The Most Awesome Linear Regression Project Your Class Will Love

  Does your class love Kahoot as much as my class does?  Because they REALLY love Kahoot.  During our unit on linear equations, I decided to have my class use linear regression to try to figure out the Kahoot algorithm for assigning points as our final project.

    As our discussions of Kahoot scoring began, it was clear to everyone that the two variables that impact your score are time to answer and answer streaks.  Trying to figure out how both of these variables affected your score was the foundation of our project. 

       The first thing we had to do was find a way to collect data about these variables.  My teacher's brain went into overdrive trying to figure out exactly how we could collect the data so that my students would have data to analyze.  However, rather than just organizing the data collection myself, we started the project by having a class discussion about how to collect meaningful data relating how time impacts your score in Kahoot.  I felt like having students think through the process of how to collect meaningful, useful data was very important.  I was so excited that the plan the kids came up with was basically the same thing I had planned to do. 

       Here was the plan:  Each student would be assigned a specific time at which they were supposed to answer.   Students would answer at the specified time and record how many points they received on that particular question (rather than their overall score).  The class decided that after each correct answer, you had to miss the next question so that no one had an answer streak that would impact their score.   We played through the Kahoot a few times with different time limits on the questions.  Throughout the data collection process, we used the same Kahoot.  It was a 10 question Kahoot in which every question was 1 + 1, and the right answer was always in the same place. 

        Next, we collected data about answer streaks.   This time, the entire class answered at the same time but each student had a different amount of questions they were supposed to get correct.  Once I had collected all of the time and answer streak data, I transferred it over to Google Sheets so that I could easily share it with students.  Now we were ready to get to work on our linear regression project.

       The project had several parts for students to complete: 

• Data table and graph with at least 8 points relating time and score 
• Linear regression equation relating time and score.  Students had to explain the m and b value within the context of a Kahoot game, as well as explain what the r value meant
• Data table and graph with at least 6 points relating answer streak and score
• Linear regression equation relating streak and score.  Students again had to explain the m and b values within the context of a Kahoot game and explain the r value.  In addition, students had to explain any limits to the domain (because the streak bonus eventually maxes out)
• A predicted score on a fake Kahoot game compared to the actual score--This was my favorite part of the project.  Students had to use their equations to predict their score on an 8 question Kahoot.  They had to specify when they would answer and if they would get it right or wrong.  Then we actually played the Kahoot so they could see how well the equations worked.  It was a lot of fun to hear, "My prediction was only 5 points off!" and the rest of their excitement!
• A letter explaining what the student liked about the Kahoot scoring algorithm or a suggestion to change it for the better

       Overall, I really liked this project much better than using fake linear regression data from our textbook.  If I had to do it over again, I would probably only focus the project on the time aspect and not worry about answer streaks.  Having two sets of data definitely complicated things.  Overall, this was a fun project for my linear equations unit.

       If you'd like a copy of this project, click here to join my email list and you'll get access to this project.

Your Math Class Will Love Going To the Movies

     There are lots of great scenes from books and movies that can be used to launch math activities.  Today, I'm going to focus on a few of my favorite ones from over the years.

     Probably my favorite all time movie connection actually comes from the special features of the first Lord of the Rings movies.  There is an awesome documentary where they talk about how they use forced perspective to make Frodo look shorter than Gandalf.  The clip shows how they use the actors' distance from the cameras as well as the size of sets and props to accomplish the visual illusion.  If you click here, it will take you to a link on YouTube.  The video is 15 minutes, but the first 5 minutes are the best part.
      After watching this clip, we've had some fun projects based on this.  One year, I typed up a "script" for a short scene between Frodo and Gandalf.  Then I had students in class plan out where each person needed to stand so that they could make Gandalf look taller than Frodo in our scene.
     Other times when I've done this project, I've also had the students make easy props (such as teacups) that were normal size for Frodo, but tiny for Gandalf.  The props are identical in every other way except the size.  This way, when Gandalf picked up his tiny teacup that otherwise looked exactly like Frodo's, it helps sell the illusion that Gandalf is larger.  These activities force students to use measurements, scale, as well as reinforcing student understanding of reciprocals.
      Forced perspective is also used in the movie Elf (at the beginning when Buddy is a huge Elf at the North Pole) and some in Harry Potter, to make Hagrid look larger than life.

