## I introduce key characteristics with parabolas and use the analogy of a rollercoaster. Riding once (and never a again) the Superman rollercoaster at Six Flags New England got me thinking about this. At one point the roller coaster hits ground level (a zero) and then goes underground (negative y values).

### Handout

Here is a handout I use for the introduction. Here are images showing how I use the handouts. The table helps students visualize the x-values and y-values when looking at the graph. The rollercoaster provides extra context for the various characteristics, e.g., increasing means the rollercoaster is going up. Note the scaffolding by adding context clues for each characteristics.

I start with max height of the rollercoaster. I highlight the actual graph first, then the y-values in the table. Then point out we are looking for the x-values for what we highlighted.

The issue of highlighting the vertex for the increasing and decreasing values would be addressed when writing the interval. The idea of the rollercoaster at the tip top provides context to develop the concept.

Similarly, I start with the zeroes. Again, highlight the graph, then the y-values, then the x-values.

The issue of highlighting the zeroes for the positive and negative values would be addressed when writing the interval. The idea of the rollercoaster at the ground level provides context to develop the concept.

I has been effective to have students highlight the parts of the respective axis when discussing the domain and range (not discussed yet). A common challenge is understanding that the x-values continue to the right or left when it appears they simply go down. To address this, I use a very wide parabola to show more lateral movement.

### Jamboard

Here is a Jamboard. You have a make a copy to access it (see photo at bottom). Here is a FB Reel and a YouTube video showing how it works.

## Mailbag Jan 26, 2019

### Are you a parent of a student with special needs who is struggling with a math topic? Are you a teacher figuring out how to differentiate for a particular student on a math topic? Pose your question and I will offer suggestions. Share your question via email or in a comment below. I will respond to as many as I can in future mailbag posts.

Here is a topic multiple educators and parents ask about:

I don’t want my child to be stuck in a room. He needs to be around other students.

Randy:

Often we view situations in a dichotomous perspective. Inclusion in special education is much more nuanced.

In math if a student cannot access the general curriculum or if learning in the general ed math classroom is overly challenging then the student likely will not experienceÂ full inclusion (below) but integration (proximity).

For example, I had an algebra 1 part 1 class that included a student with autism. He was capable of higher level algebra skills but he would sit in the classroom away from the other students with a para assisting him.Â  Below is a math problem the students were tasked with completing.Â  Below that is a revised version of the problem that I, as the math teacher created, extemporaneously for this student because the original types of math problems were not accessible to him (he would not attend to them).

I certainly believe in providing students access to “non-disabled peers” but for students who are more severely impacted I believe this must be implemented strategically and thoughtfully. Math class does not lend itself to social interaction as well as other classes. If the goal is to provide social interaction perhaps the student is provided math in a pull-outÂ setting and provided push-in services in other classes, e.g. music or art.

Here are the details of example of a push-in model I witnessed that had mixed effectiveness.Â  A 1st grader with autism needed opportunities for social interaction as her social skills were a major issue. She was brought into the general ed classroom during math time and sat with a peer model to play a math game with a para providing support. The game format, as is true with most games, involved turn-taking and social interaction. The idea is excellent but the para over prompted which took away the student initiative. After the game the general ed teacher reviewed the day’s math lesson with a 5-8 minute verbal discussion. The student with autism was clearly not engaged as she stared off at something else.

Inclusion is not proximity.

## Real Life Relevant Context for Students with Autism

Â

InÂ Â a lesson on functions I provided a student with autism the input and output mapping on the left as opposed to the problems like the one on the right. This student, asÂ I’ve written before, loves comics and superheroes and villains. He was tasked with matching (mapping) people with super powers with the organization to which they belong. He completed the assignment eagerly and quickly.