Category Archives: Consumer Math

Money in Authentic Settings

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.

Luisa at counter at BN

  • 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).

Luisa at table with money

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.

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Superhero Math

I was recruited to help a middle school student who is having a very rough time at this time in his life. It was shared with me that he likes Marvel superheroes and he is struggling with counting money and multiplication. Below are some ideas I presented for a test run and photos of the items I ordered for these suggested activities.

  • For multiplication

    • Put the heroes (or villains) in groups of 2 and have him count out 4 groups and compute. Use different groups and number per group. (IGNORE the numbers on the cards)

    • Get a group of 10 villain cards. Pretend heroes have to travel in groups of 2 and ask how many groups to get 10 heroes to fight the 10 villains. (IGNORE the numbers on the cards). Variations of this.

    • After gets the idea of groupings, focus on the number on the cards and show him two 5s and have him compute. Variations of this.

    • Play a game where he draws two cards and has to multiply the cards (start with very low numbers or maybe show him a 2 card and he has to pick another card to multiply by 2.

marvel playing cards

  • For Money

    • Tell him he earn money to buy these figures, one at a time – a monetary version of a token economy. Have him rank them by his favorite to least favorite and come up with a price for each with his favorite figures costing more. Start with the least favorite and make the price such that with a little practice he could count out the coins to pay for it. Maybe 17 cents with dimes and pennies. He has to count out the money correctly and independently to actually buy the item.

Avengers Figurines

  • Other options

    • If he needs work with addition you can play WAR in which 3 cards are played and each person adds to find the total. For subtraction do the same with 2 cards.

    • You can play subtraction in which one person has superheroes and the other has villains. In order for a villain to win a villain card has to be higher than a hero card by 3 or more.

You can write an 11, 12 and 13 on the J, Q, K cards respectively. All the games can be presented though Direct Instruction – I do, we do, you do. The You do can be used as daily progress monitoring. If he needs prompting this can be recorded. This can be used for your progress reports. Attached is a data sheet I use for activities.

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Authentic Work Experience

Very clever activity implemented by the teacher who runs the Life Skills program at our school. She created envelopes (below) for each teacher. The envelopes do not contain any content but are used for practice sorting mail for the students in the program. The students in the program sort and deliver them to our mailbox. We return them to this return bin for reuse.

Such experiences should be available to all of our  students who are more severely impacted. Many will need YEARS of practice to develop skills which means a transition program from 18-21 years old may not be enough.

work experience envelopes.png

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Data Collection for IEP Objectives

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.

data collecton for counting nps

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Cutting Up the Math Into Bite-sized Pieces

When I train new math and special education teachers I explain that teaching math should be like feeding a hot dog to a baby in a high chair. Cut up the hot dog into bite-sized pieces. The baby will still consumer the entire hot dog. Same with math. Our students can consume the entire math topic being presented but in smaller chunks.

bite sized pieces

My approach to doing this is through a task analysis. This is very similar to chunking. It is a method to cut up the math into bite-sized pieces just as we would break up a common task for students with special needs.

Image result for task analysis

While waiting for my coffee order at a Burger King I saw on the wall a different version of a task analysis. It was a step by step set of directions using photos on how to pour a soft cream ice-cream cone. I thought it was amazing that Burger King can do such a good job training its employees by breaking the task down yet in education we often fall short in terms of breaking a math topic down.

soft cream icecream cone task analysis

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Opportunities for Parents to Engage Students with Math

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.

sally math problem

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!

2019-01-18 18.33.56

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Authentic Activities – Money and Prices

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.

adding-money-worksheet-1

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.

mock grocery store

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Basic Skills Older Students

A widespread problem at the secondary level is addressing basic skills deficiencies – gaps from elementary school. For example, I often encounter students in algebra 1 or even higher level math who cannot compute problems like 5÷2. Often the challenges arise from learned helplessness developed over time.

How do we address this in the time allotted to teach a full secondary level math course? We cannot devote class instruction time to teach division and decimals. If we simply allow calculator use we continue to reinforce the learned helplessness.

I offer a 2 part suggestion.

  1. Periodically use chunks of class time allocated for differentiation. I provide a manilla folder to each student (below left) with an individualized agenda (below right, which shows 3 s agendas with names redacted at the top). Students identified through assessment as having deficits in basic skills can be provided related instruction, as scheduled in their agenda. Other students can work on identified gaps in the current course or work on SAT problems or other enrichment type of activities.
  2. Provide instruction on basic skills that is meaningful and is also provided in a timely fashion. For example, I had an algebra 2 student who had to compute 5÷2 in a problem and immediately reached for his calculator. I stopped him and presented the following on the board (below). In a 30 second conversation he quickly computed 4 ÷ 2 and then 1 ÷ 2. He appeared to understand the answer and this was largely because it was in a context he intuitively understood. This also provided him immediate feedback on how to address his deficit (likely partially a learned behavior). The initial instruction in a differentiation setting would be similar.

2018-12-20 11.20.25

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Pretest on Money and Spending for Consumer Math

pretest money

The photo shows a pre-posttest for a student in a consumer math class. In the course I taught we would conduct a pretest at the start of the class to determine which of the related skills a student lacked mastery. The course focus for this student was on the identified skills – highly individualized. The assessment also provided present level of performance information, allowed us to monitor progress and to evaluate instruction.

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Counting Out Total Value of Coins

The chart shown in the photo below was created and used by my former co-teacher and I to teach students in a high school life skills program how to count out the total value for coins (dimes, nickels and pennies). Here is how we implemented it.

  • The students are given a pile of coins, set next to this chart.
  • Students start with dimes (identifying dimes as the coin to start with is a prerequisite step that can be taught in isolation if necessary)
  • They line up the dimes in the dimes column as shown below.
  • They count out the total value of dimes (and can look at the number under the last dime)
  • Then the students identify the nickels as the next coin to use.
  • The place the first nickel in the nickels column, starting at the row below the dimes (you can use a highlighter to highlight the last dime row to scaffold where the student places the nickels)
  • Have the student count off 5 and place the next nickel (on the dimes column) etc.
  • Then follow the same steps to transition to pennies.
  • Have the student identify the total value by looking under the last penny.

coin chart

The idea is to fade the use of the chart and have the student count out the value without the chart. This is more possible if the task demand is incremented with pennies only, then dimes only, the pennies and dimes etc. Here is a link to handouts for those.

 

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