       Another fun (and similar) project could be based on the movie Ant-Man.  There is a fun scene in the movie where Ant-Man and YellowJacket are fighting in a briefcase.  During the course of the fight, you see giant LifeSavers, IPhones and keys flying by our tiny hero.  We are finishing our Stretching and Shrinking unit right now....so what better time to make giant versions of classroom objects!  Yesterday, I challenged my students to take an object that would fit inside a briefcase and use a scale factor to enlarge it.  (Note:  I used 10 as my scale factor, and that was REALLY big!  I would probaby recommend 5 or 6.)  When they finish, I plan to post them on a wall as a backdrop for some fun Ant-Man pictures.  Click here to get a clip of this scene.  You only really need to show from 2:00-3:00 to see what is needed for this project.
      To get a Google Slides presentation to launch this project, click the graphic below.

      Mythbusters once did an episode on zombies, and one of the tests that they did was whether it was realistic to be able to outrun a horde of zombies.  They tried different population densities and had someone see if they could run a certain distance without being "caught" by a zombie. One of our units, Comparing and Scaling, has a huge focus on unit rates.  So I used this clip to introduce the idea of population density.  We figured the population density of our classroom, gym, and cafeteria.  Then we looked at the population density of several cities.  Finally, I took my kids outside to the football field, and we tried it ourselves.....with most of my class playing zombies and the a couple trying to outrun them.  The kids LOVED it! This clip is a short version....it just the simulation for one population density.  It gives the dimensions of the field and the number of zombies.  To find the rest of the episode, here is the clip I found.  The quality is not great, but you can see it from 26:30-29:00 where it explains the other populations densities they tried.
       To get a copy of an editable lesson to go along with this video clip, click the graphic below.

Click here to find some of the other fun projects I've blogged about!

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How To Get Your Students Excited About Similarity

       Our current unit is Stretching and Shrinking, a unit about mathematical similarity.  This is one of my favorite units to teach every year, and this year I found a great way to launch it.  I decided that to launch our unit, we would have some class "grow beasts".  I am so excited about how this class activity turned out.  There were lots of great benefits for my student's learning, and it was pretty easy to implement.

       First, I'll talk about the implementation.  I had 7 different grow beasts:  2 frogs, 2 lizards, 2 skeletons and 1 shark.  Each table was assigned one of the grow beasts.  On day 1, we defined what measurements we would be taking each day.  I had a simple chart that defined measurement 1, 2, 3, 4 and 5 for each grow beast.  Students took initial measurements of their beasts.  I had students submit their measurements through a very simple Google form.  I also made initial measurements of each of the different types of grow beasts.  We also examined the claims on the package (I hung them on the wall as reference), which included the following claims:

       The next day, we organized all of the data and looked for outliers.  For each measurement that didn't make sense, we decided what to do about it.  In a few cases, we threw the data out that clearly seemed incorrect.  In a few cases, the decision of the class was that the measurement had accidentally been taken in centimeters instead of millimeters, in which case we fixed it.  We also made predictions of what we thought would happen.  This was a great chance for me to begin to understand my students thinking before we started our unit.  I tried to focus our discussion on key issues relating to similarity, such as whether all parts of the body would grow equally, and whether the angles in the figures (such as the angles of the legs in the frog) would stay the same or change as the beast grew. Student response was mixed on these issues, so the discussion was very eye-opening for me.  It gave me a good window into my students' initial thinking about similarity.  I also had students make predictions about what would be the size of each of the measurements if they all doubled, or if they all tripled.  At the end of the day, I put the grow beasts in water.

