Math Apps Students (and their Teachers) LOVE!

“Do you use IPads in the Technology/Application Station of Tabor Rotation?”

“What apps do you recommend?”

“Could I write a grant to get more technology in my classroom?”

These questions are frequently asked by Tabor Rotation teachers in math and science, since one of the Tabor Rotation Stations is the Technology/Application Station. It’s also being asked by parents who are looking for ways to help their children learn, have fun, and use their newest technology—all at the same time. My next few blog posts will feature the apps that have received the greatest reviews from my students.

The first app I introduced to in my Technology/Application Station is called Math Bingo. This app caught my attention immediately because so many students need practice in computation, but don’t want to use flashcards and timed worksheets to improve their basic skills.

The object of Math Bingo is to get a pattern of five Bingo Bugs in a row by correctly answering math problems. You can choose 4 games: Addition, Subtraction, Multiplication, and Division at three different levels: Easy, Medium, and Hard. Level 1.4 Math Bingo features a mixed Bingo game. Because this game is at varied levels and varied or mixed operations, I am able to use it with students from 1st to 8th grade.

Math Bingo is immediately rewarding and self-checking. Players get Bingo Bugs if they make a high score. A bonus to teachers is the ability to view high scores by individual players, track the items missed, and the amount of time it took the player to solve the problems.  If your students are addicted to the app, Angry Birds, then they’ll really enjoy the Bingo Bug Bungee which is similar to Angry Birds.

I have to say that Math Bingo is not only effective, but it is addictive—even for adults. This app from is well worth the .99 I paid for it. The current version, for IPods, IPads, and IPhones, has received almost 2,000 ratings with over 4 stars. My students and my own children give it a HUGE thumbs up!

Math Ninjas, by is the current favorite app of all of the students because it is the most like an arcade game. Players “use math skills to defend their treehouse against a hungry tomato and his robotic army.” The game is so highly interactive that it kept the attention, and engaged my most reluctant learners. In fact, my students liked it so much that I became suspicious of the math portion of the app and ended up playing it right along with them for over 30 minutes. (Okay, I could have stopped after ten minutes, but it really is addictive!) The computational operations selected at the beginning of the game aren’t just a side note, but are needed because it’s the only way the player can progress and move to the next level.

You can download the free version of Math Ninjas, but my students quickly reached the top levels of the free version and begged me to spend $1.99 for the full version. It was worth it! I agree with the 403 reviewers who gave it 4 stars—this app doesn’t skimp on learning or fun!!!

The last app I write about today may not have the flashiest graphics, but it is my favorite of these three. It’s a teacher favorite because it gave me a new, different, and highly effective way to help my students who have continually struggled with complex questions about number lines.

Math Tappers: Numberline is a FREE app that “challenges players to find the locations of numbers on a number line.” What was fascinating to watch was the development of my students’ proportional reasoning skills while playing the game. I’ve never had students want to practice this skill, but mine were incredibly disappointed when the Station Rotation time was up. Math Tappers also has other free math apps for telling time, elapsed time, estimating fractions, multiples, probability, and using base 10 blocks. The Math Tappers motto is “Play, Explore, Understand! This app did just that for every one of my students who used it. Bonus? The students were asking if they could play the Number Line app during their self-selection time—what more could you ask for?

And, now to answer that last question, “Can I write a grant to get more technology in my classroom?” If you use documentation like this blog to support your use of it–YES!

What can you hear in your room?

“There is no such thing as a worthless conversation, provided you know what to listen for. And questions are the breath of life for a conversation.”     -James Nathan Miller

“You were the first person to stop talking at me and give me something I could move in Algebra. Today was the first day I understood—really understood what I was doing.”     -Algebra student exploring polynomials in the Manipulative Station

The previous statement made me think about conversations that encourage, build, and are productive in an educational setting. These types of conversations are vital in a math classroom. While working with schools over the last month, I decided to listen closely in classes who use Tabor Rotation. Here are a few of the things I overheard.

“I want you to work with a partner reviewing your vocabulary cards for the next 3 minutes. After you’ve worked with your partner, we’re going to play a game to help you remember your words.”

I saw partners working together, in this classroom, during the warm-up described above and during the Whole-Group Mini-Lesson. During the whole-group lesson, the teacher would instruct for about five minutes, then give the partners a chance to explain what they were thinking to each other or solve a problem together. 100% of students were on-task and engaged.

“One of the teachers in our cluster has developed an observation chart for the coming unit so we’ll be able to better determine each student’s depth of understanding for the important concepts. This will also help us form readiness groups.”

