We have a base-10 number system. That means we can use 9 digits plus place-holder zeros to represent any quantity.
In standard form, numbers can only have one digit in each place. If there are 9 units in a place and one more is added, those 10 units will be composed into 1 unit in the next larger place.
This is the most basic understanding of numbers students develop from kindergarten through the 5th grade.
In the 3rd grade, children build on their work with number forms to compose and decompose 4-digit numbers. With rounding, this is one of the most challenging skills in 3rd grade math!
MA.3.NSO.1.2 I can compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens, and ones. I can demonstrate each composition or decomposition using objects, drawings, and expressions or equations.
Composing 4-Digit Numbers
Composing 4-digit numbers in 3rd grade can be easier than decomposing them. Since each place can only have one digit, groups of 10 smaller units (ones, tens, or hundreds) are composed to make 1 larger unit in the next greater place. 10 ones compose 1 ten. 10 tens compose 1 hundred, and 10 hundreds compose 1 thousand.
Activities to support this understanding include making bundles or groups of 10 units and regrouping them into the next place to convert a quantity into standard form with one digit in each place.
It is a little more challenging when there are multiple groups of ten in a place, or there are more than 9 in multiple places. Students should learn to work from the ones place to the left and can explore the number of steps it can take to compose 4-digit numbers.
For example, given 1 thousand, 1 hundred, 9 tens, and 22 ones, 10 ones can be composed into a ten. There is now 1 thousand, 1 hundred, 10 tens, and 12 ones. It will take two more steps of composing to have one digit in each place.
Decomposing 4-Digit Numbers
Decomposing 4-digit numbers and understanding equivalence is challenging because students have to hold more than 10 units in a place. With 4-digit numbers there can be almost unlimited combinations of units that a number can be decomposed into.
3rd grade students need plenty of opportunities to work hands-on with place value mats and base-10 blocks or place value disks before transitioning to work with numerals only.
This skill is important conceptually because numbers aren’t just collections of digits. They represent a quantity, which is a concrete collection of units that can be manipulated into multiple different forms.
More importantly, being able to hold more than one digit briefly in a place allows students to perform addition and subtraction algorithms that require decomposing or composing 4-digit numbers to obtain a sum or difference.
Standards
As discussed in an earlier post, the Common Core Standards don’t specify that 3rd graders will work with 4-digit numbers. The Texas Essential Knowledge Standard go through 5-digit numbers for 3rd graders, which is one place higher than Florida’s BEST expectations.
Regardless of the magnitude of the numbers worked with in 3rd grade, the ability to compose and decompose units across places build flexible thinking about number quantities and a deep understanding of number sense. It is also a crucial preliminary skill to adding and subtracting 3- and 4-digit numbers when composing or decomposing is needed in one or more places.
3rd graders are getting ready to transition to adding and subtracting using algorithms and multiple numeral-based strategies. Decomposing and composing 4-digit numbers will prepare them for success!
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