Numbers are mathematical entities used to count, measure, and label. They are essential in everyday life for tasks such as telling time, counting money, and measuring quantities. In mathematics, numbers are classified into different types, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Natural numbers are the counting numbers, starting from 1 and continuing indefinitely (1, 2, 3, 4, ...). They are used for counting objects and are always positive.

Whole numbers include all the natural numbers along with zero (0, 1, 2, 3, ...). They are used to represent quantities that do not involve fractions or decimals.

Integers are the set of whole numbers and their negative counterparts, along with zero (... -3, -2, -1, 0, 1, 2, 3 ...). They are used to represent both positive and negative quantities.

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They can be written in the form a/b, where a and b are integers and b is not equal to zero. Rational numbers include fractions and terminating or repeating decimals.

Irrational numbers cannot be expressed as a fraction of two integers. They are non-repeating, non-terminating decimals and cannot be written as a simple fraction. Examples of irrational numbers include the square root of non-perfect squares and constants such as π (pi) and e (Euler's number).

Understanding the different types of numbers is fundamental to many areas of mathematics and is crucial for solving various mathematical problems.

For example, in arithmetic, numbers are used for basic operations such as addition, subtraction, multiplication, and division. In algebra, numbers are used as variables and constants in equations and expressions. In geometry, numbers are used to represent measurements and dimensions of shapes and figures.

Overall, numbers play a vital role in mathematics and are essential for solving a wide range of problems in everyday life and in various fields of study.

Study GuideSubtraction Facts Worksheet/Answer key

Subtraction Facts Worksheet/Answer key

Subtraction Facts Worksheet/Answer key

Subtraction Facts Worksheet/Answer keySubtraction Facts Worksheet/Answer keyAddition and Subtraction Vocabulary/Answer keySubtraction Facts

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.

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.