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8 Popular Common Core Math Standards Explained with Examples in the Classroom

Written by Maria Kampen

Did you know?

Prodigy Math Game covers many math curricula across the world, including Common Core.

• Teaching Strategies
• Definitions for each of the eight standards
• Examples to help you seamlessly incorporate each standard into your classroom
• Suggestions for talking to parents about the new Common Core math curriculum

The dust has finally settled, and it looks like Common Core math is here to stay.

After countless political battles (and more than one Common Core math meme floating around social media), the initiative that incorporates techniques like cooperative learning and active learning has settled into the American education system.

Prodigy offers common Core-aligned math practice that your students will love. Start today!

Beginning in 2010, the Common Core State Standards Initiative (CCSSI) aimed to change the way American students were taught English language arts and mathematics by countering low test scores, inconsistent learning standards and a curriculum that was a “mile wide and an inch deep.”

Of the 45 states (plus the District of Columbia and the Department of Defense Education Activity) that fully implemented Common Core by 2015, 24 chose to revise some aspects of the program but still remain aligned with the original standards today.

What is Common Core math?

The Common Core State Standards for Mathematical Practice were designed to reform the American education system, with three main goals:

• Provide  graduating high school students with the skills they need to be successful either in the workforce or in post-secondary education
• Boost  math test scores for all American students
• Smooth out  the differences between individual state curriculums and practices

At the heart of Common Core math are the eight Standards for Mathematical Practice. These standards were created by education professionals at all levels, and are based on research, leading state curricula and exceptional international math programs.

• 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

These standards allow students to learn deeply instead of widely and build a solid foundation for advanced study . The traditional Common Core math provides guidelines for grade-specific concepts, but it’s up to individual school districts to implement a curriculum that’s in line with the standards.

Keep reading to find out what they mean, or download our free, condensed list of the eight standards and examples for teaching them!

Is Common Core math working?

Due to the massive overhaul of state education frameworks, many teachers are still scrambling to prepare. A study from the Center for Education Policy Research at Harvard University reported that 82% of math teachers are changing “ more than half of their instructional materials” in response to the new practice standards. The same study found that “three out of four teachers (73%) reported that they have embraced the new standards ‘quite a bit’ or ‘fully’.” 

Source: Center for Education Policy Research

1. Make sense of problems and persevere in solving them

When students approach a new problem for the first time, they might be tempted to go straight for the solution. After all, isn’t that the point? The first standard directly counters this impulse.

When students rush in to immediately solve a problem, they often fail to understand the underlying concepts. Rote memorization and a quick recall are essential parts of mathematical fluency, but can often lead to greater problems. If a student doesn’t understand the underlying concept behind the facts they’ve spent time learning, they might struggle with more complicated problems or ideas.

Giving students more open-ended questions or methods allows them to work with the concepts behind the problem, instead of going straight to the solution.

For example, look at this typical Common Core math problem:

Source: The School Run While it looks complicated, a number line is a Common Core math example that teaches students several essential concepts:

• The relationship between numbers in a given problem
• The potential for more than one solution
• The foundation behind shortcuts and more complex processes

Jennifer Smith and Michelle Stephan used this question to incorporate the first standard into a seventh-grade classroom:

Source: Journal of the American Academy of Special Education Professionals

The problem was presented to the class with a quick introduction, and the teachers asked students to find the greater net worth -- without explaining how. Students worked alone or in groups to discuss the question and their process, while the teachers supervised and made note of different strategies.

The teachers spent minimal time with the students, fixing only minor mistakes and encouraging them to work with their group. Every student was actively engaged in working with the problems, and explained their thinking to the class in a follow-up discussion.

2. Reason abstractly and quantitatively

There are two parts to the second standard: decontextualization and contextualization.

Decontextualization refers to the process of understanding the symbols in a problem as separate from the whole. This is where the much-loved word problem becomes essential.

Take this question as an example:

Sarah has 5 bouquets of flowers on her desk. After lunch, Steve brings her 3 bouquets of flowers. How many bouquets of flowers does Sarah have on her desk now?

Decontextualization means a student is expected to infer from the above problem that they are to solve an equation (5 + 3 = 8) without getting distracted by any additional information.

Contextualization is the opposite: it refers to the ability to step back from the problem and view it as a whole. Students would have to understand that five bouquets of flowers represent the total amount, and the three more that Steve brings are adding to that original number.

Source: Stanford Graduate School of Education

A study conducted by the Stanford Graduate School of Education found that the same parts of the brain that compare physical size also compare the abstract worth of two numbers. By linking those two processes using modular tools , the study found that students were better equipped to learn about abstract concepts like negative numbers, negative fractions and pre-algebraic problems.

Researchers used different colored blocks to represent negative and positive numbers, and asked students to find the midpoint between two sums. In your classroom, have younger students model addition and subtraction with number blocks, or ask older students to find the dimensions and volume of an everyday object using the formulas they’ve learned.

3. Construct viable arguments and critique the reasoning of others

Are your students just repeating the steps without understanding what they’re actually doing, or are they building the strong theoretical foundations they need to tackle high-school- and college-level problems? Similar to the first standard, this standard encourages critical thinking and problem-solving.

