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Why operations and algebraic thinking is important


21 December 2020

Reading Time: 3 Minutes


There are four basic operations in mathematics: Addition, Subtraction, Multiplication, and Division. They form the basis of operations and algebraic thinking.

You already know simple math problems like 25/5 = 5. But do you know what do they really mean? For example, 38=24. That’s like saying 24 is 3 times more than 8 and 24 is 8 times more than 3.

Think about it this way. Phineas has 24 crayons and Ferb has only 8 crayons. So, Phineas has 3 times more crayons than Ferb because of 8+8+8=24 or 83=24.

In this article, you will understand how operations and algebraic thinking in grade 5 are used to develop your math skills and increase your understanding of math’s basic operations.

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📥 Why operations and algebraic thinking is important


What is Algebraic Thinking?

To ensure that students flourish and succeed when they arrive at the formal study of algebra, the development of algebraic thinking is essential in the mathematics curriculum from kindergarten to high school.

Algebraic thinking includes recognizing and analyzing patterns, studying and representing relationships, making generalizations, and analyzing how things change. It would help if you learned how to use algebraic symbols efficiently to become proficient in algebra.

At a young age, children have a natural curiosity to recognize and work with patterns. They start making generalizations about patterns that seem to be the same or different. Then as they proceed to middle grades, they can connect their learned patterns to numbers, operations, and expressions.

What is Algebraic Thinking image

Operations and Algebraic Thinking for Grade 5

Operations and algebraic thinking in grade 5 involve two important aspects:

  • Writing and Interpreting numerical expressions
  • Analyzing patterns and relationships

Writing and Interpreting numerical expressions

It involves:

  • Using parentheses, brackets, braces, etc. in numerical expressions and evaluating expressions that contain these symbols. For example, 3(4+7) =311=33
  • Writing simple expressions that represent calculations with numbers and interpreting numerical expressions without evaluating them. For example, “add 4 to 3 and double the result” can be written numerically as 2(4+3).

Analyzing patterns and relationships

It involves generating two numerical terms according to the given rules and then finding out apparent relationships between the two terms. Thes two terms can form an ordered pair. This ordered pair can then be represented on the co-ordinate axis. 

For example, given the rule “add 5” and starting number 2 and given the rule “add 3” and starting number 11.

1.  2+5=7

2.  11+3=14

Observe the relationship that the term in the second sequence is twice of the term in first one.


Let’s solve some practice example questions that will help us to learn concepts better.

1. Evaluate the expression 4(9+6-2)


Let’s first evaluate the expression inside the parentheses. You should always solve the expression in parentheses first and then gradually move out. Here,


= 13

Now, multiply 4 to the evaluated term from the parentheses. 


2. Record the expression: Three times the sum of 68 and 28


Let’s focus on the latter part of the expression. You need the sum of 68 and 28. It can be written as 68+28.

Now, you know that this is not the final answer so you should put pare theses around this, i.e., (68+28).
According to the question, you need three times the sum of 68 and 28. So, the final recorded expression is 


3. Evaluate the two patterns and find the relationship between them.
    Pattern x : Starting number = 5, Rule = Add 5.
    Pattern y : Starting number = 10, Rule = Multiply 2.


Pattern x: You have to add 5 to the starting number 5. 


Pattern y : You have to multiply 2 with the starting number 10.


Pattern x evaluates to 10 and pattern y evaluates to 20. What is the apparent relationship between the two?

Yes, y is two times of x!


In this article, you learned what algebraic thinking is and how to apply it in problems. Then you learned about the concepts of algebraic thinking in grade 5 through the help of some examples and questions. 

Operations and algebraic thinking of grade 5 is easy if you have the basic functions of mathematics clear in your head. You can get better by practicing more and solving more algebraic thinking worksheets.

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FAQs on Algebraic thinking

What is algebraic thinking?

Algebraic thinking is about recognizing and analyzing patterns, studying and representing relationships, making generalizations, and analyzing how things change. A good foundation of algebraic thinking helps in further formal studies in algebra and higher mathematics.

How to learn algebraic thinking?

The best way to learn algebraic thinking is to practice the basic operations of mathematics and solving practice problems related to it from your textbooks and homework assignments. You can also take the help of resources such as youtube videos, blogs etc. to understand algebraic expressions better.

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