Exit Tickets

As math educators, we must make broad judgments daily about whether the class understood the day’s lesson before we move on with instruction the next day. The pulse of the class is taken easily because of the level of student interaction and discussion during the questioning segment of the lesson, but it’s harder to get a clear picture of what individual students have mastered and are able to do independently. Though whole group instruction may move forward the next day, it is our responsibility to ensure that all students are reaching mastery. We need to know specifically students who need small group reteaching or more support for success. Because, at CCE we are aware that retention rates for students are highest when they teach others (90%), practice by doing (75%), and partake in discussion groups (50%), many days my students are working in pairs or small groups in math. There is not always the opportunity to collect independent student work, so we needed another teaching strategy to accomplish the goal of knowing whether every student was at mastery on the day’s work.

Exit Tickets have become our answer. An Exit Ticket is a formative teaching strategy given immediately after the Math Workshop concludes which focuses students on the core content of a lesson and promotes a quick and independent assessment check. Each student answers a question or two that targets the big idea for the day. The checkpoint, taking only a few minutes, offers teachers the immediate opportunity to check students’ independent mastery of the day’s content.

Exit Tickets are simple and time efficient to create and analyze. When preparing for a lesson the teacher has to think, “If I teach this math concept or skill effectively, which question should students be able to answer at the end of the lesson?” This question or two should align with the big idea.

Typically, we create an Exit Ticket on a ½ sheet of paper for easy distribution and collection. Having it on a ½ sheet of paper makes it effortless to sort students’ work into piles once the task is complete and collected. Within minutes, you can have several stacks of student work. One stack of student work proves independent mastery of the lesson, the second stack contains student’s work where mastery is not clear and more information is needed, and the third stack demonstrates work with misconceptions or lack of understanding. Students whose work is in the first pile need no additional instruction; Students whose work is in the second pile need a teacher to confer with them so they can explain or justify their answer because the written work did not prove mastery. With this quick conferring session, the teacher can tell whether or not additional instruction is needed. If additional instruction is needed, the teacher can pull the student into a small group during the next day’s Work Session. Students whose work is in the third pile need small group reteaching to acquire more knowledge on the concept or skill. In addition, they may need more strategic questioning during whole group instruction and more feedback during the Work Session as the concept or skill is developed.

As a rule, the whole process of Exit Tickets takes little time and provides great benefit. Teachers don’t have to wait for a summative check on a math quiz or assessment, they have the formative Exit Tickets that help them prescribe instruction along the way and help prevent misconceptions or gaps in knowledge.

Third Grade Exit Ticket Example:

During a unit of study on developing and understanding fractions and fraction equivalence, students needed to be able to use models to represent equivalent fractions and identify representations of equivalence. To get started, we had students work with pattern blocks. They identified the yellow hexagon as one whole, a red trapezoid as ½, a blue rhombus as 1/3, and a green triangle as 1/6. They created equations like ½ + ½ = 1, 1/3 + 1/3 + 1/3 = 1, and 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1.

Additionally, we taught students to find ways to make one whole using combinations of halves, thirds, and sixths with pattern blocks as their tool and write equations. For example, ½ + 1/3 + 1/6 = 1.

Students quickly began to find equivalent fractions like ½=3/6, 1/3 = 2/6, and 2/3 = 4/6, and make generalizations like, all fractions that contain denominators twice as large as the numerator are equivalent to ½.

After several lessons, we played a game in which students received a recording sheet of yellow hexagons. Students rolled a fraction die and had to add that fractional piece to one of the yellow hexagon pieces. The object of the game was to fill in all their yellow hexagons.

During the two days of lessons using the pattern block manipulatives much of our discussion was in student pairs. We weren’t confident that every student had transferred our classroom conversation to independent mastery, so we used an Exit Ticket at the end of Math Workshop on Day 2 to formatively assess students. The students were given three minutes to complete the task and then we collected their work. In the first problem, students had to write an equivalent fraction for 3/3, 3/6, and 2/6, and in question number two they had to answer the following question, William had a fraction cookie with the equation ½ + 1/6 + 1/6 + 1/6. Sebatian told William that he could just write ½ + 3/6 or ½ + ½. Is Sebastian right? Explain.

