Numbers are mathematical objects used to count, measure, and label. They can be classified into different types, such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

Natural numbers are the counting numbers, such as 1, 2, 3, 4, and so on. They do not include negative numbers or fractions.

Whole numbers include all the natural numbers along with zero, such as 0, 1, 2, 3, 4, and so on. They do not include negative numbers or fractions.

Integers include all the whole numbers as well as their negative counterparts, such as ..., -3, -2, -1, 0, 1, 2, 3, ...

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. For example, 1/2, 3/4, -2/5, etc.

Irrational numbers are numbers that cannot be expressed as a simple fraction, such as the square root of 2 or pi (π).

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.