Unit Cost and Actual Shopping

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 below) 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). I 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.

Introduction to Unit Rate using Unit Cost

Unit rate is an important topic in middle and high school. Unit cost (e.g., hamburger meat on sale for $2.39 per pound or you make $13 per hour) is an example of unit rate. This post shows how to use unit cost as an effective entry point to learning unit rates.

Significance

First, unit rates and unit costs are common in life. Second, in the Common Core State Standards math categories you can see that Proportional Relationships, and Ratios and Proportions (which includes unit rate) are a 6th and 7th grade topic and are then replaced by Functions in 8th grade. The proportional relationships are an entry point for functions.

Below is a photo showing a graph of a function. The slope of a line is the ratio of vertical change to horizontal change. In context, it can model the unit rate in a proportional relationship.

Video

Unit cost can be challenging for students who need life skills math

Activity

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. Here are links to a FB Reel and a YouTube video showing how this works.

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.

Google Document

A follow up to the Jamboard is to have students use a scaffolded chart to shop for items. This will help them internalize conceptually what a rate and unit rate are.

Have them start with an item that is a pack. In the Google Document, they paste a screenshot, enter the cost and quantity, and then compute and enter the unit cost but use “for 1” before delving into volume and weight.

Accessing Jamboard

You have to make a copy of the Jamboard in order to use it.

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.