Within minutes, we had sorted the students’ work. Some students easily, accurately, and articulately answered the questions and needed no further instruction. Some students answered the questions correctly but their explanation of the equivalencies was not articulate enough to know whether they fully understood the concept. These students would need a quick conference to identify whether they fully mastered the concepts. In some cases, we found that no further instruction was needed, but in other cases, we found that there is a gap in knowledge and small group instruction is needed for mastery. The third group of students could not accurately answer the questions and we formed a small instructional group to offer more instruction and practice.

When I first heard the idea of an Exit Ticket, I jumped too quickly to the conclusion that I would gain the same information from a quiz or assessment. But, after implementing them on a trial basis consistently for several weeks, I realized that they had tremendous value for gathering data and giving immediate and consistent feedback to students. It was the difference between assessing with a summative (a quiz or test) and a formative which helps guides the next day’s lesson. I would recommend the use of Exit Tickets to any math teacher who is serious about offering differentiated math instruction to meet the needs of each of their students.

A Few New Math Ideas

A colleague and I facilitated math training for teachers in Texas in mid-February. Each training day included lesson pre-briefing and planning, a classroom math observation, and a debrief of the lesson afterward. Teachers made rich connections, gained new ideas for their instructional practice, and gained a deeper understanding of a Math Investigations unit of study. Though my main focus was on the learning of the teacher participants, I also couldn’t help but take away a few reflections of my own.

Archiving Student Work

The classrooms we visited do a stellar job of archiving students’ math work. Each student has a composition notebook with a Table of Contents in the front. The pages of the composition notebook are numbered and each day the teacher has students add the date, math title, and pages of the journal they've consumed. We could easily turn to the pages listed in the Table of Contents to see what work the student had done for that day. In the notebook, they may solve a problem, explain a solution, do an extension activity, or answer an essential question during their Closing Meeting. Providing a great way for students to reflect and a resource for studying for assessments, I loved the possibilities of this tool.

Extension Activities

At Chets Creek, we use standards to write yearly pacing guides, plan instruction, and assess students. In making our work transparent, students become familiar with the standards we expect them to master. Many times the way a teacher implements this best practice is by having an essential question, written in standards language, posted on the board. In their math lesson they go over the essential question which students revisit and answer in their Closing Meeting. At NISD, I noticed that not only did the teachers write the essential question for the day, but they also had an extension activity written next to the essential question. When some of the students finished early on their task, they didn’t say, “I’m done! What now?” instead they got to work on the extension question. What an easy way to extend student learning!

Visual Word Walls

There was one math word wall in particular that caught my eye. Instead of the word wall simply being a list of terms the students are expected to know, this word wall offered a great visual reference for remembering geometry vocabulary. This model math word wall sets the standard that we should all being striving toward.

Skip Counting on the Number Line

Number lines are a permanent artifact in our math classrooms, however this number line included colored dots that are used for the students use in skip counting. For example, if a student followed the red dots, they could easily skip count by twos, and if they read the yellow dots, they would be skip counting by fives, etc... I could easily see this as a great tool in elementary classrooms, especially in K-3rd grade. Afterall, skip counting/repeated addition is the foundational element in multiplication.

Walking into another teacher's classroom offers so much opportunity for gleaming new ideas. Whether you do it in your own building, like our Kindergarten teachers did two weeks ago, or in another school, you gain so little without consuming too much of your time or energy, and gathering just a few new ideas leaves you with a wealth of new knowledge over time. I can't wait to see if any of these new ideas are embraced at CCE. Stay tuned...

What Motivates Us?

As a Florida educator, my life's work has been dedicated toward providing children with a quality education in which to build a prosperous life full of options. As a classroom inclusion teacher, I worked tirelessly with each of my students, regardless of their exceptionally, socio- economic situation, or home life to reach their fullest potential. And, as a current Instructional Coach, I dedicate my time toward guiding professional growth and learning amongst our nearly 90 teachers to improve classroom practice and student achievement. My work and that of my colleagues matters. In fact, it may be the most important thing we ever do.


