Place Value Operations with Two Units
Place Value Operations with Two Units is a Grade 4 math skill that teaches students to perform addition and subtraction involving two different place value units simultaneously, applying the like-units principle to each column. For example, 4 tens 3 ones + 2 tens 5 ones = 6 tens 8 ones, or 68 in standard form. Students work with units in both expanded notation and standard form to build flexibility. Covered in the early chapters of Eureka Math Grade 4, this skill solidifies place value decomposition and composition as prerequisite knowledge for multi-digit arithmetic.
Key Concepts
Property To multiply or divide a number with multiple units by 10, apply the operation to each unit separately. For example: $10 \times (3 \text{ thousands } 2 \text{ hundreds}) = (10 \times 3 \text{ thousands}) + (10 \times 2 \text{ hundreds})$.
Examples Find the value of $10 \times (2 \text{ thousands } 4 \text{ hundreds})$. $10 \times 2 \text{ thousands } = 2 \text{ ten thousands}$ $10 \times 4 \text{ hundreds } = 4 \text{ thousands}$ So, the result is $2 \text{ ten thousands } 4 \text{ thousands}$, which is $24,000$.
Find the value of $(5 \text{ ten thousands } 3 \text{ thousands}) \div 10$. $5 \text{ ten thousands } \div 10 = 5 \text{ thousands}$ $3 \text{ thousands } \div 10 = 3 \text{ hundreds}$ So, the result is $5 \text{ thousands } 3 \text{ hundreds}$, which is $5,300$.
Common Questions
What are two-unit place value operations?
Two-unit place value operations involve adding or subtracting numbers that each have two different place value components, such as tens and ones. You add or subtract each unit type separately: tens with tens, ones with ones.
How do I add 4 tens 3 ones plus 2 tens 5 ones?
Add the tens: 4 tens + 2 tens = 6 tens. Add the ones: 3 ones + 5 ones = 8 ones. Combine: 6 tens 8 ones = 68. Keeping the units separate prevents place value errors.
What is the like units principle in place value addition?
The like units principle states that you can only directly add or subtract units of the same type. Tens can only be added to tens, hundreds to hundreds, and so on. This principle underlies both fraction addition and whole number place value operations.
How does place value unit notation connect to standard form?
Place value unit notation (4 tens 3 ones) makes the structure of a number explicit, while standard form (43) compresses it. Converting between these forms reinforces understanding that each digit has a specific positional value determined by its place.
Why is working with two-unit place value important in Grade 4?
Two-unit operations build the mental model needed for multi-digit addition and subtraction. Students who understand that 4 tens + 3 tens = 7 tens can extend this to 400 + 300 = 700 and handle regrouping more confidently.
What chapter introduces two-unit place value operations in Eureka Math Grade 4?
Place value operations with two units are covered in the opening chapters of Eureka Math Grade 4, which establish multi-digit place value as the foundation for all four operations introduced in later chapters.