The state of California first adopted common core math standards or principles. Later on, these standards were adopted by the 43 states. Now a question arises: What are common core math standards? These are the standards for students studying in kindergarten to class 8 students. These are the standards that students should know. It focuses on learning fewer concepts but in more depth.

These concepts were made in 2009 and 2010 by the two state groups, the National Governor Association and the Council of Chief state school offices. It took about 18 months to write these standards, and they focused on using the common core as “state tests.” These standards primarily focus on the three key features, which were:

- Focus on fewer topics
- Linking the topics and thinking across the grades
- pursue only conceptual understandings and procedural skills.

Common core is considered suitable for the education system because it not only focuses on middle-level school students but also prepares students for college and global world success. After implementing these standards, there have been many debates, and many states did not adopt them in their education system. But slowly, after seeing the result, some states changed their mind, but still, many don’t follow these standards.

**What is common core math **– Explained

Common core mathematics, or core mathematics**,** is a collection of some math standards that encourage students to think critically and solve math problems differently.

Common core math encourages students to understand the reason or intent behind the equations rather than just solving them and know why a particular approach worked to solve the equations.

## 10 **Common Core Math** Standards

**Writing and Interpreting Numerical Expressions:**

In Numerical expressions, try using Brackets, Bars, or braces and evaluate the mathematical expressions with these symbols. You need to write some basic mathematical equations that involve the use of calculation with numbers and interpret the numerical expression without evaluating it.

**Common core math example**, Express the calculation “add 2 and 7, then multiply it by 5,” so this equation in standard mathematical form can be written as 5× (2+7) = 45. You need to understand the question correctly as it says 5× (2+7) is five times as large as 2+7 without calculating the sum or the product.

**Make sense of problems and preserve solving them:**

According to the math standards, the students should always go through the problem correctly and thoroughly. They should first analyze the math problem and then try to interpret it using their mathematical knowledge. Then they should plan a pathway for the solution by thinking about the conjectures rather than simply jumping into the solution. Students must focus more on the facts behind the question rather than just memorizing it.

For example, An almirah was bought for Rs. 14360, and Rs 240 was spent on transportation. At what price should it be sold to gain 15%?

This question would seem complicated for the students, but if they go through the problem correctly and take some time to analyze it, it would become more straightforward for them.

**Analyze proportional relationships and use them to solve real-world mathematical operations:**

Students need to try the unit rates associated with the ratios of fractions, including ratios of lengths and other quantities that may be measured in the same or different units. They also need to represent and analyze the proportional relationship between the two portions and whether the amounts are proportional to each other or are in constant proportionality and then represent the proportional relationship in the form of equations.

To solve the problems of ratio and percentage, you need to use proportional relationships. The basic rule of proportional relationship states that as x increases, y also increases; when x decreases, y also decreases, and the ratio between them always remains the same. By analyzing the proportional relationship, they would be able to solve real-world mathematical problems and benefit them in their career.

**Common core math example**, A man travels at a constant rate. The man travels 300 miles in 4 hours. What is the constant rate of the man? Write an equation to represent the man’s constant rate.

The given problem can be solved by finding the miles per hour that man travels. The constant proportionality can be found by dividing the total miles by the time it is taken; 300÷4 = 75 miles.

The equation can be represented using the general proportional equation, y= 75x.

**Reason abstractly and quantitatively:**

The following common core math standard is to reason abstractly and quantitatively. Before solving any mathematical questions, students must make sense of quantities and their relationships. Students need to understand the reasoning of questions abstractly and quantitatively because it develops a problem-solving opportunity.

There are two parts to reasoning abstractly and quantitatively: Contextualize and Decontextualize. In decontextualizing, the students only need to understand the symbols from the problems rather than the whole problem itself.

For example, Sudha had five choco bars, and Meera gave her four more. How many total choco bars does Sudha have?

