# Engaging students: Word problems involving inequalities

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 Jillian Greene. Her topic, from Algebra: word problems involving inequalities.

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

The students, in pairs, are stranded on a deserted island. There’s another island nearby that has various items that they need to survive, but that island is overrun by snakes and is virtually uninhabitable. The have one canoe to get to the island and back, but it was damaged and will only last for two roundtrip voyages to the other island. Luckily, the students possess a certain clairvoyance that tells them the weight that the canoe can hold, as well as the weight of each supply. The numbers will vary for each group, but the canoe will hold something like up to 37 lbs (after the weight of the person on the canoe) for the first trip, and 25 lbs for the second trip. There will be weight for individual fire-building supplies, food, water, an old radio, weapons, etc. and will then be left to the students to find the different combinations they can transfer. They then have to choose which items, how many of each item, and what combination they think would benefit them the most. To add a fun element, the teacher might even have a correct answer as to which materials will save them. This activity would be a fun way for student to take numbers given to them and organize them in a way that they’re excited about.

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

If this is an algebra 1 class, this concept will be new to them. If this is algebra 2, then they should have seen this in geometry already. However, this is a fun way to look at how inequalities help us with very base level geometry. Assuming this is algebra 1, the students will discover the triangle inequality theorem and then be informed that is a big concept that they will discuss next year in geometry. They can do the activity where they’re given uncooked spaghetti noodles and break a piece into three pieces and see if it makes a triangle. They can measure the pieces and see when a triangle does work and when it doesn’t, describe their findings using words, and try to formulate the necessary inequality from that (the third side must be less than or equal to the sum of the other two sides.) If the students are learning this in Algebra II, then they can see how the description connects to the equation, and it will be interesting for them to build off of prior knowledge.

How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

This activity is not as much deciphering the inequality from a word problem as it is understanding what inequalities mean in a graphical sense. However, it is indeed a situation involving inequalities, and a TV clip. I do not have the clip available to me right now (legally) but it’s in an episode of Numb3rs called “Blackout” where an attacker is causing blackouts throughout the city and then committing the crimes during the blackouts. The investigators found a code for where the attacks take place and they’re given two inequalities that they need to graph to find region in which it might take place.

https://mathstrategies.wordpress.com/numb3rs-activities/

This will not only allow for a solid practice on how inequalities look on a graph, but for the (kind of) practical application of using things like this. The teacher can ask a few fun questions, like “why do you think the attacker is choosing this region?” or “how would it affect the graph if all of the area between Ramirez St and Gateway Plz was closed due to construction?” This will make the “less than” and “greater than” signs actually hold some amount of meaning.