Predicate Logic and Popular Culture (Part 193): Randy Travis

Let T be the set of all time, and let L(t) be the proposition “I am going to love you at time t.” Translate the logical statement

\forall t \in T (L(t)).

This matches a chorus of the famous Randy Travis song.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Engaging students: Area of a trapezoid

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 Lissette Molina. Her topic, from Geometry: finding the area of a trapezoid.

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

I believe most students in America all discovered finding the area of a trapezoid with one very easy and simple activity. Students are to receive a trapezoid of some different sizes. They are then asked to find area by cutting off the triangular sides. The student then finds that all trapezoids are composed of triangles and a rectangle. This is a very quick activity that requires students to come up with a formula that works across all trapezoids. Learning about finding the area of a shape with hands-on discoveries keeps the formula and how it became embedded into students’ memories. This activity may also work with most polygons.

 

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How does this topic extend what your students should have learned in previous courses?

Find the area of a trapezoid does not require much information from previous courses. One major topic the student should be able to have learned before coming into a geometry class should be area. However, very rarely, students do not know what area is already. So, the student should be able to apply what they know about area into finding the area of a trapezoid. This involves finding the area of a rectangle and a triangle. It is important that a student understands exactly where a formula is derived, so it is also important that students know that the trapezoid contains two shapes and that finding the area of those two shapes will help them find the area of the resultant trapezoid.

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

One helpful website or program is Desmos (desmos.com). There are usually modules made for students often made by teachers. I have not yet come across one already made, but here is what I have in mind. Desmos is primarily made for graphing, but there are so many functions in this website that it can be manipulated to perform other things such as the unit circle. One very helpful idea would be to make a shape of a trapezoid by combining two triangles of different sizes off each of a rectangle’s sides. Since these shapes are placed on top of a graph, students would be able to calculate the area by counting the square units. WIth triangles, students can count the number of half, quarter, etc. square units. This way, students can find the area of a trapezoid by counting the squares, and realize that it would be easiest to find the area of those two triangles and one rectangle and combine them.

Predicate Logic and Popular Culture (Part 192): Overwatch

Let P be the set of all people, let H(x) be the proposition “x is a hero,” and let D(x) be the proposition “x dies.” Translate the logical statement

\forall x in P (H(x) \Rightarrow \lnot D(x)).

This matches a line from the videogame “Overwatch.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 191): Bebe Rexha

Let P be the set of all people, let p be the proposition “I’m paying,” and let S(x) be the proposition “x shows up.” Translate the logical statement

\not p \Rightarrow \forall x in P (\lnot S(x)).

This matches a line from “I’m a Mess.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 190): Eastside

Let T be the set of all things, and let D(x) be the proposition “We can do x if we put our minds to it.” Translate the logical statement

\forall x \in T (D(x)).

This matches a line from “Eastside.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 189): Mana

Let W(t) be the proposition “At time t, you want me as I am,” and let R(t) be the proposition “At time t, you reject me for what I was.” Translate the logical statement

\forall t<0 (\lnot W(t) \land R(t)).

This matches a line from the Spanish-language song “Tengo Muchas Alas / I Have Many Wings.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 188): Talladega Nights

Let p be the proposition “You are first,” and let q be the proposition “You are last.” Translate the logical statement

\lnot p \Rightarrow q.

This matches the famous catchphrase from “Talladega Nights: The Ballad of Ricky Bobby.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 187): Naked Eyes

Let T be the set of all times, let H be the set of all things, and let R(x,t) be the proposition “At time t, x is there to remind me.” Translate the logical statement

\forall t \in T \exists x \in H (R(x,t)).

This matches a phrase from the chorus of this 1980s classic.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 186): Nickleback

Let M(t) be the proposition “Somehow, I will make it right at time t,” where t=0 is now. Translate the logical statement

\lnot L(0) \land \exists t > 0(M(t)).

This matches a line from “Someday” by Nickleback.

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 185): Westworld

Let W be the set of this world, and let M(x) be the proposition “x is magic.” Translate the logical statement

\forall x \in W(M(x)).

This matches a line from season 1 of HBO’s “Westworld.”

Context: Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.