Lesson 3: Name numbers within 1 million by building understanding of the place value chart and placement of commas for naming base thousand units.

Property

Large numbers are read by grouping digits into periods of three, starting from the right, with commas separating each period. Each period has a name (e.g., million, thousand). Read the number within each period from left to right, followed by its name, omitting the name for the ones period.

Examples

• The number $452,198$ is read as "four hundred fifty-two thousand, one hundred ninety-eight". You read the number in the thousands period ($452$) and then the number in the ones period ($198$).

Property

Adding place value units can result in a sum of 10 or more of that unit, which can be bundled to compose the next larger unit. For example, 10 tens can be bundled to make 1 hundred, and 10 hundred thousands can be bundled to make 1 million. This is the foundation of carrying over in addition.

Examples

• $2 \text{ hundred thousands} + 8 \text{ hundred thousands} = 10 \text{ hundred thousands} = 1 \text{ million}$
• $5 \text{ ten thousands} + 6 \text{ ten thousands} = 11 \text{ ten thousands} = 1 \text{ hundred thousand} + 1 \text{ ten thousand} = 110,000$
• $23 \text{ thousands} + 4 \text{ ten thousands} = 2 \text{ ten thousands and } 3 \text{ thousands} + 4 \text{ ten thousands} = 6 \text{ ten thousands and } 3 \text{ thousands} = 63,000$

Explanation

This skill focuses on adding numbers expressed in unit form. When you add quantities of the same place value unit, you can sometimes create a group of ten, which allows you to "bundle" them into the next larger place value unit. This is the same principle as carrying over in standard addition and reinforces the relationship between adjacent place values. Understanding this helps you perform mental math and builds a flexible understanding of how numbers are composed.

Property

Each place value is 10 times greater than the place value to its immediate right.
Therefore, multiplying a number by 10 shifts each of its digits one place to the left, increasing the number's total value by a factor of 10.

Examples