 ## Grade 4 Math: Place Value and Expanded Notation

### Read and Write with Place Value to 10,000

Place value concepts for 4-digit numbers are reviewed, using the Place Value Table used in earlier lessons. The basic concept is that the place of a digit in a number represents the value of that number, and that a unit in each place to the left represents ten units in the place to its right.

The ten thousands place is introduced. A digit in the ten thousands place is used to indicate ten thousands.

Three ways of writing numbers is illustrated: 1) the number of units in each place in the Place Value Table, 2) the value of each number in each place in the Place Value Table expressed as a sum (expanded notation), and 3) the number written in standard notation.

Students are then required to write numbers illustrated in a Place Value Table in each of these forms.

### Identify Place Values to 10,000

In this lesson, students use what they learned in the prior lesson about place values in four-digit numbers. They learn to make each of two judgments, given a four-digit number:

• They identify the name of the place value of a specified digit in a four-digit number.
• They identify the digit that has a specified place value in a four-digit number.

### Find Missing Number in Expanded Notation

In this lesson, expanded notation for five-digit numbers is introduced. Students extend their knowledge of place value for four-digit numbers by learning to write four-digit numbers in expanded notation.

They learn to identify the missing value in a number written in expanded notation. Special attention is given to numbers that have zeros in one or more places.

In the last lesson, students learn to identify the value of a single digit in a five-digit number when it is written in expanded notation. In this lesson, students extend their understanding of expanded notation for five-digit numbers by writing the entire five-digit number in expanded notation.

They learn to rewrite a number with up to five digits given in expanded notation in standard notation. Special attention is given to numbers that have zeros in one or more places.

In this lesson, two additional place values are introduced: hundred thousands and millions. Students learn to read six- and seven-digit numbers in a Place Value Table and write them in standard notation.

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