Wednesday, July 22, 2009

Guided Math...

As a child I truly struggled with math. I HATED math, couldn't understand it, was never good at it. Oddly, now that I am a teacher, math is one of my favorite subjects to teach.

I started my teaching career teaching splits. I did a 1/2 split for two years followed by a 2/3 split for two years. The first year I taught I nearly had a breakdown. I was running back and forth between two grades. Teach a mini lesson to one group, get them working on their independent practice, run over the other grade, teach them, get them settled, go back to the other group, help them, run back to the other group. It was back and forth for over an hour. It was exhausting!

When I knew I was going back to a 1/2 split the next year, I had to search for a different, more effective way to teach math. After searching the internet I came across some teachers talking about math groups. There was and still is no real professional development books on how to teach math groups or on the subject of guided math (hmmm, can I see my future here, maybe?)

Even now as I teach a singular grade, I can't go back to teaching math whole group. The benefits of meeting with small groups are numerous. I get to really see if each student is understanding the lesson each day. Students cannot hide amongst the crowd. In a small group I am able to very quickly pick up on who gets it and who doesn't. My groups can be tailored to needs and I can do as basic or as challenging of a review/lesson. The second part of doing math groups is what they are doing when you are teaching small group. Well, they are practicing math using math card games and math games.

Here is description of how my grouping and lessons work...

10-15 min- Whole Class Lesson Introduction (would include Math Message and or review and a brief introduction of the days lesson)

15-20 min - Group Rotations

Group 1 Group 2 Group 3 Group 4
1-Guided Lesson -Math Game -Math Card -Individual
2-Individual -Guided Group -Math Game -Math Card
3-Math Cards -Individual -Group -Math Game
4-Math Game -Math Card -Individual -Group

Group Lessons- Meet at kidney table. I have a small white board next to the table to show work on, students love to "play teacher" and show the group what they know on the white board during group lessons. I also usually have individual whiteboards for each student for practice. The lesson will include continuation of days lesson and guided practice- usually follow along with Everyday Math Journal Practice Pages

Individual- Students complete Everyday Math Journal- Math Boxes and coordinating Practice Pages, Skill Link pages or individual worksheet practice. They may not leave this station unless all work is completed. They will have to stay at this station, the next rotation until completed.

Math Game- I have a variety of math board games, file folder games, etc. I got a lot through DonorsChoose donations. Somedays I tell students what they must play and other times I give a category, such as any multiplication game or any money game.

Math Cards- At the beginning of the year and throughout the year I teach students addition/sub/mult/div/place value card games. You can play with any standard deck. You can even purchase specific place value/fraction/money playing cards through LakeShore Learning, for a more specific skill game.

In the past I have forgone the beginning mini-lesson and just did straight small groups. Sometimes it depends on the day and the lesson that needs to be taught. Needless to say my math block never is shorter than 75 minutes, most times 90 minutes long.

We have been meeting with reading groups for years. The idea and concept of meeting with math groups is very hard for teachers to undertake. I think we will see an upcoming trend of teaching math groups, but I think it is a very long road ahead.


Let me say this first and foremost... The first several weeks are critical in correctly teaching students the procedures and expectations for guided math. Not following through or cutting corners can lead to frustration and guided math failure. As most teachers know the key to a good system is practice, practice, practice. As with your literacy stations-centers; you wouldn't just sent kids to the station and say, "Have fun!" You teach and practice what is expected of them, for weeks.

Typically I introduce guided math the very first day of school. I gather the kids around and say that they are about to experience math different than what they might have in the past. (as I am the only teacher in my school who has done it, have since converted a couple teachers)

I briefly describe what the guided math block of time will look like.
- You will be in math groups. Groups might change over the course of the school year.
- Each math time you will rotate through 4 stations.
-You will spend about 15-20 minutes at each station.- You have a different task to accomplish at each station. I then explain each one; card station, game station, independent work station, and lesson with me.

At this point I only introduce one station at a time. I usually start with the card station because they games are easy to teach and easy to model correct behaviors. Here is what a typical introduction would look like.

"Students today we are going to learn our very first station! Today we will be practicing the math card station. Remember this is the station where you get to play card games that help you out with your math skills. I will tell you what card game to play each day. One day a week I will let you have free choice!"
I label the top of a piece chart paper : MATH CARD STATION

I then make a T chart. Labeling one side, Student and the other side Teacher.

"Boys and girls let's take a look at this chart. I thought we could start by brainstorming some good things that you would expect to see from your classmates when they are at the card station."

Students start the list:
1. Take Turns
2. Play Fairly
3. Clean Up All Materials
4. Put Back All Materials Where They Belong
5. Get Started Right Away
6. Work Quietly
7. Play The WHOLE Time

Notice that I tend to use positive statements, not statements that begin with Don't or Never. These are just a few staple statements that I want to include on my chart. Students can usually think of a couple other important good behaviors.

"Now, these are things that you are doing when you are working. Let's take a look at the other side of the chart. Notice that it says, Teacher. Who can raise their hand and answer this question? Your job is to play cards following all these rules. What do you think is my job while you are doing this?"