Challenging your students to look at data, solve problems, draw conclusions and debate with their classmates is a great way for them to ask new questions and develop a solid understanding of definitions and processes.

The best way to develop the third standard is through structured classroom discussion. Before you start working on the solution to a problem with your class, brainstorm some strategies: Put the simplest answers on the board first, then move on to more advanced strategies. Talk through each strategy as a group, and discuss what was right or wrong about the approach.

Some more tips for having a great classroom discussion:

• Ask students to write down answers to questions, like “what did you find difficult about this problem?” or “what did you learn during this activity?” before sharing out loud
• For a more lively class, consider implementing a “talking stick” or other object to let students know who has the floor
• Read our post for more ideas on  effective classroom management

4. Model with mathematics

Different types of learners respond best to different instruction styles, and it can be difficult to respond to the personalized learning needs of each student.

However, many different types of learners respond well to seeing their textbooks brought to life. That’s exactly what high school math teacher Dan Meyer illustrates in this TED Talk:

It’s not just teachers who can show students the real-world applications of math. Reversing the processes can have a valuable effect on how students engage with problems and the world around them. Challenge students to take a problem from the page to real life using number lines, diagrams, o r classroom technology .

This is also a great time to try out project-based learning strategies , like third grade teacher Renee McFall did with her classroom.

In order to bring math to the real world, she challenged her students to raise money for a local charity by selling bracelets. Students were responsible for making and selling bracelets, calculating the amount of supplies they needed, making a budget, and pitching their best business ideas to teachers. With real-world consequences, students were encouraged to be precise in their calculations, measurements and planning, because mistakes could cost money.

5. Use appropriate tools strategically

Students today have a huge variety of tools available to them, and knowing which to use is half the battle. Depending on the problem, students could use anything from scrap paper and a pencil to more advanced technology resources. When students know how to find what they need, they develop problem-solving skills and become more comfortable looking for new solutions in the future.

One practical way to get your students familiar with the appropriate tools is to challenge them to figure out what they need themselves. At the beginning of the lesson, ask them to make a list of the tools they need and gather them up.

Some options to include:

• Pencils and paper
• Calculators
• Modular tools
• Worksheets with key formulas

Ask more advanced students to brainstorm a list of sources to draw research from, like books, websites or even podcasts. Afterwards, have a discussion about the tools used. Were there any differences between what students chose? What worked and what didn’t? What tools would they consider using next time?

6. Attend to precision

Precision is one of the most important skills to develop early on in math study. Even if most first graders would rather finger paint than write numbers, it builds a solid foundation for more advanced math problems . Encouraging students to use correct symbols and challenging them to accurately communicate their process to others gets them comfortable with the “language” of math.

In younger grades, students can practice precision by explaining their thinking to classmates, using either words or modular tools. As students get older, they can begin to accurately define units and equations, both in writing and speaking about math.

Have students start a math journal to practice precision and communication. Younger students can respond to prompts of “what they did” and “what they learned.” Older students can use their journal space to engage more with the topic and ask questions about concepts they don’t quite understand yet.

Write prompts on the board to get your students started:

• Write a letter to a family member explaining your process
• Do you have any more questions you want answered?
• Where did you get stuck in this problem? Why?
• What tools did you use to solve this problem?
• What will you do differently next time?

Be aware that students might need some time to adjust to writing about math. Make sure to model it to the class and provide students with lots of prompts to get them started.

7. Look for and make use of structure

Seeing repeated patterns gives students the tools to reason through new, more challenging problems.

Sean Nank , recipient of the Presidential Awards for Excellence in Mathematics and Science Teaching, defines the understanding of patterns and structure as being key for math fluency:

“ I would define fluency as being able to recognize patterns, so people can do math quickly -- which is not to say memorization is bad. It’s still something that is needed. But, you can only memorize so many math facts. If you know the patterns behind them, you can break them down really fast ."

Structure allows students to understand that complicated equations are not whole entities, but rather composed of several smaller, more accessible objects. This understanding gives them the confidence to attempt more difficult equations.

One of the best ways to develop an understanding of structure is through a daily math practice. Prodigy is an engaging, game-based math platform aligned with Common Core math curricula. It’s an exciting online resource that challenges students to answer math questions every day as they duel characters, play with their friends and collect exotic pets.

To see an even greater impact on your classroom, use the teacher tools to set assignments that help students build confidence in a particular skill.

Other great options for building a daily math practice include challenging your students to solve a daily math problem when they arrive in the classroom, or setting aside time in your lesson for students to model problems with modular tools so they can see the patterns for themselves.

8. Look for and make use of repeated reasoning

The seventh and eighth standards are closely related, but it’s important to distinguish between them. Instead of focusing on the repeated structure of an object, the eighth standard encourages students to use past problems as a model for present ones .

When students can demonstrate repeated reasoning, it means they’re able to try different solutions for the same problem and adjust as needed. Students can see which elements stay the same and which are variable by testing different methods repeatedly. This process develops both attention to detail and oversight -- controlling the small parts of the problem while making sure that overall, they’re on the right path to a solution.

A great way to promote repeated reasoning is through the use of “ fact families .” When students write an equation, challenge them to write two or three more equations that directly relate to the original, like this:

Source: Teachers Pay Teachers

As students progress and become more advanced, this provides a solid foundation for more complicated equations that include fractions, integers and algebraic elements.

