Understanding the Sum

In mathematics, the term "sum" refers to the result of adding two or more numbers together. It is a fundamental concept that is often introduced in the early stages of learning arithmetic. Understanding how to find the sum of numbers is an important skill that lays the foundation for more advanced mathematical operations.

Finding the Sum

To find the sum of two or more numbers, you simply need to add them together. For example, to find the sum of 3 and 5, you would perform the following addition:

3 + 5 = 8

So, the sum of 3 and 5 is 8. When adding more than two numbers together, you can simply continue to add each number to the running total. For example, to find the sum of 2, 4, and 6:

2 + 4 = 6

6 + 6 = 12

So, the sum of 2, 4, and 6 is 12.

Study Guide for Finding the Sum

Here are some key points to remember when finding the sum of numbers:

Start by writing the numbers in a vertical column, with the ones digits aligned.
Begin adding the numbers from the rightmost column (the ones place) and move to the left, carrying over any excess to the next column.
Continue this process until all numbers have been added together.

Additionally, it's important to practice finding the sum of numbers regularly to build fluency and confidence in this fundamental arithmetic operation.

By understanding the concept of the sum and practicing addition regularly, students can develop a strong foundation in mathematics that will support their learning as they progress to more advanced topics.

◂Math Worksheets and Study Guides First Grade. Commutative Property

Vocabulary/Answer key

Commutative Property

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.

Connect number words and numerals to the quantities they represent, using various physical models and representations.

Understand meanings of operations and how they relate to one another.

Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.

Understand the effects of adding and subtracting whole numbers.

Compute fluently and make reasonable estimates.

Develop and use strategies for whole-number computations, with a focus on addition and subtraction.

Develop fluency with basic number combinations for addition and subtraction.

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Illustrate general principles and properties of operations, such as commutativity, using specific numbers.

Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.

Use mathematical models to represent and understand quantitative relationships.

Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.

Grade 1 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing understandings of addition and subtraction and strategies for basic addition facts and related subtraction facts

Children develop strategies for adding and subtracting whole numbers on the basis of their earlier work with small numbers. They use a variety of models, including discrete objects, length-based models (e.g., lengths of connecting cubes), and number lines, to model 'part-whole,' 'adding to,' 'taking away from,' and 'comparing' situations to develop an understanding of the meanings of addition and subtraction and strategies to solve such arithmetic problems. Children understand the connections between counting and the operations of addition and subtraction (e.g., adding two is the same as 'counting on' two). They use properties of addition (commutativity and associativity) to add whole numbers, and they create and use increasingly sophisticated strategies based on these properties (e.g., 'making tens') to solve addition and subtraction problems involving basic facts. By comparing a variety of solution strategies, children relate addition and subtraction as inverse operations.

Connections to the Grade 1 Focal Points (NCTM)

Number and Operations and Algebra: Children use mathematical reasoning, including ideas such as commutativity and associativity and beginning ideas of tens and ones, to solve two-digit addition and subtraction problems with strategies that they understand and can explain. They solve both routine and nonroutine problems.