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 Camp....my 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 sturdiness....one 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 topics...like 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!)

Saturday, October 7, 2017

Homework

    About three years ago, I completed overhauled my homework system.  I switched to a system of a single weekly review assignment, rather than the short daily assignments I had been accustomed to giving before that.  Here are the four reasons why I'm so glad that I changed to weekly homework.

  • #1:   Students have a chance to get help on homework.  When homework is due the next day, students really have no chance to get help if they don't understand something.  Currently, I assign homework on Friday and it is due on Thursday.  I feel comfortable that students have plenty of time to ask questions if they have it....and if something is left blank, I feel totally comfortable telling them that it is their responsibility to make sure they ask for help.   
  • #2:  This lightens the load and gives students a chance to practice time management.  As the mother of a student who works VERY slowly, I know what it is like to face a homework assignment every night....and it is not a good feeling.  Weekly homework gives students and families a chance to figure out what works for completing homework, and to build in plenty of time instead of knowing you only have one chance to get it done on time.  7th graders are notoriously bad at time management, and I feel like this is a good chance to start learning.  I can still remember the student I had many years ago who always struggled to finish anything that wasn't due the next day.  I remember him saying, "If you would just make it due tomorrow, I would remember to finish it."  I could practically see the light bulb go on for that boy when I told him that he could decide to make it due for himself the next day, even if my deadline was later.    
  • #3:  I like having a built in chance for spiral review.  Since the homework is not just over what we did in class that day, it gives me a great chance to frequently spiral back and review skills.  I really think it helps keep the skills fresh.  
  • #4:  I don't lose as much time grading homework, since we only have to check it once a week.  This is huge for me.  My class periods are only 46 minutes long, so losing 5 minutes every day is a lot.  But taking 10 minutes one day is much better.
      Now that I have done this for a few years, I have learned some lessons to make it work better in my classroom.  I will talk about those in my next blog post!  But I will say, I have finally figured out a way to do homework that I love and think is good for my students.

Tuesday, September 19, 2017

Talk Like a Pirate (and Practice Order of Operations!)

    Today was the best day.  One of those days that your lesson goes exactly like you want it to, the kids are amazed at what you're doing, and it all just falls into place.

     The first part of the day that was so awesome was related to the fact that is was International Talk Like a Pirate Day.  I've been looking forward to Talk Like a Pirate Day for awhile for two reasons.  Reason #1...my son has an awesome pirate hat that I looked forward to wearing to school.  I also had an old Pi Day shirt (Pi-Rate, When Good Numbers Go Bad) to wear...so perfect!

Reason #2....I had this idea this summer of making a pirate name generator.  I figure I could make up a problem (I used an order of operations problem) and the kids could roll dice, and plug the numbers into the problem.  The answer to the problem then generated the kids' pirate names.  So for example, in the first problem, the kids rolled 4 numbers and plugged them into this expression (___ + ___)^2 + ___*___.   So let's say you rolled 4, 2, 3 and 5 then your answer would be 51.  Then I had a table that told them different names for different number ranges.  So 51 meant the first part of your name was "Thieving".

Click on the picture if you're interested in purchasing this pirate name generator.

My pirate name generator had two parts.  My absolute favorite nickname of the day was Salty Fishlips!  Some of the other awesome nicknames:  Parrot Plankwalker, One-Eyed Devil, Jolly Dog, Bearded Cutlass, Gold-Toothed Buaccaneer....it was a blast!  And the kids got a little bit of order of operations practice in.  As I walked around, I really enjoyed hearing students explain to their classmates how to do the problem as they tried to get their pirate name.  

The only disappointment was that I really wanted a name that involved Scurvy Legs or Plankwalker, and the dice never let that happen for me!

Now, the other really awesome part of today's lesson was the part where I showed the kids how to use a spreadsheet....and they got it, and they were as amazed as I thought they should be at the power of spreadsheets.  But I'll leave that for another post!



Friday, July 7, 2017

Area Model in the Middle School Classroom

In my last post, I talked about using the multiplication chart as a tool in the middle school classroom. I really love this idea of building on elementary tools and techniques in our middle school classrooms. Making these connections to prior knowledge is important for students, and it makes our lives easier. So, today I want to talk about another elementary tool that can be useful in the middle school classroom: the area model. When students are first learning multiplication and area,  the area model are foundational for building understanding. Here are a few ways that I like to use the area model to help teach middle school concepts:

 1. Distributive Property--We all know that this is an important concept moving forward, but it can sometimes be tricky for students to wrap their minds around. I use lots of different strategies to help kids understand the distributive property, but the area model is definitely one of them.
The representation below can be seen as two rectangles, a 5 x 8 with an area of 40 and a 5 x 12 with an area of 60.  Or you can see this as one rectangle, a 5 x 20 with an area of 100.  This is a concept that is understandable for students, and it is a good way to reinforce our abstract ways of showing this concept.
          
area-model
area-model
Learning abstract representations of math can be one of the major challenges as students transition from elementary to secondary math, so connections like these can be helpful.

2.  Factoring--This is the natural extension of using area model to teach distributive property.  By simply leaving out the shared side length, we encourage students to factor, and help them see the connection between factoring and the distributive property.

It's good to start with an example that only shares one common factor, like this one.
area-model
         Students can see that the side length has to be the same number.  Next, we want them to make the connection between the same side length and a common factor of 35 and 56.  Student thinking might be like this: 
 What 5 times what equals 35?  8 times what equals 56?  
Finally, we want to students to make connections between the picture and the to the abstract work: 
35 + 56 = 7(5 + 8).  

Now, you can move to examples that have more than one common factor that could be factored out. 
area-model

40 + 60 = 5(8 + 12).  
Connecting the drawing back to the work is important....where do you find the 40, the 5, the 8, and so on in the picture?   

3.  Battling Common Misconceptions--If you give your students the problems (8)(4.5), would you be surprised to have some students give the answer of 32.5?  Me neither!   But the area model can again help us out.  
If students have been using area model to show the distributive property, this representation should be familiar.  This shows that the area is 36 and gives a visual illustration of why we can't multiply 8 x 4 to get 32 and simply add 0.5.

4.  Reinforce proportional thinking--If I had to pick one topic that was the most important thing we do in middle school, it would be proportional reasoning.  Every chance I get, every way I get, I want to reinforce proportional reasoning with my students.  I want to give them different ways to see it.  So what about this?
Since the side of 3 is the same for both rectangles, if you double the 4 to get 8, it also doubles the area from 12 to 24.

5.  Move towards algebraic thinking--Ultimately, our middle school students need to be ready for the demands of algebraic thinking.  The area model can also give us another way to get students using variables in middle school.  Consider the progression of the examples shown below.



If students are consistently using the area model as a representation in our middle school classrooms, hopefully the jump to the last two representations will be easier.  

      So we've looked at multiplication charts and area model...what other elementary models and tools can continue to be helpful in middle school?