Fun Amongst Linear Regression Labs
Wednesday, October 9, 2019
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My Algebra 2 students simply finished amongst our 2nd unit of measurement of the twelvemonth on linear functions. The unit of measurement didn't just become equally I had planned. Their prior noesis of linear functions was shockingly low. They knew it had something to hit amongst y=mx+b, but they couldn't tell me what k too b stood for. They knew at that spot was about formula for gradient that involved x1, x2, y1, too y2, but they could never scream back the order.
So, I basically ended upwards starting from scratch amongst these students which took much to a greater extent than fourth dimension than I had planned on devoting to this unit. I volition portion the interactive notebook pages too specific activities nosotros did later, but I hit desire to portion the linear regression labs I did amongst my students. I wishing I could tell that my students loved these, but they didn't. They regularly told me how deadening algebra was. I think the twenty-four hr menses I heard the most complaints was the twenty-four hr menses nosotros performed a linear regression on information nosotros gathered past times eating twizzlers. How tin move eating twizzlers inwards math flat last anything but exciting?!?
To innovate my students to linear regression, I had them hit the True Colors Personality Test that I wrote almost this summer. I had wanted to hit this amongst my students at the starting fourth dimension of the schoolhouse year, but after 2 days of getting to know you lot activities, I was ready to restrict straight into about mathematics! So, I saved the activity for afterwards inwards the semester. We spent almost 2/3 of the fifty-minute flat menses taking the personality exam too learning almost or results. My kids got actually into this! I may direct maintain encouraged their involvement a footling past times telling them this personality exam would assist them ameliorate sympathize their boyfriend/girlfriend. I ended upwards having to brand copies of what each color agency to give to the students because too then many of my students wanted to give the personality exam to someone too translate the results.
The final 3rd of the flat menses was total of information collection too graphing figurer action. I made a tabular array on the Smart Board. Number of People vs. Time. I asked i educatee to volunteer to occupation the stopwatch on their telephone to fourth dimension the students for this activity. The students at tabular array i took turns proverb their cite too their color from the personality test. We stopped the fourth dimension too recorded the pose out of students too total time. We repeated this amongst tabular array i too tabular array two. We repeated it i time to a greater extent than amongst the students at tables i through three. Eventually nosotros got a fourth dimension for the students at all v tables proverb their cite too color.
Next, nosotros had a brusk give-and-take almost which variable was theme too which variable was independent. I direct maintain been making a HUGE bargain almost independent too theme variables this year. This was our firstly fourth dimension e'er to explore the spreadsheet business office on our TI-Nspires. We entered the pose out of people inwards column H5N1 too the amount of fourth dimension inwards seconds inwards column B. My favorite affair almost the TI-Nspire is the procedure that you lot direct maintain to become through to brand a scatter plot. First, you lot move into your information inwards the spreadsheet. Then, you lot insert a novel Data too Statistics page inwards your document. This volition brand the figurer identify your information points randomly on the screen. Once you lot figure out what your independent variable is, you lot click on the x-axis too pick out the independent variable. The information points volition start dancing across the covert to their proper homes. Then, you lot click on the y-axis too pick out the theme variable. After about to a greater extent than dancing, your scatter plot is done! It's fun to watch, too I dear that students actually direct maintain to think almost which variable belongs on which axis!
Together equally a class, the students walked through the procedure of performing a linear regression of the shape y=a+bx. This summer, I went to 2 split week-long workshops that told me that I should halt pedagogy y=mx+b too start pedagogy y=a+bx. The firstly fourth dimension I heard that, I wrote it off equally crazy talk. After all, y=mx+b too I direct maintain been friends since middle school. But, the 2nd fourth dimension I heard that, I started to think that at that spot powerfulness last about merit to the idea. This year, I am experimenting amongst pedagogy y=a+bx for the firstly time. I'm notwithstanding non quite certain how I experience almost it, though. I gauge fourth dimension volition tell. (I also would direct maintain never thought that I would direct maintain given upwards my trusty TI-84 for a TI-Nspire, but that has also happened. I was helping a educatee amongst their TI-84 on Friday, too it was such a weird experience. I've started to forget where about of the buttons are already!) We discussed the gradient too the y-intercept too their pregnant inwards this situation. We also discussed reasons why our information was non perfectly linear. The bell rang earlier nosotros could delve much deeper into it.
