Three ways to represent perimeter: I taught a lesson on perimeter to a 5th grade class. First I had them create a rectangular pen for their animals and they counted the number of fence pieces. Then we drew a rectangle to represent the pen. Finally we looked at the formula. This allows a deeper conceptual understanding of the concept. This is known as Concrete-Representation-Abstract – representing the concept at all three levels.

## Representations of Concepts

**Tagged**Bruner, concrete, CRA, hands-on, kinesthetic, perimeter, representations

[…] photos below are used to introduce length and area as part of a CRA approach. First a student is asked to build a Lego garage. He first builds the bottom row of a wall […]

[…] the “mathy” way of talking about it. This follows the Concrete-Representation-Abstract (CRA) approach to presenting […]

[…] 2 sided tokens to support his work with integers (red for negative and yellow for positive) in a CRA approach. The color coding and tokens were like the swimmies in the photo above of the child in the […]

[…] Lego model is the concrete representation in CRA. In this lesson I subsequently had students use fractions trips (on a handout) and then number […]

[…] Below is a video of a lesson I recorded on function notation using the Explain Everything app. The lesson starts by addressing the concept of function notation by connecting it to the use of the notation “Dr.” as in Dr. Nick of Simpson’s fame. The lesson builds on prior knowledge throughout with a focus on color coding and multiple representations. […]

[…] graduate students). I suggest using this after manipulatives and before visual representations in a CRA sequence. It is hands on but it includes the symbolic representation (numbers) as opposed to just base 10 […]

[…] The sequence of manipulatives, drawings then the actual “mathy” stuff constitutes a Concrete-Representational-Abstract (CRA) model. Concrete = manipulative, Representational = picture, abstract = symbolic or the […]

[…] math symbols (below). Addressing the concepts, vocabulary and the process with this approach is a concrete-representational-approach (CRA). The equations below would not be addressed until the conceptual understanding was developed. […]