By the decontextualization process, students need to only focus on numeric values ignoring the other given facts, 5+4= 9

Whereas Contextualization is the opposite of decontextualization, where the students need to go through all the given information from the above example, they need to understand that Sudha had a total of 5 choco bars and Meera by giving her four more means adding to the original number.

**Create equations that describe numbers or relationships:**

Create the equations and inequalities in one variable and use them to solve the problem. The equations of mathematics can be formed using quadratic or linear equations. Try to make equations with two or more variables to represent the relationships between the quantities. Also, the equations can be expressed in graphs or coordinates for better understanding.

To solve an equation is to find the variable’s value that satisfies the equation. For example, solve for x

0.3x+0.4= 0.28x+1.16

To find the value of x, we need to use the transposition process,

0.3x-0.28x= 1.16-0.4

0.2x= 0.76

Therefore, x= 38 is the solution of the given equation

**Use of appropriate tools strategically:**

Students should know the tools needed to solve a particular problem. Today, various tools are available for students, and finding out the tool that would help them solve a problem is the first step toward finding the solution to the question.

So to use the tools strategically, students should list the tools like pencils, compasses, protractors, calculators, and many similar tools. Doing this helps students not to waste time by searching for tools; it would also be the first big step towards solving any question.

**Common core math examples**, Draw a line parallel to the line and pass through a point.

So, now students need to figure out the tools required for this construction: a scale, a pencil, and a compass.

**Understand solving equations as a process of reasoning and explain the reason:**

It is advisable for the students that before solving any equation, try to understand it by giving various reasons like what formula can be used, what can’t be used, and many more. Doing this helps students understand the concept better than memorizing formulas and equations.

This will help students to remember the concept for a long time, and they will be able to apply practical knowledge for the same. For example, What will be the sign of the product if we multiply together 299 negatives and 20 positive integers?

Since we know that whatever may be the number of positive integers, it will not affect the sign of the product. Since it is given that 299 is an odd number and the product of an odd number of a negative integer is negative, so the given product is negative.

**Attend precision:**

In math study, the essential skill students must develop attending precision. Students from the early class must be taught the language of mathematics because later on, further studies become difficult for the students.

Students learning math language is considered the foundation for most advanced problems. Teachers should give a good understanding of math symbols that are used in the equations.

For example, what will be added to 5, so the number becomes thrice 3?

This question is totally in a math language, so students who are well aware of the math language could solve it quickly. The number 4 must be added to 5 to make the number equal to thrice of 3.

**Look for and make use of structure:**

To solve the most difficult or complex problems, students need to go through the question structure properly so that they will be able to understand the question pattern and try to solve it more straightforwardly. They must go through the structure carefully and smartly to find the solution for the question.

Doing this from a very young age would help the students once they grow up and be given some complex problems. So teachers should help them with this from the very start.

**Common core math examples**, 7×8 is equal to 7×3+7×2

**Define, evaluate and compare mathematical operations:**

Students should be able to define all the mathematical operations they are using in their day-to-day life and also be able to assess them. Since all the mathematical operations are different, some are more complex than others. So, students need to develop this feature of defining it, evaluating it, and comparing it with other mathematical operations.

Doing this will help students in their academics and future learning as well, and they will be able to understand that well throughout their lifetime.

For example, in Linear and quadratic equations, both mathematical operations are different from each other, and both have different functions; in a linear equation, there must be one variable, whereas, for the quadratic equation, there must be two, and more variables.

You may also like to read- Unique ways on how to teach math better

## Final thoughts:

The education system significantly shifted from the commencement of common core math standards. It took a long time to implement these standards, which are considered the best for the education system as it mainly focuses on practical knowledge rather than theoretical knowledge.

The teachers, parents, and students should thoroughly review these standards and try to implement them. The significant role to be played here is by teachers; they should be able to make students understand these practical problems well so that they never get any confusion related to their subject. Parents should also understand what exactly teachers teach their students tricks.

Overall the implementation of these standards has made the education system better. Only a few states have adopted these, but soon they will be adopted worldwide, and students will gain more practical knowledge in mathematics.

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