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?





Thursday, June 22, 2017

Multiplication Charts in the Middle School Classroom

     Every year when I put up my posters, I put a multiplication chart near the front of my room.  Until a few years ago, it kind of bugged me.  You know how it goes...kids coming in to middle school should know their multiplication facts, why should I need this, etc....   But then I finally realized I needed to start looking at the good old multiplication chart not for what it might have been in elementary school (although, yes, some kids still use it like that), but for what I could use it to show in middle school.  Because now what I see when I look at that multiplication chart in the front of my room is patterns, patterns, patterns!  That's what math is all about.  Here are some of my favorite ways to use a multipication chart in my middle school classroom.

1.  Equivalent fractions--The multiplication table is filled with row upon row of equivalent fractions.

Here you can see a simple multiplication table that I created on Google Sheets.  The thing I love about my Google Sheets multiplication table is that I can customize it in whatever way is useful.  So if I want to talk about equivalent fractions for 3/8, I can highlight those rows.  But then I can easily change to something else.    What a great way for my students that may struggle with equivalent fractions to have a quick reference to find them, but also a visual way to see that the reason by 12/32 is equivalent to 3/8 is because both 3 and 8 were multiplied by 4!  These realizations that may at times seem to be no big deal for teachers can absolutely blow the minds of our students.

2.  Equivalent ratios/ratio table--Just as we can use the multiplication table for equivalent fractions, it can also be used for scaling ratios up and down to find equivalent ratios.  So now our students are trying to answer some proportional reasoning question:  "It takes James 4 minutes to solve 7 problems.  How many problems can James solve in 12 minutes?"  Again, this idea of using the multiplication chart flexibly, even attaching a label or meaning to some quantity, can be a stretch for kids at first.
This would also be a great way to teach students to think about if the answer to a proportion question like this is even reasonable.  For example, what if the question had been, "It takes James 4 minutes to solve 7 problems.  How many problem can James solve in 11 minutes?"  Now the answer is not actually on the multiplication table...but a sense of what is reasonable sure is.  If 8 minutes is 14 problems and 12 minutes if 21 problems, then the answer must be between 14 and 21 (but closer to 21!).  That sort of amazing proportional reasoning can be supported by a great visual tool like the multiplication chart.

3.  Proportional relationships versus non-proportional (but linear) relationships--Let's say you were focusing on the proportional relationship of 6x = y.  What about showing the multiplication chart as a place to see this?
The multiplication chart can show the table of values for a proportional relationship by simply looking at the column with the correct constant of proportionality.   This gives another way to think of a proportional relationship....it is a relationship that if you had an infinitely large multiplication table, it would have a row on there.  You could also build the connection between 6x = y and 6x + 1 = y by having students add one to all of the values in the 6 column.

       Ok, and honestly, some students will use the multiplication chart because they don't know their multiplication facts.  As much as I wish this weren't true, it just it.  So rather than fighting against it, I've decided to help all of my students see that the multiplication table can be a great tool to help us learn about a lot of middle school concepts far beyond simply multiplying.  After writing all of this, I think this year, we just may create a digital multiplication table in the first few weeks of school to establish right away what a great tool it can be.

How do you think multiplication tables can be helpful in middle school?  What other "elementary" tools do you rely on to make your classroom a better place?

Wednesday, June 14, 2017

Beginning of Class Routine Revamp

        At NCTM, I got several ideas that I wanted to incorporate into my beginning of class routine, and I've been finding others as well.  Here is my beginning of class routine for next year.



Wonder Monday:  This idea is the culmination of a lot of reading and listening that I have been doing.  Jo Boaler's Mathematical Mindset, as well as her growth mindset course have really opened up my eyes to the need for math to be an open and creative field.  I've also been reading "Becoming the Math Teacher You Wish You'd Had", which talks about the importance of a "notice" and "wonder"...what do kids notice about a problem?  What do they wonder about?
           So this is my thought for how to get kids thinking creatively, as well as how math is woven in to so much that we do.  My plan here is to find a crazy or interesting picture each week, and just letting the kids start to wonder about it.  I think it will get their creative juices flowing, and hopefully start to see math as an open subject, with a place for interesting questions.  I think this will be a fun way to start each week!