      I also made a graph with all of the initial measurements, as well as a line showing the measurements for growing 3 x bigger and growing 6 x bigger.  I had original measurements as my x variable and growing measurements as my y variable.  I started by putting all of the original measurements on the x-axis.  I made it on a big sheet of chart paper.  This graph became a central place for me record all of the results and became the guide for many of our discussions.  I was so glad to have this graph to refer to throughout our grow beast project.  I also really liked that it was a great way to introduce the concept of proportionality, although we didn't formally use that language.  For someone teaching 8th grade or Algebra, this might also be an interesting way to look at trend lines.  I definitely found that each day's data made a somewhat linear pattern on the graph, although measurement accuracy (or lack of) might be a problem.  You could also use Desmos to graph your data.

       Our warm-up each day was to measure the grow beasts.  I usually gave them the first 5 minutes of class to get their measurements submitted.  If you're going to do this, you'll want to make sure that you have a towel around to dry off the beasts before you measure them.  The kids got really excited to see how they grew.  Each day I would put up the chart that listed the different measurements, and the kids continued to complete the same Google Form over and over with the measurements for the grow beast.  This project definitely reminded me that having students measure is so important, and they REALLY need the practice!  I also liked having students give the data via the Google Form.  It allowed me to easily sort the data by the animal type, and then by date so we could really see the trends in growth.

       At the end of each day, I also measured the grow beasts and add the new data to the class graph.  I had each figure color coded on the graph, but it was really cool to see how you could see a trendline of growth for all of the figures.  I loved the fact that I had already put the tripling line and 6 x bigger line on the graph, so when I showed it to the kids we could compare it to those benchmarks.


       One interesting (and fortunate) thing that happened to me was that one of my frog grow beasts did not grow for some reason. That group of students was kind of bummed out, but as a teacher it was terrific!  We had initially debated whether the angles of the legs would stay the same, and this way we actually were able to check it out.  If you plan to do this project, if possible, you might get one grow beast that doesn't go in the water to compare back to.

           

       We let our grow beasts grow until they stopped.  For us, that was about 7 days.  They were close to triple in size, but none of them quite made it.  This did make a great impression on my class.  It also sparked a fantastic discussion about mathematical similarity.  By the time we finished the project, I had introduced 2-D similarity (Wumps, for you all CMP users!) and we had a great discussion of what the grow beasts had to do with Wumps and everything that we had learned about the characteristics of similar figures.

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The Best Math Christmas Project Ever

    Ok, this will be a short post.....but I just have to tell you how excited I am about my classroom Christmas tree this year.

     We decided on a 3:1 ratio of green pyramids to other colored pyramids for the "decorations".

     I'm excited.  The kids are excited.   What a win-win!  And it's been pretty easy.  The only supplies I've needed are colored copies of a net for a triangular prism and tape.  One day for my warm up, I reviewed the surface area and had every kid fold up one pyramid.  And that is the only class time I've taken to do this.  The rest was kids taking these home to work on, or kids that wanted to work during our advisor/homeroom time at the end of the day.

     I will definitely do this again next year.  I think one thing I will change is that I will use the chance to more fully review surface area and make kids draw the height in on the base of the pyramid.  Then I'll have them find the surface area.  I'll probably also give them 10 minutes or so to decorate their pyramid, but you wouldn't have to do that.

Patterns.  Geometry.  Math.  Art.  Beauty.  Creativity.  Christmas Decorations.  It's perfect!

Update:  When I did this last year, I just used a basic pattern for a triangular pyramid printed two per page.  This year, I'm going to make it a bit fancier.  I have several patterns for students to use.  Some of them have clip art that kids can color.  One pattern reviews area of triangles and has students find the surface area of the pyramid.  One pattern focuses on acts of kindness and one focuses on different things about the student.  I think I will have each kid make two of these....one of their choice and then everyone will do the area of triangles one.    I'm also excited that I think I have the other 7th grade teachers on board to do this as well, so I think we will be able to take this to the "next level" and have an even bigger tree!

       It's easy to do this project with a simple triangular pyramid that you can easily find with a Google search.  Click here for a video tutorial explaining how to put the pyramids together.  If you'd like the patterns shown above, click here to see this at my Teachers Pay Teachers store.

