What is CRA you ask? It stands for concrete, representational, and abstract, and it’s a research-based instructional sequence that results in a deeper understanding of mathematics concepts.

- Concrete learning is hands-on. It’s using manipulatives to make meaning of a new concept.
- Representational is showing that same concept using pictures.
- Abstract is representing a concept using symbols.

This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend. Now that I’ve set the stage, let’s talk about place value.

I talked with both 2nd and 3rd-grade teachers today, and both grade levels are starting the year with place value. In 2nd grade, they will use groupable manipulatives, linking cubes, to model numbers with tens and ones (a review from 1st grade). Van de Walle recommends groupable manipulatives prior to using traditional base-10 blocks, because they can physically be joined together and broken apart. Traditional base-10 blocks are actually a little more abstract because, for example, you can’t break the tens rod apart into ones–you have to trade it for ones. 2nd grade will then transition from the linking cubes to base-10 blocks as they extend their learning to hundreds.

In 3rd grade, my good math buddy Jeremy wanted a place value mat that the kids could use to work with base-10 blocks (concrete) and that also had representations of each place value (representational), so I whipped up this PV mat for him. Note that it prints on 11 x 17 so the columns fit the base-10 blocks. Of course, you can scale it down to print it on letter-sized paper, but the columns won’t fit the manipulatives. I love how he wanted the ten-frame for the ones! Great bridge to prior learning. Click here to grab yours and read on for suggested uses and another freebie.

For a whole-group lesson, Jeremy called out numbers and the students built them on the mats. Here Jeremy shows us 225. If you have a document camera or interactive whiteboard, extend this lesson by showing different forms of the numbers: standard form (numbers), word form, and expanded form.

Let’s throw a little problem solving in. After building the number 225, Jeremy asked students to add 7 more to the number, resulting in a mat that looks like this. Notice that the ones have spilled over the ten-frame. Hmmmm, what to do?

Yes! That’s right. Let’s slide ten of the ones to the tens column

Now we can trade those ten ones for a ten.

And to complete the picture, let’s slide the two ones into the ten-frame. Hmmm, I wonder what would happen if we added 8 tens… 🙂

So this is a great whole group mini-lesson, now let’s move the place value mat into a workstation for a little game of Race to 100. I wonder if I could beat Jeremy… 🙂

Click __here__ to grab a copy of the I Can card instructions.

This is something I’ve done in my intervention classes (2nd gr.) for place value and addition/subrtration w/regrouping. For several years, now, it has been pretty effective. One difference- I use 2 ten frames. Would there be an advantage to using just one ten frame for the ones place?

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Funny you should mention that! When Jeremy first showed me his rough draft of the PV mat, he had a double ten-frame. I suggested the single ten-frame, because I thought that the visual of some spilling over off the ten-frame would be easier for the kids to understand–like if it fills or spills over the ten-frame, you have to trade. I think it could really go either way.

How can I modify the place value mat for kindergarteners?

Hey Iris,

So, for Kindergarten, you want to focus on numbers from 11-20 and the structure of tens and ones. A great tool is a double ten frame, because the kiddos see a number like 14, for example, as a ten and 4 “leftovers”. You can also start to group objects into groups of tens and leftover ones. For example, using 18 beans, students put 10 beans in a cup and have 8 leftover.

Wow! That’s crazy! I blogged about the same thing http://mathswithmeaning.blogspot.com.au/2012/08/quick-place-value-freebie.html – I have my set laminated and we use them all the time!

Great minds think alike!

Alison

Hey Allison,

Okay, so I’m going to have to ask. What is MAB? Is this some Aussie thing, or is it something I should know about? Very cool that we both blogged about the same idea! I think that means I should come visit you in Australia so we can compare notes, don’t you think? 🙂

Haha! Definitely! I always accept US visitors!

MAB are the blocks that you showed in your pictures? I used them when I taught in the US too and had no idea you didn’t call them that!!!!! We also call them Place Value Blocks – maybe I should have called them that in my post! Stands for Multi-base Arithmetic Block…

This is so helpful, Donna! Thank you so much for sharing! Your blog is wonderful! I look forward to your posts each time!

Linda

AroundtheKampfireThanks so much, Linda! I’m glad you find my blog useful. I’m following your blog now. 🙂

So happy to find your blog today! I have u bookmarked! Love this!

Of COURSE I use technology! I just hopped over to your blog and I’m a follower now. 🙂

I love doing this as a dice game. At first, we play together and roll 1 die for the class while everyone plays on their board. Then, I let them play in partners, adding the number they roll, and ‘race’ to 100. I can circulate for assessment and mini lessons one on one!

I also loooove using Goldfish Colors to represent the places in a ‘code’ as our next step. I wrote about it last week on my blog!

Jenny

Luckeyfrog’s Lilypad

Great way to scaffold their learning! I hopped over to your blog to read the fishie story. Cute!

I love the idea of using a ten-frame in the ones column. I’m new to primary, so that’s one of those things I’m figuring out as I go! 🙂 I am your newest follower!

~Erin

Mrs. Beattie’s Classroom

Welcome, Erin! I’m so glad you found something useful! 🙂

I used this mat for some reteaching with 4th graders this year. Thank you for your resources, and your blog ! I have many fourth graders who struggle with the place value concepts for hundreds and thousands – understanding that one thousand four hundred is equal to 14 hundreds. They can do it with manipulatives, but struggle with the concept in pictures or when asked to apply this in problem solving. Do you have any other suggestions about moving them from concrete manipulatives to more abstract understanding? Are there any anchor charts that relate to this? Thanks !

So glad you mentioned using ten-frames first! Research shows that, even though ten-frames are often pictorial rather than concrete, they help students develop an understanding of a number in relation to ten more than base ten blocks. Once students have reached this level of understanding, they are ready for the linking cubes and, later, the more abstract base ten blocks. Thank you so much for your wonderful ideas! I was a math specialist for 4 years and now teach junior Kindergarten. I enjoy following your blog and have been able to use your resources. Keep inspiring good math teaching!!! It is very encouraging!

I teach fifth grade and for many years, more than I want to think, I’ve used base ten blocks to teach decimal place value. The flat becomes a one, the rod is a tenth, and the cube is the hundredth. I approach decimal place value just as you would whole numbers. I also love doing riddles such as build two wholes, five tenths, etc. and make sure some will require regrouping. Number sense and place value are so important to the understanding of any mathematical content.

Yes, Patty, students need to see that the base-10 blocks can represent different things with decimals! Definitely leads to flexible thinking and helps students better understand the relationships in our place value system.

Hi Donna,

I’m a new TK- 5 math coach. I’d like to talk to you about the curriculum that you use in Texas for CPA. I’m not satisfied with the curriculum our district is looking at and I want to know what y’all use in Texas.

Thanks,

Susie

Congratulations on the new position! Of course I can’t speak for all of Texas, because each district and even school is different, but to me CRA is just using lots of manipulatives and then pictorial representations. Any curriculum will have to be supplemented, because the best a textbook can do is pictorial. Sometimes textbook programs include suggestions for hands-on lessons, but I usually don’t find those to be enough. Manipulatives…pretty much every day.

How would you use this approach with decimals up to the thousandths?

Great question! You redefine the value of the base-19 blocks. Check out this blog post for more information.

I cannot download the instructions.

Are you getting an error message of some type?

I tried to download the file of the place value chart and it says it is in the owner’s trash. How can I get a copy of this?

My bad!! Try now, I’ve restored it. Thanks for letting me know!