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
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.