Counting is the process of determining the number of elements in a set or group. It is a fundamental concept in mathematics and is used in various mathematical operations and problem-solving situations.

Counting numbers, also known as natural numbers, are the set of numbers used for counting and ordering. They start from 1 and continue indefinitely (1, 2, 3, 4, ...).

There are several counting principles that are used in mathematics, including:

**One-to-One Correspondence:**This principle states that each item in one set can be paired with exactly one item in another set without leaving any out or pairing any item with more than one item.**Counting by Multiples:**This involves counting numbers by adding a fixed number each time (e.g., counting by twos: 2, 4, 6, 8, ...).**Counting Backwards:**This involves counting in reverse order, subtracting a fixed number each time.

There are various techniques used for counting, including:

**Counting by Tally Marks:**Tally marks are used to count by making a mark for each item counted, with groups of five marks represented by a cross mark.**Counting by Grouping:**This involves grouping items into sets of a fixed number and counting the sets to determine the total count.**Counting using Number Lines:**Number lines can be used to visually represent the counting process and determine the position of numbers in relation to each other.

- Count the number of apples in the following image:
- If you count by threes starting from 3, what is the 6th number you would say?
- Using tally marks, count the number of birds you see in the park: |||| ||| ||

By understanding the principles and techniques of counting, you can develop a strong foundation in mathematics and apply counting skills to various real-world scenarios.

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.