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.
This lesson brought in something totally new for my students: how to turn a function rule into an equation to deal with a specific case. I wanted my students to recognize that once a function has been written, I can use the function to find a missing equation easily once more information is provided.
In this lesson, students may get bogged down or frustrated the calculations. So, an important thing to do in the closing is to highlight this big idea: we started by describing functional relationships with rules, and then we could easily use those rules to write equations to solve problems. After I highlight this idea for students, I ask them to:
I find that asking students to work back through a problem and reflect on their work helps them connect their work to the mathematical concepts.