Making Math Meaningful in the Home

“There are no secrets to success. It is the result of preparation, hard work, learning from failure.”     -Colin Powell

Building conceptual understanding for math can be done through almost anything. I’ve witnessed the most powerful understanding of fractions by cooking with my children. When we double or half the recipe it develops fractional understanding at the middle school level.

Simply dump the change in your pocket or wallet and see how fast your children can count how much money you had in all. If you did this every day, they would have an amazing amount of experience counting change. (Their second grade teacher will appreciate your efforts in this area since that is one of the most challenging concepts they teach.)

To develop a sense of time, hang analog clocks around the house and ask questions like, What time is it? How many more minutes till bedtime? How many more hours till dinner? What time will we need to leave if we have to be there at 7am? After you ask the question, really listen to how they respond and then ask them,

“How did you know that?”

“Tell me what your brain did.”

“Could you teach me how to do that?”

Many parents have asked me about my Hmmm-Home Meaningful Math Management. Hmmm is modeled after the Meaningful Math Management System that was extremely effective with my students.  This is a system used to cultivate math skills, life skills, and personal accountability in the home. We began using it in our home three years ago and have elevated our children’s level of economic understanding. When one of our children wants something, then we help them determine a way to earn it. Whatever they receive means so much more when we don’t just give it to them.

I’ve posted a slideshow explanation of the system and tools to assist parents in implementing Hmmm! in their home. To continue on my mission to help families, too, I’ve also added a lot of activities, games, and workmats to the parent section of the FREE RESOURCES page of my website. I’d love to know what happens when you begin to use these ideas in your home!

“When you discipline yourself to do what is hard, you gain access to a realm of results that are denied everyone else. The willingness to do what is difficult is like having a key to a special private treasure room.”     -Steve Pavlina

“We’re not allowed to use number sense.”

Go ahead and read the title of this blog again. I’ve been thinking about it for almost 24 hours. It’s what my 4th grader told me last night after dinner. He and his sisters were allowed to choose anything they wanted for dinner. They chose a famous chef’s ravioli concoctions. After heating them in the microwave and declaring them the best thing they’ve ever tasted, he said he wanted that kind of meal every night. I explained that we simply couldn’t afford to eat that kind of prepared food all the time.

“Well,” he said, “exactly how much did it cost?”

Never wanting to miss an opportunity to meaningfully apply mathematical concepts, I asked him to think about it and tell me how much the meal cost. We looked at the receipt and noted that each container cost ninety-seven cents. Two of our children ate two containers. The smallest one ate only one container. After less than a minute he confidently said,

“It costs four dollars and eighty-five cents.”

I was fascinated by his immediate and sure response and asked him how he figured it out.

He described the following steps:

  1. I know that there were two of us who had two containers and one of us had one. That makes five containers of food.
  2. Ninety-seven cents is really close to a dollar. I know that five times a dollar is five dollars. But, that’s just close to the answer. It’s not the answer.
  3. Ninety-seven cents is three cents away from a dollar. There were five containers. Five times three is fifteen.
  4. Five dollars minus fifteen cents equals four dollars and eighty-five cents.

“That was easy. And, if you ask me that’s a pretty cheap way to feed all of us without having to cook. All you had to do was heat it up and it was less than five bucks.”

Being a math educator, I’ve taught all of our children standard algorithmic procedures and divergent problem-solving procedures, but I’ve also taught them how to use good number sense to determine answers. I was relieved that he had used his knowledge of money and multiplication instead of demanding a sheet of paper and a pencil.

I praised him for being so smart and for using all he knew to help him determine the answer. I told him that his teacher this year would be impressed by his ability to think mathematically and use great number sense. That’s when he made the shocking statement,

“We’re not allowed to use number sense at school. They take off points if you try to use number sense. We’re supposed to use the test-taking strategies and show in our work that we did. If we don’t, we get points taken off—even if we have the right answer.”

Do we think about the messages we are giving students? Are we encouraging our students to become mathematically intelligent or just test takers? What is good number sense and how can I help develop it?

Skip Fennel writes about the importance of number sense in this article,

Numeracy Blocks talks about number sense being the foundation for everything else one learns about math, yet we take for granted its complexities.

