It’s heartbreaking when a student not only doesn’t know a fact like 8 + 4, but also has no strategy for figuring it out. Especially when that student is a 5th grader. How do you know they have no strategy? Because you ask them what 8 + 4 equals and it’s a good 10 seconds before they come up with an answer. No counting on fingers, no head bob indicting they are counting on, just ten agonizing seconds. But even in 5th grade, it’s not too late to help students learn their basic facts. Enter strategy-based instruction.

You may have heard of strategy-based fact instruction, but what exactly does it mean? It boils down to helping kids become flexible thinkers. Helping them to use what they know to figure out what they don’t know. It gives them a place to start. Here are some examples of strategies for basic addition facts.

**COUNTING ON** Yes, this is a strategy. It’s not the most efficient, but it’s better than counting all. For example, one way to find 8 + 4 is to count 1, 2, 3, 4, 5, 6, 7, 8 and then 9, 10, 11, 12. So counting on from 8 (8, 9, 10, 11, 12) is definitely more efficient. And it is a strategy to know that when solving 4 + 8, I can count on starting at the bigger number. Take my 5th grader in the introduction–it doesn’t take 10 seconds to count 8, 9, 10, 11, 12, so it seems like this student didn’t even have the most basic strategy.

**MAKE A TEN **This is a powerful strategy for students who understand composing and decomposing numbers. Basically, you split one addend to make a ten out of the other addend. For example, to solve 8 + 4, I would split the 4 into 2 + 2, use 2 to make a 10 with the 8, and then add the other two. So…

8 + 4 = 8 + 2 + 2

**USE DOUBLES **Kiddos learn their doubles (2 + 2, 3 + 3, 4 + 4, etc.) quite easily. Knowing their doubles can help with near-doubles facts, like 6 + 7. I’ve watched a student stumped by 6 + 7 and asked them: What’s 6 + 6? Almost automatically they will say 12. So what is 6 + 7? the light bulb goes off and they answer 13 with a smile. It’s like you just taught them a magic trick!

**THINK +10 FOR +9** Those 9s are such difficult facts! But, adding 10 to a number is easy. So when I see 9 + 6, I can think 10 + 6 and then just subtract 1.

So you might be thinking, don’t we want students to have automaticity with their facts? Absolutely–automaticity with facts is essential. Teaching strategies leads to automaticity along with a deeper understanding of numbers. Timed fact tests and flashcards don’t help a student who doesn’t know how to figure out 8 + 4.

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Have I piqued your curiosity? Wondering how you can get started? You might want to check out this blog post for more about the Make a Ten strategy and this post for the Using Doubles. Both posts include freebie workstations for practice. The book Mastering the Basic Math Facts in Addition and Subtraction: Strategies, Activities, and Interventions to Move Students Beyond Memorization is a great phenomenal resource. It includes literature links, games, and mini-lessons. Oh, and there is one for multiplication and division also!

I love to hear your success stories with strategy-based fact instruction! Be sure to leave a comment. 🙂

I’d love ideas for students with documented dyscalculia.

Thank you for your doubles + 1 and make 10 practice cards! I’m also wondering how best to assess:

“1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decompose a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums.”

I was thinking of some timed assessments for 1-10? For problems with 1-20, maybe I just leave space for them to solve, encouraging them to solve using the strategies we taught? Maybe if I list the strategies on each problem and have them identify which strategy they used?

Any ideas/thoughts?

My favorite assessment of the basic facts is to interview the students using flash cards. I use one card from all of the +1 through +9 cards. I don’t use the “turn around” cards for time sake. For the addition facts, this is 36 cards. You can decrease the number of cards, but be sure you have a good sampling of each strategy. I use a fact matrix to record the student responses. If the student responds within 3 seconds (mastery) I mark a diagonal line. I mark a horizontal line for a correct response that took longer than 3 seconds. I circle incorrect or no responses. I also note which strategies the student is using. I can tell by observing and for some facts I ask, “How did you get that answer?” Afterwards I highlight all the facts not mastered on the matrix. This enables you to easily see which facts and strategies have not been mastered yet. This is an easy way to progress monitor the basic facts. I wated to attach a picture of a matrix to show you the system in action, but I’m new to this site and can’t figure out if there’s a way to attach a picture with my post.

The book referenced in the post covers all the facts up to 20. It is a wonderful resource! It has literature links, games, and assessment suggestions. I’m a big believer in not reinventing the wheel!

Hi. I’m a big fan of your blog and your resources. I’m using a strategy based approach with my 2nd graders but I always end up overwhelmed by the students’ wide range of skills and how to make sure I’m giving every child time at their level to practice their strategy, especially as we get going in the year and many kids are taking off, but just as many need a slower pace. Any suggestions? I do Number Talks, whole group minilessons (EnVisions curriculum), and small group rotations. Students not at the table with me are doing workstations or independent practice. Thanks!

