Mathematics
Grade 6
15 min
Complete addition and subtraction sentences
Complete addition and subtraction sentences
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1
Introduction & Learning Objectives
Learning Objectives
Identify the unknown value in an addition or subtraction sentence.
Apply inverse operations to solve for the unknown in addition sentences.
Apply inverse operations to solve for the unknown in subtraction sentences.
Solve addition and subtraction sentences involving positive and negative integers.
Verify their solutions by substituting the unknown value back into the original sentence.
Construct addition and subtraction sentences from given word problems.
Ever wonder how detectives solve mysteries? 🕵️♀️ In math, we're often detectives too, trying to find a missing number!
This lesson will teach you how to find the missing number in addition and subtraction problems, turning incomplete math statements into complete, true sentences. Mastering this sk...
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Key Concepts & Vocabulary
TermDefinitionExample
Mathematical SentenceA statement that shows the relationship between numbers and operations, often an equation or inequality.5 + 3 = 8 or x - 2 = 7
Unknown/VariableA symbol (usually a letter like x, y, or n) that represents a missing or unknown number in a mathematical sentence.In 7 + n = 10, 'n' is the unknown.
EquationA mathematical sentence that states two expressions are equal, using an equals sign (=).12 - x = 5
Inverse OperationsOperations that 'undo' each other. Addition is the inverse of subtraction, and subtraction is the inverse of addition.To undo adding 5, you subtract 5. To undo subtracting 3, you add 3.
Balancing an EquationThe principle that whatever operation is performed on one side of an equation must also be performed on the oth...
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Core Formulas
Rule for Solving Addition Sentences
If $a + x = b$, then $x = b - a$.
To find an unknown addend, subtract the known addend from the sum. This involves performing the inverse operation (subtraction) on both sides of the equation to isolate the unknown.
Rule for Solving Subtraction Sentences (Unknown Minuend)
If $x - a = b$, then $x = b + a$.
To find the unknown starting number (minuend), add the subtrahend (the number being subtracted) and the difference (the result). This is done by adding 'a' to both sides of the equation.
Rule for Solving Subtraction Sentences (Unknown Subtrahend)
If $a - x = b$, then $x = a - b$.
To find the unknown number being subtracted (subtrahend), subtract the difference (the result) from the minuend (the starting number). This can...
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Challenging
In the equation a - b = c, if 'a' is a negative integer and 'c' is a positive integer that is larger than the absolute value of 'a', what must be true about 'b'?
A.b must be a negative integer.
B.b must be a positive integer.
C.b must be zero.
D.b can be positive or negative.
Challenging
The solution to the equation 15 - x = 32 is the same as the solution to the equation y + 8 = k. What is the value of k?
A.k = 25
B.k = -9
C.k = 9
D.k = -25
Challenging
A student is solving 20 - n = -5. Their first step is to write '-n = -5 + 20'. What conceptual error did they make?
A.They used the wrong inverse operation for 20.
B.They should have added n to both sides.
C.They did not keep the equation balanced.
D.They made a sign error on the -5.
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