The Florida Department of Education gives some great ideas for developing number sense.

Wichita State University Department of Math and Science students in the 750J Workshop offered examples of number sense in the animal world.

As for me, I breathed in for a couple of seconds. (Okay, the statement almost knocked the wind out of me and I had to count to thirty before answering him.) Knowing that it won’t help our children for me to be critical of the requirements of their school system and teachers, I answered,

“Well, you can use number sense everywhere else but in school.”


“Common sense is instinct. Enough of it is genius.”    -George Bernard Shaw

More Tabor Rotation Trainer Tips

Yesterday’s blog gave the first half of tips and “aha” moments from participants in Tabor Rotation Training of Trainers Institutes. Here’s the second half. may they encourage you to try using small-group, differentiated instruction in your school.

Tip #16: Every learner ‘s brain craves moving from the concrete to the pictorial to the abstract. I need to make sure I do this in Teacher Time and in Readiness Groups each week.

Tip #17: I like calling the Teacher Time table and the table where I meet with students for guided math instruction the WHISPER TABLE. I may even meet with students for no reason at the WHISPER TABLE just for fun!

Tip #18: Tiering isn’t really that difficult. You just take an on grade level assignment. Think of the key concepts and skills in it, then simplify for the students who might not understand how to do it and sophisticate for the students who will already know how to do it.

Tip #19: Planning is the most important part of successful use of Tabor Rotation. This isn’t something you can do on Sunday night or on the way to school that morning…

Tip #20: You can’t say you’re trying to do small groups in math the right way. It’s like standing up. You can half-way stand up. You either stay sitting or you get up. You either do Tabor Rotation or you don’t. You can’t half-way do it!

Tip #21: Assessment is critical! If you create the unit’s final assessment, then the pre-assessment, you’ll start with the end in mind and focus your attention on what needs to be learned. And, this justifies my results!

Tip #22: Although learning all 14 Essential Elements of Tabor Rotation and how to plan for a full week of Tabor Rotation is challenging at first, with an open mind and clear vision for student improvement, the training will be the most valuable time you’ve ever spent!

Tip #23: Planning for Tabor Rotation helped our teachers work better as a team. Everyone has ownership for the learning of all of our students.

Tip #24: By putting in Team Roles and Leadership Academy into our classrooms, our students are learning responsibility, collaboration, and personal accountability.

Tip #25: Readiness groups can’t be skipped. I tried that last year because I thought I was doing enough just by having math stations. My students need time and attention “where they are.” Readiness groups are essential!

Tip #26: Teacher Time is my students’ favorite part of Tabor Rotation. They told me that my class is the one time during their day that a teacher actually listens to them. If you do nothing else, find a way to have Teacher Time with your students!

Tip #27: There’s a reason why the 14 Essential Elements are called “essential.” If you do all of them it makes a difference.

Tip #28: Planning for Tabor Rotation has helped my team organize their instruction so that it is specific, informed, and focused. I feel empowered!

Tip #29: This is the platform I’ve been looking for to help me and my team make small groups work. It’s like Microsoft Windows…for our math program.

Tip #30: Tabor Rotation will cause a paradigm shift.  It will challenge what teachers know and force them to truly reflect and collaborate, but it is well worth the obstacles and challenges.

Tabor Rotation Tips from Trainers


The following tips and “aha” moments came from participants in Tabor Rotation Training of Trainers Institutes. They allowed me to share them with you in hopes that they might ignite your fire for sophisticating the use of guided math groups, math stations, and differentiated instruction in math using The Tabor Rotation Framework.

Tip #1: Use Thursday and Friday to front load or pre-teach students who normally only receive remedial or intervention assistance. This gives these students the chance to be ahead instead of always feeling like they’re behind.

Tip #2: Mathematician’s Circle on Fridays is a great way to end the week. This will be the time that my class turns into a community of learners.

Tip #3: Add test prep questions to the Exit Questions after each station rotation. By doing this I’m always preparing them for the state test.

Tip #4: Self-reflection is essential, too. My on-going assessment isn’t just for my students, it’s also for me.

Tip #5: I can use FREEZE words in the classroom to get my students’ attention.  I say the FREEZE word and they stop and put their hands on their shoulders.

