Top Teaching > Beth Newingham > Math Workshop: Using Developmental Grouping to Differentiate Your Instruction

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Math Workshop: Using Developmental Grouping to Differentiate Your Instruction

JacobIn the past, I taught my math lessons as an entirely "whole-class" event.  I found myself at the front of the classroom teaching while my students sat at their desks trying to understand the new concepts.  There were always some students who found the lesson too easy and, likely out of boredom, tried to do the work before I even finished teaching the lesson.  On the other hand, there were also those students who struggled to understand the concepts and felt lost unless I stopped teaching and went to their individual desks to help them.  For these reasons, I found that teaching math was frustrating.  I was never able to meet the needs of all of my students.  That is when my teaching partner suggested we do Math Workshop after attending Alice Murphy's professional development seminar.  I have no idea why I had not been doing this all along!  I am so passionate about Reading and Writing Workshops because I can provide my students with the differentiated instruction that is so important in elementary school.  Math Workshop now allows me to do the same thing, as I use developmental grouping to differentiate my daily instruction. 

READ ON to learn how I use developmental grouping, math rotation stations, and math games to meet to the needs of my students during Math Workshop.

 

The Math Workshop model was created seven years ago by a teacher in my county, Alice Murphy.  Some of the information in this post was derived from her presentations and professional development seminars. Visit Alice's Math Workshop Web site to find detailed information about Math Workshop, as well as Everyday Mathematics lesson plans for using this approach in your classroom.  You will also find her contact information so that you can invite her to train teachers at your school or in your district.

 

How Does Math Workshop Work in Our Classroom?

  

Developmental Grouping:  Before each unit, we pre-test the students to determine their prior knowledge about the concepts in the unit we are about to teach.  Using that information, we create three groups (high, medium, low).  The students obviously are not told what group they are in, and the groups do change throughout the year as we move through each new unit.  Students are assigned to a group with a name that goes along with our theme.  (See "Math Rotation Stations" picture below.)  We are careful to make sure that the group names change after each unit so that, for example, the high group is not always "The Titanic."

 

Rotation board

 

 

 

Everyday Math Daily Lessons:  We use Everyday Mathematics in our school district.  It is a great program because it includes lots of math games for the reinforcement of new concepts, and it provides teachers with materials to meet the needs of both gifted and remedial students.  We teach the lessons in the order that they are introduced in the book.  However, we alter the lessons when necessary to meet the needs of our highest math students and our lowest math students by using the "enrichment" and the "readiness" resources provided in the program. (See picture below.)

 

Differentiation options

 

Math Rotation Stations: Once the students are divided into three groups, they rotate through three different stations during our daily math period.  Students are typically at each station for 20 minutes.  Below are the descriptions of the three stations.

   

  • Work With Teacher: At this station, students sit close to me and engage in an interactive lesson that is geared to their needs. I use a small dry erase board, and the students sit on the carpet in front of me so that I can see exactly what they are doing. Students often use portable dry erase boards to practice the concepts we are learning, or we may work together on pages in the math journal.  (I am excited to have a new SMART Board to use during this rotation to make my instruction more interactive and effective!)

Teaching



 

  • Independent Practice: Students are at their desks during this rotation, working on pages in their math journal (Everyday Mathematics' term for a math workbook).  They may also be working on teacher-created worksheets or math packets.

Ind work


 


  • Math Games: At this rotation, students play Everyday Mathematics games or other math games that help them practice the concepts they are learning in each unit.  Students usually play the games with a partner in their group.  However, there are times when the games can be played as a whole group or in larger groups of three to four students.  This rotation can also be a time for students to work on math projects and/or investigations that span multiple days. (Everyday Mathematics even has online games that students can play on the laptops.)

Game1 Game2




 

In What Order Do the Groups Rotate to Each Station?


 

Rotation #1:

 

Lap boards The low group starts with me at the Work With Teacher Station.  I work with this group first so that they are taught the lesson before being asked to work independently or play a game related to the concept I am teaching.  I use a small dry erase board or the interactive whiteboard for my instruction, and the students sit in front of me on the carpet.  They bring their math journal with them because I often have them work on the math journal pages with me during the lesson.  If I notice right away that they are struggling with the concept, I will use the "readiness" materials provided in the Everyday Mathematics lesson or create my own "remedial" resources.  I often copy the "readiness" materials to use just in case I need them if I think they are worthwhile.