Fact families encourage students to maintain a focus on the overall equation, while also manipulating the individual numbers and examining the relationships between them. Working with fact families to express repeated reasoning in early elementary gives students the skills they need for later elementary, high-school level and post-secondary math.

Tips for explaining Common Core math to parents:

All set! You’ve seamlessly integrated Common Core in your classroom, your students are working together and discussing their ideas, and things are going smoothly. But what about their parents?

Parents want their children to get the best education possible. Common Core math is quite a large shift from how they were taught as children, and some of the processes and techniques might be unfamiliar to them.

With that in mind, here are three ways to get parents on board with new Common Core math standards:

• Send home an information sheet or link parents to a web resource  that explains the standards behind Common Core math and how they work in the classroom. Parents are less likely to be alarmed by dramatically different-looking homework when they’ve been given a head’s-up and an introduction to the reasoning behind the change.
• Let parents know that their children might ask questions and struggle while they get used to the new curriculum . A recent study from  Psychological Science  found that when parents expressed negative feelings about math, their children were also more likely to underperform. Encourage parents to model a positive attitude and to work through difficult problems with their children.
• Consider taking a few minutes during a parent evening to go over the most important points of the new curriculum,  and encourage them to keep in touch and to reach out if they have any questions. Supporting an open dialogue with parents is a great classroom practice, no matter which subject you’re teaching.

Education doesn’t happen in isolation — in fact, one of the key indicators for students’ success is how engaged their parents are with their schooling. Keep parents in the loop to avoid major frustration and confusion and ensure a positive learning environment for all your students.

Common core math standards: Final thoughts

Such a large shift in curriculum and teaching habits is bound to have a few growing pains, and certainly won’t happen overnight. However, with a little bit of time, patience and hard work, you’ll begin to see confident and engaged learners.

The biggest strength of the Common Core math standards is their versatility -- they overlap and complement each other to ensure all children are confident in their math skills.

“I see the Common Core as a way to provide teachers with strategies,” says Sean Nank, “so that students can see the beauty of math -- the how it works and the why it works and the patterns.” Encourage your students to keep looking for the how’s and the why’s, and watch them flourish.

Create or log in to your free teacher account on Prodigy – an engaging , game-based learning platform for math that’s easy to use for educators and students alike. Prodigy is aligned with curricula across the English-speaking world and filled with powerful teacher tools for differentiation and assessment.

Mathematics Assessment Project

Common core state standards, mathematical practices for all grades.

Choose the standard set (Content, Practices and MAP task types) above. Choose a set of materials on the left to see links to example tasks or lessons.

Common Core State Standards

From this page, you can browse the Common Core State Standards for Mathematics (CCSSM), and see which Formative Assessment Lessons or Summative Assessment Tasks relate to them.

• Using the menu on the left, you can browse the CCSSM Standards for Mathematical Practice and Standards for Mathematical Content .
• Use the drop-down menu at the bottom of the to choose whether you want to see links to the Formative Assessment Lessons (Classroom Challenges) or the Summative Assessment Tasks.

You can also view two classifications used by the Math Assessment Project: Lesson Types distinguish between the two main styles of Classroom Challenge - “Problem Solving” and “Concept Development”. Assessment Task Types describe how the Project classifies assessment tasks to balance between assessing routine content knowledge and fostering development of the mathematical practices.

State, district and CCSSI standards appear courtesy of their respective authors. All other material Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham.

Common Core State Standards Initiative

Standards for Mathematical Practice » Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

• Standards for Mathematical Practice
• How to read the grade level standards
• Introduction
• Counting & Cardinality
• Operations & Algebraic Thinking
• Number & Operations in Base Ten
• Measurement & Data
• Number & Operations—Fractions¹
• Number & Operations in Base Ten¹
• Number & Operations—Fractions
• Ratios & Proportional Relationships
• The Number System
• Expressions & Equations
• Statistics & Probability
• The Real Number System
• Quantities*
• The Complex Number System
• Vector & Matrix Quantities
• Seeing Structure in Expressions
• Arithmetic with Polynomials & Rational Expressions
• Creating Equations*
• Reasoning with Equations & Inequalities
• Interpreting Functions
• Building Functions
• Linear, Quadratic, & Exponential Models*
• Trigonometric Functions
• High School: Modeling
• Similarity, Right Triangles, & Trigonometry
• Expressing Geometric Properties with Equations
• Geometric Measurement & Dimension
• Modeling with Geometry
• Interpreting Categorical & Quantitative Data
• Making Inferences & Justifying Conclusions
• Conditional Probability & the Rules of Probability
• Using Probability to Make Decisions
• Courses & Transitions
• Mathematics Glossary
• Mathematics Appendix A

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Common Core Math Explained: 8 Common Core Math Examples To Use In The Classroom 

Samantha dock.

Common Core math examples can be a tricky world to navigate for teachers trying to meet the individual needs of their students. Having a bank of Common Core math examples to hand can be helpful when planning your lessons. 

Embraced by the majority of states in the U.S., the Common Core math standards help to develop students’ conceptual understanding, problem-solving skills, and real-world applications.  In this article, we explore what Common Core math is, 8 Common Core math examples and top tips for educators teaching Common Core math.