Tip #6: Even during the daily Whole-Group Mini-Lesson you need to stop every 5-6 minutes to let students process what they have learned so far. You may need to write this into your lesson plans so you don’t forget. (I did last year, so this year I’m writing it down!)

Tip #7: If differentiated instructional experiences are based on readiness levels, learning styles, and interests, then I have to figure out my students’ learning styles and I have to build activities based on their interests.

Tip #8: I should always be open to new ideas. I want to be green & growing instead of red & rotting on the vine.

Tip #9: We don’t have a moment to spare in a school year. For example we should be sponging up minutes waiting in line by playing games that students can use non-verbal signals to answer.

Tip #10: Tabor Team Names should come from a list of really important tested words. Every student in the room has to know what the team name means and examples of it. If the team names change once a month, that’s at least 32 words they’ll master before the test.

Tip #11: Highly able, gifted, and on-level students are still at-risk if they never receive additional assistance to challenge them in ways that are best for them. They are the untapped resource in every school.

Tip #12: Just because a school is exemplary doesn’t mean that they are doing what is best for every student. If a student begins 4th grade at level 7.1 in math and leaves 4th grade at level 7.0, then we didn’t do our job. They should have been at least at level 8.1. State tests never reflect this lack of growth…

Tip #13: Tiered station activities should be the goal of every teacher beginning to use Tabor Rotation. Just begin tiering one station at a time until you’re doing all four stations.

Tip #14: I need to use a timer when teaching the Whole Group Mini-Lesson. If I don’t, my mini-lesson will turn into a maxi-lesson!

Tip #15: If I do Tabor Rotation the way it’s designed, then I’ll have at least 30 minutes meeting in a small group setting with EVERY student—that is way cool!

Readiness Groups in Tabor Rotation

“Every success is built on the ability to do better than good enough.”

I’m beginning to understand Tabor Rotation, but what are readiness groups and why are they important?

The Tabor Rotation Framework asks teachers to flexibly group students in a variety of ways. Each week includes partner work, whole-group instruction, teachable moments with individual students, small group work with students of mixed abilities, and working with small groups of students who are grouped together according to their level of understanding of the concepts that are being explored that week.

Students are grouped heterogeneously for the rotation through the four stations on Days 2 & 3 of the Tabor Rotation Framework. This type of grouping promotes the communication between students in the group and between the teacher and the students. If students who are at-promise in general ability in mathematics sit between a couple of other students who have a little bit greater ability, then the teacher/leader/co-leader isn’t the only person in the group who can explain or clarify how to process a concept. This varied perspective gives students a chance to learn from each other at the other stations.

Just as important is the homogeneous grouping of students on the continuum of readiness for the concepts that are being explored that week. The students’ placement on the continuum is determined by pre-assessments, curriculum compacting, informal assessments, formative assessments, and clipboard cruising. Readiness grouping takes place on Thursdays and Fridays. After Vivid Vocabulary and the Whole-Group Mini-Lesson, all students are involved in an application of a simple or previously learned concept. Sometimes teachers use a tiered Application Menu of Concepts to engage all learners in an appropriately differentiated practice. As all students are working, the teacher uses the information gathered during the week to pull readiness groups.

On Days 4 & 5 of Tabor Rotation, the first readiness group called is the “Above-Level” Group. These students have mastered the week’s concepts at an abstract level and are ready to be qualitatively challenged with different work. The teacher meets with these students for 8-10 minutes and sends them back to work on the tiered assignments or on a different set of assignments designed to challenge their deepened level of understanding.

Next, the teacher meets with the “On-Level” Readiness Group for 8-10 minutes. Why meet with them? They are on level and have a basic level of understanding of the week’s concepts. Here’s why…if a teacher will meet with these students and build on their interests and learning styles to challenge them, they will become highly able learners. Typically,  these students are never met with at all because the perception of a district is that these students will “pass” so they are just fine. I believe these “woodwork” students are the untapped gold mine of a school. We have no idea what they could do with a little bit of individualized attention, because they have rarely received individualized attention.

