SWBAT create a function to describe the relationship between two variables.

In this lab, students will once again be gathering data in order to describe the relationships between two variables. This time, however, the correlation is negative.

5 minutes

For today's Warm Up, I have provided students a graph that has no axes labels. I want students to create a story that matches this graph. I want students to pay close attention to the slopes of the various graphs sections and write their corresponding story accurately.

Once the timer sounds, I ask some "pre-selected" volunteers (ones I have picked out and asked beforehand while taking roll) to share their stories. After each story is shared, I ask students to respond with thumbs-up (agree), thumbs-down (disagree) or thumbs-sideways (not sure).

30 minutes

In this activity, student pairs or trios use teacher-created slinky stretchers to gather data. The lab sheet lists all the materials needed to conduct the lab: meter sticks (2 per group), ruler, a bag with two sets of 12 coins (e.g. 12 pennies and 12 quarters...FYI, dimes are too close in mass to pennies, so I would not use these two coins in the same bag), masking tape, and slinky stretchers.

I direct students to review the procedures while I demonstrate: Tape one end of one of a yardsticks from the end of the table (60 cm overhang is best). Suspend the slinky from the end of the yardstick by sliding two coils onto the yardstick. Next, remove 12 coins of the same type from your baggie. After measuring the height of the cup from the floor with no coins and recording your data in a table, add one of the coins. Measure the new height of the cup from the floor. Continue adding coins one at a time and measuring the height from the floor until the cup touches the floor.

I explain that after they finish collecting the data, they will create a scatter plot, a line of best fit for each coin, and an equation for the line of best fit for each coin.

I ask for any questions, then start the 30-minute work timer.

10 minutes

When the work timer sounds, I ask students, "What word would you use to describe the pattern that you see in your data?" I then ask each to justify the words suggested.

Next, I show a slide on which I have listed penny, nickel, dime, and quarter. I ask for students to volunteer the equations of the lines they wrote for the coins they used. We then compared the equations. I am careful to remind students that scatter plots and lines of best fit are imperfect representations, but hopefully, with practice, we are improving our precision.

I then move on to the second question on the lab sheet, "Describe what each of your lines on your graph represent." I ask this question because students often lose track of the math in the activity and fail to process what data is being represented.

I close by giving each student a notecard and asking them to predict the equation of the line if we used Sacajaweah dollar coins (I show the students an example). I am interested to see if students are able to transfer the knowledge from the other coins to the one with which they have no experience through reasoning.