What is CRA you ask? It stands for concrete, representational, and abstract, and it's a research based instructional sequence that results in 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.
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.
|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... :)|
here to grab a copy of the I Can card instructions.