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Middle School Math: Playing with Ratios

What do Barbie dolls and slime have in common? Both toys can be used to teach math lessons about ratios, according to math learning specialist, Maleia Clarke.
Students were recently engaged in using measuring tape and calculators to find out what a real-life Barbie would look like. Turns out, she’s over 7-feet-tall and wears the shoe size of a toddler. 
 
“The Barbie Doll Proportions Lab is a great way to practice manipulating ratios,” said Mrs. Clarke. Mathematicians measured the doll’s height before creating a doll to human ratio using 64 inches as an average woman’s height. Once the ratio was determined, they went on to measure and calculate equivalent ratios (proportions) for limbs, torso, face, etc. by solving for the unknown measurement of the “life-size Barbie.” Finally, they took their life-size Barbie dimensions and drew a figure on a large sheet of paper to visually represent their calculations.
 
Next came the slime. To determine the importance of accurate ratios when making recipes, students were asked to deliberately “mess up” a slime recipe by changing the quantities of all ingredients by increasing or decreasing each ingredient by a specific scale factor -- for example, increasing the glue measurement by a scale factor of 1.5. After mixing the botched batch, students observed the results. Was the mixture too runny or too stiff? Finally, their end goal was to find equivalent ratios needed in order to correct their botched batch. Ideally, if they were able to do so using their mathematical problem solving and knowledge of ratios, they were able to take a good batch home. 
 
“I love when students engage and interact with mathematics in a non-traditional way and take their learning beyond the textbook or traditional algorithm,” said Mrs. Clarke. “It allows for multiple connections, attaching their learning to pre-existing knowledge, and some fun to boot.”
 
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Graland Country Day School

Graland Country Day School is a private school in Denver, Colorado, serving students in preschool, kindergarten, elementary, and middle school. Founded in Denver in 1924, Graland incorporates a rich, experiential learning approach in a traditional classroom setting, emphasizing the development of globally and socially conscious leaders who excel academically.