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Teaching Place Value with Base-Ten Blocks: Free Place Value Mats & Activities

If you’re not familiar with CRA, it stands for Concrete, Representational, and Abstract. It’s a research-based instructional sequence that helps students develop a deeper understanding of mathematical concepts.

  • Concrete: Students use hands-on manipulatives to make sense of a new concept.
  • Representational: Students represent that same concept using pictures or visual models.
  • Abstract: Students use numbers and mathematical symbols to represent the concept.

If you’d like to learn more about the CRA instructional sequence, check this out. In this post, let’s explore what CRA looks like when teaching place value.

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.

Students begin building place value understanding long before they reach second grade. In first grade, they use groupable manipulatives, such as linking cubes, to model numbers to 120 and develop an understanding of tens and ones. If you’d like to see what that progression looks like, you can read more about it in this post.

By the time students reach second grade, they may or may not have had experience using base-ten blocks. Even if they have, they don’t always understand what the blocks represent. A valuable introductory lesson is to connect linking cubes to base-ten blocks, helping students see that both models represent the same quantities. Making that connection helps students understand what the base-ten blocks represent before they begin using them with larger three-digit numbers. You can read more about that lesson in this post.

Place value mats are a great tool for organizing base-ten blocks during small-group instruction, guided practice, and place value games. They help students keep each digit in the correct place while making clear connections between the concrete manipulatives and the values they represent. The column headings include pictures of the corresponding base-ten blocks, and the ones column features a ten-frame to help students organize their ones and recognize when it’s time to regroup for a ten.

I’ve created two versions of this place value mat. The hundreds version prints on legal-sized paper, while the thousands version prints on 11 × 17 paper to provide plenty of room for base-ten blocks. Keep reading for ideas on using the mats effectively, and you’ll find the free download at the end of the post.

place value math to hundreds and thousands with ten-frames to hold unit cubes for the ones

This activity works especially well during small-group instruction. At the beginning of the year, your small groups should be based on students’ readiness, using assessment data to determine how well they have mastered the previous year’s place value standards. Even in a small group, have students work in pairs so they can discuss their thinking as they build each number.

In the example below, I simply say, “Build the number 225,” and students use base-ten blocks to represent the number on their place value mats. As partners finish, encourage them to explain how they know each block belongs in a particular place value and how the model represents the number.

picture of a place value mat and base ten blocks showing the number 225

If you want to extend the lesson beyond the concrete stage, have students use whiteboards to record the number in standard form (225), word form (two hundred twenty-five), and expanded form (200 + 20 + 5). This provides a natural bridge from concrete models to more abstract representations.

The same activity also works well as a whole-class lesson. Display the number under a document camera or on an interactive whiteboard while students build it on their own mats and discuss their thinking with a partner.

Once students are comfortable building numbers, it’s time to add a little problem solving. After students build the number 225, ask them to add 7 more using their base-ten blocks. Their mats will look like the one below. The ones have spilled over the ten-frame. Ask students, “What do you notice? What should we do next?”

picture of a place value mat and base ten blocks showing the number 232

This is where having students work with a partner really pays off. Give partners a few minutes to discuss what they notice and what they think should happen next. Students already have the background knowledge that ten ones can be regrouped as one ten, so they have everything they need to solve the problem. It’s okay if not every pair arrives at the solution. The goal is for every student to grapple with the problem and listen as classmates explain their reasoning. A few partnerships will likely recognize that it’s time to regroup, giving the class an opportunity to discuss why that makes sense.

Now we can trade those ten ones for a ten.

picture of a place value mat and base ten blocks showing the number 232

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… 🙂

picture of a place value mat and base ten blocks showing the number 232

Once students have had opportunities to build numbers and regroup with the place value mats, they’re ready to use them in a game. Remember, the best time to introduce a game that will eventually become part of your math workstations is during small-group instruction. This gives you the opportunity to model the game, observe students’ mathematical reasoning, and make sure everyone understands how to play before they’re expected to play independently.

instruction card for a place value game called race to 100

In Race to 100, partners take turns rolling a number cube and deciding whether to use the number rolled as tens or ones. As they build their numbers on the place value mats, they’ll regroup whenever they fill the ten-frame in the ones place. The strategy comes from deciding whether to add tens or ones as they try to get as close to 100 as possible without going over.

Building a strong understanding of place value takes much more than memorizing the value of each digit. Students need opportunities to model numbers, regroup, solve problems, and talk through their thinking with classmates. I hope these place value mats and activities help your students build a deeper understanding of our base-ten system. Be sure to download the free place value mats and Race to 100 game before you go!

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28 Comments

  1. 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?

    Reply

    2. 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.

      Reply

    1. 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.

      Reply

    1. 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? 🙂

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    2. 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…

      Reply

  6. 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

    Reply

  8. 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 !

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  9. 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!

    Reply

  10. 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.

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    1. 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.

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  11. 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

    Reply

    1. 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.

      Reply

  13. 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?

    Reply

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