Develop Number Sense with Number Talks

One of the reasons Number Talks are so important is that they give students, and adults, a whole different perspective on mathematics—a perspective that turns out to be critical for future learning.”  ~Jo Boaler, Professor of Mathematics Education, Stanford University

In Cathy Humphreys and Ruth Parker’s Making Number Talks Matter and their newest companion title, Digging Deeper: Making Number Talks Matter Even More, teachers learn not only how to use Number Talks to develop number sense, but how these short, daily routines can help create a thriving classroom community where students actively share their thinking and teachers become expert listeners.

What Are Number Talks?

Number Talks are routines in which students reason mentally with numbers. It is a time when students put their pencils and paper away to think about and try to solve a problem mentally, then share their thinking and strategies with their peers. The teacher’s role is to listen, to record the students’ thinking on the board, and to hold back on explaining or correcting. This can be difficult for some, but it is essential to making Number Talks work. “Number Talks turn students’ roles in math class upside down. Now they are supposed to figure something out rather than be told the steps to follow. Now they are supposed to explain what they think rather than waiting for us to explain” (Humphreys and Parker 2015).

Why Are Number Talks Important?

Number Talks allow students to take back the authority of their own reasoning, but they also bring interest, excitement, and joy back into the math classroom. Number Talks allow students to make sense of mathematics in their own ways by practicing making convincing arguments while critiquing and building on the ideas of their peers. “As students sit on the edge of their seats, eager to share their ideas, digging deep into why mathematical procedures work, they come to like mathematics and know that they can understand it,” (Humphreys and Parker 2015). Number Talks can help students build competence, flexibility, and confidence as mathematical thinkers.

How Do I Start Digging Deep Into Number Talks?

For practical guidance as to how to start Number Talks in your classroom, pick up a copy of Making Number Talks Matter, an introduction and how-to guide to Number Talks. In order to get a full grasp of Number Talks, however, and see exactly what they look like, Digging Deeper is a must-have. This essential companion book uses extensive video footage of teachers and students practicing Number Talks in real classrooms. This personal and accessible book shows teachers:

  • The kinds of questions that elicit deeper thinking
  • Ways to navigate tricky, problematic, or just plain hard exchanges in the classroom
  • How to more effectively use wait time during Number Talks
  • The importance of creating a safe learning environment
  • How to nudge students to think more flexibly without directing their thinking.

“The process of engaging students in reasoning with numbers is one we hope you will consider as a problem-solving venture—an investigation that will help you to learn to listen to your students and learn along with them as you build your lessons around their thinking” (Humphreys and Parker 2015).

Ruth Parker co-created Number Talks with Kathy Richardson in the early 1990s. Cathy Humphreys has been instrumental in extending Number Talks to the secondary level. Together, Cathy and Ruth have developed a deep knowledge of the best ways to teach Number Talks with students of all grade levels. Their extensive knowledge is packaged nicely into these two highly accessible books. Order them HERE today.

REFERENCES

Humphreys, Cathy, and Ruth Parker. 2015. Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4 – 10. Portland, ME: Stenhouse.

Add comment December 3rd, 2018

Here’s What’s Happening at NCTM, 2018 in Seattle, WA!

Stenhouse authors come to the National Council of Teachers of Mathematics (NCTM) annual conference each year bringing new resources and delivering innovative and inspiring presentations. This year will be no different with the release of new exciting titles, such as Necessary Conditions by Geoff Krall and Digging Deeper by Ruth Parker and Cathy Humphreys and an invigorating opening session with Christopher Danielson.

Below is a rundown of the not-to-miss presentations by Stenhouse authors, and don’t forget to go to booth # 415 and preview the new titles!

