In recent years there has been a huge shift away from rote memorization of math facts and toward a strategy-based approach for *learning* math facts. There’s a big difference between memorizing and understanding. Sure, we want kiddos to have automaticity with their facts. Knowing math facts is similar to knowing sight words–it frees up the mind to solve *real* math problems. If a child has to struggle to solve 8 + 3, they have no mental energy (or desire) left to grapple with the types of problems that will increase their capacity as a mathematician.

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A great resource for strategy-based fact instruction is __Mastering the Basic Math Facts in Addition and Subtraction: Strategies, Activities, and Interventions to Move Students Beyond Memorization__. There’s one for __multiplication and division facts__, too.

A big problem with teaching kids facts is that we often jump to the abstract (symbolic) level of instruction too fast. This does two things: (1) produces children who can recite their math facts, but have no real understanding of what they mean, and (2) children who get left behind because they can’t memorize. I’d be hard-pressed to say which is worse.

Learning facts begins in Kindergarten (or PreK) when students are exposed to __dot patterns__ and __five-frames__. When a child can see 2 dots and 3 dots on a card and know without counting (__subitize__) that there are 5 dots, that’s the foundation of learning math facts.

The concrete for the foundation sets (or doesn’t…) in first and second grade. __Ten-frames__ are magical! Not only do they help students see how the ability to compose and decompose numbers helps connect facts they know with facts they are learning, but they also plant the seed for place value.

Students should have extensive exposure to the combinations that make ten using objects or drawings in Kindergarten (CCSSM K.OA.4). This skill goes by many names: friends of 10, making ten, tens partners. But it’s an absolutely essential skill–move it up to the top of your to-do list! Raise your right hand and repeat, *I will not let my kinders become firsties without knowing their combinations for ten!* Why is it so important? In 1st grade students are expected to add and subtract within 20 *with fluency to 10* (CCSSM 1.OA.6). That means they should have automaticity of the facts within 10 by the end of 1st grade. Why? Because in 2nd grade the standard is for fluency of facts within 20 (CCSSM 2.OA.2). Do you see that beautiful progression? Do you also see, however, how critical it is that students master their grade-level standards? And what happens after 2nd grade? Multiplication, of course, but that’s a post for another day.

Which finally brings me to today’s activity, which utilizes the Using Tens strategy. We want students to be so familiar with their combinations for ten that they automatically use them. When a child is trying to add, for example, 9 + 4, a great strategy is to split (decompose) the 4 into 3 and 1, use the 1 with the 9 to make a 10, and then add on the 3 to make 13. Likewise, to add 8 + 3, split the 3 into 2 and 1, use the 2 with the 8 to make 10, and add on the extra 1. All this is a mental process, of course, but it begins with lots of work on ten-frames–first with counters and then by drawing. Look at the picture below that illustrates 9 + 4. Don’t you see the splitting of the 4 into 3 and 1?

The paper-and-pencil activity shown below is an assessment I created for my 1st-grade teachers. Note that it is an assessment to be used after students have had lots of practice with the concept.

I hope I’ve given you some food for thought today and helped you to better see the progression of fact mastery through the early grades. I’d love to hear your comments! Click here to grab the freebie assessment.

I LOVE your posts! I could not agree more with what you had to say. Being a first grade teacher, it’s become so apparent this year how important it is that these kiddos have a solid foundation for their basic math facts…and a true understanding that’s building that foundation! I use a website a few times a week where I flash different tens-frames up on the SmartBoard and student’s tell what number they saw, and then explain “how the saw it” (The number is 12…I saw 10+2…I saw 5+5+2).

Thank you so much for all of your inspiring & informative posts – I check them regularly to help with my math instruction!

Thanks so much for the lengthy comment! Number talks, like you describe, as so important. 🙂

Thank you for all your posts, but especially those geared towards the early years of elementary school. I feel that I’ve deepened my own mathematical understanding so much more this past year reading your blogs, fb, twitter and exploring your recommended resources (still digging through the NC Ed website). You’ve also reinforced my instincts about the importance of number sense and have given me many more ways to work with my Title 1 kiddos, who often need more than your average student. Sue

Wow! I can’t tell you how appreciative I am of your comment, Sue! I’m so pleased that my work has been so useful to you and benefited your kiddos!

As always, you have put into words what I have been trying to say! Thank you for all that you do and share!

My pleasure, Jennifer! 🙂

Love your ideas! Thanks for sharing. You have given me food for thought many times. I have included many new understandings that I have gleamed and used them in my inclusion 2nd grade classroom.

Love this freebie. We are going to be sharing all of our 2nd graders into new groups for RTI work a few times a week. We will be working on building number sense for very challenged students all the way to our proficient/advanced students. I plan to use many of your ideas, coupled with our district initiatives.

Jeanne

Thanks so much, Jeanne! I love hearing how my resources are used in the classroom! 🙂

Great way to look @ what’s really going on with math.

Thanks so much!

Rekenreks are such a great tool for this, too, especially once kids are accustomed to ten frames but need to work with bigger numbers.

