## At a Glance

Over the course of three days, cosmetology students at Indiana County Technology Center first receive instruction on ratios and proportions from the math instructor and then complete activities in which they must accurately mix and dispense colors and chemicals by applying those math concepts in the lab.

## Overview

Because mixing color and chemicals in Cosmetology usually requires combining two products together to obtain a specific chemical mixture, students must not only be able to do the math calculations but also be able read the labels on the chemical bottles, and then dispense the correct amount. At Indiana County Technology Center (ICTC), the cosmetology and math instructors collaborated to create a three-day lesson focused on mixing and dispensing colors and chemicals in order to help students correctly apply the mathematical concepts of ratio and proportion from paper and pencil to real world situations in the lab. (The lesson plan and activities are attached.)

On the first day of the lesson, the math instructor teaches students how to use ratios and proportions to mix color and other chemicals. The lesson focuses on two real world scenarios one in which the students know the amount of one ingredient needed, and a second in which the students only know the total amount of final product needed. Both scenarios require students to use proportions, but they are set up slightly differently.

On day two, students apply the concepts learned on the previous day to practical situations. They work in pairs to complete seven Cosmetology Mixing Stations, each of which requires students to read the label of a specific chemical to find the mixing ratio and then use the ratio to answer questions. Each station focuses on a different color or chemical that is used in the salon and the proportion method that was learned during the previous lesson.

On the final day of the lesson, students work in pairs again and this time they complete an activity focused on dispensing color from color tubes (Color Squeeze Activity). Using refillable squeeze tubes and frosting, the instructor simulated a color tube. (It is necessary to write the ounce markings on the outside of the tube). Using the frosting in the color tubes, students practice dispensing product without wasting valuable color. (Graham crackers are usually supplied so students can dispense the frosting onto them and then eat them following the activity.) This activity provides students the opportunity to practice dispensing product from a partially used tube. For example, they practice how to squeeze 1 1/8 of an ounce if ½ of an ounce has already been squeezed out of the tube.

## Origin / Implementation

The cosmetology instructor observed that while students often were able to correctly complete math problems involving ratios and proportions in the classroom setting, they frequently were unable to accurately apply those concepts in the real world setting of the lab. This resulted in frustrated students and in wasted products. For example, students often struggled with understanding that ¾ of an ounce did not mean ¾ of a tube and with how to dispense ¾ of an ounce from a tube if ½ of an ounce already had been dispensed. In order to address this problem, the cosmetology instructor and the math instructor collaborated to develop a hands-on lesson that would help students better understand the math concepts.

Math integration was not a new concept for ICTC instructors. ICTC began using the Push-In Integrated Math Program in 2003. As part of this program, the math instructor pushes into each program area once a week to teach a math lesson relevant to that program area. Because this level of math integration and collaboration with the math instructor is well established, program area instructors are comfortable sharing their ideas, struggles, and concerns with the math instructor on a less formal basis. Therefore, when the Cosmetology instructor first expressed concerns about her students ability to do the math necessary to mix product, read labels, and dispense the correct amounts, she and the math instructor began developing an integrated lesson that would target those concepts. The three-day lesson was first implemented during the 2011-2012 school year.

## Results / Impact

The cosmetology instructor reports that after completing the three-day lesson on mixing, students make fewer mistakes and waste less product as a result.

## Contact

Indiana County Technology Center

Cathy L. Jones, Mathematics Instructor

Email: cjones@ictc.edu