Students usually can guess this one right away (ok, depending on the grade level :)

"That's right, I am working with students. So boys and girls, let's put on this side; Working with groups or individual students."

"And guess what? That is what my main job is the whole time. If you keep up your job, then I can do my job." (I sometimes go into the whole interruption speech, what happens to the poor kids I have to stop teaching because I have to go tell you to stop your bad behavior.)

"So now we are going to have three students model what they think working at the card station would look like. "

I give a verbal overview to those three students as to what they are going to do first. Go get the cards, go to the designated card playing area, get started right away, play nicely, clean up and return materials when I say stop.

I then have those students give a short (no more than 2 min) overview of what the whole process looks like. The go and pretend they are at that station. I then call, "Ok, card station is over." (or whatever system you use to indicate it is switch time or the end of math).

The students come back to the group. We look at our chart. I go down the list calling out each behavior. Students give me a thumbs up or thumbs down to show if the group demonstrated that behavior.

Next is the fun part. Choose a few students to show the wrong way. Yes, I do show the wrong way, because every year a student demonstrates something the kids might not recognize as the wrong way. I ask this group to go wild, be noisy, toss the cards, don't get started right away, and don't clean up. The kids have a blast (obviously :) Showing this one. I then again signal for them to come back, and we go over the chart, but this time we all give thumbs down.

Now most importantly, you need to follow up with another group showing the correct way again. "Boys and girls, I need three more volunteers who can show the last group how the real card station should be done. Who thinks they can do it?"

At the end of all this I then introduce their first math card game. Something simple, very easy to play and to teach. I then give students a chance to work with a partner or two and show me how they all can practice the good behaviors on our chart.

This sequence goes on for several days. So the next day, this is what it looks like in short review...

-Gather kids, ask them if they remember what some good things are that we should see when we are at the math card station.
-Review chart and get any that they may have overlooked
-Have group model, good, bad and then good again.
-Show new card game
-Have students practice

Yes, this does take a good chunk of time and will each math time until you are ready to begin stations. I follow this same format when I introduce all four stations. At the end all four stations will have its own chart that can be shown somewhere in the room for student reference.

Now when you are ready go begin introducing the math game station. I usually do a quick review of expected behaviors at the card station and then introduce the game station.

The next day same thing.

A few days in, I will split the time between practicing card and then game. Really you set the time on this one, how long you want them to play and practice the games (10 mins max to begin with I would say, build your time stamina).
I know some of you are thinking where does fitting in the actual math manual lessons work when introducing stations. I teach the lesson first, then do the practice of the stations.

This is just a guideline on how to get it started. A lot of you have your own ways and tips and tricks you have learned throughout the years. Use it! Do what works for you, but remember like I said at the top, guided math will not be successful unless you take the time to teach behavior and model them over and over again.

To see the full series of Guided Math posts check out this...


Jenn Tanaka said...

I am planning on teaching math in guided small groups as well! This will be my first attempt, so I'm glad to hear that yours has gone well. I will be starting the Daily 5 for reading, so I figured, "Why not math too?" It's funny, I was the opposite when I was younger. I loved math (until I got to high school and where it was much harder!) and loathed the language arts. Now it's reversed. I actually got my BA and MA in English. Must have had a shift in brain management!!! Best of luck to you this year!

Laney Sammons said...

In April of this year, my book Guided Math: A Framework for Mathematics Instruction was published by Shell Education. As you were, I was amazed that nothing had been written on this subject before now. I'm sure there is room for more books on the subject! Thanks for sharing your ideas in your blog. There is also a Yahoo Guided Math group where members share their ideas and questions. The website is

Robyn P. said...

I love the idea of Math Groups. In my classes I usually have a very large range of really high kids, and super-duper low kids. How do you differentiate your instruction using the guided math groups in conjunction with the whole group mini-lesson?

MeMimi said...

Jen- Good luck with teaching math groups this year, you are going to lvoe it!
Laney- I had no idea there was a book now! I think you are going to start seeing a lot more in the near future.
Robyn -For differentiation of my group instruction I still stick with the main focus of the lesson, but make the problems easier or harder. I know my lowest group still needs basic one digit multiplication, while my highest group came do two. You can really make it as complicated or uncomplicated as you want. About mid-year I start to mix up the groups. I sometimes still think the lower ones need some modeling and guidance from the high ones, especially during the math games and math cards.
Thanks for all the great comments!

dr. nicki said...

I think this is such an important discussion. Guided math is really the wave of the future. It allows us to reach all learners where they are and bring them to the next level. I want to engage in more discussions specifically about guided math and so I've started a blog just for that at Keep us posted about how your groups are going and what new discoveries you make this year!

Anonymous said...

I have been using small group math instruction for about ten years. I would encourage everyone to continue using heterogeneous grouping and not get trapped in ability grouping that leads to tracking. Remember the DMI model of purposeful talk. We need to differentiate in the moment. Differentiation does not mean different lessons but meeting the students at there understanding level and then stretching them with math talk. During the independent work time, is a great opportunity to differentiate with specific skills.