The identity property, also known as the identity element, is a fundamental concept in mathematics that applies to both addition and multiplication.

**Identity Property of Addition:**The identity property of addition states that when you add a number to zero, the sum is the original number. In other words, the identity element for addition is 0. This can be written as:

a + 0 = a

where "a" is any number.

**Identity Property of Multiplication:**Similarly, the identity property of multiplication states that when you multiply a number by 1, the product is the original number. The identity element for multiplication is 1, and it can be expressed as:

a * 1 = a

where "a" is any number.

These properties are important because they help us understand the behavior of numbers when they are combined using addition or multiplication. They provide the foundation for more complex mathematical operations and are essential in algebra and higher-level mathematics.

.Study GuideRegrouping Worksheet/Answer key

Regrouping Worksheet/Answer key

Regrouping Worksheet/Answer key

Regrouping

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.

Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Connections to the Grade 3 Focal Points (NCTM)

Number and Operations: Building on their work in grade 2, students extend their understanding of place value to numbers up to 10,000 in various contexts. Students also apply this understanding to the task of representing numbers in different equivalent forms (e.g., expanded notation). They develop their understanding of numbers by building their facility with mental computation (addition and subtraction in special cases, such as 2,500 + 6,000 and 9,000 - 5,000), by using computational estimation, and by performing paper-and-pencil computations.