Mathematics
Grade 6
15 min
Related addition facts
Related addition facts
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1
Introduction & Learning Objectives
Learning Objectives
Identify the commutative property of addition and apply it to simplify calculations.
Apply the associative property of addition to efficiently group numbers for easier sums.
Recognize and utilize the inverse relationship between addition and subtraction.
Use related addition facts to solve for unknown variables in simple equations.
Develop mental math strategies based on the properties of related addition facts.
Explain how related addition facts can be used to verify the correctness of addition and subtraction problems.
Ever notice how changing the order of numbers in an addition problem doesn't change the answer? 🤔 Or how knowing 5 + 3 helps you solve 8 - 3 instantly?
In this lesson, you'll explore 'related addition facts,' which a...
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Key Concepts & Vocabulary
TermDefinitionExample
Related Addition FactsA set of addition and subtraction equations that use the same three numbers, showing their mathematical relationship.For the numbers 3, 5, and 8, the related facts are 3+5=8, 5+3=8, 8-3=5, and 8-5=3.
Commutative Property of AdditionThe property that states that changing the order of addends (the numbers being added) does not change the sum (the total).$a + b = b + a$, so $7 + 4 = 4 + 7 = 11$.
Associative Property of AdditionThe property that states that changing the grouping of addends (using parentheses) does not change the sum when adding three or more numbers.$(a + b) + c = a + (b + c)$, so $(2 + 3) + 5 = 2 + (3 + 5) = 10$.
Inverse OperationsOperations that undo each other. Addition and subtraction are inverse operations.If $5 + 2 = 7$, then...
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Core Formulas
Commutative Property of Addition
$a + b = b + a$
You can swap the order of any two numbers being added, and the sum will remain exactly the same. This property is useful for rearranging numbers to make mental calculations easier.
Associative Property of Addition
$(a + b) + c = a + (b + c)$
When adding three or more numbers, you can group them in any way (using parentheses to show which operation to do first), and the final sum will not change. This helps in combining numbers that are easy to add together first.
Inverse Relationship of Addition and Subtraction
If $a + b = c$, then $c - a = b$ and $c - b = a$.
Addition and subtraction are opposite operations. Knowing an addition fact immediately provides you with two related subtraction facts, and vice-versa. This rela...
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Challenging
Based on the Associative Property of Addition, what must be the value of n in the equation (41 + 19) + 25 = 41 + (n + 25)?
A.41
B.19
C.25
D.60
Challenging
A fact family involves the integers -8, 5, and -3. Which of the following equations is NOT a valid member of this fact family?
A.-8 + 5 = -3
B.5 + (-8) = -3
C.-3 - 5 = 8
D.-3 - (-8) = 5
Challenging
To most efficiently calculate the sum 350 + 188 + (-50), what is the best first step and which property justifies it?
A.Add 350 + (-50) first, justified by the Commutative and Associative Properties.
B.Add 188 + (-50) first, justified by the Associative Property.
C.Add the numbers from left to right as they appear.
D.Subtract 50 from 188, justified by the Inverse Property.
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