This type of statement from a faculty is amazing and speaks to the high level of professionalism at this school. Not only did these teachers plan for pre-assessment, give the pre-assessment, use the pre-assessment for planning their unit of study, but then they planned for consistent and meaningful on-going assessment. They truly believe in teaching what is needed only to those who need it.

“You have a Menu of Options for the rest of the week. The materials you need are in the buckets with the corresponding number on the menu. If you have any questions, please see the leader or co-leader of your team.”

After the teacher briefly reviewed the tiered Application Menu of Options for Days 4 & 5 of Tabor Rotation, the students immediately made their choice and went to the correct location for their materials. The materials were in numbered buckets and were also color-coded for easy identification. This grade level was well organized in the independent/partner work so they could meet with more readiness groups formed to meet specific needs of students.

“You have your chapter quiz on your desk. While you are working the co-teacher and I may pull you for a few minutes to work with you at your level. You’ll have plenty of time to finish the quiz and go on to Anchoring Activities.”

What a wise use of time during a short quiz and while a co-teacher was in the room. The sound level in the room never rose above a whisper and there wasn’t a minute of wasted time in the classroom. Both teachers were working with small groups and said that planning together for their readiness groups made the difference to the students.

“Materials Managers, please collect the geometry foldables that were used as reference during the test.”

This is an example of a Tabor Rotation teacher sponging up every spare minute. He taught until three minutes before the bell rang, but had plenty of time for clean up because every student in the class has an active role in the classroom and knows how to do their job. Before the bell rang, the classroom was back in order and the students were practicing simultaneous interaction by sharing what they learned that day with a partner.

“I can’t figure this out…but if you’ll explain it to me again, I might get it!”

This statement was made by a student who was playing a game with her team. The teacher had given an overview of the rules to the entire class and the team leader had explained the rules, but the student still didn’t understand. It said volumes about the atmosphere established in this classroom that a student would feel comfortable sharing this with her team. Being actively engaged with a team gave this student the medium for this type of discussion.

“I know you’re up there in your ability with these concepts, so I want you to try the top line of the Application Menu of Options. You can do it!”

A truly differentiated classroom is guided by a teacher who has anticipated different levels of understanding of the concepts for the week and has prepared for that difference. The Application Menu of Options in this class had on-level activities, approaching level activities, and above-level activities. The teacher was circulating in between readiness groups when he made this statement to a student who was hard at work. He was qualitatively challenging this student at her level of understanding.

“We’d really like to thank one of our teachers for developing real-world activities for the concepts. It really helps us teach difficult concepts to students when they have a connection.”

If the brain learns best when it makes a connection to the information, how do you do this when teaching complex, higher-level concepts? This faculty knows how important it is for the student to make a real-world connection and spent time, before the unit began, developing real-world activities that would help the students make connections to the concepts. So many adults wish they had this type of instruction in high school. These teachers are ensuring that their students have a deep understanding of the concepts and know why they’re learning them!

“The first table ready for rotations earns $10. If every table is ready when the timer goes off, then every table wins.”

This teacher is using extrinsic motivation to encourage his students to transition into the new class period and be ready for the rotations to the four stations that will explore the week’s concepts. The activities at the stations were engaging and the teacher used both intrinsic/engaging and extrinsic/rewarding methods to make the most of his mathematical minutes.

What can be overheard in your classroom? Does the conversation reflect that you are trying to move every student just a little bit further than they were the day before?  Hope so…


“Anyone who thinks the art of conversation is dead ought to tell a child to go to bed.”     -Robert C. Gallagher

“No man ever listened himself out of a job.”     -Calvin Coolidge

 “Listen. Do not have an opinion while you listen because frankly, your opinion doesn’t hold much water outside your universe. Just listen. Listen until their brain has been twisted like a dripping towel and what they have to say is all over the floor.”     -Hugh Elliott

The Power of Teacher Observation

Maria Montessori says, “We cannot create observers by saying “observe,” but by giving them the power and the means for this observation.” I cannot agree more and that is why Clipboard Cruising is one of the 14 Essential Elements of the Tabor Rotation Framework. Clipboard Cruising, or constant and consistent teacher observation is complimented by two other Essential Elements of Tabor Rotation, Exit Questions and Math Journal Writing. All three are a part of the on-going assessment and feedback process in the Tabor Rotation Framework and are essential elements in ANY classroom.

As teachers move along on the continuum of effective implementation of Tabor Rotation, they begin asking these kinds of questions:

“I’d like to learn how to better target my instruction for each level of student in my classroom.”