Wednesday, 11/28

5:30–7:00 p.m. Christopher Danielson, author of How Many? and Which One Doesn’t Belong? and Melissa Gresalfi will kick off the conference with their opening session: “Play is the Ninth Mathematical Practice!” They will explain how mathematicians’ work and children’s mathematical play are connected through exploration guided by curiosity and a pursuit of something interesting and beautiful. (Ballroom 6ABC)

Thursday, 11/29

8:00–9:15 a.m. Geoff Krall, author of Necessary Conditions will host a workshop called “Necessary Conditions: Essential Elements for Secondary Math” where participants will examine the three crucial elements of a successful secondary classroom: quality tasks, effective facilitation, and academic safety. (4 C4)

9:45–11:00 a.m. Allison Hintz, author of Intentional Talk will join two other presenters to host a workshop called “Story Time STEM: Engaging Students in Sense-Making Discussion Through Children’s Literature” where you will think about how to approach literature with a mathematical lens and support students’ sense making through discussion of stories. (608)

9:45–11:00 a.m. Christopher Danielson will present “The Hierarchy of Hexagons: An Example of Geometry Inquiry,” a general inquiry session in which participants will develop hexagon classification schemes, ask about relationships, and maybe even prove a few new theorems! (602/603)

1:30–2:45 p.m. Megan Franke, co-author of Choral Counting & Counting Collections, will explore how attending to the details and partial understandings of children’s thinking can enable teachers to engage students in learning together, making use of the resources that each student brings in her session, “Children’s Thinking (CGI): How We Notice, Support, and Extend to Enhance Equity.” (4 C4)

3:00–4:00 p.m. Michael Flynn, author of Beyond Answers, will explore how to mathematize hands-on science as participants launch rockets, mix chemicals, and program robots in his session “Modeling with Mathematics in Science Class: Maximizing Opportunities to Enrich the STEM Experience.” (4 C3)

5:00–5:30 p.m. Michael Flynn, in this burst session, “Powerful Moments in Math Class: Why Certain Experiences Stand Out and How We Create More of Them” participants will learn how to create memorable mathematical experiences for all students. (613/614)

Friday, 11/30

3:15–4:30 p.m. Elham Kazemi, co-author of Choral Counting & Counting Collections, will work with participants and a team of educators to learn, plan, and rehearse a routine instructional activity, playing out how to respond to students’ ideas and cultural funds of knowledge in the workshop, “Experience the Power of Rehearsals & Teacher Time-Outs to Grow in Our Visions of Teaching for Equity.” (606)

If you are unable to attend the conference this year, be sure to follow us on Twitter @stenhousepub and get live updates directly from the presentations, as well as photos of your favorite authors!

Add comment November 27th, 2018

Three Elements of a Successful Secondary Math Classroom

This is the first in a series of posts where we take a deep dive into the three elements of a successful classroom from the upcoming book, Necessary Conditions by Geoff Krall.

We want kids to like math. We want kids to be mathematical thinkers. So why is it that math is often the barrier that prevents students from having a rich secondary or post-secondary experience? That is the question author and educator, Geoff Krall, tackles in his new book, Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation.

“As challenging as it is to teach math, a high-quality mathematical school experience can unlock a person’s academic identity…I’ve found that the biggest drivers of a high-quality math experience are teachers dedicated to their craft and to their students.” ~Geoff Krall

In his research visiting schools across the country, Krall found secondary mathematical ecosystems where learning is thriving; students are confident in mathematics and demonstrate high achievement. He found that all the classrooms he visited had a common thread: the teachers are implementing high-quality mathematical tasks, facilitating effectively, and attending to the students’ social and emotional well-being and self-regard in math. In Necessary Conditions, Krall explores these three elements of a successful math classroom. Here’s a brief description. We will go into more detail in subsequent blog posts.

Academic Safety

Academic Safety exists when students are in a safe environment where they have the allowance to ask questions, make mistakes, and try something new. Being proactive about academic safety is especially crucial in mathematics because students often arrive with negative prior experiences and already-low self-esteem. It is the teacher’s responsibility to create and maintain an environment that invites all students into challenging mathematics. Through real classroom stories and thoughtful analysis, Krall describes specific teacher moves and routines we can use to create academic safety.

Quality Tasks

For students to build and develop their own mathematical identity they need to hone it with quality tasks. Tasks are what you see students working on in the classroom. A quality task is one that is intrinsically interesting and allows all students to access it. Students cannot realize their mathematical potential without being provided opportunities to grapple with and successfully solve quality tasks.

