Engaging students: The quadratic formula

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Storm Boykin. Her topic, from Algebra II: the quadratic formula.

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How could you as a teacher create an activity or project that involves your topic?

Learning the Quadratic Formula can be quite a tedious process for students. They have to learn the why and how, but still need to be able to recall the Quadratic Formula fairly quickly. Students cannot use it as a tool to solve quadratic equations if they cannot remember it. The chart below is to be a card sort from a mnemonic device that was passed down by a former teacher. The idea is that the students will have these cards mixed up, and then they will have to match the story with its’ mathematical counterpart. Then, using the mnemonic device, the student can put the story in order, and will have the quadratic formula before their eyes.


The negative boy -b
couldn’t decide ±
if he wanted to go to the radical party  √
but the boy was square b^2
and missed out on four awesome chicks -4ac
it was all over by two am /2a


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What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

Quadratics began to come about around 2000 BCE because mathematicians needed a way to make “architectural floor and wall plans.” Quadratics have been worked on by various cultures since then. While working on quadratics, Pythagorus found that the square root of a number did not have to be an integer. However, he didn’t believe that imaginary numbers existed, and had one of his associates killed for even suggesting to the public that “non- integers” existed. They idea of a quadratic formula was touched on by hindu and islamic mathematicians, but did not come into form as our modern day formula until 1637, when Rene Descartes published it in his geometric works.



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How can this topic be used in your students’ future courses in mathematics or science?

All algebra and calculus courses will have quadratic equations in them. Students will have a much easier Physics experience if they have the equation at their disposal. Quadratics are used to calculate velocity and height of objects in the air. Real world examples involving velocity and height are the perfect blend of physics and science! Students will also need the quadratic formula for the SAT and PSAT.




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