw from PARCC. Georgia withdrew from the consortium test in July 2013 in order to develop its own. Michigan decided not to participate in Smarter Balanced testing. Oklahoma tentatively withdrew from the consortium test in July 2013 due to the technical challenges of online assessment. And Utah withdrew from the Smarter Balanced Assessment Consortium in August 2012.
Adoption and implementation by states
The chart below contains the adoption status of the Common Core State Standards as of May 12, 2015. Among the territories of the United States (not listed in the chart below), the U.S. Virgin Islands, Guam, the Northern Mariana Islands, and the American Samoa Islands have adopted the standards while Puerto Rico has not adopted the standards. As of May 12, 2015, three states have repealed Common Core. Nine additional member states have legislation in some stage of the process that would repeal Common Core participation.
|Alabama||Formally adopted||State school board voted to rescind the agreement that commits the state to adoption. However, state standards are still aligned with Common Core State Standards.|
|Arizona||Repealed||The Arizona State Board of Education voted to reject Common Core on October 26, 2015. The vote was 6–2 in favor of repeal.|
|District of Columbia||Formally adopted|
|Florida||Non-Member||Dropped in favor of "Florida State Standards", which are based on Common Core standards.|
|Indiana||Repealed||Implementation paused by law for one year in May 2013 and under public review;formally withdrew in March 2014, but retained many of the standards.|
|Kansas||Formally adopted||Defunding legislation passed Senate, narrowly failed in House in July 2013.|
|Louisiana||Formally adopted||Governor signed executive order to withdraw state from PARCC assessment program. (June 2014).|
|Massachusetts||Formally adopted||Delayed Common Core testing for two years in November 2013. Ballot question on future of standards in 2016 has been ruled against by Massachusetts Supreme Judicial Court as of August 12, 2016.|
|Michigan||Formally adopted||Implementation was paused for a time but was approved to continue.|
|Minnesota||Partially adopted||English standards only, math standards rejected.|
|Mississippi||Formally adopted||Withdrew from PARCC testing on January 16, 2015.|
|New Hampshire||Formally adopted|
|New Jersey||Repealed||Adopted New Jersey Student Learning Standards in lieu of Common Core beginning in the 2017-18 school year.|
|New Mexico||Formally adopted|
|New York||Formally adopted||Full implementation of assessment delayed until 2022.|
|North Carolina||Under review|
|North Dakota||Formally adopted|
|Oklahoma||Repealed||Legislation restoring state standards signed June 5, 2014.|
|Pennsylvania||Formally adopted||Paused implementation in May 2013.|
|Rhode Island||Formally adopted|
|South Carolina||Repealed||A bill to repeal the Standards beginning in the 2015-2016 school year was officially signed by Governor Nikki Haley in June 2014 after deliberation in the state legislature.|
|South Dakota||Formally adopted|
|West Virginia||Formally adopted|