Let's Dig Into the CRA Model
Concrete - Representational - Abstract
The purpose of teaching through a concrete-to-representational-to-abstract sequence of instruction is to ensure students truly have a thorough understanding of the math concepts/skills they are learning. When students who have math learning problems are allowed to first develop a concrete understanding of the math concept/skill, then they are much more likely to perform that math skill and truly understand math concepts at the abstract level.
CRA Model vs. GRR Model
While the GRR Model is a gradual release of responsibility, the CRA model is a sequenced and gradual increase in mathematical knowledge, allowing students to grow toward independent practice. The end goals are the same!
UNIT PLANNING
Each grade level has a unit planning day coming up. The CLEAR protocol is used to develop a high level of clarity for the content taught in a given unit. While planning math, allow the CRA model to rest in the background of that planning. It will shift to the foreground as you think about resources needed during a unit, but otherwise it will rest in the background.
As you plan your daily lessons is when the CRA model will come to the foreground of your planning.
So first, build clarity with the content taught in a given unit with the CRA model in the background.
DAILY PLANNING (My example is from Grade 3, Module 5, Lesson 8) - Represent parts of one whole as fractions with number bonds
As you develop your lesson plan, understand a few things:
- You have a total of 70 minutes dedicated to math.
- Each Eureka lesson is slated to last 60 minutes, which includes math fluency as part of the 60 minutes.
- Each Eureka lesson embeds the Representational and Abstract. Some also embed the Concrete!
- Use of the CRA model must fit into the daily lesson. We can't afford to extend a given lesson, thus altering the math pacing. Extending a lesson isn't necessary. Trust me on this!
What does a Eureka lesson, infused with the CRA Model look like?
- Fluency Practice should take no more than 12 minutes.
- The Application Problem should be trimmed from 10 minutes to 5 minutes. I recommend that you give the students that problem for the sole purpose of seeing what they do with it! Give it and observe! Write down what they are doing, how they are solving it, and what their misconceptions are. You will use that knowledge during the Concept Development.
- The extra five minutes from the Application Problem can be added to the Concept Development. Under the Concept Development, you will see Problems that are written in bold. The narrative (T:... S:...) that follows can be thought of as a safety net if you need it. Think of it as you do the Calkins narrative. Use it as you see fit while teaching the lesson.
- Start by showing students the Abstract, for example, 3/8 + 5/8 = 1. The Abstract will be visible as you go through the Concrete and Representational.
- Start with the Concrete. Using "The Fraction Tower" I will model how 1 can be broken into 8 unit fractions. I will model how 8 unit fractions is the same as 1 whole unit. I will model how 3/8 and 5/8 equal 1. See images below.
- Move to the Representational using pictures. Keep the Abstract visible - 3/8 + 5/8 = 1. See the images below (these are typically shown in the teacher manual).
- Using the "Fraction Tower," invite pairs of students to show another way to organize the 8 unit fractions using the "Fraction Tower" blocks and drawing representations. For example 1/8 and 7/8, 2/8 and 6/8, 4/8 and 4/8. Invite pairs to do the same with tenths and fifths (collaborative practice).
- When the students are ready, they will complete the Problem Set, which integrates the abstract. Allow students to use the "Fraction Tower" if they choose to use it.
- Do the Student Debrief.
- End with an Exit Ticket.
1 is broken into 8 unit fractions
1 and 8 unit fractions are the same
3/8 + 5/8 = 1
Build Your Toolbox
The C-R-A Model may be new to you. Take time to learn more about it! Remember, an important part of Domain 4 and more importantly, something great teachers do, is to continue to learn and grow. Here are some resources:
https://mscastillosmath.com/2018/05/03/scaffolding-instruction-through-the-cra-approach/
http://www.therecoveringtraditionalist.com/how-to-use-representation-in-the-cra-method/
My Goal For You
My goal is to use the upcoming Unit Planning to plan with CRA in mind.
By the end of January I would like each grade level to provide to me a list of manipulatives needed for purchase.
By the end of February I would like to see lessons written with the CRA model evident.
I will conduct walk-throughs in March providing feedback on the CRA model for the purpose of supporting teachers.