The medium group starts at the Math Games Station.  They are often playing the game that is part of that day's Everyday Mathematics lesson, but they may also be playing a game that they have played in the past that corresponds to the concepts in the unit.  Sometimes students are also doing projects at this center, especially during the fraction and geometry units.


The high group starts at the Independent Practice Station.  I have them start at this station because they are often able to do the math journal pages without much instruction.  Each day, they are asked to complete the journal pages that correspond to the lesson I will be teaching.  When they finish those pages, they can also do the math boxes that correspond to the day's lesson.  (Math boxes are practice pages in the math journal that provide students with extra practice on previously learned concepts.)  The high group is also given a math packet created by our "Gifted and Talented" teacher because they often finish the math journal pages before it is time to rotate to the next station.



Rotation #2:


Ind work 2 The low group moves right from the Work With Teacher Station to their own desks at the Independent Practice Station to finish the journal pages we started together.  When they finish those, they can then complete the math boxes for the day.  I have them move to the Independent Practice Station right after working with me so that the new concepts are fresh in their minds.


The medium group now comes to me at the Work With Teacher Station. I always plan to teach the lesson from the book to the medium group.  However, they will sometimes catch on quickly and need to be challenged.  If this happens, I can either do some enrichment with them or just challenge them by giving them some problems similar to the ones in the lesson but making them a little more difficult.  I have a set of portable dry erase boards at my station, so students can work right on their laps.  I like this because they are working right in front of me, and I can immediately see how they are doing.  This group will usually start the journal pages with me, but they will complete most of the work independently at their desks if I feel they are understanding the concept. 


The high group goes to the Games Station to continue practicing the concepts that were introduced in their journal pages.



Rotation #3


Game3 The low group moves to the Games Station now that they hopefully understand the concept that was introduced for the day. Playing the game gives them an additional way to practice what they have learned.


The medium group moves to the Independent Practice Station at their desks to complete the assigned journal pages that correspond to the daily lesson and then the math boxes when they are done with the assigned journal pages.


The high group is the last group I see at the Work With Teacher Station.  Since they have already completed the journal pages for the day's lesson, I take a quick look at those first.  If it looks as though most students in the group already understand the concept, I will use the enrichment materials from the Everyday Mathematics curriculum, or I will do some sort of enrichment that I create on my own.  If the students in this group did not do well on the journal pages, I will teach the regular lesson and make sure that they understand the new concept.

 

 

Daily Schedule for Math Block


We have one hour and 20 minutes scheduled for math each day (80 minutes).  Below is exactly what we do during that precious time.

Math on the Water: (810 minutes) This is a student-led activity that is explained in greater detail in a later section of this post. 

HollyLesson Preview & Directions: (58 minutes) During this time, I briefly introduce the concept I will be teaching for the day, specify the journal pages students will be completing in their math journals, announce any materials they will need to do their daily work (rulers, protractors, etc.), and explain the game that students will be playing at the Games Station (if necessary).

 

Rotation #1: (20 minutes)

 

Rotation #2: (20 minutes)

 

Rotation #3: (20 minutes)

 

Closing: (5 minutes) At the end of math, I call the class back together quickly to reinforce the day's concept.  If there is time, we will correct the daily math journal page as a class.

  

 

Don't Always Let the Teacher Edition Determine What You Teach


Math lesson

Once I have completed a lesson, I decide what to do the next day.  If the majority of students in all three groups understood the concept, I will move on to the next lesson with each group.  If the low group needs more practice, however, I will spend another day with them on the same concept.  I can either move ahead with the other two groups or just do additional enrichment.

 

There are even times when I feel the entire class could use an extra day on a concept.  In this case, I create work for the Independent Practice Station since students would have already completed their Everyday Mathematics journal pages.



 

Create Your Own Math Games to Enhance Math Workshop


While Everyday Mathematics does provide materials for many games in each unit, my teaching partner and I have also created many games of our own and have purchased some additional math games at teacher stores or online to supplement the Everyday Mathematics games for some of the units.  There are great resources available from the Scholastic Teacher Store that can be used to enhance your Math Games Station, such as Scholastic professional books with reproducible math games and math center ideas.


Website math games

 

You can also have students play Everyday Mathematics online games or Scholastic online math games if you have computers or laptops in your classroom.

 

Make Your Math Games Reusable

 

We copy, cut, and laminate all of the Everyday Mathematics game boards (and any game boards that we use from the Scholastic professional books) so that they are sturdy enough to be used by multiple groups during the year and in years to come.  We also mount and laminate the directions so that students do not need to interrupt us while we are working with another group.