What is Common Core math?

Common Core math standards are a set of educational standards for mathematics adopted by forty states in the United States. Each standard outlines the math knowledge students should know and be able to do at each grade level, from kindergarten through to high school. 

These standards aim to provide a more focused and coherent set of learning goals for students, emphasizing conceptual understanding, problem-solving, and critical thinking skills.  

Often, Common Core math involves multiple strategies and approaches to solving problems. In turn, this encourages students to understand the underlying concepts rather than simply memorizing algorithms.  

One aim of the Common Core State Standards is to move away from traditional memorization of procedures and algorithms towards a deeper understanding of connections between mathematical concepts.  

Common Core math standards are organized by grade level and cover a wide range of mathematical topics, including:  

• Arithmetic 
• Probability

Each standard is divided into domains, which represent broad categories of mathematical content such as: 

• Counting and cardinality
• Operations and algebraic thinking
• Numbers and operations in base ten
• Measurement and data

3rd to 6th grade Common Core math test

Help your students prepare for their state math test with these Common Core practice math tests for 3rd - 6th grade.

Common Core math standards have been controversial in some areas due to concerns about curriculum changes, standardized testing, and complexity. But some argue that these standards provide a more coherent approach to mathematics education and better prepare students for higher education than traditional math. 

Read more: Why is Math Important?

How is Common Core math different from traditional math?

Common Core math and traditional math represent two different approaches to teaching mathematics.

Traditional math typically refers to methods of teaching mathematics that were used before the adoption of the Common Core standards. These methods often focused on rote memorization of formulas and procedures, with less emphasis on understanding the concepts or on real-life application of mathematical skills.

Here are some key differences between the two:

Focus on Conceptual Understanding vs. Memorization

A strong emphasis is placed on developing students’ conceptual understanding of math concepts under the common core. It aims to help learners understand the “why” behind mathematical procedures rather than just memorizing algorithms. Traditional math often focuses more on rote memorization of formulas and procedures without necessarily understanding the underlying concepts needed to approach math questions.

Problem-Solving and Critical Thinking vs. Rote Practice

Common Core math problems encourage critical thinking skills. They promote multiple approaches to solving new math problems and require students to justify their reasoning. Often, traditional math involves repetitive practice of standard procedures with less emphasis on problem-solving and critical thinking.

Real-World Applications vs. Abstract Exercises

Connections between mathematical concepts to real-world situations is valued under the common core. This helps students see the relevance of the math skills they are learning. Tasks and problems require the application of mathematical skills in practical contexts. Traditional math lessons focus more on abstract exercises and textbook problems that may not always have clear real-world connections.

Depth of Understanding vs. Breadth of Coverage

Rather than covering a wide range of topics, Common Core math aims for depth of understanding and maths mastery. Fewer topics at each grade level allow for deeper exploration and mastery of key concepts. In contrast, traditional math tends to cover a broader range of topics in less depth.

Flexibility and Multiple Strategies vs. One Correct Method

Students are encouraged to use multiple strategies and approaches to solve problems through the Common Core math standards. Flexibility and creativity are valued when approaching problem-solving. Emphasis on a single “correct” method or algorithm for solving problems is the general approach in traditional math. Overall, Common Core State Standards aim to develop students’ mathematical proficiency in alignment with the demands of the modern world. This includes the need for critical thinking, problem-solving, and application of mathematical concepts to real-world situations

Overall, Common Core State Standards aim to develop students’ mathematical proficiency in alignment with the demands of the modern world. This includes the need for critical thinking, problem-solving, and application of mathematical concepts to real-world situations. 

Third Space Learning provides one-on-one math instruction for students who need it most. Personalized one-on-one math lessons are designed by math experts and aligned to your state’s math standards — including the Common Core State Standards. 

Common Core standards and 8 Common Core math examples

1. make sense of problems and persevere in solving them.

Students should not only be able to understand problems and make sense of them, but persevere in finding solutions. 

Finding solutions may involve math skills such as: 

• Analyzing problems
• Making conjectures
• Planning approaches to solving math problems 

Common Core math example 1

A student is faced with a word problem about finding the area of a garden. They must take the time to carefully read and understand the problem before attempting to solve it. 

This problem may require several approaches to answer the math question. Small group work and discussion can encourage students to persevere through the challenge and try different strategies until they find a solution.

2. Reason abstractly and quantitatively

In order to reason abstractly, students need to be able to make sense of quantities and their relationships in mathematical situations. 

This will be easier for students if they can take abstract information from context and quantify information. Being able to decontextualize and contextualize mathematical ideas will benefit students.

Common Core math example 2

A graph shows the relationship between the number of hours worked and the amount earned. Students can analyze the graph to determine patterns and make predictions about future earnings based on proportional relationships between hours worked and money earned. 

For example, if John worked for 13 hours, how much money would he earn?

3. Construct viable arguments and critique the reasoning of others

Introducing math vocabulary in the classroom helps students construct viable arguments and critique the mathematical reasoning of others. Exposure to mathematics language and sentence stems will help students to reason mathematically, construct arguments, and justify their thinking, without creating cognitive overload. 

Common Core math example 3

During a class discussion about strategies for solving a particular math problem, you might ask students to present their solutions — justifying and explaining their reasoning. 

