Thursday, January 11, 2018

Student Issues with Complementary and Supplementary Angles

        One of our first units of the year is Shapes and Designs.  Part of this unit involves teaching angle relationships, such as complementary and supplementary angles.  As with any topic, there are a few things that can cause issues for students when learning about angle relationships.

      Issue 1:  Remembering the vocabulary.  One pretty obvious issue is that students have to remember the definitions of complementary and supplementary.  I have a pretty effective (although geeky) way that I help my students remember this.
      For complementary angles, I ask my students, "You all like compliments, RIGHT?".  At first they look at me confused.  Then I ask again, and I start to get a lot of  "I see what you did there" kind of nods as students realize way I said RIGHT so loud!  So this becomes a mantra in our class for a week or two.       
Getting silly often helps my kids remember things!

     Now if you thought complementary was a geeky way to remember, hold your socks....supplementary is even better!  :)  For supplmenetary, I tell my students that I'm going to introduce a new "mathematical" way of greeting one another.  You walk up to someone, with both arms held straight out (the straight line in supplementary angles) and say "WSUP?".   At this point, I get quite a few groans and eye rolls, but as I walk in to class for the next couple of weeks, I will be greeted by a chorus of WSUPs!

     Issue 2:  Understanding what the vocabulary means.   This issue was less obvious to me at first.  I was working with a student at study hall, and he could tell me the definitions of complementary and supplementary, but he couldn't do much else related to complementary and supplementary angles.  At first, I was struggling to figure out the problem.  Finally, after telling me what complementary meant, I told him to draw me a picture of what complementary angles looked like.  This kid looked at my like I had grown another head!  In all of our work with complementary and supplementary angles, the pictures had been provided.  When I had him draw his own set of angles, a light bulb went on and he really made that connection to what the definition really meant.  The longer I teach, the more I realize that having students create or even just visualize their own models of situations is very powerful, rather than always providing them for them.

     Issue 3:  Arithmetic errors.  Now this one is pretty silly, and pretty easily corrected....but can we just take a moment and groan for all of the times that my students told me that the complement of a 32 degree angle would be 68 degrees.   Students rush and forget to borrow when they subtract.  The good news here is that usually a simple question like, "So 32 + 68 is 90?" and students quickly realize the mistake.

     Issue 4:  Setting up the equations.   I had a few students that could easily find the complement or supplement, but going from that to a problem with an equation was difficult.

I found that having the student repeat the definition, and then use their own words to frame a question was really helpful.  It would go something like this:
                    Me:  Are these complementary or supplementary?
                    Student:  Complementary
                   Me:  What does complementary mean?
                   Student: Two angles that add up to 90.
                   Me:  So what two things add up to 90 in this picture?
For many of my students, this was enough to help them make the connection and set up the equations.

     Issue 5:  Understanding what the answers meant.   When we started working with equations, many students were confused about solving for the variable in equations like above, and the actual measure of the angle.  We had many class discussions about this, and I made it a practice to ALWAYS ask for both the value of the variable and the measure of the angle.

What issues have you had with angle relationships, and how did you help your students?  Comment below!

If you need some stations, notes or games to teach angle relationships, click here to see what I have in my TpT store.  There's a free angle relationships golf game, as well lots of other stuff!

Thursday, December 7, 2017

"Math-y" Christmas!

    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 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!

NOTE:  When I get a chance, I'll post a pattern for the pyramid, but you can Google search and find one pretty easily.

Sunday, December 3, 2017

Math in Movies Lesson Ideas

     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 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 of 10 to enlarge it.  When they finish, I plan to post them on a wall as a backdrop for some fun Ant-Man pictures.  We will be working on this when we have free time between now and winter break, so I'll post pictures as we finish some props!  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 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.

I hope you enjoy trying these movie-themed lessons in your classroom!


Sunday, November 12, 2017

Celebrating National STEM Day by Putting the M in STEM

    November 8 was National STEM Day.  When a colleague came in my room a couple of days before that to ask what I was going to do for National STEM Day....I'll be honest.  My first thought was, "I'm so far behind my pacing guide....I can't afford to do ANYTHING!".  But as I sat and thought about it, I came to the same conclusion I've come to several times since attending Space job is not only to teach kids math skills, but to inspire them to want to learn math.  My job is to show them that math could be a part of their future, and that it could be a good thing.

