Tag Archives: money

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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Introduction to Slope

which-jobSlope is one of the the most important topics in algebra and is often understood by students at a superficial level. I suggest introducing slope first by drawing upon prior knowledge and making the concept relevant (see photo above).  This includes presenting the topic using multiple representations: the original real life situation, rates (see photo above) and tables, visuals,  and hands on cutouts (see photos below).

10-dollars-per-hour-graphA key aspect of slope is that it represents a relationship between 2 variables. Color coding (red for hours, green for pay) can be used to highlight the 2 variables and how they interact –  see photo above and below.5-dollars-per-hour-graph

The photo below can be used either in initial instruction, especially for co-taught classes, or as an intervention for students who needs a more concrete representation of a rate (CRA). The clocks (representing hours) and bills can be left in the table for or cut out.cut-outs-hours-bills

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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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Assessment for General Curriculum Math Topics

In special education there is a tool called a task analysis. It is a formal approach of identifying the steps taken to demonstrate mastery of a skill. For example, putting on shoes with Velcro straps involves the following steps: get shoes, sit on chair, match shoes with feet (right to right), insert foot into respective shoe etc.

I have applied this approach to general curriculum math topics from counting money to solving using the Quadratic Formula. Below are the iterations of my task analysis for the objective count TENs, a FIVE and ONES (dollar bills) to pay a given price. The first shows a rough draft of notes I took as I actually counted out the money, going through each little step. The second shows the steps written out on a task analysis table I created. The third shows the final, typed version.

paying price with bills task analysis rough draft

paying price with bills task analysis rough draft on table

paying price with bills task analysis final

The table is used for assessment, collection of data and progress monitoring. The steps that are problematic can be targeted individually, e.g. skip counting by 10s.

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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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Streamlining Differentiation

Photo below shows a grid I use to identify the daily activities for my 12 high school Consumer Math students (all with IEPs) in an 86 minute block.IMAG3910

Our daily agenda is comprised of a warm up puzzle (to get them settled and to allow me to coordinate with the other adults – between 2 and 4) and two rounds of activities. Each column is used for a student. The “C” indicates computer use (we use IXL Math mostly and have 4 computers in the room) and the colors indicate the adult supervising.

Each student has a manilla folder which contains all handouts needed, including the daily puzzle, and the IXL modules to complete taped to the inside front cover.

IMAG3911 

In a given day we may have different students counting nickels and pennies, identifying coins, identifying bills needed to pay a given price, computing sales tax and total price and creating a monthly budget on Power Point, with photos. The system allows me to track the many details.

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Adding Money First Steps

The following shows steps to introducing the concept of the value of money and of adding coins.

The concept of a dime is presented as 10 pennies (see below). The dime is compared to a penny, nickel and quarter using these representations. Repeated use of these representations leads into an intuitive understanding of the coins.dime and ten penny bag

Next is determining the value of multiple coins. The place to start is with pennies, which is relatively easy as the number of pennies represents the value. The next step is to count dimes because counting by 10s is relatively easier than counting by 5s or 25s.

Dr. Russell Gersten is a guru in special ed. At a presentation at the 2013 national Council for Exceptional Children he explained that number sense is best developed using the number line. With this in mind I created a CRA approach using the number line.

First, the student lines up the dimes on the number line (see photo below) then skip counts to determine the cardinal value, which is the value of the coins. money number line dimes

Upon demonstrating mastery of counting dimes, the student moves from using coins (concrete) to a representation – see photo below.

IMAG3828

This approach is used for nickels and then a combination of nickels and dimes (corresponding blog post forthcoming).

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Conceptual Presentation of Percents

 

 

 

Percents is a very challenging concept for students often because it is presented in symbolic terms, e.g. 40% of a 25 is what? Students typically understand what 100% and 50% mean. The concept of percent can build on this intuitive understanding. Here is my approach using a Concrete-Representation-Abstract approach (from a lesson taught today).

First, I ask the students to match common terms used for various percents on a percent number line. The students typically understand the first four terms.

percent number line words

 

 

I build on their knowledge of 50% first by having them cut (see below) a pizza into 50% then 25%. Then they cut $200 into 50% then 25% and then count the money.

 

percents cut outs

 

Many struggle with 1/4 and 3/4 (25% and 75%). The little less than half is the building block because it is the first step away from 0%, 50% and 100%. Here’s how I use this step (below). The students compute 50% or half of the $200 then estimate 40% which is “a little less than 50%.” If a student struggles with this step, we go back to the cutout money and they cut a little off of the 50% and guess how much money is left.

money on percent number line

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