 

Math game boards


We organize all of our math games in manila envelopes and store them in a cart with drawers so that we know all of the games we have available for each unit and can easily locate them when necessary.


Math Cart



Use Parents as Math Helpers!


Many teachers ask how I manage all three groups when I am only teaching one group.  It does take a few weeks at the beginning of the school year for students to learn to work independently at the Independent Practice Station and work cooperatively and quietly at the Games Station.  One helpful solution is to ask parents to volunteer to be your math helper during math time each day.  The math helper in our classroom works at the Games Station.  He or she can help students understand the directions, manage the groups as they play the game, and hold students accountable for their learning.  There are times when students will not put forth as much effort as they should when the teacher is not looking over their shoulder.  Having a parent watching them as they play the math game helps ensure that students are getting the most out of the activity.  Also, if students have questions about the game they are playing, they do not need to interrupt my teaching. These parents also help out with projects at this station when students are doing collaborative projects as opposed to math games.

To round up parent volunteers for math helpers, we send home a sign-up calendar each month.  We almost always have a parent helper at the Games Station to make sure students are getting the most out of the games they play or the projects they are doing. 

 

 

Assessment in Math Workshop


Math Skills Checklist

While we do give unit tests at the end of each unit to check the students' understanding of the concepts we taught in the unit, our overall assessment is ongoing (just as it is in Reading and Writing Workshops).  As my teaching partner and I meet daily with each group at the Work With Teacher Station, we keep a clipboard that has a checklist of skills for the unit.  We have each child's name listed on the checklist so that we can keep track of students who are struggling with any of the concepts we are teaching.  We try to find time to meet individually with struggling students to reteach the difficult concepts or at least check in on their progress.  If an entire group is struggling with a concept in a particular lesson, we will reteach the skill to all students in the group during Math Workshop on another day.

On the sample checklist to the right, you can see that we use "S," "P," and "N." "S" indicates that a child is "secure" with the concept, "P" means the child is "progressing," and "N" means the child "needs additional support." (Please know that this is a sample checklist I made that does not feature real students.)

 

Math on the Water (Daily Math Review)

 

We begin Math Workshop every day with what we call "Math on the Water" to go along with our Pier 13 theme.  (Last year we called it "Martian Math" to go along with our space theme.)  During this time, a student teaches the class a short math review lesson that includes three to five skills that have been taught during the current unit or previous units.  See the photos and information below to understand what this time of our day looks like.

 

Board-full

 

Each day a new student has the job of "Captain Math."  It is this student's responsibility to complete parts of the math activities on the Math on the Water board during morning work time. Since students have about eight minutes to teach their lesson, we suggest they pick three to five math problems to do on the board each day.  The student will then complete the problems with the help of the class at the beginning of Math Workshop.  For example, if a child chooses to do a "frames and arrows" activity, he or she might not fill in the rule and just add enough numbers for students to determine the rule and add the missing numbers.

 

Preparation

 

 

We do math first thing in the afternoon.  Captain Math wears a captain's hat and leads the lesson while the rest of the class sits on the carpet.  Students raise their hands to help Captain Math solve the problems, and the class agrees or disagrees with the final answers.  (Captain Math is also expected to have solved all problems prior to the lesson so that he or she knows the correct answers.)

 

Rija

 

The Math on the Water board is a magnetic dry erase board that changes on a regular basis to reflect the new skills we learn in each unit.  At the beginning of the year, we have things on the board that the students are expected to have learned in 2nd grade.  However, by the end of the year, the board has everything from fractions and decimals to geometry and double-digit multiplication to reflect all that students have learned.  The board is constantly changing.

 

Emma

 

Many teachers want copies of all of the things we have on our Math on the Water board.  This would be nearly impossible, as we have hundreds of different concepts we put on the board throughout the year.  Many of the items we use come straight from the Everyday Mathematics curriculum.  These include things like frames and arrows, number grids, "What's My Rule?" charts, number story diagrams, place value charts, name collection boxes, etc. (We enlarge things from the Math Masters book.)  We also use clocks, magnetic money, magnetic geometric shapes, fraction pieces, etc.

 

Function machine Measurement

Capacity 
 
 
All of the activities on the board are printed on colored card stock and then laminated so that students can write on them with Vis-à-Vis markers and clean them off at the end of the day to be used again.

 

Martian Math

 

Share Your Math Ideas!