I direct maintain also done this activity without having the students portion results. At i workshop, nosotros called this "Pass the Buck." The presenter took a dollar pecker out of his wallet too gave it to someone sitting at the firstly table. That someone said their cite too passed the buck to the adjacent person. We stopped at the halt of the firstly tabular array too recorded the time. The buck made it's way dorsum to the master copy person, too nosotros timed the amount of fourth dimension it took to move past times the buck to the halt of the 2nd table. This procedure continued until the buck had made it to every table.
This lab was about other activity that I learned almost through the OGAP Common Core Training I attended this summer. It is based on an Illuminations activity from NCTM. Students are given a lawn tennis ball to bounce for 2 minutes. Every 10 seconds, the pose out of bounces is recorded. I learned a lot from doing this activity for the firstly time.
1. When you lot instruct inwards a edifice that was built inwards 1919 too your room is on the 2nd floor, it's non a proficient thought to hit this lab inwards your classroom. The scientific discipline instructor whose classroom is direct beneath you lot volition mail a educatee upstairs to inquire you lot to halt doing whatever you lot are doing because it is distracting them. Oops... I gauge v bouncing lawn tennis balls tin move brand quite a flake of racket. We ended upwards going downwards the hall to the auditorium too doing our bouncing on the stage.
2. Do non mitt out the lawn tennis balls to the groups until the final infinitesimal possible. Otherwise, students volition start their exercise bounces earlier you lot demonstrate the proper way to bounce a lawn tennis ball for this lab. Then, you lot volition notice yourself inwards a scenario similar this.
Student - Can nosotros direct maintain about other lawn tennis ball?
Me - What did you lot hit amongst the lawn tennis ball I simply gave you?
Student - We powerfulness direct maintain lost it?
Me - How could you lot lose it? I simply gave it to you lot a few seconds ago!
Student - Well, I entirely bounced it once, but...
Immediately, all eyes inwards the classroom were drawn to the ceiling. Other perks of working inwards such an one-time edifice are that at that spot are incredibly high ceilings too random pipes running EVERYWHERE. Okay, perhaps entirely i of those is a perk. I looked upwards to a higher identify the lite fixtures to run into the lawn tennis ball resting on about pipes. If you lot expect closely, you lot should last able to run into it.
I told the students that they would non last given about other lawn tennis ball. If they could acquire the lawn tennis ball upwards there, they could notice a way to acquire it down. Eventually, i of the students stood on top of their desk too used an umbrella to dislodge the lawn tennis ball.
3. Even if you lot demo students the proper way to bounce a lawn tennis ball too then their information is linear, they volition non listen.
4. The provided tabular array asks students to count the pose out of bounces inwards each ten-second interval. Then, afterwards, they are supposed to fill upwards inwards a 3rd column amongst the cumulative pose out of bounces. This volition confuse students INCREDIBLY. Have students grade out the middle column too ONLY tape the cumulative pose out of bounces.
5. Yes, having each educatee collect their ain laid of lawn tennis ball information sounds similar a keen idea. But, you lot volition last much saner if you lot direct maintain each grouping collect i laid of data. That was a lesson learned the difficult way!
Here is the handout I created to occupation amongst my students. I took the activity a pace further than Illuminations did too used it equally an chance to review a lot of the concepts that nosotros had started working amongst inwards Unit 1. Students were asked to form out variables equally theme too independent, calculate the charge per unit of measurement of alter betwixt diverse intervals, form out a scatter plot equally linear or non-linear, create upwards one's heed if the produced scatter plot is a function, depict the relation equally increasing or decreasing, perform a linear regression using their calculator, translate the pregnant of the gradient too y-intercept inwards this item situation, too occupation the regression equation to brand predictions. Once students were done amongst the lab, their page could last folded inwards one-half too glued inwards their interactive notebooks.
The Twizzler Lab was non an master copy idea. I stole the thought from here too modified it to stand upwards for my grouping of students too their needs. The thought is simple. Give students a twizzler to eat. Before students accept a seize amongst teeth from their twizzler, they mensurate its length. After each bite, they remeasure the twizzler until they direct maintain eaten the entire thing. They occupation this information to create a scatter plot too perform a linear regression.
