Adding 9 Facts: Make 10 Strategy and a Simple Finger Trick

Adding 9 facts is a major milestone in first-grade math and one of the trickier ones to teach. The standard approach uses a make-10 strategy that works well for many students, but it requires specific prerequisite skills and can be hard to simplify for younger learners.

My kindergartner zoomed through his curriculum and hit a wall at exactly this point. The rest of this post covers the prerequisite skills, how the make 10 strategy works, and the simple finger shortcut I found when the full model had too many moving pieces.

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 fact that makes 10, and that needs to be made explicit. Students also need to know that 9+___=10 and to know that something is 1. It’s not just that 9+1 is 10, but that the missing piece of the equation is 1. That missing piece can be difficult to grasp.

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 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, and 10+2. Not only do students need to know the answers to these expressions, but they also 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 students is to show them a number card, 1-9, although focus on 2-8. Have students tell you what 10 more is. 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 and moving one object from one ten-frame to the other.   It looks like 9 + 7 = 10 + 6, represented in number form and with objects.  

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 addition facts.

I have a 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. 

When the Traditional Approach Has Too Many Steps

The above strategy and model are what students are taught in a traditional math lesson. They’re solid 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 for making 10-fact tables, recognizing patterns in writing numbers, and 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 the other has 7. Not only do students have to look at a model with 9 circles, each representing an individual unit, but they also have to move a circle to make 10. Then count the remaining circles in the other ten frame, or if they’re good at subtilizing, just know that it’s 6. After that, they add 10 + 6 to get 16. That’s a lot of steps.

There’s nothing wrong with the process, but as I tried to explain it using base-10 blocks, ten frames, or any other manipulative, my son got lost with all the pieces. When I wrote it down as 9+7 and 10+6, he could solve the problems, but he didn’t use the make 10 strategy 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 didn’t let him revert to counting all the pieces.

There were too many moving parts that didn’t encourage the use of a strategy.

A Simple Finger Shortcut for Adding 9 Facts

The following is a little trick that I discovered while working with my son on 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.

How to Use the Finger Shortcut for Adding 9 Facts

Here is the shortcut, step by step, using 9 + 7 as an example:

1. Look at the number being added to 9. Show that many fingers. (Show 7 fingers.)
2. Lower one finger. That 1 is going to the 9 to make 10. (6 fingers showing.)
3. Note how many fingers are still up. (6)
4. Add 10 to that number. (10 + 6 = 16)

The short version: show the smaller number on your fingers, take one away and give it to the 9, then add 10 to what’s left.

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 his 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 manipulatives and drawing circles to make 10 are great, they 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 they’re the best tool they have for solving math equations.

The basis of this trick is compensation, which I explain in more detail in the blog post titled “Developing 10 as a Benchmark Number.”  This is our application of that strategy using fingers.

When looking at a problem like 9+7, I tell my son to just look at the 7 and make 7 with his fingers. Since he knows that he needs 1 to make 10, he lowers one finger from the 7 fingers shown. There are now 6 fingers shown. He adds 10 + 6 in his head and says 16.

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, a few prerequisite skills are needed to successfully 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 This Finger Shortcut Works

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 placing it on our fingers, we have reduced the problem to its basic components.

More Resources for Developing Single-Digit Addition Strategies

Here are a few more resources that may be helpful as you support your students in developing a variety of strategies for single-digit addition.

• Strategies that Develop 10 as a Benchmark Number
• Using 10 to Add +9 & +8 Games and Activities
• Addition & Subtraction within 20
• Addition Go Fish