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Inside The Classroom:
Stretching and Shrinking with Berhane Zerom

Guy Parsons and Peter Ferraro work together to find the height of their object as Mr. Z checks in.

Determining similar triangles? Using shadows to find out the height of a towering skyscraper? It’s all in a day’s work for sixth graders in Berhane Zerom’s math class.

“Today we’re going to talk about how we can use shadows to find height,” says Zerom, affectionately coined Mr. Z by his students. “Here we have two triangles—assume they are similar. What are some of the things that we know for sure are similar about these two triangles?”

“They have a similar scale factor and the angle measure should also be the same,” pipes up Amy Roberts.

“True...and what other things do we know?” Zerom asks as his question is met with blank stares.

 “I'm going to give you a clue. The word starts with A...D...J....”

“Adjacent!” the class shouts in unison.

“Exactly! The ratio for adjacent sides should be proportional,” Zerom says, his face brightening as he witnesses his students grasping the concept.

Today’s lesson is about using shadows to determine the height of an object, all part of the “Stretching and Shrinking” unit that focuses on geometry and teaches students to understand and use the concepts of mathematical similarity. In the sixth grade math curriculum, each unit is tied together, allowing the students to go back and reflect on what they did previously, Zerom says, which helps them make connections among the concepts they have studied so far.

“This unit is all about the question of what do you do when you have a certain shape and you shrink it to a certain size,” Zerom says. “The same thing has to happen to all the sides or you will not have a similar shape. We also introduce students to the concept of an object being similar, but not always the same. It can be the same in shape, but the size has to be different. If it’s the same, then they are congruent. Now we are at the point where we are making connections to real life as well. If you know how to apply the similarity rule to figure out a missing side or a missing angle, then you can use that in real life.” 

Broken up into small groups, students are asked to sketch an object and determine its height based on the concept of similarity. The goal of the exercise, according to Zerom, is to have students explore relationships among figures that have been stretched or shrunk, and the resulting changes on properties of the figures, such as area and perimeter, which they covered in their last unit. By the end of the lesson, students will know how to create similar figures, how to determine whether two figures are similar, and how to predict the growth of the lengths and areas between two similar figures.

“When the sun hits a certain object at a certain time the angle of the rays are always the same no matter how tall or how short the object is," Zerom reminds the class as they eagerly sketch their objects and get to work with their partners before sharing their answers with the class.

“We are doing this in math class but this has a practical application in life,” Zerom says. “Of course you can use this to determine the height of a building, but this application is also used in science. How do astronomers, for instance, figure out the distance from the sun to the earth? They use indirect measurements to figure out how far apart the two objects are. What about the atom? Is it possible to measure an atom with a protractor? No. Again, science uses the application of similarity.”

Born in East Africa, Zerom arrived in the United States ten years ago, where he obtained his master’s in teaching at Harvard before teaching at Cambridge Friends School for eight years. Although this is his first year at BB&N, Zerom says he has quickly settled into his role, and loves the enthusiasm and hard-working nature of his students.

“I want students to leave my class with an appreciation of math and look at it in a way they haven’t looked at it before,” he says. “In my class, math is not taught in a ‘here are the facts, memorize them’ way. They have to make connections, and it helps when they make connections on a personal level. And they do. You’ll hear kids say, ‘Oh, that’s what my dad was doing at his job.’ I want them to appreciate what they are doing and once they leave the classroom, to not stop thinking about math...to look at an object, and say, ‘Oh, that’s what Mr. Z was talking about.”