## Fractions! Meaning Making for Comparing Fractions

Fractions is one of the most challenging math topics. Many high school and college students struggle to some degree with fractions.  The Common Core of State Standards (CCSS), despite all the criticism, includes components to address the conceptual understanding of fractions. Below is a photo showing a 4th grade Common Core standard regarding fractions along with an objective for a class lesson I taught at an elementary school in my district. I subsequently presented on this at the national CEC conference in 2014. Notice the bold font at the bottom, ¨justify…using a visual fraction model.¨ The photo above shows an example of a model I used in class.

The photo below shows a handout I used in the lesson. The first activity involved having students create a Lego representation of given fractions. These would eventually lead to the photo at the top with students comparing fractions using Legos. The students were to create the Lego model, draw a picture version of the model then show my co-teacher or I so we could sign off to indicate the student had created the Lego model.

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 lines – see photos below.

In lieu of a school having to make technology available for vast numbers of kids it is possible to use personal technology. The apps identified here can be useful in a math course.

Polls would allow personally relevant data collection and could lead to modeling opportunities (not on the runway, models like linear functions).

Plinky would allow a high tech version of an exit slip.

Group Tweet would allow collaboration on a project and provide details for a student who is absent. You could match kids with kids at another school…maybe another country!

I would love to field some input from readers.

## Visual of Inclusion

This image is making the rounds through various social media outlets. I think it is a wonderful representation of the various settings and situations encountered in special education. I will share my take on each of these.

Full inclusion is the ultimate LRE (least restrictive environment) but is simply not the appropriate placement or LRE for some students. My son Gabriel rarely encounters this model because it is simply would not work for him. Even when it is the appropriate LRE it is incredibly challenging to enact for various reasons which I’ll enumerate.

Special ed teachers are often overwhelmed with responsibilities to provide the support for a full inclusion environment.

Administration does not allow for the factors necessary for implementation, e.g. providing a student with the individual attention necessary.

For the most part, general ed teachers simply do not know how to or do not take responsibility for providing accommodations necessary, especially ones not listed in the IEP.

The other models are both useful and misused as well. Exclusion can refer to how students in special education either are denied access to or could not make use of many opportunities or classes. Segregation would represent a self-contained placement. It has its place in services. My son Gabriel has situations in which it is necessary and desired. The integration model is also perfectly valid. Some students are not capable of being fully woven into a class but they can benefit from proximity to peers.