Effective Facilitation

Effective facilitation involves the series of teacher moves that guide students to construct, enhance, and communicate their mathematical insight in a quality task. It is the launch of a rich task that captures all students’ interest; the question that pushes a collaborative group of students to think more deeply; the framing of the whole-class discussion afterward to promote sense making. Facilitation appears as singular moments in a classroom and as structures and norms that develop over months.

If a student enters post-secondary education requiring remediation (most typically in math), that student is much less likely to graduate. Of students who require remedial courses at four-year universities, only 35 percent go on to graduate within six years (Complete College America 2012). Let’s work to change this statistic by giving our secondary students a better math experience.

Click HERE to see a preview of Geoff Krall’s new book, Necessary Conditions.

Add comment November 12th, 2018

Toward a Math Pedagogy

There’s that famous yarn about how if someone time traveled from 100 years ago everything would look different except classrooms. That’s not really true. At least, not now. In fact, if this time traveler walked along the hallway of a math department, they’d see all sorts of disparate things. Sure, some classrooms might have desks in rows with the teacher lecturing at the board. But in other rooms students would be working in groups. In other rooms still students would be plugged into a piece of instructional software. This would-be time traveler would have no idea what’s going on!

When I walk down the hallways of a school, I notice these differences. In a 9th-grade Algebra class, students are using physical textbooks, while right across the hall in a 10th-grade Geometry class (or even a different 9th-grade Algebra class), I see hands-on activities. We’ve never had more varying math classroom experiences: project-based learning and instructional software, tracking and de-tracking, group work and packets.

We have so many pedagogies, we don’t have any pedagogy.

So I sought to find a pedagogy. What are the universal elements for a quality math experience? What are the things we as teachers can get better at? What are the things students bring to the table that help or hinder their mathematical identity?

In my work as a traveling instructional coach, I saw three consistent elements in successful math classrooms. The three elements are listed here, with much-too-brief definitions:

  • Academic Safety – the social and self-regard of a student’s mathematical status
  • Quality Tasks – the items that students are working on and toward
  • Effective Facilitation – the short- and long-term moves that allow for learning to occur

We’ll dig into these three elements in my forthcoming book, Necessary Conditions. Each of these elements receive a deep dive individually, with analysis of where these elements interact with one another. These aspects exist in everything students experience: from problem-solving to assessment, from lesson planning to room design. We can create a system that carves the path for our three necessary conditions, or we can create a system that works against them.

Combining research, classroom observations, and student voices, the book contains practical examples of how to assess and improve each of these conditions in your classroom and how you can imbue them in every lesson.

You can check out a preview of the book here. You can read stories of students who have been lifted up by incredible math teachers. You can see concrete examples of lessons and routines that yield deep mathematical learning. You can gawk at the ridiculous number of appendices.

So give it a look and see if we can really make that time traveler have something to marvel at.

This blog post was written by Geoff Krall, educator and author of the new title, Necessary Conditions: Teaching Secondary Math with Academic Safety, Quality Tasks, and Effective Facilitation.

Add comment November 5th, 2018

Blogstitute 2017: Which Comes First in the Fall–Norms or Tasks?

In this last post of our Summer Blogstitute series, Tracy Zager, author of Becoming the Math the Teacher You Wish You’d Had, shares her ideas for kicking off the school year in your math classroom ready to notice, imagine, ask, connect, argue, prove, and play.

Which Comes First in the Fall–Norms or Tasks?
Tracy Johnston Zager

I periodically hear discussion about whether it’s better to start the new school year by establishing norms for math class or to dive right into a rich mathematical task. I’m opinionated, and I’m not shy about my opinions, but in this case, I’m not joining one team or another. They’re both right.

The first few weeks of math class are crucial. You have a chance to unearth and influence students’ entrenched beliefs—beliefs about mathematics, learning, and themselves. You get to set the tone for the year and show what you’ll value. Speed? Curiosity? Mastery? Risk-taking? Sense-making? Growth? Ranking? Collaboration? You get to teach students how mathematics will feel, look, and sound this year. How will we talk with one another? Listen to our peers? Revise our thinking? React when we don’t know?

