- Research and evidence based
- Clear, understandable, and consistent
- Aligned with college and career expectations
- Based on rigorous content and the application of knowledge through higher-order thinking skills
- Built upon the strengths and lessons of current state standards
- Informed by other top-performing countries to prepare all students for success in our global economy and society

According to the best available evidence, the mastery of each standard is essential for success in college, career, and life in today’s global economy.

**The standards focus on core concepts and procedures starting in the early grades, which gives teachers the time needed to teach them and gives students the time needed to master them.**

** (******* FYI- this is extremely important!!!)**** **

**The standards draw on the most important international models, as well as research and input from numerous sources, including educators from kindergarten through college, state departments of education, scholars, assessment developers, professional organizations, parents and students, and members of the public.****Because their design and content have been refined through successive drafts and numerous rounds of state feedback, the standards represent a synthesis of the best elements of standards-related work in all states and other countries to date.****For grades K-8, grade-by-grade standards exist in English language arts/literacy and mathematics. For grades 9-12, the standards are grouped into grade bands of 9-10 grade standards and 11-12 grade standards.****While the standards set grade-specific goals, they do not define how the standards should be taught or which materials should be used to support students. States and districts recognize that there will need to be a range of supports in place to ensure that all students, including those with special needs and English language learners, can master the standards. It is up to the states to define the full range of supports appropriate for these students****.****No set of grade-specific standards can fully reflect the great variety of abilities, needs, learning rates, and achievement levels of students in any given classroom. Importantly, the standards provide clear signposts along the way to the goal of college and career readiness for all students.**

High standards that are consistent across states provide teachers, parents, and students with a set of clear expectations to ensure that all students have the skills and knowledge necessary to succeed in college, career, and life upon graduation from high school, regardless of where they live. These standards are aligned to the expectations of colleges, workforce training programs, and employers. The standards promote equity by ensuring all students are well prepared to collaborate and compete with their peers in the United States and abroad. Unlike previous state standards, which varied widely from state to state, the Common Core enables collaboration among states on a range of tools and policies including the:

- Development of textbooks, digital media, and other teaching materials
- Development and implementation of common comprehensive assessment systems that replace existing state testing systems in order to measure student performance annually and provide teachers with specific feedback to help ensure students are on the path to success
- Development of tools and other supports to help educators and schools ensure all students are able to learn the new standards

**Mike Petrilli:**

“Now, what you won’t hear us argue is, first of all, that Common Core is going to solve all of our nation’s educational problems because, of course, it won’t. You’re not going to hear us say that Common Core is perfect. They were not handed down from Mount Sinai, they are not set in stone, right, or we’re going to hear plenty of concerns about this individual standard or that individual standard, so you won’t hear us say that they’re perfect. And you’re not going to hear us say that it’s all going perfectly out there around the country, because, of course, it’s not all going perfectly out there around the country. This is a big country, 50 million kids in public schools, 100,000 of those schools, and like any ambitious reform, it’s a work in progress, okay? But what you are going to hear us argue is that despite all of that you should still embrace the Common Core.

In our view, to embrace the Common Core is, first of all, to embrace the idea that our schools should have standards, all right, that doesn’t sound so radical, and that the standards that we have should be set at a high enough level to indicate that our students are ready for what comes next.

States did have standards before the Common Core, but, by and large, they were set at a very, very low level. And so what that meant is that students could meet those standards, they could pass the standardized tests connected to those standards, but it didn’t mean that they were ready for success later on. In fact, in many states it didn’t even mean that they were at grade level

Today…it’s not that schools are failing, it’s that our schools, by and large, are mediocre when compared to schools overseas.

This is our chance to embrace the Common Core, is to fix all of that, to move to a system with much higher standards but also better tests that give better information but that also encourage better teaching and learning in the classroom.

Common Core….is not perfect. There’s issues, and there is bumps in the road, but they talked about these higher expectations for their students that some of these kids, they couldn’t — you know, four years ago they couldn’t believe that the kids could perform at the level that they’re performing now, but these higher standards have pushed them in that direction.

The old standards gave teachers a set of specific and sometimes constricting direction on where to turn, when to turn, and how fast to go. The Common Core standards instead give us mileposts to aim for, tell us where we should end up but not how to get there.”

**Carmel Martin **

“Common Core has moved from paper to practice, from the ideal to the real."