     So I decided that I would do a STEM activity, because my students needed that chance to be creative, and work collaboratively, and do so many other things that STEM can do in the classroom.  And I did work in some important math from my standards (even if it wasn't exactly what my pacing guide said I should be doing!).

     The challenge for my students this time:  To build a tower with a shelf at the top that could hold at least two quarters.  Students had a limited amount of "credits" to spend, and they got bonus points for unspent credits.  They also got bonus points if their tower could hold more than two quarters.  Each group had to draw three cards that guided their building.  The cards had inequalities that gave students criteria they had to meet for tower height, base area and shelf area.

      I don't know about your students, but in 7th grade, many of my students still struggle with inequality symbols.  There were many discussions throughout the day about the meaning of the cards.  "Does this mean our tower can be 5 inches, or does it have to be taller?"  "Does the area of the base have to be more or lesss than 6 square inches?"  "How big is 3 square inches?"  I find the open-ended activities like this are a great chance for formative assessment for me, if I listen to the students having conversations with each other.  For this lesson, I could definitely tell that many of my students didn't fully understand inequality symbols, as well as the difference between inches and square inches.

     After a short introduction, my students ended up with about 30 minutes to work on this STEM challenge.  That seemed to be just about the right amount of time.  Because students got extra points for unspent credits, they were very careful about material use.  That was one nice thing about this STEM challenge....the materials ended up being really cheap!  The things I had available were graph paper, index cards, tape, staples, straws, foil (cut in 2" squares) and pipe cleaners.

     My student creations were AMAZING!  I had one group that used a single piece of paper, and built a 5 inch tower that held 15 quarters.  I had groups in every hour that build towers so sturdy that 30 quarters wasn't enough to topple them (I realized in 1st hour that I had to put a limit on how many extra points they could get for group of boys built a tower that held 5 huge library books and still hadn't toppled!).  Students were engaged, creative, and working hard....STEM for the win!

     The next day, I used this as a chance to teach kids how to graph inequalities on the number line.  In each class, I had a handful of students that remembered learning this in 6th grade, but the majority did not.  Using the cards from the STEM challenge, student quickly understood how to graph inequalities.   I feel like this made it well worth it to have take the time to do the STEM challenge.

If you're interested in this Inequality STEM Challenge lesson, you can get it at my TpT store.

Tuesday, November 7, 2017

Homework Part 2

    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 because 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 a second part to my grading system.  Each individual homework assignment is still entered into my gradebook 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 the 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 6th grade content.  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.

Sample Homework
Homework Quality Rubric

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

Saturday, October 28, 2017

4 Ways to Give Feedback to your Class

      There is so much research that supports the effectiveness of giving feedback to improving student performance.  In order to be effective, feedback needs to be both specific and timely.  That makes perfect sense, but that can also be a real challenge.   Here are a few ways that I like to give feedback to my class.

1.  Games--Games are such a great way to get students engaged, but also a great way to give feedback, especially when answers are wrong.  There are so many fun games to play.  One simple game I played last week I called, "Get 5".  I  decided to do this in the middle of class when my planned lesson was NOT going as planned.  Anyway, it was pretty simple.  I challenged my class to get 5 questions in a a row correct. I put a problem on the board and gave everyone a chance to work with their partners to answer the question.  Then I rolled a 30-sided die to randomly call on a student to give me the answer as well as how they got it.  If the class could get 5 in a row correct, I gave them a stamp for our school-wide PBIS program.  It worked great....lots of conversations, and students knew that everyone at their table needed to understand.  Kids were giving each other feedback, and I could give feedback based on conversations I heard or answers given.