Jenny

Luckeyfrog’s Lilypad

Absolutely, Jenny! Rekenreks are great tools! 🙂

Fluency and flexibility with facts is something we’re definitely grappling with. Thanks for the additional strategies.

❀ Tammy

Forever in FirstYou’re welcome, Tammy. It’s something we ALL grapple with! Ha ha.

I love this post. Thank you for the assessment. I’m going to use it with my first graders. It will be interesting to see how they do. I work with a student teacher who is getting a specialty certificate in math. This will be great for her to see.

Mona

First Grade SchoolhouseYou’re welcome, Mona!

Very well said! It’s scary to see kids in second grade that don’t have that basic number sense that you described. Thanks for posting this!

Sally from Elementary Matters

Thanks, Sally. I think things are definitely changing for the better! 🙂

I LOVE your post and this book!

Thanks so much for all you share!

It’s my pleasure, Heidi! Thanks for your sweet comment. 🙂

Donna,

I loooove this post and can’t wait to share it with our math instructional specialist. She has been trying to get teachers to see math in the early years as number sense for the past couple of years. We work with our ten frames every morning during our calendar time. They are perfect visuals and manipulative enough to keep kids focused and organized.

Do you think now that we need to get parents on board? They want flash cards and time tests. Do you have a good “parent connect” explaining the reasoning behind what is very new to them? I would soooo appreciate it!

Thanks for the assessment!

And thanks for all you do!

Nancy

firstgradewow.blogspot.com

Nancy,

So glad the post was useful! You are totally correct that sometimes it’s hard to get parents on board! I don’t have a parent letter or communication, but some great ways to address parent questions and concerns are through a Math Night, during Open House or Curriculum Night, or even as part of your classroom newsletter. Hope that helps a little! 🙂

I love your posts about early numeracy. I have been doing a lot of professional development with teachers this year around early numeracy activities and building capacity for additive reasoning. Posts like these give me a quick and easy way to spread the knowledge with other teachers. Thanks!

Tara

The Math Maniac

Thanks, Tara! I appreciate all your sweet comments! 🙂

I wish I had seen this last week! Our whole math topic was doing this. Those that got it, got it and those who didn’t seemed to be missing the whole idea. We have had this program for 5 years and I am still trying to figure it all out and find the best way to explain it to my kids, which is hard since math is my least favorite area to teach. But, I have to say, I have become a better math teacher by having to figure it all out myself!

Better late than never, right? Now you have new knowledge to file away and pull out as needed. 🙂

I wanted you to know how much all your posts mean to me. As soon as I read this post, I clicked on the link and purchased the book. It arrived today and I have read all except the last section (I teach kindergarten). I am super impressed with this book! I love the way it ties in literature. Thank you so much for the post and all the book recommendations, keep them coming!

Jennifer Tilton, kindertrips

Thanks so much, Jennifer! I simply love sharing about great math and awesome math resources, and it’s always nice to hear that teachers find it useful, because that means students are benefiting!!

LOVE this post! It sums it up in a nutshell!!! Thanks so much for the time you put in to writing such inspiring, thoughtful, helpful, AWESOME, practical, useful…(I could go on and on)posts. You are amazing! Thank you!!!

Thanks for the sweet comment, Colleen! I love being part of such an awesome online learning community!

I saw this post from your Facebook page today. One of my goals this summer is to work on teaching fluency in math facts. This will help and I thank you very much!

First Grade Frame of Mind

I love the dedication that teachers display! So many teachers work throughout the summer to provide students with an even better learning environment in the fall. Kudos to you!

Donna, just wanted to say a HUGE thank you for your posts and your selfless willingness to share your substantial knowledge. I am homeschooling my 8 yr old daughter who has Nonverbal Learning Disorder – difficulty with maths is a huge part of this disorder and I have found your posts extremely helpful. I am even going to include some of your ideas, strategies and reference material in her homeschooling plan for next year. Thanks sooooo much!! [email protected]

Wow, thanks so much for taking the time to comment! I absolutely love that my posts are helping with your daughter’s understanding! Keep up the good work!

I love your blog and your products! I feel that in my district, we are the blind leading the blind. We have been given minimal training and absolutely no materials. Your blog and products have really helped me to understand this new approach to teaching math. (At least it’s new for me) 🙂

perfectly timed-as always! I really need help with counting on(or up). any ideas? I wish you earned all the money for a Math curriculum! Your ideas are having a ripple effect-hope you know that! THANKS!

the only way I can send comments is as an anonymous reader.( not sure how to use the other choices) send me any ideas to [email protected]

Counting is really a rote activity, so lots of practice is what’s best. Practice using a hundred chart, a count around (each child saying one number), and small group instruction. If the only counting your class does is whole group, some kiddos just won’t participate and won’t get it.

I just recently came across your blog on automaticity and this approach really makes sense. Thanks for sharing your ideas.

As a retired high school math teacher who currently tutors elementary, middle, and high school students, I couldn’t agree with you more!!! Students must have concrete experiences and develop number sense. Those who just memorized arithmetic facts usually don’t expect to understand math, and are unwilling to trust that they can reason,