Numbers are mathematical objects used to count, measure, and label. They can be used to represent quantities, order, and patterns.

There are several types of numbers, including:

- Whole Numbers: 0, 1, 2, 3, ...
- Integers: ... -3, -2, -1, 0, 1, 2, 3, ...
- Rational Numbers: Numbers that can be expressed as a fraction, such as 1/2, 3/4, 5/2, etc.
- Real Numbers: All rational and irrational numbers, such as √2, π, etc.

Numbers have various properties, including:

- Commutative Property: a + b = b + a
- Associative Property: (a + b) + c = a + (b + c)
- Distributive Property: a * (b + c) = a * b + a * c
- Identity Property: a + 0 = a, a * 1 = a
- Inverse Property: a + (-a) = 0, a * (1/a) = 1

Numbers are made up of digits, and the position of each digit in a number determines its value. This is known as place value.

For example, in the number 3,215, the digit 3 is in the thousands place, the digit 2 is in the hundreds place, the digit 1 is in the tens place, and the digit 5 is in the ones place.

Basic number operations include addition, subtraction, multiplication, and division. These operations follow specific rules and properties.

Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves. Composite numbers are numbers that have more than two positive divisors.

Even numbers are integers that are divisible by 2, while odd numbers are integers that are not divisible by 2.

Study GuidePatterns Worksheet/Answer key

Patterns Worksheet/Answer key

Patterns Worksheet/Answer key

Patterns Worksheet/Answer keyPatterns and Algebra

Algebra (NCTM)

Understand patterns, relations, and functions.

Describe, extend, and make generalizations about geometric and numeric patterns.

Represent and analyze patterns and functions, using words, tables, and graphs.

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.

Analyze change in various contexts.

Identify and describe situations with constant or varying rates of change and compare them.

Connections to the Grade 4 Focal Points (NCTM)

Algebra: Students continue identifying, describing, and extending numeric patterns involving all operations and nonnumeric growing or repeating patterns. Through these experiences, they develop an understanding of the use of a rule to describe a sequence of numbers or objects.