In Becoming the Math Teacher You Wish You’d Had, I wrote about a mini-unit Deborah Nichols and I created together. We called it, “What Do Mathematicians Do?” and we launched her primary class with it in the fall. We read select picture-book biographies of mathematicians, watched videos of mathematicians at work, and talked about what mathematics is, as an academic discipline. We kept an evolving anchor chart, and you can see how students’ later answers (red) showed considerably more nuance and understanding than students’ early answers (dark green). [Figure 2.1]

Figure 2.1

Throughout, we focused on the verbs that came up. What are the actions that mathematicians take? How do they think? What do they actually do?

In the book, I argued that this mini-unit is a great way to start the year if and only if students’ experiences doing mathematics involve the same verbs. It makes no sense to develop a rich definition of mathematics if students aren’t going to experience that richness for themselves. If professional mathematicians notice, imagine, ask, connect, argue, prove, and play, then our young mathematicians should also notice, imagine, ask, connect, argue, prove, and play—all year long.

In June, I saw this fantastic tweet in my timeline.

It caught my eye because Sarah’s anchor charts reminded me of Debbie’s anchor chart, but Sarah had pulled these actions out of a task, rather than a study of the discipline. I love this approach and am eager to try it in concert with the mini-unit. The order doesn’t matter to me.

We could (1) start with a study of the discipline, (2) gather verbs, (3) dig into a great task, and (4) examine our list of mathematicians’ verbs to see what we did. Or, we could (1) start the year with a super task, (2) record what we did, (3) study the discipline of mathematics, and (4) compare the two, adding new verbs to our list as needed. In either case, I’d be eager for the discussion to follow, the discussion in which we could ask students, “When we did our first math investigation, how were we being mathematicians?”

Whether we choose to start the year by jumping into a rich task on the first day, or by engaging in a reflective study about what it means to do mathematics, or by undertaking group challenges and conversations to develop norms for discourse and debate, we must be thoughtful about our students’ annual re-introduction to the discipline of mathematics.

How do you want this year to go? How can you invite your students into a safe, challenging, authentic mathematical year? How will you start?

1 comment August 1st, 2017

Now Online: Becoming the Math Teacher You Wish You’d Had

becoming-the-math-teacher-you-wish-youd-hadTracy invites you on a journey through this most magnificent book of stories and portraits…This book turns on its head the common misconception of mathematics as a black-and-white discipline and of being good at math as entailing ease, speed, and correctness. You will find it full of color, possibility, puzzles, and delight…let yourself be drawn in.

— Elham Kazemi from the foreword

While mathematicians describe mathematics as playful, beautiful, creative, and captivating, many students describe math class as boring, stressful, useless, and humiliating. In Becoming the Math Teacher You Wish You’d Had, Tracy Zager helps teachers close this gap by making math class more like mathematics.

Tracy spent years observing a diverse set of classrooms in which all students had access to meaningful mathematics. She partnered with teachers who helped students internalize the habits of mind of mathematicians as they grappled with age-appropriate content. From these scores of observations, Tracy selected and analyzed the most revealing, fruitful, thought-provoking examples of teaching and learning to share with you in this book.

Through these vivid stories, you’ll gain insight into effective instructional decision making. You’ll engage with big concepts and pick up plenty of practical details about how to implement new teaching strategies.

All teachers can move toward increasingly authentic, delightful, robust mathematics teaching and learning for themselves and their students. This important book helps us develop instructional techniques that will make the math classes we teach so much better than the math classes we took.

Add comment December 15th, 2016

Now Online: Which One Doesn’t Belong?

Danielson’s book reveals the wonder and freedom of expression that many children don’t often experience in mathematics. A single, simple question puts children in a position to speak mathematically even at early ages. Ask students of all ages “Which one doesn’t belong?” and revel in the reasoning and conversation that results.
—Dan Meyer

How can I recommend this highly enough? Christopher Danielson emphasizes the stimulation of curiosity and that math is about making precise things that we—and children—can informally observe, without having to learn any mathematical language first. Which One Doesn’t Belong? is a glorious book for adults and children to explore together, and the Teacher’s Guide makes it into a profound mathematical resource.
—Eugenia Cheng, pure mathematician, University of Sheffield and School of the Art Institute of Chicago, and author of How to Bake Pi

Which One Doesn't Belong student bookWhich One Doesn’t Belong? is a children’s book about shapes. More generally, it’s a book about mathematics. When children look for sameness and difference; when they work hard to put their ideas into words; when they evaluate whether somebody’s else’s justification makes sense—in all of these cases, children engage in real mathematical thinking. They build mathematical knowledge they can be proud of. They develop new questions. They argue. They wonder.

