Engaging students: Absolute value

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 Deanna Cravens. Her topic, from Pre-Algebra: absolute value.

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

A great way to teach absolute value is to do a discovery activity. A blogger and teacher, Rachel, posted on her blog, called Idea Galaxy, a great step by step on how to do a discovery activity for absolute value of integers. First the students will start out by showing the distance between two numbers on a number line, such as the distance between one and three.


They will do a few of these examples to build upon the prior knowledge of the students. Then the class will transition to another page. This one will also have number lines and will ask them problems like ‘what does negative four and four have in common?’ Some scaffolding can also be used like asking them to mark both numbers on the number line and look for similarities related to distance. After completion, students will discuss with one another about the observations they noticed. Lastly, the teacher will give them the term of absolute value and then ask students to rewrite it and put it into their own words.

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How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

This short video YouTube video discusses absolute value and then explains one standard way that absolute value is used in real world applications. First it explains absolute value in terms of distance away from zero. It gives a few concrete examples to display, for instance -4 and 4 both have a distance from zero that is 4. So the absolute value bars will always make the number positive. Next, the video uses an example that shows a real world example. It shows a student, Lucy, who is traveling to go to a tuba lesson. She accidentally drops her sheet music and has to go back to get it. This video does a great job of showing what it would the distance would be in terms of number of blocks walked, and how far she is from where she started or her displacement. This can easily be shown at the beginning of class either as an introduction or a review. It can spark more discussion by asking for other real world examples to help show that math really is relevant and needed for every day use.

 

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

Absolute value can show up in many areas of future math classes. It comes up when learning about the absolute value function, working with inequalities, proofs and so much more. One specific way that absolute value is used, is in calculus. After students have learned how to take derivatives, they will learn how to take antiderivatives. If a student is given ∫1/x dx, they need to find the antiderivative. Students will know that the derivative of ln x is 1/x, however this is not the case when you take the antiderivative of 1/x. The domain of 1/x is everything except zero, so negative numbers must be taken into consideration. However, if one was to say the antiderivative is lnx, it only accounts for positive numbers. Thus, in order to make the domain match 1/x, the absolute value must be brought in. Therefore, the ∫1/x dx = ln|x|+c. Thus a very basic concept becomes for important within calculations at higher level mathematics.

References:
http://ideagalaxyteacher.com/teaching-absolute-value-discovery/
https://www.youtube.com/watch?v=wrof6Dw63Es
https://www.khanacademy.org/math/ap-calculus-ab/ab-antiderivatives-ftc/ab-common-indefinite-int/v/antiderivative-of-x-1

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