They can also be encouraged to critique each other’s approaches, identify strengths and weaknesses in their arguments and offer alternative methods. 

4. Model mathematics

Math lessons should prepare students to use math to solve real-world problems. It may help students to do this if you represent mathematical concepts with visual models and math manipulatives . 

Common Core math example 4

Subtraction of fractions is a skill that many students struggle with. Using a visual model to describe and analyze the word problem can release cognitive load for students. 

For example, Paul had 11 ⅔ yards of twine. He used 6 ½ yards to make macrame wall hangings, how many yards of twine does Paul have left?

5. Use appropriate tools strategically

To solve math problems effectively and efficiently, students must be able to select and use appropriate tools. This includes recognizing when and how to use tools, as well as evaluating effectiveness and efficiency.

Common Core math example 5

When solving a complex geometry problem, students should recognise the effectiveness of using a protractor and ruler to accurately measure angles and lengths. 

For example, Given an angle ABC where point B is the vertex of the angle, construct an angle bisector of angle ABC using a ruler and a protractor. Then, using the angle bisector you have constructed, draw a line segment from point B to the bisected angle’s line that is exactly 5 cm long. Measure and report the angle sizes of the two new angles created by the angle bisector.

6. Attend to precision

Calculations need to be carried out precisely. To do this, students need to be aware of key mathematical terminology for the Common Core Standards they are studying. This involves using appropriate units and labels and stating mathematical results clearly.

Common Core math example 6

A student ensures that their work is clear and organized. They pay attention to detail, avoiding errors and inaccuracies in their calculations. Below is a worked example of a student showing how to solve a word problem involving multiple percentages.

7. Look for and make use of structure

Solving math problems accurately means students need to recognize and use mathematical patterns and structure. They should be able to identify relationships between mathematical ideas and make connections between different mathematical representations.

Common Core math example 7

When solving a multiplication of decimals problem, a student recognizes that breaking down the whole numbers and decimal parts into their factors makes the problem easier to solve. They identify the underlying structure of the problem and use it to their advantage.

8. Look for and express regularity in repeated reasoning

Identifying and generalizing patterns and regularities in mathematical situations is key to proficiency in problem soving and reasoning . Students should be able to notice repeated reasoning and use it to solve math problems efficiently. 

Common Core math example 8

Example: A student identifies similarities between a problem they’re working on and a previous math problem. They utilize the patterns in the prior example to complete the new problem. This also helps them to solve similar problems in the future.

Tips for teaching Common Core math

Teachers need to understand Common Core math standards to recognize the appropriate instructional strategies and promote a growth mindset in the classroom .  

Here are 8 tips for maximising student progress when teaching the Common Core State Standards:

1. Understand the Common Core State Standards

Familiarize yourself with the math Common Core State Standards for your specific grade level. Take the time to understand the mathematical practices, domains and teaching strategies required for your grade.

2. Focus on conceptual understanding

Prioritize conceptual understanding over rote memorization. You can achieve this by helping students understand the “why” behind math concepts and skills. Always encourage them to explain and justify their reasoning.

3. Promote multiple approaches

Offer your students a range of math strategies and approaches to problem-solving. The more methods in their math bank, the better equipped they are to find a solution. Asking students to share their thinking process helps those who are not grasping the content from the math instruction.

4. Real-world connections

Connecting mathematical concepts to real-world situations makes learning more meaningful and relevant. You can do this by implementing math problems where students work collaboratively to solve complex, open-ended word problems with real-world relevance. 

5. Use visual representations

Diagrams, models, and manipulatives support students’ understanding of mathematical concepts by making abstract concepts more concrete and accessible. For example, you could use algebra tiles when students are first learning how to solve algebraic equations and inequalities to help them contexutalize the abstract nature of algebra.

6. Encourage discourse and collaboration

Promote a classroom environment where students feel comfortable sharing their ideas, asking questions and engaging in mathematical discourse. 

Encourage discourse by using techniques such as turn and talk, or the 3 reads method for word problems.

7. Assess progress

Use formative and summative assessments to monitor students’ progress and understanding of mathematical concepts and adjust instruction accordingly based on assessment data.  

Some examples of a formative assessment are: 

• Exit tickets
• Rating scales
• Thumbs up or thumbs down 

Summative assessments include: 

• Check for understanding quizzes
• End-of-topic quizzes

Assessment resources:

• Practice state assessments  

8. Professional development

Continuously seek professional development opportunities to deepen your understanding of Common Core math and improve your teaching practices. Collaborate with colleagues and participate in workshops, conferences, and online courses.

Common Core math and the wider world

Embracing Common Core principles can help equip students for future challenges

Educators’ commitment to teaching Common Core math goes beyond math instruction. It’s about nurturing critical thinking and problem solving, ensuring students are prepared for the wider world. 

Math lessons are no longer simply giving students math worksheets and grading them on the correct answer. The American education system has developed a math curriculum that anchors mathematical concepts in real-world relevance, promotes diverse problem-solving strategies, and encourages a collaborative learning environment.  

Educators have a responsibility to ensure students have the tools and mathematical literacy they need to succeed.

