Grade 1 · Operations · MAT-01-OPS-004
Commutative Property of Addition
Recognize that changing the order of addends does not change the sum.
Learning objectives
What you should be able to do
- Recognize that changing the order of addends does not change the sum.
- Use the commutative property to turn a harder addition fact into an easier equivalent fact.
- Explain the property with objects, equations, and arrays or grouped models.
Prerequisite check
Make sure the foundation is ready.
Checks addend/sum understanding.
Learn
Build the idea from meaning, not memorization.
Order does not change the total in addition
If three red counters and five blue counters are combined, there are eight counters. If we describe the blue group first, 5+3, the same eight counters are present.
The property creates equivalent facts
2+7 and 7+2 have the same sum. This lets learners place the larger addend first for efficient counting on.
The property is about addition, not every operation
Although 3+5=5+3, subtraction does not generally work that way: 8−3 is not equal to 3−8 in Grade 1 whole-number work.
Models make the property visible
Swapping the order of two groups changes their position, not their members. The combined quantity stays constant.
Interactive math lab
Change it. See what stays true.
Ten-Frame Lab
Fill the frame from left to right and connect the visible amount to the numeral.
5 filled; 5 empty; 10 spaces altogether.
- build two groups
- swap position
- compare sum
- choose efficient order
Worked examples
Twenty different ways to see the concept work.
2+3 and 3+2.
Both 5Same addends, reversed order.
1+6 and 6+1.
Both 7Order does not change sum.
4+5 and 5+4.
Both 9Same combined quantity.
3+7 and 7+3.
Both 10Reversing addends keeps ten.
0+8 and 8+0.
Both 8Zero can switch positions.
Which form is easier for counting on: 2+7 or 7+2?
7+2Start larger, count two.
Rewrite 1+9 using commutative property.
9+1Same sum, easier one-more strategy.
Rewrite 3+6.
6+3Same two addends.
If 5+4=9, find 4+5.
9Commutative pair.
If 2+8=10, find 8+2.
10Order does not affect total.
Two groups have 4 and 3 objects. Swap their left-right position.
Total remains 7Location changes, membership does not.
Does 6+1 equal 1+6?
YesBoth combine six and one.
Does 8−3 equal 3−8 in Grade 1 whole numbers?
NoSubtraction is not commutative.
Why does 4+4 look unchanged when swapped?
The addends are equalReversing equal values produces identical expression.
Use property to solve 2+5.
Rewrite 5+2=7Count on two from five.
Use property to solve 1+8.
Rewrite 8+1=9One more than eight.
Which expression matches 3+4: 4+3 or 4−3?
4+3Commutative property stays within addition.
Explain with apples/bananas: 2 apples+3 bananas vs 3 bananas+2 apples.
Both total 5 itemsThe groups are the same.
Can commutative property change the addend values?
NoOnly their order changes.
State the property in words.
Changing addend order does not change sumThis is the commutative property of addition.
Practice
Guided practice with hints
01Rewrite 2+6.
Hint: Swap addends.
Answer: 6+2
02If 7+1=8, what is 1+7?
Hint: Use same sum.
Answer: 8
03Which form is efficient: 3+6 or 6+3?
Hint: Start with larger addend.
Answer: 6+3
04Does property work for 5−2?
Hint: Compare with 2−5.
Answer: No
05Explain 4+2=2+4 with counters.
Hint: Swap group order.
Answer: Total remains 6.
06What changes under commutation?
Hint: Only order.
Answer: Addends keep values; sum stays same.
Practice
Independent practice
01Rewrite 1+5
Answer: 5+1
02Rewrite 2+8
Answer: 8+2
03If 6+3=9, then 3+6
Answer: 9
04If 4+5=9, then 5+4
Answer: 9
05Does 7+0=0+7?
Answer: Yes
06Does 7−2=2−7?
Answer: No
07Why use commutative property?
Answer: To connect equivalent facts and choose efficient order.
08What stays unchanged?
Answer: The sum.
Common mistakes
Learn to catch the error, not just the answer.
Use the exact same addends, only reversed.
Test with a simple example to see subtraction order matters.
Count members; location does not change quantity.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Reorder addends mentally to count on from the larger number.
- Recognize equivalent totals when two categories are listed in different orders.
Challenge problems
Why is 2+8 useful to rewrite as 8+2?
Counting on two from eight is more efficient.
Give a counterexample showing subtraction is not commutative.
For example 5−2=3 but 2−5 is not 3 in Grade 1 whole numbers.
If a+b=10 for two whole-number addends, what is b+a?
10
Explain commutativity without symbols.
Joining the same two groups gives the same total no matter which group is named first.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Swap & Solve
Swap addends, prove the sum stays the same, and choose the easier order for mental addition.
Practice
Mastery check
01Rewrite 3+6.
Answer: 6+3
02If 2+7=9, then 7+2?
Answer: 9
03What stays same when addends swap?
Answer: Sum
04What changes?
Answer: Order
05Does property apply to subtraction?
Answer: No
06Use property to solve 1+8 efficiently.
Answer: 8+1=9
07Explain with groups why 4+3=3+4.
Answer: Same seven objects are combined.
08State property.
Answer: Changing order of addends does not change sum.
Terminology
Words to know
- commutative property
- A property stating that changing addend order does not change the sum.
- addend
- A number being added.
- sum
- The result of addition.
- equivalent
- Having the same value.
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 fluency, properties, and strategy progression.