It sounds like you’ve got it all going on, Jenny!! Do you have them practice fluency in one of their workstations? Many teachers have one rotation devoted just to fact fluency. You could differentiate the tasks in the fluency workstation to address the different needs of your students.

I am a passionate supporter of teaching math facts strategically as well as Jo Boaler’s growth mindset to eliminate myth that there is a connection between being good at math and being fast at math. I truly believe that automaticity will be achieved the more we relieve the pressure of timed tests and focus instead on games and activities that develop the strategies. Dr. Nicki Newton has written a book that will be published this spring called Running Records. She has developed a running record assessment for each of the operations. I have given hundreds of them now K-5 and it is absolutely amazing! For addtition we follow the progression of Plus 1, Plus 0, Count on 2 or 3, Make 10, Plus 10, Doubles, Doubles plus 1, Doubles plus 2, Decompose with 9 to make 10, and finally Decompose with a 7 or 8 to make 10. When I interview the students I asked them one problem from each category to get a sense of speed and accuracy but there is NO TIMER. Then, I go back and ask them about each of the strategies until I find one that they need to work on. For example, I begin by asking “What happens when we add 1 to a number”. I am looking to see if they know that it is the next counting number. For Count on 2 or 3, I give them the expression 2 + 6 to see if they know it is more efficient to start with the larger number and count on the 2 or 3. If I find a child is counting all the fingers for 2 and then 6 and then counting them all up, I know they need to work on this. So, then we have those children who need help on that strategy play a Bump game where they roll a regular die and then another one that only has 2 or 3’s on it. They then need to add the 2 or 3 to whatever they rolled. It has been amazing! I am seeing such growth with our students K-5. Spending time on this is crucial to form the foundation for everything. In a grade 2 classroom the other day students were working on adding two 2-digit numbers and having trouble with adding tens when the sum went over 100. I then had the teacher work with them on how much 5 tens is, 8 tens, and 14 tens. Then, they would see 80 + 40 and say 8 tens plus 4 tens is 12 tens which is 120. The kids did awesome with it. All these foundational skills are embedded within the more difficult problems. So, so crucial!

First of all – I love your site. I have been a math coach for 3 years now, and found your site when I first started! I am presenting the Mastering Basic Math Facts and Number Talks to a committee next week. I see the benefit of both and would like to know how you would approach implementing both. I have read several people use Number Talks as a way to teach basic facts. I feel they are two separate programs that both show promise to changing the way our students see math. Any clarity on implementing both programs would be much appreciated!

Thank you!

Hi I am a teacher from NSW Australia. We use a program called TEN (teaching early numeracy) in our k-2 classes. Your incredible ideas support this program and constantly remind me about teaching the how. I have students who are 7 telling me time and time again “I know 5 and 5 is 10 so 5 and 6 is 11” etc etc etc. I just want to say tank you for your logical explanation of strategies. I love teaching how numbers work together and seeing those little light bulbs come on. So all the way on the other side of the world, your work is making a difference. Thank you

Fiona Tickle -year 1 teacher.

Hello. I admire your instructional expertise in math. Are you familiar with the GoMath Program? If you are, what is your opinion? I will be using it to teach second grade next school year. Thank you for any insights you have.

Sincerely,

Lisa

I only know GoMath from reviewing it during our adoption process. I think the key with any textbook is to use it as a resource, and not necessarily the primary resource. It’s really hard to give the students as much hands-on activities as they need only using a textbook, but many of the activities in the textbook can be enhanced. Likewise, the center activities and games are often great for math workstations.

another great resource-I would like to ditch my Math pages and use your helpful samples. perfect timing as always. I only have 45 min for Math. How about others?

We have at least an hour – I usually go over!

Once you use a strategy based approach, you’ll never go back! Boo, 45 minutes is too short for math. 🙁

I have 45 minutes with my fifth graders. Do you have any suggestions for using number talks in that short amount of time?

I can say that time spent on Number Talks is time well spent, Ann. Also, if you are familiar yourself with the number talk strategies, you can incorporate them into your whole and small group instruction.

The book you mention for fact fluency sounds wonderful. Is it CCSS aligned? Thank you !

Thank you! That helps. I’m concerned as my second graders seem to forget facts like 7+4 while they determine the strategy. It is not coming quickly or automatically. Is it ever appropriate to use flash cards? I use “mad minutes” to determine – by observation- how they are solving simple addition facts. I encourage them to simply do better each time and not worry about their total compared to others. Thoughts?

It does not have specific references to CCSS, Patrice, but it certainly supports this 1st grade standard:

“1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decompose a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums.”

Can you recommend any resources for math talks?

Thanks,

Laura

Laura, you need to check out Number Talks, by Sherry Parish. It is the gold standard!

