*tens*and

*ones*on the table in front of him (see the photo). He put the 4 back and took out a 10. I asked him how many tens he had, and he told me 1. I then asked how many dots were on the ten-frame, and he told me 10. I asked him where he should place the 10, and he told me under the tens. Next I asked him to show me another 10, so he took another ten out of the kit. I repeated my questions–how many tens? how many dots (ones)?–and he told me 1 ten and 10 dots and put the 10 next to the other one under the

*tens*heading. Then I asked him how many tens he had under the

*tens*heading, and he told me 20. Hmmm, I think I see 20 dots, but how many groups of 10?

*Two.*Great! So there are 2 tens and how many dots on those two tens?

*Twenty.*His responses were still no where near automatic. That is, he really had to think about his answers. I repeated this process until we had 4 tens. Finally, I asked him what he would need to add to make the number 43. He considered the question, looked at the ten-frames in his kit, pulled out a 3, and placed it in the

*ones*column. To tie it all together we wrote that 43 is 4 tens and 3 ones, and we also wrote it in expanded form, 40 + 3. We repeated this same process for several more 2-digit numbers.

Truly understanding place value requires students to be able to *unitize.* What this means is that they must be able to understand that a group of ten ones can be counted as a single unit, called a ten. That’s a huge mathematical step, because the idea is so abstract. As with any abstract concept, students need lots of varied hands-on experiences building tens and ones and talking about the meaning to develop a true understanding. That means ten-frames and counters, linking cubes, beans on a stick, linking chains, etc.–as many different representations as you can think of.

__ten frame kits__can be a bit pricey, but you can create your own students kits using

__this file__. I also uploaded a

__B&W version__, in case you want your kiddos to color their own. If you need ten-frames to use with counters, download those here.

Margaret Quigley says

Thank you so much for these tens frames counters!! I think they may just be the perfect manipulative to help my struggling First Graders!! I will try them out in my Intervention groups on Tuesday!!

Donna Boucher says

Perfect! I’m glad it’s something you can use right away, Margaret!

Barbara Knox says

I love the organization of the ten frame numbers in pockets. I am going to make some for my first grade teachers using the baseball card plastic sleeves. I love your blog!

Julie says

Barbara, I know this post is several months old, but I would love to know how you used the baseball card pockets. I’ve got lots of them on hand, and half the summer left. Would you be willing to share how you did this?

Thanks!

Julie

Kim says

Hi Donna!

Working with kids in fifth grade, I am finding a similar problem–especially when it comes to decimal fractions. (Out come the manipulates once again!)

I love that you share the conversations you have with kids–it always gives me ideas about how to structure my own chats.

Thanks for another great post. I am passing it along to a first grade teacher friend for the nifty ten frames.

I hope you enjoy this special day!

Kim

Finding JOY in 6th Grade

Donna Boucher says

Oh, yes, Kim! Decimals and fractions are such abstract concepts. Teachers must extensively use manipulatives and multiple representations for students to truly understand. Concrete learning is for ALL grade levels, not just the primary ones!

Carol says

Metric measurement makes decimals concrete!! US needs the metric system!!!

Jessica says

Hi I was wondering what the holder is that you put the ten frames in and where did you get it? Thanks so much. Jessica

Donna Boucher says

That is the student ten-frame kit that you can buy, Jessica. It includes the plastic ten-frame tiles and the wallet. The link is in the blog post.

Kari Augustine says

If you have a laminator at your school, you could use the cut off double-thick plastic to sew narrow strips into a wallet for kids. Felt might be good for the outer wallet material. Set your stitch very long and use a sharp needle. I like the idea of having students color in their own cards – lots of thinking gets done at the same time as the coloring.

Donna Boucher says

Good idea, Kari! Thanks for sharing. 🙂

Michelle Cota says

I use trading card protector pages–it has 9 pockets on it. Perfect for fitting sets of cards, they are 3-hole punched so they fit nicely in a 3 ring binder. 🙂

Robin Ryan says

Donna,

Once again, I find something that I can immediately use in my first grade classroom. For free! Thank you so much for your generosity and your expertise. I can’t wait to use these with my first graders. I really love your blog!

Robin

Donna Boucher says

My pleasure, Robin! We’re all in this together!

Rhonda Gamboa says

Please advise where you purchased the blue holder in the photo for housing the place value cards.