The last readiness group called is the “Approaching-Level” or “At-Promise” students. These students have not mastered all of the concepts for the week even though they experienced the concepts in varied modalities and met with the teacher in Teacher Time. The students are given a different experience with the week’s concepts so they may continue on their way to mastery.

Why use mixed grouping at the Tabor Rotation Stations? Why keep a constant check on students to determine their level of understanding & form readiness groups…because…ALL students deserve qualitatively challenging, respectful, and meaningful work. ALL students need time to meet with the teacher in a small group setting and receive additional and appropriate assistance. Varying the grouping is a great way to make sure this occurs!

“The greatest danger a team faces isn’t that it won’t become successful, but that it will, and then cease to improve.” -Mark Sanborn

“Success always comes when preparation meets opportunity.” -Henry Hartman

Application Menus

“The doors we open and close each day decide the lives we live.” -Flora Whittemore

“My basic principle is that you don’t make decisions because they are easy; you don’t make them because they are cheap; you don’t make them because they’re popular; you make them because they’re right.” -Theodore Hesburgh

“This framework doesn’t really meet the needs of all my learners. Just sending them to stations isn’t going to cut it!”

My blog post today is about engagement of students during readiness grouping on Days 4 & 5 of a week of Tabor Rotation using Application Menus. However, the concern above is typically expressed by at least one member of a faculty who has the required opportunity of using the Tabor Rotation Framework.

Let’s address this first concern. My response will always be, “You’re right! Just sending them to stations a couple of days a week isn’t going to meet all their needs. But, it’s a great place to begin differentiating instruction in mathematics and is so much better than whole-group instruction every day of the week.” Now that you’ve begun to use stations and vary the modality through which you students learn mathematical concepts, then you’re ready to layer on Readiness Grouping.

Take a look at some of my blog posts concerned with Clipboard Cruising. You also might want to look at the clip below from the new Tabor Rotation Training Series.

Clipboard Cruising, and other on-going assessment techniques, helps the teacher determine the varied levels of mastery of the week’s concepts and form readiness groups. Now, we’re ready for the next set of questions…

“What do you mean by Application of Concepts on Day 4 of Tabor Rotation?”

“What do I do with the rest of the class when I’m working with my differentiated, readiness groups on Thursday and Friday?”

These are some of the most frequently asked questions about Tabor Rotation, especially when the participants have only had one session at a conference. I’m glad teachers ask it—that means they are differentiating the instruction of the mathematical concepts that week based on pre-assessments, on-going assessments, and observation while “clipboard cruising.”

After Vivid Vocabulary Instruction and the Whole-Group Mini-Lesson on Thursday and Friday, there are several options for the independent or partner work for the entire class. This is the chance for task to become its own reward and for the student to do most of the learning because they are doing most of the work.

Some teachers assign pages from a text, have students work on an individualized dictionary of math vocabulary, play one of the games from the Games Station, complete a list of assignments, or select a tiered assignment from the Application Menu of Options.

This type of menu provides students with a choice of which options to select and in which order. It can also be tiered at novice, pro, and master levels. The following Application Menu Templates and Application Menu Example might be helpful as you begin to create your Application Menu of Options for Days 4 & 5 of Tabor Rotation.

Tabor Rotation Application Menu, Elementary Level

Tabor Rotation Application Menu, Secondary Level

Sample Tabor Rotation Application Menu

Why would you put so much time and effort into something like this? Because your composition, your work, and your masterpiece are the students whom you teach. Maybe because we should hold ourselves under the ancient Roman standards…

“The ancient Romans had a tradition: whenever one of their engineers constructed an arch, as the capstone was hoisted into place, the engineer assumed accountability for his work in the most profound way possible: he stood under the arch.” -Michael Armstrong

Grouping in Math Using Tabor Rotation

“Always behave like a duck-keep calm and unruffled on the surface, but paddle like the devil underneath.” -Lord Barbizon

“Help! My class is so much BIGGER this year…
…what do I do?”

“I just found out that I have 28-30 students. How do I use math stations now?”

“Which is better—a larger group with an even number or a small group with an odd number?”

“Is it better to have more math stations since I have more students?”