I used almost the exact same laid of questions from the lawn tennis ball lab amongst the twizzlers lab. I was surprised past times the pose out of students who claimed to non similar twizzlers. I mean, I don't similar twizzlers, but I figured most teenagers did. I'm to a greater extent than of a chocolate someone myself! I told those students who didn't similar twizzlers to direct maintain someone else consume their twizzler for them. But, they notwithstanding had to participate too accept the measurements.
Files tin move last establish here.
So, I basically ended upwards starting from scratch amongst these students which took much to a greater extent than fourth dimension than I had planned on devoting to this unit. I volition portion the interactive notebook pages too specific activities nosotros did later, but I hit desire to portion the linear regression labs I did amongst my students. I wishing I could tell that my students loved these, but they didn't. They regularly told me how deadening algebra was. I think the twenty-four hr menses I heard the most complaints was the twenty-four hr menses nosotros performed a linear regression on information nosotros gathered past times eating twizzlers. How tin move eating twizzlers inwards math flat last anything but exciting?!?
Linear Regression Lab 1: Personality Test Results
The final 3rd of the flat menses was total of information collection too graphing figurer action. I made a tabular array on the Smart Board. Number of People vs. Time. I asked i educatee to volunteer to occupation the stopwatch on their telephone to fourth dimension the students for this activity. The students at tabular array i took turns proverb their cite too their color from the personality test. We stopped the fourth dimension too recorded the pose out of students too total time. We repeated this amongst tabular array i too tabular array two. We repeated it i time to a greater extent than amongst the students at tables i through three. Eventually nosotros got a fourth dimension for the students at all v tables proverb their cite too color.
Next, nosotros had a brusk give-and-take almost which variable was theme too which variable was independent. I direct maintain been making a HUGE bargain almost independent too theme variables this year. This was our firstly fourth dimension e'er to explore the spreadsheet business office on our TI-Nspires. We entered the pose out of people inwards column H5N1 too the amount of fourth dimension inwards seconds inwards column B. My favorite affair almost the TI-Nspire is the procedure that you lot direct maintain to become through to brand a scatter plot. First, you lot move into your information inwards the spreadsheet. Then, you lot insert a novel Data too Statistics page inwards your document. This volition brand the figurer identify your information points randomly on the screen. Once you lot figure out what your independent variable is, you lot click on the x-axis too pick out the independent variable. The information points volition start dancing across the covert to their proper homes. Then, you lot click on the y-axis too pick out the theme variable. After about to a greater extent than dancing, your scatter plot is done! It's fun to watch, too I dear that students actually direct maintain to think almost which variable belongs on which axis!
Together equally a class, the students walked through the procedure of performing a linear regression of the shape y=a+bx. This summer, I went to 2 split week-long workshops that told me that I should halt pedagogy y=mx+b too start pedagogy y=a+bx. The firstly fourth dimension I heard that, I wrote it off equally crazy talk. After all, y=mx+b too I direct maintain been friends since middle school. But, the 2nd fourth dimension I heard that, I started to think that at that spot powerfulness last about merit to the idea. This year, I am experimenting amongst pedagogy y=a+bx for the firstly time. I'm notwithstanding non quite certain how I experience almost it, though. I gauge fourth dimension volition tell. (I also would direct maintain never thought that I would direct maintain given upwards my trusty TI-84 for a TI-Nspire, but that has also happened. I was helping a educatee amongst their TI-84 on Friday, too it was such a weird experience. I've started to forget where about of the buttons are already!) We discussed the gradient too the y-intercept too their pregnant inwards this situation. We also discussed reasons why our information was non perfectly linear. The bell rang earlier nosotros could delve much deeper into it.
I direct maintain also done this activity without having the students portion results. At i workshop, nosotros called this "Pass the Buck." The presenter took a dollar pecker out of his wallet too gave it to someone sitting at the firstly table. That someone said their cite too passed the buck to the adjacent person. We stopped at the halt of the firstly tabular array too recorded the time. The buck made it's way dorsum to the master copy person, too nosotros timed the amount of fourth dimension it took to move past times the buck to the halt of the 2nd table. This procedure continued until the buck had made it to every table.
