Learn the 6 addition strategies your child needs to know to master all of the addition facts. Clear explanations and illustrations, plus a free printable.
Why Addition Strategies?
When I taught elementary school, my students’ parents sometimes wondered why I was teaching their children addition strategies. “Why not just memorize the facts?” they would ask as they crouched in the child-size chairs at conferences.
Here’s what I would tell them:
- Learning strategies makes the addition facts less overwhelming. Instead of memorizing every addition fact individually, all it takes is 6 simple strategies.
- Focusing on strategies is more efficient. Children learn the facts much more quickly–and remember them much better–when they use strategies to find the answers.
- Children develop confidence in their math skills as they realize that math is for understanding, not just memorizing.
Think of addition strategies as stepping-stones. Stepping stones aren’t there for you to stay teetering on; they are there to help get you across the stream.
Math fact strategies serve the same purpose as stepping stones. They are there to help kids get to their ultimate destination: mastering all of the addition facts!
Below, you’ll find a brief explanation of the most important addition strategies. But if you’d prefer to watch a video in which I explain all 6, just scroll to the video at the bottom.
The 6 Most Useful Addition Strategies
With just these 6 strategies, your child can master all of the addition facts from 1 + 1 up to 9 + 9. To teach them, all you’ll need are some counters and a simple printable called a ten-frame that helps kids visualize numbers and apply the strategies.
Strategy 1: Adding 1 and 2
Use for: all of the +1 and +2 addition facts
To add 1 or 2, teach your children simply to count forward 1 or 2 from the larger number.
Example: 6+2. Count forward 2 from 6: “6, 7, 8.”
Strategy 2: Pairs That Make 10
Use for: sums that equal 10 (5 + 5, 6 + 4, 7 + 3, etc.)
Use counters on a ten-frame to help your child visualize these sums. Represent the larger addend on the ten-frame and ask your child to figure out how many boxes are empty.
Example: 6 plus what equals 10? When 6 boxes are full, 4 are empty. So, 6 + 4 equals 10.
Strategy 3: Use 5 as a Benchmark
Use for: all remaining sums less than 10
Use the dividing line in the middle of the ten-frame as a reference point and add in 2 steps.
Example: 4+ 3. First add 1 to the 4 to make a 5. Then add the remaining 2.
Strategy 4: Adding 9
Use for: all +9 facts
Use two ten-frames to model the problems. Move one counter from the bottom ten-frame to the top ten-frame to make a complete group of 10. Then, use place-value knowledge to “see” the answer.
Example: 9 + 4. Move one counter from the bottom ten-frame to the top ten-frame. Now, it’s easy to see that 9 + 4 is the same as 10 + 3, or 13.
Strategy 5: Adding 8
Use for: all +8 facts
This strategy is very similar to the Adding 9 strategy. Again, use two ten-frames to model the problems. This time, move two counters from the bottom ten-frame to the top ten-frame to make a complete group of 10. Then, use place-value knowledge to “see” the answer.
Example: 8 + 5. Move two counters from the bottom ten-frame to the top ten-frame. Now, it’s easy to see that 8 + 5 is the same as 10 + 3, or 13.
Strategy 6: Look at the Leftovers
Use for: all remaining sums greater than 10
Place counters on the ten-frame to represent the problem. Look for two groups of 5 and combine them to make a 10. Then, add on the “leftover” counters.
Example: 7 + 5. The 2 groups of 5 make a 10. Then, add on the 2 “leftovers” to see that the answer is 12.
All 6 Strategies Explained
Want to learn more about the strategy-approach to teaching the addition facts? Learn more in this video.
Want help teaching your child these addition strategies?
Check out my book, Addition Facts That Stick. It makes teaching the addition facts easy and fun, with step-by-step lessons, games, and worksheets to help your child master the addition facts.
Hey Kate!
Thanks so much for this article. I’m a new homeschool mom. We emergency homeschooled Spring semester and spent the time evaluating each of our kids. My fourth grader needs help with addition facts. My question is about the ten frame. In our math book, it is set up as two five frames stacked one on top of the other. Is there a reason you prefer the side-by-side frames over the stacked frames?
Thanks so much!
Hi Brandi,
I do prefer the side-by-side ten-frames, because they break numbers down in the same sequence that I want children to think about them. For example, take the number 7. As the child “reads” the ten-frame from left to right, she first sees the group of 5, then the remaining 2 dots. With the stacked ten-frames, she sees both parts simultaneously, and so it’s not as linear and sequential.
That said, any sort of ten-frame is better than no ten-frame at all, and I certainly don’t think there’s anything wrong with programs that use a stacked ten-frame. I see side-by-side as just a slight advantage. 🙂
Happy Math!
Kate
Hi Kate! I’m using Preschool Math at Home with my girl and love it, and hope to use your Kindergarten Math next year (but I haven’t officially decided). I realized she was getting confused because we had worked often with the 2 row frame (we had a wooden one for her to use). I agree with your preference for using a one row frame but I’m wondering whether I should reteach her using the one row or adapt the activities with the 2 row? I don’t want to complicate things. 😆
Hi Danielle,
Both types of ten-frames are great, but I do use the one row version throughout the rest of MWC, so I’d try to transition her to that version now. I’d suggest spending a little time using both and translating between the two: “What does 7 look like on this ten-frame? What does it look like on the other ten-frame?” Most children adapt fairly quickly once they see the similarities between the two models. (If you like using the wooden ones, you can also use two of them side-by-side to end up with 2 rows of 10.)
Happy Math!
