Addition works in either order
3 + 5 and 5 + 3 both make the same total.
The two parts are the same, just shown in a different order. The total stays 8.
Year 2
Show that addition of two numbers can be done in any order and subtraction of one number from another cannot
See that addition can be done in either order, but subtraction changes when the order changes.
Lesson overview
Number - addition and subtraction
Addition is commutative. This means we can swap the numbers around and still get the same total. Subtraction is different. If we change the order, we change the answer. Looking at paired number sentences helps us notice this clearly.
Subtraction changes when the order changes
9 - 4 is not the same as 4 - 9.
When we subtract, the starting number matters. Changing the order changes the answer.
Two-digit addition can also be swapped
21 + 14 and 14 + 21 give the same answer.
Addition keeps the same total even when the addends swap places.
Worked example
Compare 12 + 7 with 7 + 12, then compare 12 - 7 with 7 - 12.
- Read the first addition sentence: 12 + 7 = 19.
- Swap the numbers: 7 + 12 still equals 19.
- Now look at subtraction: 12 - 7 = 5.
- Swap the numbers: 7 - 12 does not give the same answer.
- So addition can be done in any order, but subtraction cannot.
Try it
Look at the pair of number sentences, then choose the answer that fits.
Question 1
Question 2
Question 3
Question 4
Question 5
Common mistakes
These are the slips to watch for when comparing the two operations.
- Thinking subtraction works like addition when the numbers are swapped.
- Looking only at the numbers and not noticing which one comes first.
- Assuming every operation keeps the same answer when the order changes.
Related topics
These ideas help with checking answers and seeing number relationships.
- Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100.
- Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.
- Solve problems with addition and subtraction using concrete objects and pictorial representations.