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The student uses the order and zero properties to fill blanks without computing, and knows why the sum does not change.
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Swap the addends around and the sum stays exactly the same.
Take a look at this sum: . If we flip the numbers and calculate , we get the exact same result.
Remember: When we change the order of the addends, the sum remains the same.
How to fill an equation with a missing number on each side.
Problem. Solve and fill in the blanks without performing addition:
Four order-property blanks from Worksheet 2.
For problem (a), the equation 75,361 + 2,135 = 2,135 + blank can be solved without adding. The missing number is . In problem (c), 92,501 + 123 + 111 = 111 + 92,501 + blank, the missing addend is . Looking at (d), 21,511 + 222 + 11,333 = 21,511 + blank + 222, we know the missing value is because the order does not change the sum. Problem (f) has two blanks: blank + 615 + 62 = 617 + blank + 615. By matching the numbers on both sides, the first missing number on the left side is , and the second missing number on the right side is .
Zero added to a number, either way round, leaves it alone.
Look at these simple equations: and . What do you notice? Adding zero to a number leaves it completely unchanged.
The page 22 fill-ins plus the zero items from Worksheet 2.
Just like the book shows with 7 + 0 = 7 and 0 + 15 = 15, adding zero leaves a number unchanged. For example, 25 + 0 equals , and 0 + 372 equals . With larger numbers, 75,312 + 0 simply gives , and 0 + 52,341 is . We can also use properties of addition to fill blanks on both sides of an equals sign. For instance, 5,79,301 + 0 = 0 + blank means the missing number is . Similarly, if 0 + 2,571 = 2,571 + blank, the blank must be . Finally, if 723 + blank = 723, we know we must add to keep the number the exact same.