IXL.com is a site that provides online practice for math (and other topics). It has a hidden feature that allows for very effective differentiation. This can be highly useful in a general ed math class and in settings for special education services. This includes special ed settings with students working on a wide ranges of math topics, for algebra students who missed a lot of class or enter the course with major gaps, and for the general algebra population to meet the range of needs. IXL can be used before the lesson or after, for intervention.

By way of example, assume you have a student or students working on graphing a linear function using an XY table (image below). Using a task analysis approach, this topic can be broken up into smaller parts: completing an XY table, plotting points and drawing the line, interpreting what all of this means. I will focus on the first two in this post.

IXL has math content for preschool up to precalculus. For the topic of graphing (shown above) many of the steps are covered in earlier grades. For example, plotting points is covered in 3rd grade (level E), 4th grade (level F), and 6th grade (Level H). To prepare students for the graphing linear functions, they can be provided the plotting points assignments below to review or fill in gaps.

The tables used to graph are covered starting in 2nd grade (level D) and up through 6th grade (level H). These can also be assigned to review and fill in gaps.

When it is time to teach the lesson on graphing a linear function, IXL scaffolds all of the steps. For example, the image below in the top left keeps the rule simple. The top right image below shows that the students now have an equation in lieu of a “rule.” The bottom image below shows no table. All 3 focus on only positive values for x and y before getting into negatives.

The default setting on IXL is to show the actual grade level for each problem. I did not want my high school students know they were working on 3rd grade math so I made use of a feature on IXL to hide the grade levels (below), which is why you see Level D as opposed to Grade 2.

Several special ed teachers identified solving multi-step equations as the most challenging math topic to teach in middle school math. Here is my approach to teaching multi-step equations like 3m + 4m + 1 = 15. .

First, I use a task analysis approach to break down the math topic like we cut up a hotdog for a baby in a high chair. MOST of the steps involved are prior knowledge or prerequisites skills. I present these in a Do Now (warm up, bell ringer, initiation) – see image below. This allows me to fill in the gaps and to lay the foundation for the lesson. The prerequisite skills include simplifying expressions and solving 2 step equations. I also present meaning for the equation with a relevant real life problem that is modeled by this equation. By attempting the walkathon problem without the “mathy” approach, the students will more likely understand the equation and why they add 3m and 4m.

After reviewing the Do Now I use Graspable Math, which is a free online application that allows users to enter their own expressions and equations. These can be manually simplified and solved by moving parts around. Here is a tutorial on how to do this. This allows them to manually work with the simplifying and the equation before working on the handout, in a concrete-representational-abstract approach.

This is followed by a scaffolded handout with the use of color coding. I have student work on the first step in isolation as that is the new step (the other steps are prior knowledge and were addressed in the Do Now). This avoids all the work on the other steps that can result in sensory overload and allows me to address mistakes in the new content immediately.

This handout can have the equations removed and be used as a blank template to follow. In turn this would be followed with regular solving worksheets.

A common scenario involves a school official reporting out the grade level in math for a student. For example, a 7th grade student I was helping had tested at a 4th grade level. As a result, the student spent much of her 7th grade year working on 4th grade math.

There are a couple problems in establishing a grade level in math. First, unlike reading, math is not nearly as linear. The image below shows a breakdown of the Common Core of State Standards math categories, called domains. In a video, I use this graphic to unpack why it is more challenging to determine a single level of ability for math. In short, the reason is the student could be doing well in some categories and doing poorly in others. Second, the testing used to establish ability level can be problematic for the student. For example, the student may not have the stamina or attention span to endure a longer assessment.

If you are presented with a single grade level as an indicator of math ability, I recommend that you ask for a breakdown by category and how your student will be provided differentiation to address gaps. This is more appropriate than plowing through all of the math at a lower grade level.

I used this site, Explorelearning, with a 7th grader with Aspergers who tested at a 1st grade math and reading level. We used the Photo Synthesis Lab (screen shot below) to gather experimental data on the hypothesis “what helps flowers grow?” He won at the school level and went on to district competition.

(As of April 2020 you can get free 60 day unlimited access.)