Common Core math examples FAQ

1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

1. Focus: Emphasizes focusing deeply on a smaller number of key topics at each grade level. This is done to ensure students develop a deep understanding of foundational mathematical ideas. 2. Coherence: Emphasizes the importance of coherence in mathematical instruction. This is done to support students in making meaningful connections between different mathematical ideas, helping them see how concepts are related and reinforcing their understanding over time 3. Rigor: Focuses on increasing the rigor of mathematical instruction by demanding that students engage in conceptual understanding, procedural fluency, and application of mathematical concepts in real-world contexts. In this context, rigor means ensuring that students develop a deep understanding of mathematical concepts, are able to apply their knowledge in various contexts, and can solve complex problems through reasoning and critical thinking.

Forty states have fully adopted Common Core math, while Minnesota partially embraces it. South Carolina, Oklahoma, Indiana, Florida, and Arizona initially adopted but later repealed Common Core. Alaska, Nebraska, Texas, and Virginia never adopted it.

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Ultimate Guide to Problem Solving Techniques [FREE]

Are you trying to build problem solving and reasoning skills in the classroom?

Here are 9 ready-to-go printable problem solving techniques that all your students should know, including challenges, short explanations and questioning prompts.

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Implementing Common Core Standards for Mathematics: Focus on Problem Solving

Utilizing action research as the methodology, this study was developed with the ultimate goal of describing and reflecting on my implementation of one aspect of the Common Core State Standards for Mathematics ( CCSSM) in an algebra classroom. This implementation focused on the Problem-Solving Standard of Mathematical Practice (SMP) as described in CCSSM (Making sense of problems and persevere in solving them). The research question that guided my work was the following: How is the Common Core State Standards for Mathematics ( CCSSM ) Problem-Solving Mathematical Standard enacted in an algebra class while using a Standards- based curriculum to teach a quadratics unit?

I explored this by focusing on the following sub-questions:

• Q1. What opportunities to enact the components of the Problem-Solving Mathematical Standard are provided by the written curriculum?
• Q2. In what way does the teacher’s implementation of the quadratics unit diminish or enhance the opportunities to enact the components of the Problem-Solving Mathematical Standard provided by the written curriculum?
• Q3. In what ways does the teacher’s enactment of problem-solving opportunities change over the course of the unit?

Reviewing the literature related to the relevant learning theories (sociocultural theory, the situated perspective, and communities of practice), I outlined the history of CCSSM, National Council of Teachers of Mathematics ( NCTM), National Research Council (NRC), and the No Child Left Behind Act of 2001 . Exploring the details of CCSSM ’s Standards of Mathematical Content (SMCs) and Standards of Mathematical Practice (SMPs), I discussed problem solving, the Problem Solving Components (PSCs) listed in the Problem-Solving SMP of CCSSM , teaching through problem solving, and Standards- based curricula, such as College Preparatory Mathematics (CPM) which is the algebra curricula I chose for this study.

There are many definitions of the construct problem solving. CCSSM describes this construct in unique ways specifically related to student engagement. The challenge for teachers is to not only make sense of CCSSM ’s definition of problem solving and its components, but also to enact it in the classroom so that mathematical understanding is enhanced. For this reason, studies revealing how classroom teachers implemented CCSSM , especially in terms of problem solving, are necessary.

The Critical Theoretic/Action Research Paradigm is often utilized by researchers trying to improve their own practice; thus, I opted for an action research methodology because it could be conducted by the practitioner. These methods of data collection and analysis were employed in order to capture the nature of changes made in the classroom involving my teaching practice. I chose action research because this study met the key tenets of research in action, namely, a collaborative partnership concurrent with action, and a problem-solving approach.

While I knew how I wanted to change my classroom teaching style, implementing the change was harder than anticipated. From the onset, I never thought of myself as an absolute classroom authority, because I always maintained a relaxed classroom atmosphere where students were made to feel comfortable. However, this study showed me that students did view my presence as the authority and looked to me for correct answers, for approval, and/or for reassurance that they were on the right track. My own insecurities of not knowing how to respond to students in a way to get them to interact more with their group and stop looking to me for answers, while not being comfortable forcing students to talk in front of their peers, complicated this study. While it was easy to anticipate how I would handle situations in the classroom, it was hard to change in the moment.

The research revealed the following salient findings: while the written curriculum contained numerous opportunities for students to engage with the Focal PSCs, the teacher plays a crucial role in enacting the written curriculum. Through the teacher’s enactment of this curriculum, opportunities for students to engage with the Focal PSCs can be taken away, enacted as written, or enhanced all by the teacher. Additionally, change was gradual and difficult due to the complexities of teaching. Reflection and constant adapting are crucial when it comes to changing my practice.

Degree Type

• Doctor of Philosophy
• Curriculum and Instruction

Campus location

• West Lafayette

Advisor/Supervisor/Committee Chair

Additional committee member 2, additional committee member 3, additional committee member 4, usage metrics.

• Algebra and number theory

In 2018, after visiting Suzdal I visited Vladimir, which was the capital of Russia from the mid-1100s to the early 1200s, when it was sacked by the Mongols and never fully recovered its importance (Moscow took over). Like Suzdal, Vladimir is one of the cities in the Golden Ring. Unlike Suzdal, Vladimir is a real city.

The bus terminal also sold an array of useful products, like the cologne "Sasha" and C3PO-sponsored "Durasell" batteries.