“I wish I had a systematic but simple way to measure and monitor the growth of all of my students—even if I have over 120 of them!”

“How do I teach everything I need to teach in my subject and my level when some of my students don’t have the prerequisite skills?”

“Can’t you put your observation sheet into a spreadsheet format so it’s easier to modify and record on?”

The fact that so many teachers have emailed me with these requests amazes me. A teacher who asks these kinds of questions is truly being a reflective practitioner and assessor of the effectiveness of their own instructional practices. I think Yogi Berra summed it up well, “You can see a lot just by observing.”

Below are some helpful hints as you fine tune the observational process with your students:

1.    Simplify the process so you can form and use readiness groups.

Remember, readiness groups are the flexible groupings of students who meet with a teacher based upon their level of understanding of the concepts and skills being explored. Homogeneous groups are part of Days 4 & 5 of the Tabor Rotation Framework and are necessary is a teacher is meeting the needs of all students—no matter their level of understanding. One way to simplify the process is to get a clipboard for every class you teach.

2. Pick the tools that will make you want to pick them up and use them.

I always choose clipboards that are colorful. I also select pens which are my favorite writing tools. It may sound crazy, but I tend to go Clipboard Cruising more when I write with a metallic gel pen than if I were writing with a plain, fine-point pen. Using my favorite tools makes me smile.
Start off your observations by simply noting at least 3-5 behaviors in a day. Gradually increase to 10 behaviors. Then move to observing groups or students.

3.   Only observe what cannot be assessed more easily using some kind of paper-and-pencil tasks.

An example of this is when a teacher completes a direct instruction in a Whole-Group Mini Lesson and asks the students to work 2-3 problems that apply the skill they’ve just learned. The exit cards are handed to the teacher as the students leave the room and give the teacher immediate feedback on the level of understanding of the students.

This information could then be used, by the teacher, to form an approaching-level readiness group the next day. He might meet with this whisper group during the warm-up or bell work time. Based upon the exit card responses, the teacher notes that 4 of the students in a class are making the same error in procedure. He knows that if he shapes this procedural knowledge before it’s internalized, then his students will learn the skill and the concept attached to it with correct automaticity.

3.    Target the big ideas of the chapter or unit of study that all students MUST HAVE in order to be successful in their conceptual development in the subject matter.

A teacher who tries to observe everything tends to be quickly overwhelmed. Targeting big ideas, instead of every single skill or concept in a unit of study, allows you to conduct consistent observations of the depth of understanding for what’s most important.

5.    Give a short quiz at the end of a class period and circulate to observe your students as they are working.

Not only will this be a check for understanding and a form of on-going assessment, but it will give you the chance to circulate and ask specific students questions about the procedures they are using to work a problem. This short quiz could also be used for a daily grade.

6.    Focus on observing the students you meet with during small-group, guided instruction or Teacher Time and in Readiness Groups before trying to observe the entire class.

Just narrowing the number of students you’re observing makes it more likely that you will be able to conduct regular observations. The information you gather about your students in Teacher Time is invaluable. This is the time, in The Tabor Rotation Framework, when teachers meet with ¼ of the class at a time to instruct the most difficult concepts for the week.

You can note what strategy students use, the challenges they are facing, or the high level of understanding and application of the concept they already have. Remember, observation is done with all students–not just the ones who are struggling. All students deserve to be respectfully and meaningfully engaged with qualitatively challenging work that is at their instructional level.

7.    Select 4-5 students a class to observe instead of trying to observe everyone.

Some teachers divide their class into quadrants and observe a specific section each day. Some teachers decide to observe one row in their classroom. When you narrow the number of students to observe, then you’ll be more likely to accomplish your observational goals.

8.    Schedule observations into your daily routine.

The age-old teacher saying is true. If you fail to plan for observations, then you’ll fail to conduct observations. Write it into your daily and weekly lesson plans so that you know when you should stop instructing and start observing.

9.    Resist the temptation to stop and “fix it.”

One of the greatest challenges, when teachers begin to rigorously and systematically observe students, is resisting the temptation to stop and fix an error a student is making. If the adjustment or instruction is going to take over two minutes, then you probably need to meet with them in a readiness group instead of during clipboard cruising. If you’re regularly assessing, observing, and using this information to form readiness groups, then you know that you’ll be working with those students the next day.

10.    When it comes to on-going assessment, observations, and clipboard cruising, keep this Nike mantra in mind…JUST DO IT!

