# Engaging students: Solving one-step and two-step 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 first student submission comes from my former student Jesse Faltys (who, by the way, was the instigator for me starting this blog in the first place). Her topic: how to engage students when teaching one-step and two-step inequalities.

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

1. Index Card Game: Make two sets of cards. The first should consist of different inequalities. The second should consist of the matching graph. Put your students in pairs and distribute both sets of cards.  The students will then practice solving their inequalities and determine which graph illustrates which inequality.
2. Inequality Friends: Distribute index cards with simple inequalities to a handful of your students (four or five different inequalities) and to the rest of the students pass of cards that only contain numbers. Have your students rotate around the room and determine if their numbers and inequalities are compatible or not. If they know that their number belongs with that inequality then the students should become “members” and form a group. Once all the students have formed their groups, they should present to the class how they solved their inequality and why all their numbers are “members” of that group.

Both applications allow for a quick assessment by the teacher.  Having the students initially work in pairs to explore the inequality and its matching graph allows for discover on their own.  While ending the class with a group activity allows the teacher to make individual assessments on each student.

B. Curriculum: How does this topic extend what your students should have learned in previous courses?

In a previous course, students learned to solve one- and two-step linear equations.  The process for solving one-step equality is similar to the process of solving a one-step inequality.  Properties of Inequalities are used to isolate the variable on one side of the inequality.  These properties are listed below.  The students should have knowledge of these from the previous course; therefore not overwhelmed with new rules.

Properties of Inequality

1. When you add or subtract the same number from each side of an inequality, the inequality remains true. (Same as previous knowledge with solving one-step equations)

2. When you multiply or divide each side of an inequality by a positive number, the inequality remains true. (Same as previous knowledge with solving one-step equations)

3. When you multiply or divide each side of an inequality by a negative number, the direction of the inequality symbol must be reversed for the inequality to remain true. (THIS IS DIFFERENT)

There is one obvious difference when working with inequalities and multiply/dividing by a negative number there is a change in the inequality symbol.  By pointing out to the student, that they are using what they already know with just one adjustment to the rules could help ease their mind on a new subject matter.

C. CultureHow has this topic appeared in pop culture?

Amusement Parks – If you have ever been to an amusement park, you are familiar with the height requirements on many of the rides.  The provide chart below shows the rides at Disney that require 35 inches or taller to be able to ride. What rides will you ride?

(Height of Student $\ge$  Height restriction)

 Blizzard Beach Summit Plummet 48″ Magic Kingdom Barnstormer at Goofy’s Wiseacres Farm 35″ Animal Kingdom Primeval Whirl 48″ Blizzard Beach Downhill Double Dipper 48″ DisneyQuest Mighty Ducks Pinball Slam 48″ Typhoon Lagoon Bay Slide 52″ Animal Kingdom Kali River Rapids 38″ DisneyQuest Buzz Lightyear’s AstroBlaster 51″ DisneyQuest Cyberspace Mountain 51″ Epcot Test Track 40″ Epcot Soarin’ 40″ Hollywood Studios Star Tours: The Adventures Continue 40″ Magic Kingdom Space Mountain 44″ Magic Kingdom Stitch’s Great Escape 40″ Typhoon Lagoon Humunga Kowabunga 48″ Animal Kingdom Expedition Everest 44″ Blizzard Beach Cross Country Creek 48″ Epcot Mission Space 44″ Hollywood Studios The Twilight Zone Tower of Terror 40″ Hollywood Studios Rock ‘n’ Roller Coaster Starring Aerosmith 48″ Magic Kingdom Splash Mountain 40″ Magic Kingdom Big Thunder Mountain Railroad 40″ Animal Kingdom Dinosaur 40″ Epcot Wonders of Life / Body Wars 40″ Blizzard Beach Summit Plummet 48″ Magic Kingdom Barnstormer at Goofy’s Wiseacres Farm 35″ Animal Kingdom Primeval Whirl 48″ Blizzard Beach Downhill Double Dipper 48″ DisneyQuest Mighty Ducks Pinball Slam 48″ Typhoon Lagoon Bay Slide 52″

Sports – Zdeno Chara is the tallest person who has ever played in the NHL. He is 206 cm tall and is allowed to use a stick that is longer than the NHL’s maximum allowable length. The official rulebook of the NHL state limits for the equipment players can use.  One of these rules states that no hockey stick can exceed160 cm.  (Hockey stick $\le$ 160 cm) The world’s largest hockey stick and puck are in Duncan, British Columbia. The stick is over 62 m in length and weighs almost 28,000 kg.  Is your equipment legal?

Weather – Every time the news is on our culture references inequalities by the range in the temperature throughout the day.  For example, the most extreme change in temperature in Canada took place in January 1962 in Pincher Creek, Alberta. A warm, dry wind, known as a chinook, raised the temperature from -19 °C to 22 °C in one hour. Represent the temperature during this hour using a double inequality. (-19 < the temperature < 22) What Inequality is today from the weather in 1962?