"Because the Common Core requires children become problem solvers and good communicators, the new tests aligned to them will measure complex thinking, reading, writing, communications, and problem solving kids’ skills. As a result, teachers will no longer be driven to narrow the curriculum or teach to a bad test. There have always been standards and always will be standards. There have always been tests and there always will be tests. It’s time to get them right. For that reason, I ask you to “Embrace the Common Core.”

**Kenneth Chang**

“In many ways, it (the Common Core Test) is a better test than the fill-in-the-bubble multiple-choice exams of my youth. With a computer-based test, the questions can be more complicated but still easily graded. Both consortiums also offer paper versions for the time being, because not all schools have enough computers and Internet connectivity.

Some questions require several calculations to come up with the answer, testing a deeper level of understanding. For example: “Hayley has 272 beads. She buys 38 more beads. She will use 89 beads to make bracelets and the rest to make necklaces. She will use 9 beads for each necklace. What is the greatest number of necklaces Hayley can make?”

Here, the student would scribble calculations on scratch paper and type in the final answer.

But for other questions, the test provides a more complex equation editor — rows of buttons including numerals, mathematical operations like add and subtract, a tool to enter fractions — for entering the answer.

A keyboard and mouse is not a natural way of doing math, and I wondered whether these questions would be more a test of computer interface.

Laura Slover, the chief executive of Parcc, asked me if I had done the tutorial before taking the practice test. I had not. I asked if it was reasonable to expect that all students would have the time and opportunity to do that. She said the organization encouraged taking the tutorial, and that in the field test last spring, students who practiced beforehand did not find the computers an obstacle.

Hint to parents: If your children are to take one of these tests, make sure they puzzle out the interface first.

P.S. Hayley could make 24 necklaces.”

**William McCallum**

“What Common Core actually requires is fluency in the simple skills of adding and subtracting that critics are calling for. “

**Sara Garland**

Common Core math Standards for Second Grade:

1) A requirement that students understand place value, for instance, that “100 can be thought of as a bundle of ten tens — called a ‘hundred.’”

2) That students be able to “add and subtract within 1000, using concrete models or drawings and strategies based on place value … and relate the strategy to a written method.” Also that they “understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.”

3) That they can “explain why addition and subtraction strategies work, using place value and the properties of operations.”

4) And that they can “represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.”

In general, being able to explain how you arrived at an answer – not just memorizing a formula is a key goal for Common Core.

**By**

**Kathleen Porter-Magee**

Here’s a puzzler: Why are the Common Core math standards accused of fostering “fuzzy math” when their drafters and admirers insist that they emphasize basic math, reward precision, and demand fluency? Why are CC-aligned curricula causing confusion and frustration among parents, teachers, and students? Is this another instance of “maximum feasible misunderstanding,” as textbook publishers and educators misinterpret the standards in ways that undermine their intent (but perhaps match the interpreters’ predilections)? Or are the Common Core standards themselves to blame?

My take is that the standards are in line with effective programs, such as Singapore Math, but textbook publishers and other curriculum providers are creating confusion with overly complex explanations, ill-written problems, and lessons that confuse pedagogy with content.

Many of the “fuzzy math” complaints seem to focus on materials that ask students to engage in multiple approaches when tackling arithmetic problems. But to understand whether the confusion stems from the standards or the curriculum, let’s start by recalling what the CCSS actually require.

Any honest reading of the standards must recognize that in grades 4, 5, and 6, the Common Core demand that students master standard algorithms. In grade 4, students should “fluently add and subtract multidigit whole numbers using the standard algorithm.” By grade 5, they are expected to multiply whole numbers using the standard algorithm. And by grade 6, they are expected to divide whole numbers and to add, subtract, multiply, and divide decimals, again using standard algorithms.

The standards themselves are unambiguous that students will master the best and most efficient ways to do arithmetic, and any curriculum that does not give top billing to standard algorithms in the pertinent grades is not aligned with the Common Core.

Because math users and teachers want more than procedural fluency from students (because they want young people actually to *understand* the math problems they answer so that they are ready for more advanced math), the Common Core leave plenty of room for teachers to go beyond the standard algorithm to ensure that students understand how numbers work. The standards ask that students understand what it means to add to and subtract from; the difference between parts and a whole; and to be able to demonstrate these understandings in more than one way.

