I previously shared that grocery shopping has a lot of tasks that are overlooked. One is working with unit costs. There are two math tasks related to unit cost, interpreting what a unit cost is and computing the total cost for buying multiple items.
When I take a student into a grocery store to work on unit costs, where is what I do. I start with a pack of items (photo on the left) and ask the student to compute the cost for 1 item, in this case, “what is the price for the pack of chew sticks, how many in a pack, how much for 1 chewstick?” Then I prompt the student to compute the total if he buys 3 packs. This allows the student to differentiate between the two tasks. The cost per items is easier to grasp and then is followed with the same prompts for a jar of sauce (below right).
I then have the student compare unit costs for the large vs the small jars and ask, “do you want to pay $4.99 per ounce or $5.99 per ounce.” This language is more accessible than “which is a better deal?” You can work towards that language eventually.
These tasks can be previewed at school with a mock grocery store. The price labels can be created on the computer.
As a parent of a child with a disability and as a math educator, I am repeatedly struck by the fact that a group of adults (educators and professionals) convene to discuss and plan how to help a child. A great deal of time, resources, and money is concentrated on that child. Awesome! Unfortunately, in math education I frequently encounter situations in which this collective energy is concentrated on math that is more about boxes to check than engaging the student in math that he or she will need in post-secondary life.
IDEA enumerates the purpose of special education, with the transition goals aligned with employment, living skills, and future education that are desired for each individual student. This is explicit and aligns with the goal most teachers likely have, to make a difference in the lives of their students.
Despite this, when I am called in to help with math programming for a student I often find the math being presented to the student is not aligned with the post-secondary goals and often appear to the result of following the general ed curriculum, by default. Here are some examples.
I co-taught an algebra 1 class with a student impacted by autism to the point that he needed a paraprofessional guiding him through the daily work. He worked in isolation with the para and struggled with the basic elements of the course. It was not until his junior year that he was moved to a consumer math class.
A senior was in a consumer math course I taught. The course was for students who could not access the general curriculum, yet her transition goal for education was to attend a community college. This setting likely require a math course (that did not have consumer math topics) and a placement test.
Over 25 years of teaching math I have periodically heard educators minimize the struggles of students with math with the rationalization “they will never need this math.” My response is to ask why “then we are presenting this math to them?!”
So what math do they need? Here is a list of blog posts that address this question. In short, here is what I share with IEP teams, educators, parents, and special ed teacher candidates I teach.
If the goal is a career that involves a 4 year degree, then boxes must be checked. The student will have to have the math courses needed to get into the college and to prepare for the math in his or her major. This is the “mathy math” that will be on a college placement test as well.
For a 2 year degree at a school with open admissions, the focus of the high school math can be narrowed to the math course required (if any) and on the placement test. Typically, this would involve a focus on algebra. For the aforementioned 10th grader, we did not cover geometry and prioritized the algebra topics to cover.
For another middle school student whose goal was to have a job and to be as independent as possible. He loved sports and his mother said he would love to work in a sports related store. For him I recommended data and statistics (not the mathy type but meaningful and applied stats and data) to help him make sense of and discuss sports stats. This was complemented by a recommendation for consumer math.
I recently worked with a student on an online grocery shopping activity – finding ingredients for mac and cheese. We had the ingredients listed in a column on a Google Doc (allows both of us to edit the doc simultaneously) and then he cropped and pasted a photo of each ingredient (see photo below). The goal was for him to identify the total he need and the total cost in planning for actual shopping or to continue with the online shopping. Note: he wasn’t actually buying anything at this point but this was a step in preparing him to do so.
This activity is dense with math tasks and shopping related tasks. The math tasks include the following:
Identify the price (vs quantity of the item or unit price).
Interpret the quantity for the ingredient.
Identify the units (oz and cups)
Compare amount in box with amount needed.
Determine how much more is needed, if any.
Compare choices before selecting the item, (Barilla Pasta vs another brand).
To convert units, the “mathy” approach can be used or the student may simply use an app. For this student we chose an online unit converter (see below). This is more complicated that it appears. The student must choose the units and the order (in this case convert cups to ounces or vise versa), distinguish between imperial and US cups, understand that you enter the quantity (the search results in 1 US ounce appearing by default), and then interpret the decimal (keep in mind the ingredient quantities are in fractions).