In the accompanying teacher’s guide, author Christopher Danielson equips teachers to get maximum benefit from Which One Doesn’t Belong? Through classroom stories, he models listening to and finding delight in students’ thinking about shapes. In clear, approachable language, Danielson explores the mathematical concepts likely to emerge and helps teachers facilitate meaningful discussions about them.

You can preview portions of the teacher’s guide online now!

2 comments August 4th, 2016

Taking apart the “key word” strategy

Today we have a guest blog post from Christine Moynihan, author of the recent math books Common Core Sense and Math Sense. Christine takes a close look at the often-used “key word strategy” and explains why it might not be the best way to help your students get to the right answer.

Taking apart the “key word” strategy
By Christine Moynihan

Christine Moynihan

Christine Moynihan

“Does your answer make sense?” Can you estimate how many times you have asked your students this question in regard to word problems? Even if you are a beginning teacher, I am willing to bet that it has been, on a daily basis, several times a day, five days a week, 180 days a year! Do the math and you will find that you have asked that question of your students a staggering number of times.

Even if your students answer in the affirmative — “Yup, my answer makes sense”!what may pass for their answers making sense is that they’ve  checked to see if their computation is correct; if it is, they assume they are good to go. Tucking their answers back into the context of the problem after they have completed the computation still may not come naturally to them, even though you and their previous teachers have tried to build it into your practice, their practice, and the practice of mathematics in general.

In my pre-service math methods classes, I was told that when I was helping students learn to solve word problems, I had to support them first in making sense of the problem so that they could then determine which operation they had to perform. One way to do this, considered good teaching practice, was to tell them to search for key words.  The next step was to get them to underline those key words, underline the numbers in the problem, and then to use the key words to write a number sentence to solve the problem.  My guess is that many of you may have had the same experience in pre-service as well as having been taught that way when you were in elementary school yourselves.  A few of the key words/phrases you most likely learned are: for addition – in all, altogether, total, increase, combined; for subtraction – difference, left, fewer, decrease, gave away, take away; for multiplication – of, times groups, twice, double; for division – per, groups, share, out of.

So what’s wrong with the key word strategy?  I have had to answer that question countless times in my previous roles of mathematics curriculum specialist and building principal, as well as in my current role of educational consultant. The short answer is that using the key word strategy has limited scope and value.  Further, it can be incredibly misleading and steer students to wrong answers that make no sense at all within the context of the problem.  Additionally, it sends students the wrong message in terms of them thinking that solving problems can be done routinely, formulaically, and without much deep thought.

Let me share a recent experience I had with one of the fourth grade students with whom I have worked for two years.  We were going over a sheet of problems he had done in class, as he had to make corrections to the ones he had gotten wrong.  Now Jared is a very bright fourth grader who excels in reading, is highly engaging, and knows a great deal of information about a wide variety of subjects.  He likes to work fast, think fast, move fast, and complete his work fast.  Mathematics is not always his favorite subject and he often shuts down his thinking if he cannot see a solution path quickly.  Here is one of the problems he had done:

Mr. Smith bought 14 new globes that his students could

use in class as they studied Earth.  Each globe cost $76.

How much did the new globes cost in all?

Jared’s answer?  I bet many of you can predict what his answer was.  If you thought that he had written $90, you would be correct.  I had him read the problem aloud and asked why he thought his answer made sense.  His response was, “I did the right thing because 14 plus 76 equals 90.  I did it in my head, but I know it’s right and I even put a dollar sign in front!”