In the center of Vladimir, one of its most important monuments is the "Golden Gate" shown below. It used to serve as a gate to access the city, which of course by now has grown completely around it. The current version is a reconstruction. The original gate was replaced in 1795 after being deemed to be in too poor a condition to maintain.

Close to the Golden Gate is the Trinity Church, which was constructed right before the Russian Revolution. Next to the church, workers are building what looks like a fountain.

Up a street from the Golden Gate is the following old water tower, which has an observation deck on the top and houses a historical museum about Vladimir below that: the photo is from 1880 and the carvings with moveable pieces on the inside were made from a single piece of wood.

Near the water tower I saw the following well-dressed local on the left in a cafe. On the right, a family is carrying blue bags from Vladimir Zhirinovsky's political party. Someone was running around giving out these free bags of party swag (must have been some election coming up). He approached me and I made it clear I had zero interest.

On Bolshaya Moskovskaya ("Big Moscow") street is a tobacco store named after Sherlock Holmes.

Off that street is a Museum of the Spoon. Its entrance is the door in the first photo below. Note the blind person eyeglass symbol, and below that a button for people in a wheelchair to be let in. It is admirable for the museum to make itself accessible to the handicapped, but if they were really committed to this they should find a better location: the museum is down a steep and bumpy asphalt road that even able-bodied people need to walk along carefully! A better view of the road than what I show in the photo is at Google maps here .

According to the museum's website (in Russian), it opened in 2015 and has the biggest spoon collection in Russia. The second photo below has a spoon with a hole in it; this is what you use if you are on a diet. A lot of the spoons in this small museum are part of spoon collections that different companies once sold. If your grandmother ever got spoons from the Franklin Mint, there is probably a copy of them here.

At the Soho Pub Steakhouse (that's Soho as in London, not New York), the menu shows where all the parts of a steak come from: sirloin, flank, and so on. I knew what part of a cow a rib steak comes from, but some of the other information was new to me.

In a park where artists could sell their work, one guy displayed the carving below. It is a parody of the painting shown after it, which everyone in Russia knows. The painting is called "Bogatyrs" (the Russian analogue of knights) and hangs in the Tretyakov Gallery in Moscow.

At a museum near the park I found 15-puzzles with removable pieces for sale and bought one of them (I wrote about another one on the page about Suzdal ).

Georgievskaya street, a pedestrian area, was rebuilt in 2016 with new brick paths, new benches, new building facades, and a few bronze statues. Here is one of the statues: a 19th century fireman outside the local fire station. (A news article about its installation is here if you know Russian.) This is interactive, since if you push the wooden handle up and down, a stream of water comes out of the hose that the statue is holding.

A kiosk off this street had the following Trump-era US currency holder for sale.

By far the most interesting tourist activity in Vladimir is a visit to Borodin's blacksmith shop, where you can forge your own nail if you visit on Friday, Saturday, or Sunday. Before the lesson began, I tried on the chain mail and helmet in the waiting area, shown below. The mail weighs almost 50 pounds, with its main pressure being on the shoulders. Taking it off made me feel so much lighter!

Behind the chain mail and helmet above is a shield. In Russian, the word "shield" is щит (shcheet). There is an Uzbekistan power company Щит Энергия (Shcheet Energiya) which translates its name into English not as Shield Energy, but as Shit Energiya. I am not making this up. You can see their name in English at the top and bottom of a Wayback Machine copy of their 2018 homepage . Strictly speaking, Shit Energiya is an LLC, and that abbreviation is translated into Russian as OOO, so the full name in English is the more impressive OOO Shit Energiya, as you can see at the top of a Reddit page on Engrish . In 2014, Ben Stiller visited the Russian late-night talk show Evening Urgant and, without knowing Russian, participated in a skit where he had to guess what presents different children asked him about in Russian. A child asked to get a shield, and Stiller was astonished by the word he (thought he) heard. This skit was posted to the show's YouTube channel here , but that link stopped working for me after the show was shut down in February 2022. I found an archived copy of the skit on Facebook here (the part about the shield starts at 1:55).

For some reason, the waiting area also had a copy of a "Felix" pinwheel calculator. The name is from Felix Dzerzhinsky, who organized a factory to create them based on an earlier model (see here ) while he wasn't busy killing people. The Felix calculator at the blacksmith is on the left, and a shinier version I found at the Computer History Museum in California a few months later is on the right.

Here are the blacksmith's forge (furnace), anvil, and work tools.

The lesson (or "master class") was led by Alexei Borodin, who began by discussing the important role of blacksmiths in the era before mass production of consumer goods. They made everything a household used that was metallic: pans, utensils, keys, horseshoes, scales, nails, iron wheel tires, etc. After discussing a minimal set of tools a blacksmith would use, he asked "What else does a blacksmith have to use?" "The head!"

This metal decorative piece took him 2 months to create.

Below, our instructor discussed weighing heavy and light items; the metal scale on the right is over 100 years old.

Now he heated up a metal rod to demonstrate for the audience how to make a nail.

He hammered the end of the rod to get a sharp tip, cut off the end, and hammered the top of the tip (with the rest of the nail held in place in a bar called a nailheader) to create a nailhead.