The fire that was ignited in me as a young teacher still burns strongly. I continue to think that anything can be changed and decisions in the best interest of students and teachers will prevail. Some are cynical, they have lost hope, but in the interest of my own two boys and the thousands of children that walk through our school doors each year, I simply can't and won't give up. Maybe, I'm acting like a cornered pitbull ready to fight, but I have hope for the future of public school education in Florida.

I don't move with a blindly optimistic attitude toward the future. I will admit that I'm fearful of poor decisions left in the hand of politicians which could cripple our profession. The writing appears to be on the wall with Senate Bill 6. Legislators without any classroom experience, never walking a mile in our shoes, will likely make a decision this year that will push the best, brightest, and most noble out of our profession. The bill erases teachers' pay on years of experience and advance degrees, and proposes to pay teachers based on their students' state test scores collected in just a few days of the 180 they are in attendance. Wanting to hold teachers fully accountable for their students learning, they overlook circumstances beyond our control.

Merit pay would rid the profession not of the poor teachers but of the exceptional ones. Some who serve our neediest learners, our learning disabled children, our non-English speaking students. Teachers who tutor on their own time, offer Tiered Interventions at every turn, buy classroom supplies when the schools can't afford to supply them, and spend hours upon hours on weeknights and weekends planning quality lessons. These are the teachers that will be most frustrated and dishonored.

For the past thirteen years, I've been serving at Chets Creek, and some of our most amazing teachers never receive the small portion of merit pay that is currently passed out. dayle timmons, a life-long Special Education teacher and 2004 Florida Teacher of the Year has never qualified for merit pay. The current merit pay system is broken and unfair. Senate Bill 6 will only escalate and intensify the problems. Educators see the glaring flaws; Senate Bill 6 may destroy the Florida teaching profession.

I work in a school with transcendent purpose and complete collegiality; We set out each and every day to change the world, one child at a time, having no doubt that we can and will achieve our goals. Embracing every child regardless of their circumstances is our moral calling, and we have the creative and innovative teachers, that with the right level of support, can reach them all. A learning organization led by a principal who implicitly trusts her teachers as professionals and gives them the autonomy needed to produce impressive qualitative and quantitative results. Just looking at our state test scores only marginally gives you a picture of who we are and what our teachers and children can achieve. Looking five years down the road, I wonder if this will be the same learning community utopia of today. It seems like our funds are drying up and our hands are being tied. Will a school like mine, full of passionate dedicated and exceptional teachers, be here for the unborn child of my principal? Or, instead will the best and brightest flee local private schools or other professions?

Politicians pass laws every year, they claim to base decisions on research. I'm wondering whether they would be supporting Senate Bill 6 if they watched this Daniel Pink video which highlights the conclusions of studies done by economists and psychologists who explain, "When the profit motive gets unmoored from the purpose motive, bad things happen." If you really want to make a change in an organization, pay people enough to take money off the table. When money is off the table that is when people can think about the work. The research shows that the best results are achieved by people who are motivated, and what they are motivated by are autonomy, mastery, and purpose. Our Florida children deserve teachers who are motivated to improve student achievement by these motivations. Merit pay will not promote the collegiality our profession needs to make significant improvements.

This video is worth every minute and I hope you will leave me a comment with your thoughts or connections.

Developing Young Mathematicians

As an educator, my math classroom is significantly different from the one in which I was raised. I think many of our students’ parents feel the same way. In fact, during conferences, I’ve had several parents proclaim, “That’s not how I learned math.” To reassure them, I’ve explained my perspective as an educator and a parent. Many times, the explanation starts at the beginning-what they know to be true about their own math experiences.

Rewind twenty-five years to the math classrooms of my youth and most likely theirs; Situated neatly in rows, desks faced the front of the room. A math textbook lay open. On the left side of the page, there were step by step procedures for solving problems, and on the right page 25 or 30 practice problems with one or two word problems at the bottom. The teacher’s lesson began by working out the practice problem step by step while the students watched and memorized the procedures. Our task during class was to mimic perfectly the procedure and to work out the other practice problems independently. At the end of the period, we would pass our papers to the front of the room for the teacher to assess our progress.

I was a good math student, always able to follow the teacher’s directions and mimic the procedures. And, it didn’t take me long to realize that I didn’t even need to read the word problems at the bottom of the page, I just needed to pull the numbers out of the paragraph and use the same procedure for solving.

