Inequalities are one of my favorite units to teach. For my grade 8 students, this is mostly a review, since they have been exposed to one variable inequalities in pre-algebra. They also see how they can use skills from solving equations and apply them to inequalities.
One of the most difficult things for my students, who are all English language learners, is vocabulary. They “get” the words greater than and less than. Adding in other words that can be sued to represent inequalities, and they have no idea what the correct symbol is. This is mainly because my students are Vietnamese and are all learning English while being taught in English. Within my classes, there are varying degrees of English proficiency, from near native speaker to almost no English.
In order to have students recognize these phrases and write inequalities, I use a story. I can’t take credit for this story; I found it many years ago, and have since modified the wording. Each year, I make a few changes. (Here's a link to a version I found online. This is not Susan's current version. Susan's current version is shown in the picture above.)
Students work in pairs for this activity. Together, they read and highlight the inequality phrases within the story. They discuss the ones they are unsure of. I always have a few tricky ones in the story! For some of my students, this is a very easy assignment. They can figure out many of the phrases. For others, this is a more challenging activity.
The follow up comes when students have to then write the correct inequalities. They write the phrases as word phrases, and then have to translate them into symbols. The final part of the activity has students translate phrases that have nothing to do with the story.