Tag Archives: unit cost

Introduction to Unit Cost (Unit Rate)

Unit rate (e.g., hamburger meat on sale for $2.39 per pound or you make $13 per hour) is an incredibly important topic in middle and high school. First, unit rates and unit costs are common in life. Second, in the Common Core State Standards math categories you can see that Ratios and Proportions (which includes unit rate) are a 6th and 7th grade topic and are then replaced by Functions in 8th grade. Below is a photo showing a graph of a function you can see that the slope in an application is a unit rate.

The unit rate is also conceptually challenging whether it is in a function or is a unit cost at the store. This is a major sticking point for many students in special ed who have fallen behind. To address this, I used the approach below.

First, I present a pack of items the student likes (4 pack of Muscle Milk for this student). Use a Jamboard to show a 4 pack and the price of the 4 pack (photo on left). Then I “pull out” the 4 individual bottles and divide the $8 among the bottles to show $2 for each bottle. Finally, I have the student shop for packs of items at a grocery store or Amazon and compute the price for 1 item using a mildly scaffolded handout.

I Follow the same steps for ounces or pounds but show how 4 oz is divided into single ounces (in lieu of a pack divided into single items). Then the student shops for items that can easily be divided to get a unit cost.

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Life Skills Math – Not So Easy

As I wrote previously, shopping is dense with math tasks as are grocery stores. Here are some division situations that are sneaky challenging and require a student to know when and why to divide before even reaching for the calculator. I will use these to help illustrate the fact that life skills math is not simply counting money or using a calculator to add up prices. There is a great deal of problem solving and thinking skills that need to be developed.

For example, if a student has $60 to spend on gifts for her 3 teachers the student needs to understand that she can spend up to $20 per teacher (before even talking about taxes).

An entry point for division can involve a dividing situation the students intuitively understand, e.g., sharing food. Start with 2 friends sharing 8 Buffalo wings evenly (below).

This can lead into the 3 teachers sharing the $60 evenly (below). In turn, this can be followed by the online shopping shown above.

This approach can be used to develop an understanding of unit cost (cited in the shopping is dense post). Start with a pack of items to allow the students to see the cost for a single item before getting into unit cost by ounces, for example.

I have had success with teaching these division related concepts using sheer repetition as much of our learning is experiential learning. Using a Google Jamboard as shown in the photos allows for the repetition.

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