My favorite thing about writing this blog is hearing from other teachers.  Please share the ways that you teach math in your own classrooms!  My fellow "Top Teaching" blogger, Angela Bunyi, conducts a form of Math Workshop in her classroom and is also available to answer any questions you might have.

 

Reader Request

In some of the comments below, readers asked what my lesson plans look like. So I'm linking to a weekly lesson plan file from early in the school year. It includes all subject areas, but you can see how I plan my differentiation in math.

Comments

  • #1 Beth Newingham

    Sunday, June 20, 2010 at 01:07 PM

    Kelley,

    Math fact practice is incorporated into "Math on the Water" daily (see my post), but we also do timed tests each week where students must memorize their multiplication facts. They move up a level each time they can do 30 problems in a minute. I have never been a huge proponent of timed tests, but I was finding that students were not truly memorizing their facts unless they were held officially responsible. Our fourth grade teachers are very grateful that we do this in our 3rd grade classroom because they are better prepared for 4th grade math!

    With all of the awesome technology you have in your classroom, I think you will find that Math Workshop will help you really use those tech tools to improve your math instruction and really meet the individual needs of your students!

    Good luck!

    -Beth

  • #2 Beth Newingham

    Sunday, June 20, 2010 at 01:02 PM

    Beth,

    Math Boxes are a component of Everyday Math, the program we use in our district. They are simply a page in the students' math journal that has 6 boxes, each one with a math problem that helps them review what they have learned in previous lessons. They are not anything fancy, but I don't think I am allowed to share them on the blog. I do not create the Math Boxes myself, so it would be a copyright issue. Here is a link to the Everyday Math website where you can find more information about the program: http://everydaymath.uchicago.edu/about/

    -Beth

  • #3 Beth Newingham

    Sunday, June 20, 2010 at 12:58 PM

    Jen,

    You can just use parts of the final tests for your pre-tests if necessary. The last Math Boxes page in each unit is also a good tool to use since it focuses on upcoming concepts. My teaching partners and I have created some pre-tests using the assessment creator CD, but we are constantly tweaking them to improve them for the following years. I would like to use them and know that they are "perfect" before I post them as resources for other teachers to use.

    I hope you enjoy doing a math workshop in your classroom next school year!

    -Beth

  • #4 Kelley Hawksley

    Sunday, June 20, 2010 at 12:34 AM

    Beth,

    How do you incorporate math fact practice into your day and math workshops? Two years ago I was transferred from high school math to a 3 grade classroom and your website saved me! After one year in 3rd grade I was then transferred to 6th grade. I just go the news on Friday that next year I will be in 4th grade and the first thing I did was look you back up! Our district uses the Saxon math program and I do have a smart board, wireless slate and a set of "clickers"...student response systems. I would love to try the math workshop but after being in 6th grade for two years I know how weak the students are in their facts .... your comments would be greatly appreciated. Thanks for all you do...you are truly an inspiration.

    Kelley

  • #5 melissa

    Saturday, June 19, 2010 at 11:19 AM

    You have a great website. I do have a question though. I am beginning to use Math Workshop in my class and was wondering if you could give me an idea about finding some great stroy problems to use. I am having a hard time coming up with some for place value in particular.
    Thanks,
    Melissa

  • #6 Jen

    Friday, June 18, 2010 at 06:31 PM

    Hi Beth,
    You have the greatest ideas, and your students are so lucky to have such a creative and passionate teacher!

    I was curious...regarding the pre-tests, are these tests you have found somewhere online, or did you create them yourself? If possible, could you share your resource? I teach using Everyday Math, and think your setup would be perfect to reach my students better and keep them engaged! (I don't know why no one has thought of it before!)

  • #7 Beth Waggoner

    Thursday, June 17, 2010 at 04:52 PM

    I love the idea of math stations and I will start using them next year. However, I was wondering if you could send or post a sample of math boxes-- I would not mind making my own.

  • #8 Beth Newingham

    Wednesday, June 16, 2010 at 02:49 PM

    Sarah,

    You asked what we do when we have students performing well beyond a third grade level in math. You wanted to know if they still do the math journal pages. We are fortunate in our district that the teachers who do our gifted and talented program created challenge packets for each unit in Everyday Math. When necessary, some students will work on these packets during the independent work rotation.

    -Beth

  • #9 Beth Newingham

    Wednesday, June 16, 2010 at 02:46 PM

    Jillian,

    Good luck with your move from Title 1 to 3rd grade. I think you will love being in the classroom full-time, and your experience working with small groups will be perfect when implementing a math workshop in your new classroom!