Try using these observation recording sheets to help you get started. Good luck!

Planning for Readiness Groups

Spreadsheet for Observations & On-Going Assessment

“Opportunities are often things you haven’t noticed the first time around.”    -Catherine Deneuve

Texas Drought Benefits Math Concepts

“We don’t stop playing because we grow old; we grow old because we stop playing.”     -George Bernard Shaw

The Texas drought may have dried up our pond, but it offered our two youngest children the opportunity to play in the biggest mud puddle they’d ever seen. I told them they could play in the mud puddle as long as they wore their boots and didn’t get too messy. All moms reading this blog are chuckling to themselves…you know that it wasn’t five minutes before the first child went in past the top of their boot. At that point, I quit worrying about the muddy mess and decided to make it into muddy math.

“It is paradoxical that many educators and parents still differentiate between a time for learning and a time for play without seeing the vital connection between them.”     -Leo Buscaglia

I talk to teachers and parents about simple ways to develop mathematical concepts in every situation.  I emphasize that the greatest tool they have is their ability to ask questions, make a real-world connection, and engage their children and students in math that’s FUN. The following list is comprised of what might have caused parental alarm and a negative parental response, but was transformed into meaningful math conceptual development.

1. The children tried to go all the way across the pond without their water going into their boot.

If your boot is 12’’ tall, how deep do you think the water is?

2. Both of the children don’t make it across the pond and are standing in water that is pouring into their boot.

Since there’s water pouring into your boot, use what you know about the height of your boot and the height of the water on your leg to estimate how deep the water is. Use this same information to see how much deeper the water is at different locations in the pond.

3. One of them stands in the middle of the pond too long and his boot is stuck. He’s about to fall over—especially when he starts laughing because his foot came out of his boot.

How deep do you think the mud is? Compare that depth to the depth of the water. Where do you think the mud is the deepest? Why?

4. Both children can barely make it out of the water because there is so much water in their boots.

How much water is in your boot? What is the type of measurement you are making when you estimate the amount of liquid something can hold?

5. Now that their boots are completely wet and most of their clothes are wet they decide to complete the drenching of their clothing by racing each other across the pond.

How fast can you run across the pond? Do you think you can run as quickly with your boots full of water? Why or why not? Try it and see if you’re right.

6. Since they’ve begun to run across the pond laughing, the inevitable is going to happen….complete immersion.

How long will it take before someone falls in?

7. After immersion of at least one child, they sit on the side of the pond to wring out their clothes and dump their boots for the hundredth time.

Did filling your boots with water and drenching your clothing make a difference in the amount of water left in the pond? Why not? How could you measure the amount of water in the pond?

8. While they dump their boots they notice that the water is flowing down certain portions of the bank faster.

How many seconds does it take for water to go from the top of the hill to the giant puddle? Which goes faster—crevasse or flat surface? What is that called?

9. They’ve grown tired of running across the pond and are taking turns pouring water out of their boots down the hill.

What is the difference between kinetic and potential energy? What does the pond represent? What does the pouring of the pond water represent?

10. The language of science appeals to my daughter who knows that math and science go together and that both are everywhere and in everything.

How many different things can you see near the pond that have potential energy? Kinetic energy? (Their favorite form of kinetic energy is themselves running down the hill. Their favorite form of potential energy is stopping just short of falling in the pond…of course, one of them does happen to fall in.)

11. One of them comes up to me and shows me how wet they are and how little water and mud is stuck to their hair.

I ask them, “What is a good probability word that describes the likelihood of you having to take a shower? What is the percentage chance of you having to use soap?”

As we trudge back up the hill and away from the pond we pass an armadillo digging in the dirt. We decide that the likelihood of the armadillo taking a shower is never and we sit down in the dirt to watch him finish his hole. The experience had brought all of us a little mud, a little math, and a LOT of fun!

“You can discover more about a person in an hour of play than in a year of conversation.”     -Plato

“It’s the GREAT Pumpkin, Charlie Brown!”

“I’ve learned there are three things you don’t discuss with people: religion, politics and the Great Pumpkin.”     -Linus

Out of all of the Peanuts comic strips and television specials, this one is my favorite. As a child I thought that waiting for the Great Pumpkin was much more fun than waiting for Santa Claus.

As a teacher, my grade level was never the one who went to the local pumpkin patch to pick pumpkins. So, when a friend told me he ran a pumpkin patch in Delaware (Yes, that’s where Pumpkin Chunkin’ is an art form and big competition.) I quickly volunteered to be the Pumpkin School Teacher.

