Math is a language with words and other symbols that also makes sense of the world around us. We consume and know more math than we realize or allow ourselves credit for.

When buying the latest iteration of an iPhone, we may call forth algebra. How much will you pay if you buy an iPhone for $1000 and pay $80 a month for service? Well, that depends on how many months you will use this iteration before moving on to the next iPhone. The number of months is unknown so algebra gives us a symbol to represent this unknown number of months, x (or n or whichever letter you want).

Just as there is formal and informal English (or other language), we can engage algebra formally or informally. You don’t need to write an equation such as y = 1000 + 80x to figure out how much you will pay. You can do this informally, compute 80 times 10 months + 1000 on the calculator. Then try 80 times 12 months etc.

Math provides us a means of organizing and communicating ideas that involve quantities like the total cost for buying an iPhone.

The difficulty in learning math is that it is often taught out of context, like a secret code. In contrast, a major emphasis in reading is comprehension through meaning, such as activating prior knowledge (see below).

In fact, math absolutely can and, in my view, should be taught by activating prior knowledge. My approach is to work from where the student is and move towards the “mathy” way of doing a problem.

Without meaning, students are mindlessly following steps, not closer to making sense of the aspects of the world that involve numbers.

Counting out the total value for a set of coins can be very challenging for students who struggle with money.

Here is a video showing how to use a WORD document table a former colleague and I created to support students in a life skills class. The video shows how this handout is used but does so with a virtual version the can be completed on the computer (see image below). Here is a link to the virtual document.

To help students learn how to measure with a ruler, I focus on minimizing the number of tic marks on the ruler at first. The image below shows an excerpt from a WORD document with a halves ruler that I use and an instructional strategy. It also contains a quarters and an eighths ruler that students can slide around the WORD document as shown above and in a video explaining this artifact and how I created it.

This is useful for distance learning as well as in class. Here is a link to the WORD document with the rulers shown in the video.

I will be fielding questions about math and online learning in real time. As a follow up, I will respond to questions through this blog post. If you did not catch the Instagram session and have questions, you can post them here through a comment. I will post replies on this post.

Below is a list of links to resources, e.g. online handouts, activities, which align with the discussion.

Online math games (click on the words Online math games for a post that explains each site)

Here is aĀ link to handoutsĀ to help you access Khan Academy which covers a wide range of math grade levels and other content areas, and the ACCUPLACER practice app to prepare for college placement tests.

BrainGenie is a FREE website that provides practice problems for almost all the math topics from 1st through high school. Each math topic has a link to a 1-2 minute video showing an example. Parents and tutors can choose topics to assign to a student as a Goal and the parent or tutor can click on the results to see student work.

Karen Linder (advocate and parent of a son with a disability) and I are collaborating on a series of Parent User Guide materials for parents. The goal is to scaffold parent efforts to use the IEP. We are presenting documents in smaller chunks to make it easier for parents to understand the steps they can take without being overwhelmed with an already challenging endeavor of advocating for your child’s needs.

Our first installment is part 1 in understanding IEP objectives (see screen shot of front page above). There is a document with templates to use and an accompanying video to provide additional support in how to use the templates. Please share feedback so we can improve our efforts to help parents.

Please feel free to reach out to us if you think we can be of service or if you have questions.

In working with students, parents and IEP teams, I find that there is an assumption that math at some point, possibly beyond arithmetic, is simply a science fiction movie that is minimally related to real life. I hear from students as well as adults, statements like, “algebra, when are we ever going to use it?” My response is, ALL THE TIME!

The math we often present in school is a “mathy” version of the math we encounter in life. For example, the top photo below shows a pizza menu and a situation that is realistic. The calculator screen shot below the menu shows how we likely would solve the problem using a calculator on our phone.

Below is the same type of problem, but solved using “mathy” math. How many of us (besides me) are doing this at the pizzeria?

The point is, we engage in algebra but maybe do not use all the symbols and vocabulary of algebra, e.g. when we typed in 2.25 repeatedly in our calculator, we were working with the math term “slope.”

This has implications for secondary students whose post-secondary plans do not include college. If the math class is teaching “mathy” math but you want your student to learn math as it is used in real life, then an alternative math course is needed. This could be addressed through the IEP.

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.

Below is a photo of a hyper-doc that I use to map out a long range plan for math services and academics for students receiving special education services. Here is a link to a video explaining how the document is organized and how it “works.” (Note, the image of the document on the video is not crisp, so I suggest you look at the handout while watching the video.)

The document contains several links to resources such as videos, websites and blog posts that provide additional information. Feel free to reach out to me using the Contact Form on this page if you have questions or would like input. I am happy to help.

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.)

Here are a variety of online math game sites I have used over the years. Break is coming up for many districts. Maybe these can fill the void and allow some learning. Several address other content areas as well.

I have also used these games for break times at school to keep students working on academics.

If you have a child learning to count money, especially at an advanced age, there are some useful money games – especially ones with coins. I have students complete problems with actual coins then enter their response online.