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

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 
  • Algebra
  • Geometry
  • Statistics
  • 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
  • Geometry
Download Free Resources

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.

Download Free Now!

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. 

Third Space Learning common core math example
Third Space Learning Common Core math lesson for 6th grade

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?

common core math example

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?

fraction worked example
number line worked example

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.

math problem explained

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.

multiplication box worked example using common core standard 7

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.

example of long multiplication
example of long multiplication using the common core standard 8

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: 

Summative assessments include: 

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

Assessment resources:

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 math strategies for 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

What are the 8 mathematical practices in Common Core?

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

What are the three Common Core math shifts?

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.

How many states use Common Core math?

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.

Do you have students who need extra support in math?
Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor.

Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way.

Personalized one-on-one math tutoring programs are available for:
2nd grade tutoring
3rd grade tutoring
4th grade tutoring
5th grade tutoring
6th grade tutoring
7th grade tutoring
8th grade tutoring

Why not learn more about how it works?


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.