    Have a great summer!

    -Beth

  • #10 Beth Newingham

    Wednesday, June 16, 2010 at 02:44 PM

    Amy,

    Good luck implementing your math workshop next year! You certainly do not need Everyday Math to make it work. In fact, we pull materials from many different resources to make our workshop as successful as we can!

    -Beth

  • #11 Sarah

    Wednesday, June 16, 2010 at 12:55 PM

    I was so excited when I found all of your valuable information on line. We just finished school for the year and I am already planning on ideas for next year...thank you for sharing! I have one quick question regarding math. What do you do if you have students beyond the norm...for example students who are really performing beyond a third grade level with certain concepts...do you still have them focus on their math journal or do you create entirely different modes of independent work for those children? Again, thank you for your willingness to share your fabulous ideas. I feel like a kid in a candy store ready to explore new things.... Thank you! Enjoy your summer and your children. I have three daughters myself and we are all ready to play.

  • #12 Jillian

    Tuesday, June 15, 2010 at 07:53 PM

    Beth,

    I love all of your ideas! Next year I will be moving from Title I to 3rd grade. I am excited and trying to get as many ideas as possible. I think I will set up my math the way you have yours. Where I was Title I, I am use to working with small groups, so I feel I will be very effective this way. My county is changing math series to "Everyday Math" this coming year. I am already planing on fixing the game cards as you suggested. Jennie A, is there anyway I could get those smartboard files? I would compensate you for your time....just email me. Thanks everyone for great ideas. jrichmond@access.k12.wv.us

  • #13 Amy

    Thursday, June 10, 2010 at 05:25 PM

    Thank you so much for sharing all of your work with us. I was just talking to my principal about implementing a math workshop since we already have reading and writing workshop well underway. I teach in 1 of the 2 schools in our districts that tested Everday Math this year. Although we are not going to be using Everyday Math as a curriculum guide and instead will go back to using our districts pacing guide I am excited about pulling some of the lessons and practice for work with my kids.

  • #14 Beth Newingham

    Thursday, June 10, 2010 at 02:51 PM

    Alison,

    We have used the CD to make some of our pre-tests. However, we have also just taken items from the final test and given that as the pre-test. We look at the students' overall performance on their pre-tests to determine which group they will be in for the upcoming unit. You can read comment #47 for more information on pre-testing.

    -Beth

  • #15 Beth Newingham

    Thursday, June 10, 2010 at 02:48 PM

    Kerstin,

    You asked about the open response questions in Everyday Math. I assume you are talking about the optional part of the unit assessments. Since we do have students complete many of the "Writing/Reasoning" questions during our daily lessons, we also like to include this section on our tests. It helps us to see if our students can truly write about HOW they solve a problem rather than just showing us the numbers. However, we have found that some of the open responses are quite difficult, so there are times when we only give it to students in the enrichment group.

    -Beth

  • #16 Beth Newingham

    Thursday, June 10, 2010 at 02:41 PM

    Gaile,

    I'm glad this post was helpful for you! Also, thanks for sharing your "Majestic Math" idea. I love it, and I'm sure your students did too!

    -Beth

  • #17 Beth Newingham

    Thursday, June 10, 2010 at 02:39 PM

    Brynne and Jen,

    I added a link at the end of the post where you can download a weekly lesson plan file from a week earlier in my school year. This is where you can see what my math plans look like. I certainly do not write out the entire lesson since it is in the Everyday Math T.E., but I do include what students will be doing at each rotation and what I will do differently for the enrichment and readiness groups.

    I hope it is helpful for you!

    -Beth

  • #18 Beth Newingham

    Thursday, June 10, 2010 at 02:36 PM

    Robin,

    There are way more problems on the "Math on the Water" board than a student will complete each day. Captain Math gets to choose the 3-4 problems he or she wants to complete each day. Also, there are some activities (blank cards)where Captain Math can make up his or her own story problem.

    -Beth

  • #19 Beth Newingham

    Thursday, June 10, 2010 at 02:34 PM

    Brynne,

    Yes, I have a chart that shows the three rotations on my main dry-erase board in the front of the classroom. Each day I write what students will be doing at each rotation and which group will be starting at each rotation.

    -Beth

  • #20 Beth Newingham

    Thursday, June 10, 2010 at 02:34 PM

    Brynne,

    Yes, I have a chart that shows the three rotations on my main dry-erase board in the front of the classroom. Each day I write what students will be doing at each rotation and which group will be starting at each rotation.

    -Beth

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