Emily and the Curious Ones Uncover Fractions
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“Emily, I want to use a former student as our next example. Emma is a young Engineer that about ten years ago was about your age and she too spent some time with us learning about fractions and other tools. She went on to college for her engineering degree and now works in the STEM field. I think you’ve probably heard of STEM as it stands for Science, Technology, Engineering, and Mathematics. You’ll learn over time that math is the lifeblood of these other fields.
Engineer Emma drives 50 miles to her job at Mechanical Auto Components. Her car uses 2 gallons of gasoline for the trip. Notice Emily how we present the data. It looks very much like a fraction with the 50 miles placed on top of the 2 gallons used. Notice how this structure is also different. In fact, what is the difference?”
50 miles / 2 gallons
“Well, I see that the 2 numbers have different units connected with them. Is that what you mean?”
“Yes indeed girl! What we have here is a new technique, similar looking to fractions and ratios but useful when looking at quantities with different units. We call this technique a Rate. We’ll see many uses for rates in just about everything we can imagine.
If we go ahead and complete the ratio by dividing we see that the result is 25 / 1. Now notice, how we state or say something about rates. Using our original data we say that Emma drove her car 50 miles per 2 gallons of gasoline. Completing the ratio we measured, at a Unit level, her mileage as 25 miles per gallon. Many times we want to express rates to a unit level. All this means is, we want to convert the rate to a divisor of 1 just as we did here. This is done to make comparisons with other rates so much easier.
So Emma’s mileage rate is 25 miles per gallon. When Emma bought the car the vehicle had a sticker on it which said the mileage rate is 30 miles per gallon. How does Emma’s driving rate compare to this advertised rate?”
“If her car is supposed to get 30 miles per gallon, and she is only getting 25 then I guess she’s missing 5 miles per gallon or something like that.”
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About the Book
Emily is having an ordinary day at Middletown Intermediate School. In Ms. Baldwin’s class, she and her friends have just finished exploring the natural world in science class and are getting ready to learn about fractions when she gets distracted by a strange spot on her math paper. Emily discovers that the spot is actually person, shaped like the number one but with a face and a voice!
It turns out this is Jackie, one of the Curious Ones. Emily takes Jackie’s hand and goes on an exciting trip to the Land of Mathesis. There, Jackie and her brother, Jack, help Emily learn all about fractions. Simple addition expands into multiplication, and simple subtraction grows into division. Emily quickly builds her knowledge of fractions, learning about ratios and rates and how they are used in modeling the real world. Soon she discovers that math can be a lot of fun!
This children’s story follows a girl on a journey through a land of mathematics, where she learns all about fractions and how they are used.
About the Author
Mr. Jack has worked as an analytical chemist, manager of quality engineers, manufacturing consultant, business owner, and special education teacher. He holds a BA and has studied management science at the graduate level. His experience in special education has given him a unique perspective in understanding how students learn basic mathematical skills.