Does this scene sound familiar? It’s the way most of today’s teachers and our students' parents were taught math. Fortunately, it’s not the way our children are learning. Instead, based on research like TIMSS (Trends in International Math and Science Studies), and teachers’ professional development through organizations like the National Council of Teachers of Mathematics, educators are learning to better prepare students to think mathematically.

Thirteen years ago, as a beginning teacher, I learned about this shift in math teaching and learning at a national conference. Phil Daro, a Senior Fellow of Mathematics, helped me understand the need for change as he explained the three-pronged math approach . A conversation that I’ve replicated with parents and colleagues throughout the years. He began by drawing a triangle on the board and printing the word SKILLS at the top. Then, continued by creating the mental image of the typical classroom of my youth. Teaching and learning, decades ago, was focused on skills as the top and sometimes only priority. All too often concepts and problem solving were omitted, creating a deficiency that students struggled to overcome as they moved on to more advanced mathematics.

To illustrate how to prevent a gap in mathematical knowledge, and create a well rounded math student, Daro drew another triangle rotated 180⁰ so concepts and problem solving were now on top. Daro explained that math is three-pronged and, “Teachers must teach for conceptual understanding, build problem-solving skills, and strengthen basic skills.” Urging educators to tip the triangle upside down and select curriculum tools with an emphasis on concepts and problem solving, and then embed skills was the way to improve math instruction he assured. The connection I made to his simple explanation was immediate; Classrooms of my youth were skill driven classrooms; I didn’t learn to understand or connect concepts, generalize my learning, or problem solve. I learned to imitate my teacher. In that moment, I vowed, as a math educator, to teach my students to think mathematically, and as a parent I committed to helping other parents understand the need for this shift.

To accomplish my goal in the classroom, I piloted a conceptually based math curriculum tool, implemented internationally benchmarked math standards along with my state standards, and embraced the three-pronged approach using a sixty minute Math Workshop format and a fifteen minute Interactive Math Skills Block. Confidently, I set forth to create a culture of student collaboration and dialogue. Growing competent and fluent young mathematicians, who understood concepts, could strategically and flexibly approach problems, were procedurally fluent, and could articulate and justify their answers captured my full attention. And, trust me when I say, teaching myself to learn in this fashion was exhausting; There were days when I was only minutes ahead of my students’ learning. However, in the end, I captured the most amazing rewards. I, with the assistance of a few colleagues, helped paved the way for my peers by creating a shift in our practice.

Now, over a decade later, this passion still consumes much of my time and provides me with just as much satisfaction. Currently, as a staff developer, I chair our Math Council to lead with our vision and mission in constant view and assist to grow math leadership capacity in others. At the same time, I embrace my role to get new math teachers started on the right path from the very beginning. I continue to share my story with anyone who will listen. After all, I have the unique pleasure of teaching children and teachers to think mathematically.

Fuel Up to Play 60 with Mojo!

To a cheering student audience, Jacksonville Jaguar player, Maurice Jones-Drew took the stage. He was at Chets Creek today to speak to third, fourth, and fifth grade students about a special program, Fuel Up to Play 60 which emphasizes healthy eating and sixty minutes of physical activity every day. A grant written by our P.E. Coaches, Estrella Bailey and Ray Robinson funded the memorable assembly which will surely be a highlight of the kids' school year.

Jones-Drew not only spoke to the kids but eagerly answered oodles of questions. Just a few of the questions our students wanted to know:
What are your favorite foods? How much time do you spend working out during the season? What do you feel like in the five minutes before you take the field? What does it feel like to score a touchdown? Who do you think will win this year's Superbowl? Who is your favorite college team? Who is your biggest opponent?

My son took the stage to ask, "Who was your childhood hero?" to which Mojo answered, "My grandfather." Later my son remembered being told that Maurice's name was Maurice Drew, but in college while playing in the Rose Bowl, Maurice's grandfather died of a heart attack. In tribute to his grandfather he added his grandfather's surname, Jones, to his own name becoming Maurice Jones-Drew. What a great lesson for my young son to learn about honoring your lifelong heroes.