My son is a first grader and we need help with addition. He has basic math knowledge he can count/add up with manipulatives but without them he doesn’t really understand what he is doing. His homework today was adding by 1 and he was trying to count dots or use the points on the actual number to figure it out and it wasn’t working. Where do I start with him??

If you want to work with him at home on a regular basis, I would highly recommend the book mentioned in the blog post. Each chapter highlights a different strategy and includes activities, games, and practice sheets you can use.

I love your comment above. I have been reading and reading and reading your blog. This year I have made time within my groups for students to work on “their number” with number bracelets, rekenreks, and shake/spill activities. My kids came to me not know the parts of 3 (in first grade). So they are starting where they are and working at their own pace. Then on top of that we are teaching strategies for those facts we don’t know automatically. They are using a lot of counting on and number lines right now. I hope that they start to use the other strategies you mention. When does this typically begin to develop? Thank you!! You have saved my math teaching.

What an awesome thing you are doing for your kiddos, Em! You will start to see the results. You might need to specifically introduce them to the strategies I mentioned. A mini-lesson format is great for that, and be sure to create anchor charts they can refer to often!

I feel like the CCSS is leading us to NOT teach fact fluency. It seems to me that they want the kids to understand how/why rather than automaticity. I am teaching first grade using EngageNY. The first module is all about number bonds and moves very fast from one number to the next. I feel like my kiddos are frustrated and confused. I would greatly appreciate your insight and thoughts. Thank you.

I am finding the exact same thing. All they have is strategies. I am not seeing any understanding being built at all. There are no connections or deeper understanding happening.They can only see trees, and have no clue they are all part of the forest. I totally agree with your (Donna’s) comment that it is this specific curriculum. That said, it takes so long because so much of it is either confusing or developmentally inappropriate, that injecting anything else is next to impossible. If I don’t do it “their way” using “their language” they don’t pass “their test.” I can help them actually understand what they are doing mathematically, but they have to be able to do it the book way. It’s a different kind of rote.

Number talksare amazing! We do them school wide–K-5–and we’ve seen a big difference.A great way to have students share their strategies about different ways they use number bonds is through the use of Number Talks. It’s a great way to bring out different strategies for kids to try.

While CCSS definitely has an emphasis on conceptual understanding, there is a component on fact fluency as well. I believe the Sprint part of the Engage NY lessons/units address this, but am not positive as I’m just getting started using them myself. Below I’ve included a link that lists out the various math fluencies by grade level, I hope it helps. Fact fluency is not something that should be put by the wayside, as it will help students focus on the concept and not get stuck in the procedure part. We want students to be out of the box thinkers, but they do have to know what’s IN the box in order to think outside of it. Good luck!

https://www.engageny.org/sites/default/files/resource/attachments/ccssfluencies.pdf

Well said! I agree that there’s still a strong need for developing fact fluency. We want the students to be able to use the strategies and explain how they’ve arrived at a number; we also want students to have facts readily at their fingertips as they progress through grade levels and need to plug facts into more challenging problems.

We are using Engage NY in our district too. This is our second year. We use the sprints and supplement with other fluency activities – games, etc. This year everyone says the kids are doing really well, much better than they expected. However, we are adopting a new math “program” for next year. I think people will be much happier with it.

It sounds to me that the problem you’re having is not with the CCSS, but with the curriculum you are using. No matter how good a set of standards is, children need time to make sense of the concepts. Composing and decomposing numbers should ideally be differentiated based on student needs. Several students might be stuck on number bonds for 5 while others are on 6, 7, or even 10. No standards can be “one size fits all”. That’s why I’m a big fan of a math workshop approach with small group instruction. It makes meeting the needs of a diverse group of students doable.

Our district wants us to assess fluency with math facts, but we’re not supposed to time them. Do you have suggestions for how to do this?

Can you set a timer and have students work to see how many they complete in the given time and work to improve their own count? So, for example, you might give them 1 minute and the first week they complete 15 facts. They next week they would be trying to get more than 15 facts correct. Each student would just be working to better their own score.

I give a 25 problem fact test and time how long my students took to finish the test. We all turn our papers face down, When I say go, they turn their papers over and start – the times is counting up. When they finish, they write the time from the timer (on the ELMO), turn their paper over and twiddle their thumbs quietly. When all are finished, we check the paper together. I call on a student to read the fact and answer. If anyone gets behind or disagrees with an answer, they say STOP. Ill say the correct answer and we move on. I’ve made “math timesheets” so they can write how long it took them to complete the test and how many were missed. This way, they compete against themselves by trying to “beat” their own time. For younger students, they will call my name quietly when finished and I will either write the time on their paper, or call it out so they can write it. We label what kind of “fact tests” we take, for example +2’s, or doubles, etc. I usually give at least 4 tests on a specific strategy so they can see improvement. They really love it and are not as stressed as worrying about a timer going off. I try to have them set a goal for under a minute.

Sorry for the long post!