I begin the lesson by presenting a hypothetical situation: I show the class a picture of a tall girl alongside a few classmates playing a scrimmage at basketball practice (see tallest girl pic). I point out that these are 8th grade students and Patricia (center) is obviously the tallest. She is already looking forward to joining the high school varsity basketball team in 10th grade. She wants to know how tall she will be in two years.
To help my students get started on helping Patricia answer this question, I ask them to write down some questions that they would like to know the answer to in order to help Patricia predict her height in two years. Some possible questions might be:
I don't respond to every question that my students ask. Many can probably be answered once students have the data set for the activity in their hands. I am most interested in preparing them to use the data thoughtfully.
Next, I form homogeneous pairs of students to work together on this task. I give each group a copy of Predicting Patricia's Height Activity Sheet. I point out to my students that the data table contains measurements of Patricia's height made by her parents on the first day of every school year (beginning in 1st grade).
All work in this part should be done without calculators or computers. My students will work with their partner for the entire activity, yet each student should complete their own Activity Sheet. Students first need to create a scatter plot with the data and then draw a best fit line. This gives students more hands on practice with skills that were introduced in the previous lesson.
Teacher's Note: Here's a great review video link for graphing data by hand and setting up your axis: graphing data by hand
As I walk through the classroom observing my students' work, I look at which data they chose for the independent variable and the scale used for the x- and y-axis. I encourage students to be as precise as possible with their plotting of points reminding them that the more precise they are, the more valid their best fit line will be, and hence, their prediction (MP4, MP6).
I encourage partners to discuss the placement of their line of best fit together. I want each student to draw their own line, but each should try to develop one that fits the data best. Here is a sample of a student's scatter plot: Student sample graph Patricia Height
In the second part of the Patricias Height Activity, I ask each student to create a scatter plot and best fit line using a graphing calculator. The calculator provides an accurate representation of the data, but, we will compare this model to the one that students created by hand.
Teacher's Note: I generally find that "change gears" or "switching from low tech to high tech" energizes my students and enables deeper engagement.
I have a set of instructions at hand for students who have never used or have forgotten how to use the calculator for creating scatter plots:
I know which students possess more calculator expertise. I ask these these students to help others that need assistance.
For the 3 2 1 Exit Pass, my students write 3 things they learned, 2 things they have questions about, and 1 thing they want the teacher to know. All of these are important, but I pay special attention to the questions students write. These often give me essential information which I can use in upcoming lessons.
I like to take the time to respond to the students' questions. I generally write my responses on the back of the slip and return the slips with responses at the beginning of the following class. This motivates my students to write good questions, which in turn helps them to reflect on their learning at the end of each lesson. I find that this routine helps me to connect with my ELL students (see my reflection ELL students and exit passes).
Homework Patricia's Height is a one problem assignment with a similar structure to today's classroom work. The scatter plot is provided, but students need to draw the best fit line, answer questions, and make a prediction.