These are some of the questions teachers submitted after conference sessions on Tabor Rotation. Teachers typically come to the Tabor Rotation sessions because they have been told to use small groups, they’ve been told to differentiate instruction at a sophisticated level, they’ve been told to respond and use intervention strategies, they’ve been told to qualitatively meet the needs of all their learners, but no one has given them a plan for how to do it all in the amount of time they’ve been given. The Tabor Rotation Framework is simply a plan to do all of the above.

Many teachers have emailed with great concern after receiving their class lists for the new school year. You may not have power over the number of students in your classes, but you do have control over how you best meet all of their needs.

The Tabor Rotation Framework came about, like any other invention, through necessity. The first Tabor Rotation classrooms had almost 40 students in a class, most of the class below grade level, and only 60 minutes to teach math. Someone had to think outside the box and start to instruct math in a way that would make the most of their minutes with students. It also needed to provide a plan to optimize varied modalities in order to develop & deepen conceptual understandings in mathematics. The Tabor Rotation Framework is what came about…it’s the answer for any size class, but was initially created for a BIG one. So, bring on the budget cuts, bring on the larger class sizes, you’ve got a way to make the most of any challenge!

The Tabor Rotation Framework is research-based, teacher-tested, and student-approved! And, implementing the 14 Essential Elements in a Week of Tabor Rotation brings about INCREDIBLE results. Check out the NEWS page of Because the framework has been implemented and tested for almost two decades, teachers have been able to report what has worked best for them.

The most success has been found when teachers create groups with even numbers so that everyone has a partner (6, 8, 10). At one point, each of my teams had 10 students in it, but it was easy to manage 4 math teams & 4 stations in the rotation process. It also ensured that the integrity of Readiness Groups on Days 4 & 5 of a week of Tabor Rotation was always maintained. Most classes are divided into smaller cooperative teams and work with partners during the Whole-Group Mini-Lesson and while learning in other subjects.

What about the number of stations? When teachers have more students they tend to create more & more stations. One teacher tried 12 stations so that she would have only 2-3 students per station. This became very, very challenging to manage and to create 12 new activities each week that meaningful engage every learner and every level, for every concept being taught.
Tabor teachers usually leave the number of stations the same & more sets of the same activities at the station. The team comes back together at the end of the rotation time and discusses the Exit Questions with their partner and other members of their team.

Creating for more than 4 stations will require the teacher to rethink the organization of Readiness Groups which are an Essential Element of Tabor Rotation. Heterogeneous groups go to the stations, but homogeneous or readiness groups are key to meeting the needs of all students during a week of instruction.

The Tabor Team Roles remain the same since the group remains working together in the same area of the room. When the team has more 4 members, the team roles are: Leader, Co-Leader, Materials Manager, & Timekeeper. With 6 members, you add an additional Materials Manager & a Reporter. With 8 members, a team may add a Whisper Monitor to maintain the sound level of the team or a Team Builder who encourages the team and builds up the team spirit.

This blog is meant to give ideas to those who are seeking them. Hopefully, something written in today’s blog provided you with an “aha” moment. One of the most important things to remember about grouping is the need to “shake up” or vary the way students experience a concept. Students should have the opportunity to learn in a whole-group setting, working with a partner, in a small group with varied levels of understanding, and in a group with students who are at the same level for the specific concepts being studied.

“Look at a day when you are supremely satisfied at the end.  It’s not a day when you lounge around doing nothing; it’s when you’ve had everything to do, and you’ve done it.”     -Margaret Thatcher

“Don’t say you don’t have enough time. You have exactly the same number of hours per day that were given to Helen Keller, Pasteur, Michaelangelo, Mother Teresa, Leonardo da Vinci, Thomas Jefferson, and Albert Einstein.”     -H. Jackson Brown

More on Readiness Groups in the next blog post…

To: All Dedicated Educators

I am always amazed and appreciative for the comments I receive from participants in my conference sessions. Here’s just a few quotes to encourage them. These educators, even though it’s the middle of their summer, are still persevering and discovering new ways to reach their students…

Slaying sacred cows makes great steaks.     – Dick Nicolose

I skate where the puck is going to be, not where it has been.     – Wayne Gretzky

Before you build a better mousetrap, it helps to know if there are any mice out there.

