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 GuideDecimals/Fractions Activity LessonOrdering Decimals & Fractions Activity LessonPercent Grids Activity LessonFraction & Percent Circles Worksheet/Answer key

Decimals/Fractions Worksheet/Answer key

Decimals/Fractions Worksheet/Answer key

Decimals/Fractions Worksheet/Answer keyDecimals/Fractions Worksheet/Answer keyPercent Grids Vocabulary/Answer keyDecimals/Fractions

Number and Operations (NCTM)

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

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

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.

Grade 4 Curriculum Focal Points (NCTM)

Number and Operations: Developing an understanding of decimals, including the connections between fractions and decimals

Students understand decimal notation as an extension of the base-ten system of writing whole numbers that is useful for representing more numbers, including numbers between 0 and 1, between 1 and 2, and so on. Students relate their understanding of fractions to reading and writing decimals that are greater than or less than 1, identifying equivalent decimals, comparing and ordering decimals, and estimating decimal or fractional amounts in problem solving. They connect equivalent fractions and decimals by comparing models to symbols and locating equivalent symbols on the number line.