Engaging students: Laws of Exponents

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 comes from my former student Jesus Alanis. His topic, from Pre-Algebra: the Laws of Exponents (with integer exponents).

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

I would create a project where the students would have to create a “poster”. First, you would give each student a strip that contains one of the laws of the exponent. On the strip, there will be 3 expressions for them to solve that involves one of the laws and have a blank space for the student to create a “rule” for their law. This is where you will let your students find out what law they got. Once they figured out their law they will create a poster that will have the name of the law, the rule of the law (by the rule I mean just using variables, for example, the Product of Powers it would be x^m \cdot x^n = x^{m+n} ), a complete sentence which explains the rule in their own words, and an example of the law which can be one of the expressions from the strip. For the poster, you would want students to use color and decorate the way they want. This will let the student’s inner artist out and creativity shine. You can have your students present their law, or you can have a gallery walk so they can look at all the different laws.

The purpose of the project is for the student to play with the expressions causing them to question which law they received and letting them create a rule that makes them understand how the law works. The sentence on the poster will demonstrate if the student understood the law. This is a project that can be used to let students find out for themselves or this could be a project to help students remember what they learned.

Something extra but you can also make this a relay race by using the strip or the whole paper where the students must at least do one expression from each of the laws of the exponent. In the end, each student in the group has at least done all three laws that were on the page. With the page from TEA, there are only three laws on there, but you could add the rest on there to make the race a little longer.  The goal is to have each student have practice with each law that is on the page, they are in a group so they can help each other and familiarize themselves with the laws and peers.

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

The way students can use the Law of Exponents in the future is that it will help write or type very large numbers towards using fewer numbers. This will not cause the value of the number to change but will be less to write. For example,

2,357,000,000,000 = 2.357 \times 10^{12}.

The law of exponents will also help with loan interest rates that can be used to predict how much you will have to pay in a certain time frame. Exponents are used to determining the pH level of substances, see the growth of bacteria, see the population of a city, and how much has it increased or decreased, and many more.

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How has this topic appeared in pop culture?

I did not really find where it appeared in pop culture, but I did find a connection of how you can use the clip of SpongeBob to the Law of Exponents. The way you can connect them is that SpongeBob says all the specific rules to blow a bubble. This is to engage students and make sure to activate their prior knowledge that goes with the rules like the way we do with the area of a rectangle we first have to find the length of the sides and then place them in the formula to be multiplied. The small clip is a demonstration that with the Law of Exponents we must “obey” the math operations so that our results are as perfect as the duck bubbles. Also, we must make the connection between rules and laws which are very similar.


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