Addition Strategies for +9 Facts – How to Add 9
Using 10 to add +9 addition facts is one of the foundational addition strategies students learn when learning their addition facts. Yet, it is also one of the most challenging since it requires a couple of prerequisite skills.
My Kindergarten son zoomed through his kindergarten curriculum, so we started him on first grade math early. He’s gotten through about half of the content, but hit a wall when we got using strategies to solve +9 facts.
For him, I discovered that using a make 10 strategy to solve +9 facts involves way too many numbers and comparisons between +10 and +9 facts. He’s really good at math
Prerequisite Skills for using a Make 10 strategy with +9 Facts
If you want students to use a make 10 strategy to add +9 facts, students need two sets of facts under their belt to be successful when adding +9.
Students need to know that 9+1=10
This math fact is generally taught and practiced when students learn all of the facts that make 10. However, when adding +9 facts, this is the only make 10
The other piece that can be difficult for students is that while they are making 10, the real part of the problem they need to hold onto when adding +9 facts isn’t this make 10 fact. It’s the 10+ fact.
Students Need to Quickly Add 10+
The second prerequisite skill students need to have before using a make 10 strategy to add +9 facts is the ability to quickly add 10+8, 10+7, 10+6, 10+5, 10+4, 10+3, 10+2. Not only do they need to know the answers to these expressions, but students need to be able to see an “8” and know that 10 more is 18. Or see 5 and know that 10 more is 15. It needs to happen quickly in their heads.
There are a couple of ways to help students master the 10+ facts. Have students write the numbers 0-20, with the first line 0-9 and the second line 10-20. Show students how to count on 10 more than the given number when adding 10+ facts. See if students can discover a pattern. While you can tell students the pattern, their ability to discover it will take them much further than a teacher making it obvious.
As students write their numbers 0-120, observe them. Do you have students who have figured out that the columns all have the same ones place? Do they write all the tens across a row at once and then go back and fill in the ones? These, and other 100s chart activities, are good precursors to mastering 10+ facts and 10+ any number.
One more activity that you can do with student is to show them a number card, 1-9, although focus on 2-8. Have students tell you what is 10 more. See how quickly they can do it. Are they counting from one? Counting on? Or do they “just know” that 10 more than 8 is 18?
Before students can successfully use a make 10 strategy to add +9 facts, they need to have automaticity with +10 facts.
Traditional Strategies for Developing +9 Facts
What are traditional strategies for teaching . +9 facts?
These strategies traditionally focus on using ten frames, moving one object over from one ten
The actual objects can vary (using small erasers is popular now) and the way the equation is written out may be different (some make two equations), but the basic idea is that students are moving objects to make a 10 and describing the relationship of the two
I have a great post about Developing Strategies to Use 10 as a Benchmark Number. In it I write about using compensation, making 10, adding 10 and using 10 to add and subtract. These strategies work for many students.
Why This Strategy Didn’t Work for Us . . . Yet
The above strategy and model are what students are taught in a traditional math lesson. They’re great math models and give students ample practice developing their math fluency and work with numbers.
However, they didn’t quite work for us. I think partly it was my son’s age and maturity level. He is at the end of Kindergarten and this is traditionally a first-grade skill. He showed aptitude in his make 10 facts, patterns in writing numbers, and in his 10+ facts, so he definitely had all the prerequisite skills.
There were just too many moving pieces with the above strategies.
Let’s say you’re using ten frames with circles. One ten frame has 9 circles and one has 7 circles. Not only do students have to look at a model with 9 circles, which are individual units,
There’s nothing wrong with the process, but as I tried explaining it using base-10 blocks or ten frames or any other manipulative, my son got lost with all of the pieces. When I wrote it down as 9+7 and 10+6 he could solve the problems but there was no use of a make 10 strategy that we had just reviewed. I needed a simpler way for him to use the strategy that didn’t require so many pieces and numbers AND that didn’t allow him to revert to counting all of the pieces.
It was too many moving parts that didn’t encourage the use of a strategy.
Our “trick” for adding +9 Facts
The following is a little trick that I discovered while working with my son in adding +9 facts. I’m sure that I’m not the only one to “discover” this trick and it’s not really a trick at all.
We call it a shortcut or a trick, but it’s really the same math strategy he learned when using the 10 frames or base-10 blocks, but without the moving pieces. The pieces were too distracting and he lost the mathematical thinking.
The reason this method works so well for us is that it takes away most of the models and numbers and puts it into the child’s head. While moving manipulative and drawing circles to make 10 is great, it also still encourage students to count one by one.
The only thing required in this strategy is the problem and fingers. Yes, I still encourage my kids to use their fingers, even my oldest. Most students have 10 fingers and it’s the best tool they have to use to solve math equations.
The basis of this trick is compensation, which I explain in more detail in the blog post about Developing 10 as a Benchmark Number. This is our application of that strategy using fingers.
When looking at a
The shortest way to explain it is to show the smaller digit on your fingers, take one and give it to the 9. Ask, “how much is left?” Add 10 to it.
As I mentioned, there’s a few prerequisite skills needed to successful use this method. One, students need to know that 9+1 is 10 and that they’re lowering 1 finger to give it to the 9 to make 10 (this is compensation). We establish this concept at the beginning, but we don’t repeat it each time.
Two, students need to know their 10+ facts to automaticity, especially the 10+2 through 10+8 facts. They need to be able to see 6 and know that 10 more is 16.
Why does this addition strategy work so well for him?
It allows him to focus on the main part of the problem. There are so many moving pieces when using 10 to add +9 facts. He got lost in all the moving pieces. The most important part of the problem wasn’t being prioritized and he wasn’t holding the right pieces in his head and letting go of the others.
We put so much emphasis on making 10 that we forget that it’s not really about the 9 or the 10. That’s part of the strategy, but not the “answer”. By focusing on the other digit and putting it on our fingers, we have simplified the problem to its basic pieces.
More Resources for Developing Single-Digit Addition Strategies
Here are a few more resources that may be helpful as you help your students develop a variety of addition strategies for single-digit addition.
Jessica BOschen
Jessica is a teacher, homeschool parent, and entrepreneur. She shares her passion for teaching and education on What I Have Learned. Jessica has 16 years of experience teaching elementary school and currently homeschools her two middle and high school boys. She enjoys scaffolding learning for students, focusing on helping our most challenging learners achieve success in all academic areas.