Increase Homework Quality with Free Rubric

    A couple of weeks ago, I wrote about why I switched to giving weekly homework.  Over the three years that I have done this, I have definitely made a couple of adjustments that have helped this system work better for me.

     One of the adjustments that I've made has to do with grading. In my class, I hand out the homework on Friday, and it is due the following Thursday.  The day the homework is due, I pass out red pens, project the answer key on the SMART Board and kids check their own work.  When I enter homework in the grade book, I enter a completion grade, rather than grade the assignment based on the number correct.

        One reason I like this system is that I feel like it lets me focus on the big picture.  When I'm entering the regular score for a homework assignment, I don't have to look closely at every problem for every student.  However, I give each paper a quick scan to make sure that it was completed.  As I grade, I look for patterns.  If I notice that one problem was skipped or missed frequently, I know that this is an area that needs more attention in future assignments, as students did not feel as comfortable with this content.  Because I'm only having to enter homework grades once a week, I have time to look for these patterns.  I also can look for students who are struggling with multiple concepts.

     However, this system was frustrating for me (and my more studious students) at times.  I know that there were a few students who put little effort into the assignments, knowing that their grade was not necessarily determined by the number correct.  This year, I have implemented another part of my grading system.  Each individual homework assignment is still entered into my grade book graded on completion.  It is usually 5 points per week.  Each week, I randomly choose about 6 students whose assignment also gets graded based on a "Homework Quality Rubric".

     This rubric looks at several characteristics of the assignment.  The rubric is based on six categories:  Assignment Completeness, Accuracy and Knowledge, Work Quality, Math Language, Legibility/Organization, and Student Reflection.   I feel this gives me a chance to reflect important characteristics on how students are doing at completely a quality piece of work.

• Are the answers correct? 
•  Did they complete every problem? 
•  Did they show their work?  
• Is their work organized and easy to follow?  
• Did they label their answers?  
• Did they use correct vocabulary? 

Because I'm only having to grade about 6 of these per class, I can take a little bit more time to look in detail at these factors.

     At the beginning of the quarter, I put student names on all of the rubrics.  Then each week I can randomly pull some from the pile to use.  Students get very specific feedback about how to improve the quality of their work, and since they don't know when it will be the week that they will be graded, there is an incentive to put quality effort into the assignment.

      The second adjustment that I've made to my homework system is new this year, and I love it!  This year, I started adding some student choice and differentiation to my homework assignments.  Each assignment is a worksheet, front, and back.  Everyone is expected to complete the entire front side.  The back side of the assignment is divided into three sections.  Two of the sections focus on skills practice.  The third section is usually called "Open-Ended Problem Solving".  This section is intended for students that don't need skills practice, as a way to push them.

This was part of the choice section on the back side.  At the top of the page, students indicate what section they are choosing and why.  During a couple of weeks prior to this, I had noticed many students confusing finding percent vs. percent change after a lesson we had done.  We were working on complementary and supplementary angles at the time, and I know some students were still struggling with this.  

       This is probably the best adjustment that I've made.  The skills sections on the back are a great way to address common errors and misconceptions that I'm seeing in class or on the homework.  At the beginning of the year, I used it to review content from previous years.  Now as the year has gone on, I am using it more to address class needs.  I love that this makes me pay more attention to what my students need.  Each week, I know that I'm going to need a couple of skills to work on for the homework, so I'm always on the lookout.  If I notice a problem that lots of students skipped or a problem that lots of students missed on a quiz, these become the skills practice areas on my homework.  I feel like this has made my homework more relevant to students, as the practice becomes an adjustment to their area of need.

      When I hand out the homework each Friday, I briefly go over the three sections.  Sometimes I might do a quick review based on the skill.  I also let students know why they might want to choose a particular section.  "If you missed #5 on the quiz yesterday, you'll probably want to complete section B".  In my experience, middle school students are not great at knowing their needs academically.  This gives this a chance to practice self-assessment and work choice.