Life skills math is more complex and challenging that parents and educators may realize. As a result, the planning for developing these skills should begin much sooner rather than later – not to mention the actual logistical tasks of shopping, e.g. finding an item in the grocery store.
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.
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.
Working independently and effectively with money is a crucial component to independent living. When I started working on math for students receiving special education I was taken aback by the number of high school students who could not work with money effectively, including counting out the total value for a given set of coins.
One of the first situations I encountered involved an upperclassman who, as reported by the parent, was learning to count money by completing handouts at school. This is NOT the way to learn to handle money. Worksheets can be used to target a specific individual skill but to learn to handle money the student has to actually handle real money.
This can take the form of baby steps – learn to crawl before walking. If a student has limited money skills here is one way to get started.
Have the student simply hand money or a card to a clerk (see photo below). This can be done while you are shopping and the student only hands over money and receives the money.
Pick a single item that costs a couple of dollars (and some change). Hand the student an appropriate number of bills (no change yet). Have the student count out the bills for a total and hand it over to the cashier. If necessary, have the student count out the money at a table or empty aisle in the grocery store then take the money over to pay. Then the student receives the coins and hands them back to you.
Same scenario but this time provide the student the bills and count out the pennies needed to pay. Choose an item that costs just a few cents, e.g. $2. 08. The student practices counting out bills and pennies.
Continue this with just dimes then dimes and pennies etc.
At some point you will want to address the concept of change returned by the cashier. To do this have the student pay with a higher bill (5 or 10 dollar bill), receive the change then count out the change at the table. Compare to what is on the receipt (see photo below).
For many of our kiddos this process can take a long time because the simple steps like counting out dollar bills takes practice. For example, students often count out money by laying the bills side by side and this takes time. This is not an effective approach to use while standing at the aisle facing the cashier.
Here is an example of what data collection can look like. (The IEP objective should have been indicated on here as well.) It shows the data, any prompting from the teacher (P with a circle around it), notes and at the bottom is 3/9 for 33% correct.
Also note that I was working on finding the value of a set of nickels and pennies only before moving onto other combinations of coins and more coins.
Math is often considered an esoteric set of information that is disjointed from the reality people face, aside perhaps from money. Sadly, in school, especially in older grade levels, math is indeed presented this way.
A situation as simple as riding an elevator provides opportunities to show and engage a student with math applied in authentic and common situations. For example, the elevator buttons address counting and cardinality (4 indicates a total of 4 floors – ignoring the R), comparison (if we are on floor 2 and need to go down, which floor do we go to?) and measurement (height above ground floor measured in floors). Such situations also provides opportunities for generalization into other settings – the important settings of every day life!
Below is a photo of a typical worksheet for money. I worked with a parent of a high school student severely impacted by autism and she explained that her son worked on nothing but worksheets when he worked on math. For students with more severe disabilities the worksheet is not real or meaningful. The photos and the setting is abstract.
Below is a photo of shelves in a mock grocery store we set up at our school for students who were in a life skills program. They would have a shopping list, collect the items in a basket then compute the total cost. We had a mock register set up (eventually we procured an actual working register) and the students made the same types of calculations they would on a worksheet but in an authentic setting, which was more concrete. We would start with simple money amounts, e.g. $1.00 then make the prices increasingly more challenging, e.g. $1.73.
It is difficult to individualize instruction in a whole class or small group setting. I created and taught the curriculum for a Consumer Math course at the high school where I teach. For a class of 10-12 students, all with an IEP, I developed an approach that allowed me to individualize the instruction for each students.
In the photo below is an example of a folder set up I used with the students in Consumer Math. Each student would have a dedicated folder, kept in the room and updated daily. The smaller paper shows the individualized agenda. The other paper shows an example of how the folder can be used as a resource. Student computer login information, accommodations like a multiplication table or notes can be secured inside the folder. The agenda would be changed out each day. (In case you are wondering about the label in the agenda, “Math Group 4.” This particular folder was used in a special education training session for teacher candidates.)