Algebra II : Unit #9 - Polynomials and Problem Solving : Lesson #1

Grandpa's Sweet Corn Problem: Day 1 of 2

Objective: SWBAT problem solve using polynomial equations.
Standards: HSA-APR.B.3 HSF-IF.B.4 MP1 MP3 MP4 MP6
Subject(s): Math
60 minutes
1 Roll Out - 15 minutes

Problem solving is a HUGE theme for my class.  To determine where students are with prior knowledge, I created a problem I call Grandpa’s Sweet Corn.  Students who have a sufficient knowledge of factoring will find the algebra in this problem easy.  The more difficult part is the set up! 

One challenge I face with my students is that they come with a “segmented” view of word problems.  Earlier in my teaching, like many others, I put off the dreaded story problems till the end of every chapter, or unit.  We would skill build, quiz, and then apply what we learned to a somewhat-real setting.  I have now learned through observation and personal reflection, this “application last” approach isn’t conducive to student learning.  By rolling out a problem, like Grandpa's Sweet Corn at the start of a unit really allows me to grasp student’s where each student is starting from and it also presents a context for learning to the students in a meaningful way (MP1). Rarely, in life you have the opportunity to skill build, skill build, skill build, re-mediate, quiz, and then apply!  In fact, this almost never happens except maybe inside the traditional classroom.  Teaching the Common Core involves teaching authentic problem solving, being presented with a problem and both determining and desiring the skills needed to accomplish the task (MP4). 

To open class, I present the students with the Entry Document and display the Grandpa’s Sweet Corn Barn and Garden Set Up.  During the 15 minutes that the students are working, I carry around a mini whiteboard and see how they are doing. Starting this way is a perfect opportunity to go around and check-up on students.  I target a range of high, middle, and struggling students to pause their work on the problem and factor a basic polynomial equation for me while having them to do their best and talk me through it.  Factoring lies primarily in Common Core Algebra however, as I have typically done for a few other concepts, there may be some need to remediate in order to ensure students' Algebra 2 success.  This is a very nice way for me to gauge the students incoming ability to work with a polynomial equation.  

2 The "Language Barrier" - 15 minutes

After allowing 15 minutes to work, I collect the entry documents to the problem, and without providing an explanation, put on the Language Barrier advertisement.  Many students get overwhelmed by mathematical terminology, and this unit full of roots, different number systems, and types of functions is no exception.  There will be a lot of new terminology for the students, especially if they have “tuned out” the mathematical lingo in the past.  I have spent time reading the Common Core State Standards, and realized that if the language is used in the standard, then it should be made accessible to students as well.  

It is important that the students and I establish a mutual agreement that we won’t settle on NOT understanding “big mathematical words” as I explain in my video narrative: The Language Barrier.

Flexibility in the Lesson
Student Communication
3 Without Totally Reteaching - What is a "zero" of a function? - 15 minutes

After telling the students to not let themselves "sink" in the mathematical lingo, and to speak up when they hear something that they don't understand, I begin to revisit properties of functions with the students. 

To begin the last fifteen minutes of class, I direct the students to Desmos and ask them to graph a quadratic - select any quadratic that factors nicely. (Many students will raise their hand and ask you to define what "quadratic" is - EVEN if it is sarcastic, take time to define it so that they know that you are very serious about their speaking up when they don't know what something means!)  I ask the students to talk about the key features of the graph, hypothesize what points they think are the zeros, and why (MP3) - all of this is a quick think-pair-share environment. This gets the students talking to each other using precise language, and allows them to take ownership of the learning... the more they talk "mathy" the more confident they will get!

After establishing what a zero is, I have the students graph the handful a handful of quadratic functions in the homework assignment (MP6).  (My assignment comes from our district adopted textbook, but a new resource for this will be posted in the future.)

Our work in Grandpa's Sweet Corn Garden continues in the next lesson.