Donna Boucher says

It comes as part of the student ten-frame kit, Rhonda. Here is the link.

Melanie says

Love this idea. Since I teach 4th grade, I would have to make these up through 100,000. Any suggestions on how to do that, or should going to 100 be all I need.

Thanks.

Donna Boucher says

At that level, base-10 blocks or place value disks are great tools! But I would make sure they really understand the concept with smaller numbers before attempting larger ones.

Mariana says

Spent my Saturday evening making seven Base Ten sets for my second graders, who are struggling with skip counting. So, I’m going back to place value! For now I have their sets in baggies, but I am planning to put them in baseball card holders. Can’t wait to use them! Thank you for your generosity.

Donna Boucher says

Yea! That was time well spent, Mariana! I’m so glad you have a new resource for your kiddos. 🙂

Mariana says

My kids were so grateful that I made these for them! And I was able to get great data on where they are with place value. We will be using these on a regular basis! Thanks!

Barbara Sader says

I love the baseball card holder idea! Thank you, Mariana.

Lee says

Thanks for this post! Do you have the students ten frames as block dots instead of red?

Donna Boucher says

No, but I think if you just print it in B&W you’ll get the same effect.

Barbara Sader says

Thank you so much for all of your wonderful blog posts and materials! I am currently a math interventionist in La Porte, TX and I am loving all the ideas that you are sharing. This is my first year to work in this position and I am grateful for your willingness to share and help others!

Barbara

Donna Boucher says

Congratulations on your new position, Barbara! I’m so glad that my blog is helping you out!

Angie says

I am working on place value with my intervention group too. I asked them to make 25 the other days using ones but they couldn’t count by ones they needed to find another way. I was hoping that they would put their ones into groups of five then push them together to make 10 to show both number fact knowledge and an understanding of teness. At first they really struggled as they wanted to count by two s but could only count to 12 but after now doing this same process for four days they have begun to see that the tens are not a single unit eg 2 tens 5 ones but still have a way to go.

Barbara says

Hello Donna-

I love your ideas and was wondering if you offer professional development at schools. Could you please let me know? Thanks so much!

Donna Boucher says

Yes, Barbara, mostly in the summer, since I work full-time. Here’s the link to my contact page.

Joel Gaspard says

Hello,

Here is a basic interactive ten frame tool with two color counters to model numbers and equations:

http://www.toytheater.com/two-color-counter-ten-frame.php

In addition you can draw on the page to write numbers and equations to match what is being modeled in the ten frame.

Cheers, Joel

Trish says

I really enjoyed reading your post about place values. I am a student right now, working towards my teaching degree. Place value and having students understand it was a big topic we covered. I loved they way you worked with the students to figure out that the 4 in 43 stood for 40. It is very important that students know how to represent place value. Knowing place values will better help students understand adding and subtracting as well as multiplying and dividing. Thank you for this post. I will take this with me so I can use it with my future students.

Marie says

Thank you for the idea of the baseball cards holder! I printed theses ten frames a long time ago and also kept them in small plastic bags. Oraganizing them will certainly make them more user friendly!

When I have my first graders match amounts to digits, I have them say the tens and ones part, and then we go into our “math language” : two-ten three or twin-ten three to twenty- three ( the -ty) part of the word is short for ten. It still takes a bit for the kids who struggle but I think constantly talking this way helps them bridge the language connection.

Jacqueline M Woodley says

I am a high school teacher in Australia, and just thought I’d share the fact that students are still struggling with the concept of place value at year 7 level…our testing comes back that place value is crucial in areas of measurement and number work. Thanks for sharing ideas and strategies.

Wendy Prout says

In making the tens frames for this activity do you have a frame that is empty to represent zero? I am not seeing it in the information that I printed. Thank you for these materials.

Donna Boucher says

No, I didn’t make a blank one. If they are using them to build 2-digit numbers, they wouldn’t really use an empty ten-frame, would they?

Wendy Prout says

That is true. We were copying the picture and thinking about how to incorporate the idea for three digit numbers. Thank you

Jennifer says

Your blog is absolutely incredible! Yet another post that shares your real life journey into helping kids develop mathematical understanding. Reading your posts has helped me greatly in my work as a learning support teacher. Just wanted to pass on my gratitude!