For example, beginning as early as first grade, students are expected to

… use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations.

More specifically, a first-grade standard asks students to

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Here, students are not limited to lining up numbers, carrying the one, or borrowing but are able to use manipulatives or drawings to arrive at answers or illustrate their understanding of what it means to add or take away one. This video gives a clear sense of how a student might use a “10 frame” or number cubes to count and to add, and it shows how useful such a model can be in helping students learn numbers.

Indeed, as the video demonstrates, such “modeling” has long been part of traditional math programs such as Singapore Math. And the appropriate, efficient use of modeling and drawing helps students understand numbers and can help them solve increasingly complex problems.

Here’s another example drawn from Singapore Math, in which a drawing is used to help pupils make sense of an elementary subtraction problem:

**? – 7 = 5**

In this problem, students are encouraged to draw the whole—which is unknown—and to show what they know. That is, some number minus 7 leaves 5. In this case, the drawing is used as a tool to better understand what the problem is asking. While a student should ultimately be able to answer problems of this sort without visual aids, this kind of “modeling” can help lay the foundation that students need to solve increasingly complicated problems through the grades.

Such “models” can be even more useful for students when it comes to making sense of fractions and answering fraction problems. Take, for example, this middle school problem, also drawn from Singapore Math:

Ronnie had 90 fish. He sold 1/2 of them and gave 1/3 of them to his friend.

- What fraction of the fish was left?
- How many fish did he give to John?

Whole

Whole, divided into six equal parts

Answer:

- First, change to fractions with like denominators. (2/6, 3/6)
- Next, using the model, show the portions sold and the portions given to John.

Using the model, it’s easy to see that Ronnie has 1/6 left.

Unfortunately—but perhaps predictably—as more publishers work to align their math programs to the CCSS, there is ample room for screw-ups. And comedian (and New York City parent)Louis C.K. gave several examples of blunders when he complained to his 3 million followers that the Common Core curriculum at his daughter’s school—with its bewildering math problems and related tests—was making her cry.

He also tweeted a few examples, including this one:

6 students are reading books for book clubs. They are reading one of the following stories:

Story A: Matilda

Story B: Magic Tree House Lions at Lunchtime

Story C: Superfudge1/2 of the students are reading Story A.

1/3 of the students are reading Story B.

1/6 of the students are reading Story C.In the model below, each box represents one student in the group. Complete the model based upon the information above. Write one letter A, B, or C in each box to represent the story each kid read.

Answer:

Louis C.K. is right: this problem (along with some others he tweeted) *is* confusing. Yet the confusion doesn’t arise from the math; it’s the fault of the English. The problem includes students (who have no names), book titles, letter labels for the books that are different from the titles, all buried in a problem that is meant to be about comparing fractions with unlike denominators. It would be easy for a student to lose his or her way and get frustrated amidst that information even if s/he gets the math.

Worse, in this example, the model or drawing has become the “goal.” In the Singapore examples, the drawings and models are means to clear-cut ends. They aim to clarify and focus on answering the problem. In other words, the model is used in service of understanding and answering a clearly defined problem.

Ultimately, math should focus on precision. If models confuse more than the math itself, they have lost their utility.

Note, too, that the Singapore problems—typical of what I’ve seen in Singapore Math—are text-lite. The emphasis is on numbers, manipulating numbers, and problem solving. In too many other examples, including those shared by Louis C.K., the math drowns in a sea of confusing text. In short: if you need that much text to explain why or how to use a mathematical model, you’re doing it wrong.

Three takeaways:

First, schools who’ve had long success with tried and true approaches, including Singapore Math, might consider sticking with them before pouring lots of money into shiny new—but possibly ill-written—curricula.

Second, publishers should emulate the clarity and precision of Singapore Math rather than reinventing the wheel and coming up with one that doesn’t roll straight. If they fail in that quest, nobody should buy what they’re selling.

Third, Common Core supporters need to understand that even as opponents eagerly pounce on any mistake that anybody makes in the name of the Common Core, that doesn’t mean that we deny or ignore such failures. Failure is an important part of innovation and a necessary step in the quest for excellence. Indeed, that we should be more exacting critics than the opponents, taking pains not to explain away implementation challenges, mistakes and missteps. Let’s resolve to be vigilant, candid, and demanding in our assessment and communication of such challenges.