If you're interested in copies of a sample of my weekly homework or the homework rubric, click below.

Homework Quality Rubric
Sample Homework

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Note:  My school uses Connected Math curriculum, so my homework follows the pacing and examples of CMP.

New Things I've Found This Year: EdPuzzle!

So, I am totally excited about EdPuzzle!  It is such a cool tool, and really gives me one more way to make the best use of Chromebooks in the classroom.

EdPuzzle is a free site that lets you take videos (from YouTube, Khan Academy, etc....) and add stuff to them for your class.

 The feature that I use the most is the ability to add questions in to the middle of the video.  So as students watch, you can have them pause the video, and answer multiple choice or open ended questions about the video.  If you give multiple choice questions, students even get feedback right away!  To make that feature even better, you can type in different feedback depending on which answer students chose.

Another helpful feature of EdPuzzle is the ability to crop a video.   So if you find a video that you like, but the intro is too long, or the concept gets too difficult, you can simply crop it out.  The only thing I didn't like about this feature is that you can only crop off the beginning or the end....I don't think you can crop a section out of the middle.

EdPuzzle also has some cool audio features.  You can add your own audio track to an existing video...basically narrating the entire thing!  Or you have the ability to add an audio note, so that you can just add your own audio comment here or there within the video.

EdPuzzle has helped me so much to have better avenues for differentiation.  It really allows me to feel like I can be in a couple of places at once.  If I need to do reteaching over multiple skills, I can assign different EdPuzzles for the skills.  My kids are engaged in something, and it frees me up to work with a small group without constantly being asked questions....AMAZING!!

Also, I signed up with Google, and it was so easy....it automatically created my classes for me.  I literally think I just had to hit one button, and I was ready to go.

Next great thing about EdPuzzle....super information about your students.  You have the ability to view the results by student, or by question.

Here is the question view.

Here is the whole class view.

When looking by student, you can see not only what they got right and wrong, but even which sections of the video the student watched multiple times.

Look at all the information you can get about individual students....which questions right, which are wrong, which part they watched over, overall percent correct....great info!

I feel like EdPuzzle is just the tool I've needed to be more effective at differentiating.  Often, I feel like I give my high kids a project and expect them to sort of figure it out on their own, while I work with my struggling students.  I think that EdPuzzle will give me a way to do a better job with the kids that I won't be working with directly when I differentiate....like I really can be in two places at once!!

Reasons I Get Excited About STEM Challenges in Math

       STEM activities are all the rage, and my goal for this year is to make time for one STEM challenge each quarter this year.  I'll be honest, I'm fairly new to the STEM bandwagon.  Prior to 2016, I hadn't done any STEM challenges and I really had no plans to incorporate STEM in my classroom.  I figured that I had enough on my plate just trying to teach all of the stuff that was in my standards.

       That all changed in the summer of 2016 when I was privileged to attend Honeywell Educators at Space Academy.  Space Camp helped me realize that I not only need to teach my kids math skills.  I also need to help them see the exciting things that STEM can open up for them.  I need to help my students see themselves as people who are capable of using math as a tool solve problems.  So began my experience with STEM challenges.

     Over the last couple of years, I've found some STEM activities that really fit my needs.  This year, I plan to do a STEM challenge every quarter.  I've become a STEM challenge enthusiast, and here are the reasons why I love STEM challenges.

1.  STEM challenges are a great way for kids to really see the real world applications of math.  Let's face it....our textbooks try to use story problems to accomplish this task, but they are often not successful.  The contexts in story problems are often too contrived to make students care about them.

The beauty of a STEM challenge, however, is that you are giving students a problem to solve.  As they complete the challenge, math can be one of the tools that they use to find and gauge their success.

2.   STEM challenges are a place to really show the need for precise measurements.  Measurement of a variable is often the key to determining success in a STEM challenge.  If the challenge is to build the tallest pipe cleaner tower, accurate measurement is definitely a key.  In other STEM challenges, students must stay within given constraints.  For example, if you are only allowed to use 6 square inches of foil in your product, you will need to measure accurately for this.