It’s easy to come up with new ideas; the hard part is letting go of what worked for you two years ago, but will soon be out of date.
– Roger von Oech

“History will be kind to me, for I intend to write it.”     -Sir Winston Cburchill

Is differentiating instruction worth the effort?

How do I know differentiating instruction works?

Will using small groups in the classroom really make a difference when they sit and listen to my lecture?

What’s the big deal about Tabor Rotation?

As one math supervisor put it,

“Tabor Rotation changes everything. It helps students think. It increases teacher efficiency and student capacity. It deepens the understanding of mathematical concepts. It provides something for everyone. And, it increases state test scores.”


Yes, it does work. Yes, it’s worth all the time and effort. Take a look at some recent results at the secondary level and results at the intermediate level. Congratulations to those schools who worked so hard this year to do what was best for all of their students and their state test scores showed it!

Tip for Small Groups in Math: Use Leaders!

“The task of leadership is not to put greatness in to humanity, but to elicit it, for the greatness is already there.”     -John Buchan

This summer I’ve had the honor of working with a great number of dedicated educators. These educators have come with a positive attitude and an open mind. Several of the schools have been sophisticating their implementation of small-group, differentiated instruction they began during the last school year.

One school was planning for the first nine weeks of the school year. The faculty decided to use the first week of school to model and shape the procedures for a week of Tabor Rotation. They also determined to begin full implementation of The Tabor Rotation Framework the second week of school.  Why?

As a member of their instructional leadership team put it,

“You can’t do small groups in a classroom half-way. We tried that last year and it didn’t work. Now I know why the 14 Essential Elements of Tabor Rotation are called Essential.”

One of the Essential Elements of Tabor Rotation that teachers tend to skip is the Leadership Academy. All the schools with whom I have worked this summer have recognized the importance of having leaders and co-leaders when using small groups in the math classroom.

A week of Tabor Rotation always includes a Leadership Academy. The Leadership Academy is the time when the teacher trains the leaders and co-leaders from each team how to play the games or work the activities at the 4 stations. After the brief overview of the stations with the whole group on Day 1, and while the rest of the class is working independently, the leaders and co-leaders from each group form a whisper group in a quiet area of the room. They explore the activities and play the games, while asking each other questions and clarifying directions. The teacher checks for understanding and answers questions periodically.

Monday night’s homework, for the leaders and co-leaders, is to study the copies of the games and activities which the teacher sends home with them. Their homework also includes answering the Exit Questions they will ask at the end of a station rotation.

Cultivating leaders and co-leaders changes everything when using small groups. A very basic result of taking the time to train your leaders and co-leaders is having eight people in the room, besides you, who know what to do when the groups are working independently.

Some of the results of having a Leadership Academy can’t be measured by test results. However, they will prove to be invaluable in cultivating your classroom community. As you inspire your leaders and co-leaders this school year, you might want to share some of the following quotes with them. I’ve read them all before, but they inspired me to write this blog today…

“Leadership must be based on goodwill. Goodwill does not mean posturing and, least of all, pandering to the mob. It means obvious and wholehearted commitment to helping followers. We are tired of leaders we fear, tired of leaders we love, and of tired of leaders who let us take liberties with them. What we need for leaders are men of the heart who are so helpful that they, in effect, do away with the need of their jobs. But leaders like that are never out of a job, never out of followers. Strange as it sounds, great leaders gain authority by giving it away.”     — Admiral James B. Stockdale

“Management is efficiency in climbing the ladder of success; leadership determines whether the ladder is leaning against the right wall.”     — Stephen R. Covey

“The older I get the less I listen to what people say and the more I look at what they do.”     — Andrew Carnegie

“The function of leadership is to produce more leaders, not more followers.”     — Ralph Nader

“The best executive is the one who has sense enough to pick good people to do what he wants done, and self-restraint to keep from meddling with them while they do it.”     — Theodore Roosevelt

Side note: I know the school I referenced above will make amazing gains in the coming year. How do I know that? Not only was every teacher actively involved in every portion of the training, but all members of their administrative team were active participants during the training and planning for next year. They’re “walking the talk” of cultivating leaders in their school, beginning with their teachers…