Adding in any order to make it easier
In 1st grade, children learn to add numbers in any order or grouping and to use facts they already know to make adding easier.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 1st grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
If you know that 7 + 3 = 10, what is 3 + 7?
- 3
- 10
- 7
Why this matters
Discovering that 3 + 8 is the same as 8 + 3 gives your child a shortcut they will use every day, and it roughly halves the number of facts they have to learn. Choosing a helpful order also makes mental math far easier. These same rules return in 3rd grade for multiplication, where 4 × 7 and 7 × 4 give the same answer, and they sit underneath the algebra children meet in middle school.
Where kids can get stuck
- Counting on from the smaller number, solving 2 + 9 by starting at 2 and counting on 9, instead of starting at 9.
- Switching the numbers around in subtraction too, believing 3 - 8 is the same as 8 - 3 and writing 5 for both.
- Adding three numbers strictly left to right, missing the ten sitting in plain sight in 7 + 4 + 3 and slipping while counting.
How you can help
- Line up two groups of toys, say 6 bears and 2 cars, count the total, then swap their places and ask if the total changed. Let your child test it a few times.
- Ask your child to start counting from the bigger number when adding in the car: "What is 2 + 8? Which number would you start from to make it quicker?"
- Hunt for ten when adding three numbers at the store. With 3 apples, 5 oranges, and 7 bananas, ask which two make 10, then add the rest to get 15.
If it’s helpful, you can watch the kid-friendly video below, or sign up for free, adaptive practice in Bobby's Math Club.
Kid-friendly explanation
Questions parents ask
Why is my child learning properties of addition this way instead of memorizing facts?
Understanding that 4 + 9 and 9 + 4 are the same, and that numbers can be regrouped to make a ten, gives your child a way to figure out facts they have not memorized yet. Memorization still happens, but it comes more easily when children see how facts connect. The goal is flexible thinking, not reciting rule names.
Does my child need to know the words commutative and associative?
Not in 1st grade. Teachers may mention the terms, but what matters is that your child uses the ideas: turning a problem around to start with the bigger number, or grouping two numbers to make 10. If your child can explain why 5 + 3 and 3 + 5 give the same total, they understand the skill.
Why doesn't switching the order work for subtraction?
Subtraction means taking away or finding a difference, so the starting amount matters. Taking 3 from 8 leaves 5, but you cannot take 8 away from 3 using whole objects. Showing this with real things, like 8 crackers versus 3 crackers, helps children see why the swap that works for adding does not work for taking away.
Make learning math fun
Bobby's Math Club turns 1st grade math practice into something fun to do together.
- Unlimited free practice
- A few minutes a day, at just the right level
- Hints when they are stuck, and a celebration when it clicks
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 1.OA.B.3: “Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)” Learn how Bobby's Math Club can help your students grow. (Common Core 1.OA.3)