2.  Partner activities--I love to do self-checking partner activities, and it allows students to give each other feedback.  Since students are checking each other's work, it frees me up to listen to student conversations and intervene as needed (or to have small group instruction).  They are fairly easy to create....the idea is that you assign each student to either be partner A or partner B.  Each student has a different set of problems.  I usually like to have about 6-8 problems, depending on what the topic is.  The key is that although the students have different problems, the answers are the same.  For example, student A might have the problem -13 + 8 and student B might have the problem -4 + -1.  Each student gets practice, and students know if they don't get the same answer that they need to check over their work.  I like to take my partner activities to the next level by creating a "second part" for each activity.  So after the partners have completed the problems and agree on the answers, then they have to use their answers together to complete another task.  For example, I might have the students from above show each of their problems on a number line, or create a story problem to represent each problem.  This is a great way to handle students working at a different pace, or just to extend the learning opportunities for the partner activity.  I have several sets of partner activities available in my store if you're interested.
3.  Dry erase---This is certainly nothing new, but having kids work problems on dry erase boards is certainly a quick, easy way to gather information about my class thinking.  It's easy to address common misconceptions using a simple feedback tool.  To do this, I'll think about the common errors that I know may happen, and I create a comment with a symbol for each, to guide students toward their error.  For example, if I was teaching adding integers, I might put the following information on the board.

Then with each problem, I could call out different answers, and tell them which feedback was appropriate for each answer.

4.  Use technology to give feedback--Technology truly can help us understand what everyone in our class is thinking, and give productive feedback to them.  One technology tool that I love (and so do my kids!) is Kahoot.  Kahoot keeps my students engaged, and I get all kinds of information about how many in my class understand.  Additionally, if you plan the incorrect answers carefully, you can sometimes customize your feedback to students, such as "If you picked green, you might have forgotten to line up your decimals.  If you picked red, you may have forgotten to carry."

          Another tool that I love to use to give feedback to my students is the website quia. I LOVE using this to give short, formative assessments to my students.  My absolute favorite thing about quia is that you can customize the feedback that students get for correct or incorrect answers.  In addition, you can change the settings so that students get feedback after each answer, instead of having to wait until the end.  I love this feature!  I know in Google Forms, you can give students feedback, but I don't think they get the feedback until they are done.  I much prefer to have them get the feedback as they work, so they can be learning as they go.  Quia does have a subscription cost of $49 per year, but for me it's worth every penny.

Sunday, October 8, 2017

Beginning of Class Routine Revamp: Part 2

A couple of weeks ago, I wrote about my new beginning of class routine:  Wonder Monday, Two Way Tuesday, What's the Question Wednesday, Number Talk Thursday and Quick Draw Friday.  This routine has gotten me through the first quarter of the year, and I have really enjoyed each of these days.  I have enjoyed the different aspects of math that they encourage.....from geometry with Quick Draw to number sense with Number Talks and Two Way Tuesday.  I've enjoyed seeing the power of What's the Question Wednesday both as a formative assessment tool, and to encourage creativity.  Wonder Monday has sparked many great discussions, and even led a student to actually find the cost of filling a pool with jello....which was over $800 by the way!

But, I have also discovered some other cool resources that would also make great warm-ups.  So I'm thinking I may introduce some of these other ideas from time to time.  Here is my next set of ideas for an interesting way to start class.

  • Math at Work Monday:  I found this awesome website that has a section called Math at Work Monday.  There are interviews with all kinds of people about how they use math at their jobs.  What a great way to open my kids eyes to the power of what we're learning!  I also found out about this cool Chrome extension called Insert Learning that lets you put questions, videos and other content into a website for students to access.  Tomorrow, I'm planning my warm up to be Math at Work Monday while I use Insert Learning!
  • Use a Picture to Prove....:  I was inspired by Jo Boaler's book Mathematical Mindsets for this idea.  One of the ways that she recommends opening up a task to make it richer is to have students make a visual to go with it.  I think this could have some real power to get at the heart of some difficult fractions!

  • Would You Rather?:  The idea is to give a choice like, Would you rather have a 1 foot stack of quarters or a $20 bill?  I got this idea from the Would You Rather Math website, which has lots of great examples.  However it's also really easy to come up with your own!

  • What's the Story (version 1):  I was so excited when I found the Graphing Stories website.  This is sooooo cool, and I think the practice graphing would be so helpful and spark tons of great discussion!
  • What's the Story (version 2):  Find a graph, and have the students write the action that matches the story.  Seems like this would alternate well with What's the Story version 1....going back and forth between seeing the action and then making the graph, vs. seeing the graph and describing the action.

  • What's the Story (version 3):  Find some data, and have students draw the conclusion or decide on the caption from it.  We are in a world with so much data, but how much practice do we give kids at deciding what the data is actually telling us?
If you would like a template for these routines, click here for a simple Google Slides that has a slide for each idea (including the ideas in my Beginning of Class Routine Revamp: Part 1 post!)