Two Way Tuesday:  This one came directly from a wonderful session I went to at NCTM.  The idea of the two-way puzzle is that you add going horizontally and vertically.  I think the puzzle aspect of this will keep kids engaged, and I can see it being useful for all kinds of review content....fractions, decimals, whole number, integers, and combining like terms are the first few that come to mind.

In this example, the missing box in the top row would be 22, since -8 + 22 = 14.  The bottom left square would be -5, since -8 + 3 would be -5.  From there, you can fill in the rest of the squares.
What's the Question Wednesday:  I got this idea from another blog I was reading.  Basically, you give the answer, and the kids brainstorm what the question might have been.   Again, I think this could encourage creativity and help kids see that there are all kinds of ways to get to any given answer.


Number Talk Thursday:  This is something else that I've been reading about, and something that I heard about at NCTM.  The idea is basically that you give kids a problem to solve mentally, and then you let kids share their strategies for how they solved the problem.  I tried this out a couple of times toward the end of last year, and I was amazed at what a great use of class time it was.  The kids were highly engaged, and had tons of great strategies.  It also allowed for great discussion as we compared strategies.


Quick Draw Friday:  This is also something that I got at NCTM.  The idea behind it is that you give kids a short look at a geometric drawing, and they try to reproduce it.  Then you give them one more look, and a chance to revise.  Then let kids share their vision for how they saw the picture, and how they re-drew it.  I think this one can really lead to some great vocabulary, and my artistic kids will love it!  The idea comes from this e-book.


       So these are the ideas that I plan to use next year. If you would like a copy of the Google Slides shown above for this beginning of class routine, click here.

One other idea that I would also love to incorporate (but ran out of days!) would be to have a day each week dedicated to looking at a graph and focusing on what story it tells.  I think this is really important as we live in a world surrounded by data, with graphs everywhere trying to convince us of one point or another.  I may try to work this in somehow to my routine, but I can't decide what to give up!  Why is there always more to do than there is time?????

What routines do you use at the beginning of class that you love?

NOTE:  I did a part 2 to this part with even more ideas.  Click here to see the rest!


Sunday, June 11, 2017

A Good Math Class Discussion: Part 2

    In my last post, I talked about my presentation norms that I use in my class.  Today, I'm going to address another important part of a class discussion:  listening.  For most kids, listening is a passive activity.  It is our job to teach them to be active listeners.  These are the strategies I use to teach my students to be active listeners in class.

1.  Listen carefully.  The first one is pretty obvious and speaks for itself.  If you're not paying attention, it's hard to hear what someone else has to say!

2.  Write down questions, comments or notes.  I think we all fall into the trap of thinking that we will remember what we want to say, what question we wanted to ask, etc.. when it is our turn to contribute.  The reality is that if we jot down notes to ourselves, we are far more likely to remember things.  Making sure that students always start with a piece of paper in front of them, even if it's just a scrap of paper or a post-it, is very important in making sure that students are active listeners.


3.  Be ready to summarize what the speaker said...    This requires a focused kind of listening.  This requires that students be more ACTIVE in their listening. As students try to do this, I think it also requires them to really think about whether or not they understand the explanation that is being give.  This leads to the second half of this expectation.

4. ......or ask the speaker a question.  It was really important to me that my classroom listening norms leave room for students to NOT understand.  I always want to send the message that it is OK to struggle and not understand, as long as you're still trying and working.  At the same time, I want students to know that not understanding doesn't mean that you don't participate.  This expectations gives students a way to stay active and involved even when they don't understand.
 
5.  Think about how your strategy compares.   I want a classroom that is open to many strategies.  By comparing strategies, students can see more clearly how strategies compare.  The more students get used to comparing strategies, the more likely they can start to pick the best strategy for the given problem.