This one time adventure turned into six years of incredible experiences teaching over 4,000 students a year all about pumpkins. I have researched the life cycle of pumpkins, types of pumpkins, the history of pumpkins, pumpkin contests, pumpkin decorations, and pumpkin recipes.  I have tried every pumpkin and every recipe I could find–just so I could tell students what it looked like, how to cook it, and what was it’s taste. I know a “scary” amount about pumpkins.

This week I once again had the honor of teaching at a Pumpkin Patch School. It was a little bit hotter and a little bit more humid since it was in Texas. However, the pumpkins fascinated the children the same way they had in Delaware. In just 30 minutes, the students were able to learn over ten math concepts, ten vocabulary words, and ten scientific facts. They not only learned them, but they brought their parents back to the patch and were telling them all about the “Baby Bear,” the “Blue Hubbard,” the “Atlantic Giant,” and the “Lumina” pumpkins. The students learned that Atlantic Giants can be the size of a small car and have been used as a boat to go across a lake–that’s fascinating information!

Because the Pumpkin School is hands-on and meaningful, the students learn and remember that pumpkins grow from seeds and the pumpkin only grows if a bee brings pollen from the male flower of the pumpkin to the female flower of the pumpkin. They can tell you about how many seeds are in a Baby Bear Pumpkin (weighs about 1 lb) and a Howden Pumpkin (weighs 5-15 lbs). They learn that gourds are inedible and just used for decoration. (The need for gourds in a pumpkin patch really stumps pre-kindergarteners. Since they can’t be eaten, why bother to grow them?) So much can be done with a pumpkin!

There are many resources on the web to help you explore pumpkins. I’ll post some of those links next week. To get you started, here’s a simple sheet with easy to do activities to develop the mathematical knowledge in your classroom or home—and, have fun at the same time!

Pumpkin Patch Fun

Charlie Brown: Oh brother. When are you going to stop believing in something that isn’t true?
Linus: When YOU stop believing in that fat guy in a red suit and the white beard who goes, “Ho, ho, ho!”

Accountability in Small-Group Instruction

“How wonderful it is that nobody need wait a single moment to improve the world.”     -Anne Frank

Many secondary teachers are fine-tuning the use of small-group instruction in their classrooms. The email below is an incredible exchange with great information. Hope it helps some of you, too.

Subject: Tabor Rotation Questions, Using a Passport

I’m beginning to use the passport with my students and have a few questions. How do you use the “Remember It” and the Vocabulary Boxes? What do the kids write and why?

**I give the kids a verbal cue the last 3 minutes of each rotation. That is their signal that they need to complete the passport for that rotation. Part of their responsibility is to fill in the “Remember It.” The purpose of the vocabulary is to help them organize their brain and connect what they did to the vocabulary. Later, when they write their journal, I encourage them to use a couple of their vocabulary words in their writing.

Passports are one way a teacher can hold each student accountable for their work and their effort during the station rotations on Days 2 & 3 of the Tabor Rotation Framework. Examples of these types of passports are on the FREE RESOURCES page of this site.

The use of the Vocabulary terms in their math journal writing solidifies the information learned and uses a different side of the brain to process the information.

How do you ensure the kids are filling out the passport with fidelity? Meaning, when do they fill it out?  How do you know they did it themselves? What’s the process? How soon do you grade it? What feedback do you give? What kind of grade do you give? Is the grade for completion or correctness?

** I grade it for a combination of completion and correctness. I try to give a little quiz at the end of Teacher Time. I count it like a class work grade. Cheating is always an issue with teenagers. I make them show their work, which helps, but I also emphasize that the most important thing to me is that they understand what they are doing. I say it a lot – they get tired of hearing, but this is working. I try to grade them by the next week.

** For the games, especially, I put a couple of questions (2-3) on the passport that represents what they are suppose to master as a result of playing the game. They complete them during the last 2 or 3 minutes of rotation. If they are caught answering them early I note it on the top of the rotation paper -they hate that.

Teachers struggle with how to obtain grades when students are working together in stations. Including a passport with a completion and participation grade is one source of assessment. Adding a couple of questions helps the students connect the meaningful activity to the abstract problem and also gives the teacher an immediate check for understanding.

Trying to make these things meaningful…

And, you’re doing an incredible job…just ask your students and all the teachers who will benefit from your questions and the advice of your colleague.

“In helping others, we shall help ourselves, for whatever good we give out completes the circle and comes back to us.”     -Flora Edwards

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!