I was a guest on special ed attorney Dana Jonson‘s podcast. Below are links to items I cited in the discussion. There is a contact information form in this post.

Here is what we are doing at home during school closure time. I created a Google Classroom (anyone with Google account can create a class on the Google Classroom app) and posted links to IXL topics (photo at bottom). (NOTE: this is one method I use to differentiate at school.) If the school is providing online work, you can enter this into the classroom as well.

The following are screen shots of online math worksheet websites I use. The variety and the options in the criteria you select for your worksheets for some of these sites allows for differentiation in the classroom.

I will start with my favorite site, Math-Aids.com. This site allows for dynamic selection of criteria for each handout (see 2nd photo below) such as choosing the types of coins in problems for counting out the total value. The coin images are outstanding! It also offers content up to Calculus.

Super Teacher Worksheets is often used elementary schools. It offers content in science and language arts as well. It requires a $25 annual subscription which I easily find to be worthwhile.

Common Core Sheets is very useful site if you want to find handouts for specific standards by grade level (see 2nd photo below). It offers multiple versions of each handout.

Dads Worksheets provides a large bank of worksheets – multiple versions of each worksheet.

Math Worksheets 4 Kids offers multiple versions of each worksheet and content in science and language arts. There are many worksheets that provide unique support in how the work is presented, e.g. the Ratio Slope worksheet shown in the 2nd photo below.

Worksheet Works is my 2nd favorite. It offers options in the criteria you choose, e.g. difficulty level (2nd photo below). They also offer unique types of handouts such as a maze with math problems to solve to find the path (2nd photo).

The students loved playing the game, it was engaging so they practiced the counting out money, I was able to collect data, and I was able to differentiate. When I co-taught a Consumer Math course, I would assign a para (instructional assistant) to facilitate the game with a couple students and to collect data.

To ensure the IEP team is on the same page as to what mastery of an objective looks like, the person writing the objective can take two steps:

provide an example problem that would be used to assess mastery (and the example problem would have the same language as used in the objective)

provide an example of a response to the example problem cited above that would be considered mastery level work

The graph below is not data. A graph is a representation of summary statistics. This summarizes the data.

The chart below does not show the actual prompts, e.g. what number was shown to Kate, but it does show the individual trials. This is data, with a summary statistics at the end of each row. Here is a link to more discussion about data, with an example of a data sheet I use.

The data shown below addresses the student’s effort to solve an equation. Problem 21 is checked as correct and the error in problem 22 is identified. I can use this data to identify where the student is struggling and how to help. NOTE: the math objective would use the same verb as the problem: solvethe linear equation.

The excerpt of a data sheet, shown below shows trials in a student’s effort to compare numbers.

Data below shows a student’s effort to evaluate integer expressions.

This applies to all areas beyond math. The chart above or the data sheet I linked above show data sheets that indicate the prompt and the results, with notes. For example, if I am asking my son to put on his shoes, each row of the data sheet is a trial with the outcome and notes.

Perhaps the vast majority of students with disabilities need support with math. Their challenges with math can be directly related to their disability or can be the result the effects of an ongoing struggle with math. The later results in what is termed secondary characteristics.

When I work with students with a disability, I first seek out background information about the student to identify what interests them, what reinforcers (rewards) can be used to enhance their performance, and what challenges and behaviors need to be addressed. Upon gather this information, I often decide to use a token sheet that is personalized for each student.

Below is an image of such a token sheet. At the start of our work together I felt the student in question needed immediate reinforcement for work completed to get him into a groove. I was also targeting a behavior in which he would draw dots on each digit he wrote, which slowed him down considerably. He would earn a Scooby (I would circle it) in the middle column for completing his work and an extra Scooby in the right column if he wrote digits appropriately (no dots). After 2 sessions, his dot writing dropped significantly to the point that I was able to remove the column on the right. As you can see at the bottom, 5 Scoobies resulted in iPad time.

This can be particularly effective for students who have more severe math anxiety, a fear of failure, or have ADHD. Such a token sheet can be included in the accommodations page of the IEP.