Linear Regression Lab 2: Bouncing Tennis Balls
 |
| Bouncing Tennis Balls Lab |
This lab was about other activity that I learned almost through the OGAP Common Core Training I attended this summer. It is based on an Illuminations activity from NCTM. Students are given a lawn tennis ball to bounce for 2 minutes. Every 10 seconds, the pose out of bounces is recorded. I learned a lot from doing this activity for the firstly time.
1. When you lot instruct inwards a edifice that was built inwards 1919 too your room is on the 2nd floor, it's non a proficient thought to hit this lab inwards your classroom. The scientific discipline instructor whose classroom is direct beneath you lot volition mail a educatee upstairs to inquire you lot to halt doing whatever you lot are doing because it is distracting them. Oops... I gauge v bouncing lawn tennis balls tin move brand quite a flake of racket. We ended upwards going downwards the hall to the auditorium too doing our bouncing on the stage.
2. Do non mitt out the lawn tennis balls to the groups until the final infinitesimal possible. Otherwise, students volition start their exercise bounces earlier you lot demonstrate the proper way to bounce a lawn tennis ball for this lab. Then, you lot volition notice yourself inwards a scenario similar this.
Student - Can nosotros direct maintain about other lawn tennis ball?
Me - What did you lot hit amongst the lawn tennis ball I simply gave you?
Student - We powerfulness direct maintain lost it?
Me - How could you lot lose it? I simply gave it to you lot a few seconds ago!
Student - Well, I entirely bounced it once, but...
Immediately, all eyes inwards the classroom were drawn to the ceiling. Other perks of working inwards such an one-time edifice are that at that spot are incredibly high ceilings too random pipes running EVERYWHERE. Okay, perhaps entirely i of those is a perk. I looked upwards to a higher identify the lite fixtures to run into the lawn tennis ball resting on about pipes. If you lot expect closely, you lot should last able to run into it.
I told the students that they would non last given about other lawn tennis ball. If they could acquire the lawn tennis ball upwards there, they could notice a way to acquire it down. Eventually, i of the students stood on top of their desk too used an umbrella to dislodge the lawn tennis ball.
3. Even if you lot demo students the proper way to bounce a lawn tennis ball too then their information is linear, they volition non listen.
4. The provided tabular array asks students to count the pose out of bounces inwards each ten-second interval. Then, afterwards, they are supposed to fill upwards inwards a 3rd column amongst the cumulative pose out of bounces. This volition confuse students INCREDIBLY. Have students grade out the middle column too ONLY tape the cumulative pose out of bounces.
5. Yes, having each educatee collect their ain laid of lawn tennis ball information sounds similar a keen idea. But, you lot volition last much saner if you lot direct maintain each grouping collect i laid of data. That was a lesson learned the difficult way!
Here is the handout I created to occupation amongst my students. I took the activity a pace further than Illuminations did too used it equally an chance to review a lot of the concepts that nosotros had started working amongst inwards Unit 1. Students were asked to form out variables equally theme too independent, calculate the charge per unit of measurement of alter betwixt diverse intervals, form out a scatter plot equally linear or non-linear, create upwards one's heed if the produced scatter plot is a function, depict the relation equally increasing or decreasing, perform a linear regression using their calculator, translate the pregnant of the gradient too y-intercept inwards this item situation, too occupation the regression equation to brand predictions. Once students were done amongst the lab, their page could last folded inwards one-half too glued inwards their interactive notebooks.
Linear Regression Lab 3: Twizzlers!
 |
| Twizzlers Linear Regression Lab |
The Twizzler Lab was non an master copy idea. I stole the thought from here too modified it to stand upwards for my grouping of students too their needs. The thought is simple. Give students a twizzler to eat. Before students accept a seize amongst teeth from their twizzler, they mensurate its length. After each bite, they remeasure the twizzler until they direct maintain eaten the entire thing. They occupation this information to create a scatter plot too perform a linear regression.
I used almost the exact same laid of questions from the lawn tennis ball lab amongst the twizzlers lab. I was surprised past times the pose out of students who claimed to non similar twizzlers. I mean, I don't similar twizzlers, but I figured most teenagers did. I'm to a greater extent than of a chocolate someone myself! I told those students who didn't similar twizzlers to direct maintain someone else consume their twizzler for them. But, they notwithstanding had to participate too accept the measurements.
Files tin move last establish here.
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