Grade 1 · Operations · MAT-01-OPS-011
Unknowns in Addition and Subtraction Equations
Solve addition and subtraction equations with an unknown in different positions.
Learning objectives
What you should be able to do
- Solve addition and subtraction equations with an unknown in different positions.
- Use part-whole reasoning and inverse operations rather than relying on blank position.
- Explain why the equals sign means both sides have the same value.
Prerequisite check
Make sure the foundation is ready.
Checks relationship reasoning.
Checks unknown quantities in context.
Learn
Build the idea from meaning, not memorization.
The unknown can appear anywhere
An equation may be 5+3=__, 5+__=8, __+3=8, 8−3=__, 8−__=5, or __−3=5. The blank position does not determine the operation; the relationship among parts and whole does.
Use the equals sign as balance
The equals sign means the left side and right side have the same value. An equation is true only when both sides balance numerically.
Fact families solve many unknown positions
If 3+5=8, then the same relationship answers 5+__=8, __+3=8, 8−5=__, and 8−__=3.
Check by substitution
After finding an unknown, replace the blank with the value and verify that the equation becomes true.
Interactive math lab
Change it. See what stays true.
Equation Balance
Adjust both sides. Equality means both expressions have the same value.
Balanced: both sides have equal value.
- unknown sum
- unknown addend
- unknown difference
- unknown whole
- substitute check
Worked examples
Twenty different ways to see the concept work.
5+3=__
8Unknown sum.
5+__=8
3Missing addend.
__+3=8
5Missing first addend.
8−3=__
5Unknown difference.
8−__=5
3Unknown subtracted part.
__−3=5
8Unknown starting whole.
7+__=12
512−7=5.
__+6=14
814−6=8.
15−__=9
69+6=15.
__−7=8
158+7=15.
9+4=__
13Compute sum.
__+4=13
9Use inverse subtraction.
13−__=4
9Other part is 9.
13−9=__
4Difference.
10=6+__
4Equality works with total on left.
12=__+5
7Both sides must equal 12.
8=8+__
0Zero makes equality true.
__−0=11
11Subtracting zero changes nothing.
Check 6 for 14−__=8.
14−6=8Substitution verifies.
Explain why blank position is not a clue to always add/subtract.
The equation relationship determines the missing valueUnknowns can occupy any position.
Practice
Guided practice with hints
01Solve 6+__=10.
Hint: Use 10−6.
Answer: 4
02Solve __+7=12.
Hint: Use 12−7.
Answer: 5
03Solve 14−__=8.
Hint: What plus 8 makes 14?
Answer: 6
04Solve __−5=9.
Hint: Rebuild the whole.
Answer: 14
05Solve 11=8+__.
Hint: Both sides must equal 11.
Answer: 3
06Check an answer of 4 in 7+__=11.
Hint: Substitute 4.
Answer: 7+4=11, true.
Practice
Independent practice
014+__=9
Answer: 5
02__+6=13
Answer: 7
0312−__=5
Answer: 7
04__−4=10
Answer: 14
0515=9+__
Answer: 6
0617=__+8
Answer: 9
079−__=9
Answer: 0
08__−0=12
Answer: 12
Common mistakes
Learn to catch the error, not just the answer.
Read the entire equality and identify known whole/parts.
Read = as 'has the same value as.'
Substitute it back and verify both sides match.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Represent missing quantities in word problems with equations.
- Use equation blanks to model unknown starts, changes, and results.
Challenge problems
Solve __+8=17 and explain.
9, because 17−8=9.
Solve __−8=9 and explain.
17, because 9+8=17.
Why is 10=6+4 valid even though the total is on the left?
Equality has no required answer side; both expressions have value 10.
Create three different equations with unknown 5 using values within 20.
Examples: 7+5=12, 12−7=5, 12−5=7.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Balance the Blank
Find unknowns in every equation position and verify by substitution.
Practice
Mastery check
016+__=11
Answer: 5
02__+7=15
Answer: 8
0314−__=9
Answer: 5
04__−6=8
Answer: 14
0513=9+__
Answer: 4
06What does = mean?
Answer: Both sides have same value.
07How do fact families help?
Answer: They connect parts and whole across addition and subtraction.
08How do you check an unknown?
Answer: Substitute it and verify the equation is true.
Terminology
Words to know
- unknown
- A value that must be determined.
- equation
- A statement that two expressions have the same value.
- equals sign
- The symbol = meaning equal value on both sides.
- substitute
- Replace an unknown with a proposed value to test it.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 1 Operations & Algebraic Thinking
Grade 1 addition/subtraction within 20, word problems, and equations with unknowns.