In the final minutes, our Principal, Susan Phillips asked, "What was your favorite subject in school?" Of course, he got a round of applause when he answered, "I am a mathematician!"

Here's to you Maurice, for not only sending the stay fit and healthy message, but also for reminding students to continually work toward their goals because anything is possible.

Purple Cow Standards Board of the Month

When you walk into our building, it's clear that we have a strong academic focus. Almost everywhere you look you see celebrations of student achievement, and unlike the holiday themed bulletin boards of yesteryear, our bulletin boards display student work samples with teacher commentary. Classroom instruction becomes transparent because of this visibility of student performance in reading, writing, math, science and social studies. Our only regret is that we've had no way of cataloging and keeping the boards for future reference, until now.

With nearly 50 bulletin boards at CCE, there is no feasible way to digitally warehouse all of them, so we've started by capturing two a month, one primary and one intermediate. After the new boards go up, teachers submit Purple Cow nominations for their colleagues' boards. A team gets together to read all nominated boards and selects one intermediate and one primary board that stands out above all the rest. The competition is steep because the boards are so creative and well done, but usually the Purple Cow is chosen because it presents a new idea that others may want to implement in their classroom or does an exceptional job capturing a moment of time in their classroom.

It's unlikely that every teacher will have the opportunity to read every board each month, but with the Purple Cow highlighted, we are hoping that every teacher will at least read the two Purple Cow Boards that can't be missed. So far, the idea has caught on and one teacher even teases that she's wearing her Purple Cow ribbon in her hair!

I'd love for you to visit our Standards Based Bulletin Board blog created and maintained by our Tech Coach, Melanie Holtsman, to read our highlighted boards. You'll see the start of what we hope will become a long tradition. Make sure you click on pictures to enlarge and print the items. I'd love to hear your comments. Stay tuned for more...

Academic Family Nights

Several times a year, we hold academic Family Nights to communicate grade level expectations with parents and answer frequently asked questions. Earlier in the year, Second grade teachers held a 2nd Grade Math Night, and this week Third grade teachers hosted an FCAT Reading and Math Information session while Fourth grade teachers held their FCAT Writes Night.

The session topics are selected with that grade level’s specific needs in mind. Typically, 2nd grade parents have many questions about the transition in math. They are curious about how math is being taught conceptually and what that means in reference to skill based teaching. They also want to know if their child will learn the standard algorithm for addition and subtraction the way they did. We begin the conversation with an overview of the three prongs of math—concepts, skills, and problem solving and explain how we use our math resources of Math Investigations, Every Day Math Counts, and Envisions to meet grade level Sunshine State Standards while teaching within each of the three prongs. Then, our teachers concentrate on explaining the strategies of addition and subtraction so parents have a better understanding of how we are teaching number sense and flexibility of thought. The session wraps with an open floor so all parents leave with their questions answered.

Third grade parents are always full of questions about FCAT and its implications. 3rd grade is the first year that students take the state standardized test in Reading and Math so this session is often packed with curious parents. The Third grade teachers provide an overview of the many facets of FCAT as well as show parents some sample problems. In addition, they discuss the embedded ways we are preparing students, like spiraling homework and formative assessments, and we clarify how we don’t stop teaching at any point for FCAT prep. Sharing strategies that parents can implement at home to help their child is a part of this gathering. Again, the evening ends with a questions and answers session.

Fourth grade parents are old hats at FCAT so just when those questions dissipate, they are curious about the state writing test. What do students have to score? What does meeting the standard look like? How are you preparing students for success on the test? How is a prompt different from the Writers’ Workshop? Is my child going to do well? These questions drive the evening’s conversation. In addition, teachers hold a fish bowl mini Writers’ Workshop with students to give parents a bird’s eye view of what is happening to prepare students in the classroom. Explaining the logistics of the 45 minute prompt write is something new to parents, and we hope they walk away feeling good about what we are doing to prepare their child. Teachers field questions as the session concludes.

Nights like these provide the platform for a deeper parent understanding of our curriculum, standards, and state assessment expectations. We hope that they leave with peace of mind and comfort in knowing that we thoughtfully and strategically prepare their students not only for the state assessment but for their future.