Applying Data Tables to Word Problems

This lesson gives students the chance to continue to develop their skill at interpreting 4-column data tables and their graphs. At this time, I am pushing students to write all the function rules in three ways: standard form, factored form and vertex form. I give students 20-30 minutes to work on today's 4-column data tables warm-up. Then, I allow them to use any extra time to work on the problem set, which will be due at the end of the week. 

The challenge of the day is to extend students’ understanding of quadratic relationships to more traditional word problems. The unique aspect of this lesson is that we will examine the relationships between quantities in the problems before looking at equations.

The first part of the Exploring Relationships Quadratic Word Problems activity asks students to describe the relationships in the problems. For example, Question A states, "Consider the produce of two consecutive integers. What is the relationship between the smallest integer and the product?" I find that my students are often unclear on what it means to describe a mathematical relationship, so I tell them that they can use any representation: a rule, a verbal description, a data table, a function rule. My idea is for the class to think about how these relationships work. After all students create representations that make sense to them, it will be easier for them to write an equation modeling the situation.

Today, it is not necessary that students do all of the problems. And, this is another task that is easy to differentiate, because students can choose which problems to focus on. It is totally fine if some students work on only 1 or two problems while other students think about all of them, as long as all students are using their time effectively.