Using Properties for Mental Addition
Using Properties for Mental Addition is a Grade 4 math skill in enVision Mathematics, Chapter 2: Fluently Add and Subtract Multi-Digit Whole Numbers. Students apply the commutative and associative properties to develop Make Ten and Add On mental math strategies for large number addition.
Key Concepts
Property The Associative Property of Addition states that changing the grouping of addends does not change the sum: $(a + b) + c = a + (b + c)$. The Commutative Property of Addition states that changing the order of addends does not change the sum: $a + b = b + a$. These properties allow us to break apart and regroup numbers to make addition easier.
Make Ten Strategy: To find $4875 + 3007$, you can break apart $3007$ into $125 + 2882$ (so that $4875 + 125$ makes a thousand). Then, group the $125$ with the $4875$ to make $5000$. $$ 4875 + 3007 = 4875 + (125 + 2882) = (4875 + 125) + 2882 = 5000 + 2882 = 7882 $$.
Common Questions
What is the Make Ten strategy for mental addition?
Break apart one addend so that it combines with the other addend to make a friendly number like 1,000. For example, 4875 plus 3007: break 3007 into 125 plus 2882, then add 4875 plus 125 to get 5000, then add 2882.
What is the Add On strategy for mental addition?
Break one addend into its place value parts (thousands, hundreds, tens, ones) and add them one at a time to the other addend sequentially.
How does the associative property help with mental addition?
The associative property lets you regroup addends so you can add the easiest combination first. For example, (4875 plus 125) plus 2882 is easier than adding in the original order.
What is an example of the Add On strategy?
To find 4623 plus 3574, add 3000 to get 7623, then 500 to get 8123, then 70 to get 8193, then 4 to get 8197.
What chapter covers mental addition properties in enVision Mathematics Grade 4?
Using properties for mental addition is covered in Chapter 2: Fluently Add and Subtract Multi-Digit Whole Numbers in enVision Mathematics Grade 4.