It was now time for people in the audience to make a nail. Everyone else who wanted to do this was a child, and I let them go first. After putting on an apron and holding a hammer, it looks like I know what I'm doing, from forming the nailhead to cooling it off in the bucket of water (quenching).

Behold my off-centered nail!

Alexei Borodin giving a version of his lesson on YouTube. He starts instructing the first "apprentice" at 26:25, and hammering begins at 28:30.

Here is Yuri Borodin's lesson on YouTube.

The last place I visited in Vladimir was a monument to Prince Vladimir (on the horse) and St. Theodore near the Assumption Cathedral. At sunset there were amazing lights and clouds behind the building.

First refuelling for Russia’s Akademik Lomonosov floating NPP

!{Model.Description}

The FNPP includes two KLT-40S reactor units. In such reactors, nuclear fuel is not replaced in the same way as in standard NPPs – partial replacement of fuel once every 12-18 months. Instead, once every few years the entire reactor core is replaced with and a full load of fresh fuel.

The KLT-40S reactor cores have a number of advantages compared with standard NPPs. For the first time, a cassette core was used, which made it possible to increase the fuel cycle to 3-3.5 years before refuelling, and also reduce by one and a half times the fuel component in the cost of the electricity produced. The operating experience of the FNPP provided the basis for the design of the new series of nuclear icebreaker reactors (series 22220). Currently, three such icebreakers have been launched.

The Akademik Lomonosov was connected to the power grid in December 2019, and put into commercial operation in May 2020.

Electricity generation from the FNPP at the end of 2023 amounted to 194 GWh. The population of Pevek is just over 4,000 people. However, the plant can potentially provide electricity to a city with a population of up to 100,000. The FNPP solved two problems. Firstly, it replaced the retiring capacities of the Bilibino Nuclear Power Plant, which has been operating since 1974, as well as the Chaunskaya Thermal Power Plant, which is more than 70 years old. It also supplies power to the main mining enterprises located in western Chukotka. In September, a 490 km 110 kilovolt power transmission line was put into operation connecting Pevek and Bilibino.

Image courtesy of TVEL

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Standards for Mathematical Practice #

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up : adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

Standards in this domain: #

Ccss.math.practice.mp1 make sense of problems and persevere in solving them. #.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

CCSS.Math.Practice.MP2 Reason abstractly and quantitatively. #

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize —to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize , to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. #

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

CCSS.Math.Practice.MP4 Model with mathematics. #

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

CCSS.Math.Practice.MP5 Use appropriate tools strategically. #

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

CCSS.Math.Practice.MP6 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.

CCSS.Math.Practice.MP7 Look for and make use of structure. #

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x_2 + 9_x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3( x - y )2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y .

CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning. #

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation ( y - 2)/( x - 1) = 3. Noticing the regularity in the way terms cancel when expanding ( x - 1)( x + 1), ( x - 1)(_x_2 + x + 1), and ( x - 1)(_x_3 + _x_2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content #

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.

The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.

In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics.

Victor Mukhin

• Scientific Program

Title : Active carbons as nanoporous materials for solving of environmental problems

However, up to now, the main carriers of catalytic additives have been mineral sorbents: silica gels, alumogels. This is obviously due to the fact that they consist of pure homogeneous components SiO2 and Al2O3, respectively. It is generally known that impurities, especially the ash elements, are catalytic poisons that reduce the effectiveness of the catalyst. Therefore, carbon sorbents with 5-15% by weight of ash elements in their composition are not used in the above mentioned technologies. However, in such an important field as a gas-mask technique, carbon sorbents (active carbons) are carriers of catalytic additives, providing effective protection of a person against any types of potent poisonous substances (PPS). In ESPE “JSC "Neorganika" there has been developed the technology of unique ashless spherical carbon carrier-catalysts by the method of liquid forming of furfural copolymers with subsequent gas-vapor activation, brand PAC. Active carbons PAC have 100% qualitative characteristics of the three main properties of carbon sorbents: strength - 100%, the proportion of sorbing pores in the pore space – 100%, purity - 100% (ash content is close to zero). A particularly outstanding feature of active PAC carbons is their uniquely high mechanical compressive strength of 740 ± 40 MPa, which is 3-7 times larger than that of  such materials as granite, quartzite, electric coal, and is comparable to the value for cast iron - 400-1000 MPa. This allows the PAC to operate under severe conditions in moving and fluidized beds.  Obviously, it is time to actively develop catalysts based on PAC sorbents for oil refining, petrochemicals, gas processing and various technologies of organic synthesis.

Victor M. Mukhin was born in 1946 in the town of Orsk, Russia. In 1970 he graduated the Technological Institute in Leningrad. Victor M. Mukhin was directed to work to the scientific-industrial organization "Neorganika" (Elektrostal, Moscow region) where he is working during 47 years, at present as the head of the laboratory of carbon sorbents.     Victor M. Mukhin defended a Ph. D. thesis and a doctoral thesis at the Mendeleev University of Chemical Technology of Russia (in 1979 and 1997 accordingly). Professor of Mendeleev University of Chemical Technology of Russia. Scientific interests: production, investigation and application of active carbons, technological and ecological carbon-adsorptive processes, environmental protection, production of ecologically clean food.   

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