Kate
My daughter (8) really struggles with switching between different addition facts. We’ve been using MUS and really love it, but she just needs a little extra help getting over the hump. I’ve been looking for new strategies to incorporate into our practice. I’m really looking forward to trying the ten frame with her to give her a new visual perspective! Thank you so much for taking the time to do the webinar! It was very helpful to me!
So glad you found the webinar helpful, Robyn! Thanks for taking the time to let me know. 🙂
Hi Kate,
After a long day investigation why my 7 years old daughter (oldest, I have 3 kids) cannot do subtraction, I found the problem was with addition by following your guidelines. The exact problem was the lack of strategy for my daughter when she faced add-up number is more than 10. She just finished year2 in Australia which means she have done 3 years in primary/elementary school. I was disappointed with my daughter’s math level but, at least, I know how to help her now. Your kids and husband are very lucky with such a fantastic mum!
Tanks and Best wishes,
Ben
Hi Ben,
I’m so glad that I was able to help! Your daughter’s pretty lucky to have a parent who takes the time to fully investigate what’s not working for her with subtraction. 🙂
Happy Math!
Kate
Hi Kate,
Thanks for sharing all this great information. I’ve discovered through your addition assessment that my fourth grader is having difficulty adding 8. I’m interested in why you don’t include using doubles or near doubles as an addition strategy as this is one he’s good at.
For 4+3 for example, its easy to see this as double three plus one or double four minus one. Is there a reason why don’t teach this as one of your most useful strategies?
Thanks
Anna
Hi Anna,
Doubles plus 1 are a great strategy for kids who have already learned the doubles and have the abstract reasoning ability needed to use them. So, if your fourth grader already knows the doubles, they’re a great strategy to use! The reason I don’t use them in Addition Facts That Stick (or this list of addition strategies) is that many younger children have more trouble with it. They often need to learn the doubles by rote, and then they find the “doubles plus 1” strategy hard to apply unless they have counters right in front of them. But, as with all strategies, whichever strategy helps your child master the addition facts quickly and efficiently is the best one!
Happy Math!
Kate
Hi Kate,
We’re going through Math Mammoth and my son is in 1st grade. We’ve completed the addition section and are currently in the subtraction section with creating two subtractions from one addition problem. He’s doing well with it, but he hasn’t mastered his addition facts. I’m wondering if I should pause where we currently are and master the addition facts before moving through subtraction? Or would you suggest seeing if he masters them by the end of first grade.
Thanks,
Lauren
Hi Lauren,
Working on subtraction can be a great way to think through and solidify number relationships, as long as he’s not feeling frustrated or counting out every problem. I’d suggest continuing to work through Math Mammoth, but do a little addition fact instruction on the side as a warm-up each day. That way, you’ll still make progress through the curriculum but know that he’s also on track to have the addition facts mastered by the end of the year.
Happy Math!
Kate
Hi Kate,
I’ve been using the Good and The Beautiful Math with my first grader, and they include all of these strategies, the 10 frame, etc. But I’m stumped because of little guy is still struggling with almost all the math facts except for 9+ which he’s seemed to grab onto for some reason.
I don’t know if he just needs to practice more, or if I should just move to flash cards because his brain doesn’t seem to grab these concepts. Do you have any advice?
Thanks!
Hi Liesl,
I’d wait a couple months to see if his brain just needs to mature a little more. Then, I’d suggest working on one small set of facts at a time, so he’s not overwhelmed and can concentrate on one strategy at a time. If that doesn’t seem to do the trick, perhaps flash cards are in order, but I’d give it more time before investing all that time and energy in them.
Happy Math!
Kate
Hi Kate,
I was looking to switch my 8.5 year old to Math with Confidence Grade 3 after using The Good and The Beautiful for 3 levels. He seems to run through math with understanding yet he has not yet mastered all the addition facts or subtraction facts, he seems to have counted on his fingers up or down to find the answers most of the time. Anyways would you go ahead with Grade 3 since that’s where he is with all other subjects or do something different or start at a lower grade?
Hi Bree,
I suggest doing Addition and Subtraction Facts That Stick first, and then move him into Third Grade MWC. The third grade level assumes that kids have mostly mastered their addition and subtraction facts, and the lessons will go much more quickly (and happily) if he has the facts down first.
Happy Math!
Kate
Dear Kate,
I am a retired teacher working with her grandchild who attends public school. Needless to say, I am impressed with your teaching strategies for the young and us adults who want to support and/or enrich those under our care.
As I view my grandchild’s homework I need teaching strategies for the following example –
Problem
44 tens is the same as _______
Sure I can multiply by 10 and get 440 but I do not think my second-grade grandson is working with multiplication.
So here is my question
how would I begin to teach using concrete, picture, and abstract strategies to solve my problem? Yes, I purchased your Teacher’s Manual as well as the student handbook for 2nd grade. Perhaps the answer to my problem is in your teacher manual, if so please direct me.
I truly thank you Kate for providing math guidance to so many.
You are a steady guiding light and I thank you,
Marie please reply by way of my email address mfsossi148@gmail.com
Up to this point I truly understand, enjoy and can teach “modern math.”
Hi Marie,
Glad you’ve found my work helpful! For that example, I’d recommend using base-ten blocks and putting together groups of 10 rods. Every group of 10 rods makes 1 hundred, and you can work up from there. After several examples, he may deduce that he can tack on a zero to find the answer, but the hands-on work will keep it from being a mindless rule. You’ll find similar work with base-ten blocks in several different units in Second Grade MWC, and then I extend it to multiplying by tens in Third Grade MWC.
Happy Math!
Kate