Linear Functions Organizer this does not include arithmetic sequences, which was earlier in the year, but I can refer back to our work with them to activate prior knowledge for this unit. The next unit will be linear regression which will include correlation, describing scatterplots, finding regression equation with technology, using the equation to predict and finally introduction to residuals.
Students started with a pre-quiz similar to the one below.
Identify Linear Functions This is a booklet with a Frayer Model for our notes, a variety of math relations to identify as linear or not and a 2-minute reflection grid on the back. Prior to beginning our notes, I gave them 1 minute to jot down anything they thought they knew about linear functions. Then we pair-shared before sharing with the entire class. Then we took our notes. (as a follow up the next day, I gave them 2 minutes to jot down all they could remember about linear functions as a small retrieval practice).
Our next task was created by cutting apart these relations and posting them around the room with a chart that asked if they agreed or disagreed with the example being a linear function. Students received stickers to place on the chart as they visited each station.
I was fairly accurate in which ones I thought we’d have to use for discussion, but a couple really surprised me. These are the 4 we discussed following the carousel activity.
I. y = 2x was the one I was not expecting. When I asked if someone would share their thinking, one student said they thought x was an exponent. Another shared they did see “the b” for y-intercept. We looked at a table of values and graph to agree, and show the y-intercept was at the origin and indeed y = 2x was linear.
The other I failed to snap a picture of was graph K, a vertical line. Yes, it’s linear, but not a function…two students got that one correct in this particular class.
Using the 2-minute reflection grid as our exit slip to see students thinking about the lesson, I was excited about some of their “I still have a question about…”
On the reflection grid, if they have no questions, nothing is confusing, I ask them to give me a caution…something to be careful or / watch for. Several of these questions encompass multiple students. Some of them I only needed to clarify what was said. Its pretty clear I was not communicating very well on a few of the. I hear my “expert blind spot” showing up…”Of course squared is not linear, we learned it was quadratic in our functions unit!” But so many students on the pre-quiz used vertical line test as their reasoning for linear…we had some side conversations about this misconception…that it shows functions, but does not prove if its linear.
Some of the questions, I allowed other students explain their reasoning to help clarify their understanding.
I know I shouldn’t have favorites, but in this list…
Why can’t you multiply the numbers by each other? We tried it. Add 2 numbers that will make 18. Create table of values, find rate of change, graph it. Yep, that’s linear! Multiply 2 numbers that will result in 18. We created a table of values of their answers, found the rate of change and graphed them. No, that’s not linear!
If an exponent is less than 1, can it be linear? We will try it tomorrow as our bell ringer. But I look forward to exploring their questions more!
I told them how excited I was about their questions and posted them on our “THINKING is not driven by answers, but by QUESTIONS” board. One student had the biggest smile and as she said, Look! I’m so proud, my question is on the board! Something so simple, yet, my hopes are that it will encourage her to ask more questions.
One student asked me, but isn’t it disrespectful to ask questions and interrupt the lesson? Nooooooo. I love when you ask purposeful, curious questions you wonder about! Finally, a break-through to get them to start asking and wondering more…