3.  The need for correct labels is clear.  I was doing a STEM challenge last year where students had to build a shelf to hold as many quarters as possible.  They were given limitations for the size of the shelf, such as less than 6 square inches.  This STEM challenge really exposed my students' misunderstandings about the difference between inches and square inches.  Even better, it gave me a way to address this misunderstanding at a time that my students needed to know that information.

4.  STEM challenges are a great chance to introduce students to the power of spreadsheets.   STEM challenges often involve data collection, and this is a good way to incorporate the technology part of STEM.  Spreadsheets are a great way to collect the data. What a great way to introduce students to the power of a spreadsheet than with a bunch of data that they collected!  Last year we did a STEM pipe cleaner challenge, and there were so many excited students when I showed them that they could enter the calculations once and the spreadsheet could do all of the calculating for them.   In the real world that we live in, much of the math that we need can be automated with a spreadsheet.  It is so important for students to begin to see that math isn't always about doing the calculations yourself, but sometimes about knowing how to get a computer to do them for you!

5.  STEM challenges are a great way to work on a variety of math concepts.  Many STEM challenges involve measurement, data collection, and data analysis.  For many STEM challenges, however, the math part stops with these things.  However, I've found ways to incorporate many other topics:

• Area, surface area, and volume:  STEM challenges often involve creating some object, so I've found that I can often incorporate area, surface area or volume.  I did a STEM challenge last year where students had to build a diving pool for a daredevil high-diver (pencil cap erasers!).  After the challenge, students had to find the surface area and volume of their pool to see who had the pool with the least surface area.
• Percent change:  This works especially well if you give students a chance to improve their original creation.  For example, lots of STEM challenges involve students building tall towers.  I've seen these with spaghetti and marshmallows, pipe cleaners, cups, or even balloons!  To incorporate percent change, have the students complete the original project and measure their tower.  Then give them time to make revisions, or wait until another day and have them try again.  Then students can compare the percent change between the first and second attempt.
• Ratios:  I did one STEM challenge where students had to build a tower from candy and toothpicks.  The catch was that they were assigned a particular ratio of candy to toothpicks that they had to use. 
• Equations and inequalities:  I've found there are often ways to incorporate equations and inequalities into a STEM challenge.  Let's say your STEM challenge is for students to build a tower that is at least 12 inches tall.  Why not use this to introduce the idea of writing inequalities?  Or you could have all students put their tower heights on a number line, and introduce the idea of graphing inequalities.  When we built our candy/toothpick towers, we wrote equations relating the number of toothpicks to candy.

6.  STEM challenges are a great way to teach a growth mindset.  STEM challenges are all about trying things out and making adjustments to make things work better.   During a STEM challenge, it is no big deal to have something not work and try something different.  What a great opportunity for teachers to reinforce the power of learning from our mistakes to figure out better solutions or understandings.  I take any chance I can to reinforce the power of learning from our mistakes with my students.  

7.  STEM challenges are great for those random days that you don't know what to do with.  You know what I'm talking about....that 2 day week before Thanksgiving when you don't want to start something new.  Or that day when fourteen kids have the flu and you don't want them to miss the lesson that is such a foundation for your unit.  STEM challenges are great to fill in these random days, and yet still be focused on math.

8.  STEM challenges are great to engage all different kinds of students.  Kids love doing hands-on stuff and even my most reluctant math students will dive into a STEM challenge.

9.  They're fun!   We get so worried about teaching standards and finishing everything that sometimes the fun gets lost.  It's nice to hear the fun and excitement of a STEM day!  It's nice to hear kids in the hall talking about how much fun math is today.  It's nice to have kids still talking about something you did in class a week later.

10.  STEM challenges are a great way to get kids collaborating.  I always have my students work in groups on STEM challenges.  STEM challenges are a great way to get kids exchanging ideas, and incorporating ideas from many students.  This is a great way to work on "soft skills"!

What is your favorite STEM activity to do in math class?  Comment below!