I asked him to draw a picture that represented the problem.  He drew 14 circles to show the globes. When I asked what the cost was for the globes, he wrote 76 under the first one and then did the same under the others.  He then said, “This won’t work.  Look at the problem – it says ‘in all’ and that means you have to add, so the real answer has to be $90.”

My next question was, “How much did two globes cost?”   He immediately replied, “Well, it could be $152 but that can’t be right!  They told me to add!”  I had him continue to work and after he had successfully solved the problem, he looked at me and said with utter conviction and even a bit of indignation, “It’s not my fault!  They put in ‘in all’ so how I am supposed to know I shouldn’t add?”

I know for certain that there isn’t anyone who teaches key words as the only and/or best problem-solving strategy. But the rigidity with which Jared applied the strategy reinforced for me just how limiting and misleading it can be. I continue to work with him with one of my goals being that he understands that the responsibility for making sense of a problem rests with him and that he needs to add to his repertoire of problem-solving strategies to ensure his answers make sense.

1 comment April 27th, 2016

Now Online: Well Played, K-2

Well PlayedK2Well Played, K-2 is the second in a series of three books by Linda Dacey, Karen Gartland, and Jayne Bamford Lynch that helps teachers make puzzles and games an integral part of math instruction.

Following the same accessible format as the first book in the series (for grades 3-5), 25 field-tested games and puzzles are each introduced with math areas of focus, materials needed, and step-by-step directions. Readers will see how they play out in the classroom and get tips on maximizing student learning, exit cards for student reflection, variations, and extensions. The rich appendix has reproducible directions, game boards, game cards, and puzzle materials, and each chapter includes assessment ideas and suggestions for online games and apps.

Get your K-2 students talking and learning more as they play games and build their thinking as mathematicians. Well Played, K-2 is available now, and you can preview the entire book online!

1 comment December 15th, 2015

Blogstitute: Got Common Core?

Today’s Blogstitute post comes from Christine Moynihan, whose latest book is Common Core Sense: Tapping the Power of Mathematical Practices. In this post Christine introduces the GOLD framework that helps make the Standards for Mathematical Practice more accessible to elementary teachers. Be sure to leave a comment or ask a question for a chance to win 12 Stenhouse books! On Twitter you can follow along using #blogstitute15.

Got Common Core?
By Christine Moynihan

FC FINAL CommonCoreSense.inddSomething I hear from many teachers is that it is challenging to be up-to-date on everything that teachers should and must know in order to be effective practitioners. This is especially true for elementary teachers, who are asked to be content experts in reading, writing, grammar, spelling, science, social studies, and, of course, mathematics. Not only do they need to have expertise in these curriculum areas in terms of content, but they must also be experts in the best instructional practices that will support their students in learning in each of these areas. (I’m not even going to go into how they also have responsibility for social and emotional growth, health and wellness, behavior management, and the list goes on. . . . )

So, as a former classroom teacher, I get it. As a former curriculum specialist, I also get it. As a former principal, I most certainly get it. As a current educational consultant, not only do I get it, I hear it all the time—there is just so much to know, so much to learn, so much to do. As a result, when I ask a variation of the “Got Common Core?” question, many teachers respond that although they “get” the basics of the Common Core in terms of the standards for mathematical content for their specific grade levels, they believe that they have a somewhat light understanding of the standards for mathematical practice. Most teachers report that what they know about the MPs has been by way of an introductory look at them at a professional development session and/or staff meeting, with little or no follow-up.

My major purpose in writing Common Core Sense: Tapping the Power of the Mathematical Practices emanates from my desire to help teachers gain a foothold in understanding the MPs and how they can affect their practice. The book is meant to be a vehicle for making the eight Standards for Mathematical Practice more accessible to elementary teachers, for I see them as the core of mathematical proficiency. As I wrestled with how to do that, I defaulted to something that has always worked for me as a learner—to devise some kind of a framework, a mnemonic of sorts, to aid in understanding and then activating that understanding. Because I had been saying over and over again that “the gold of the Common Core really lies within the mathematical practices,” I constructed the GOLD framework to help teachers see some of the major components of each MP and then think about what they may look and sound like in classrooms, and what might need to be done to support the incorporation and implementation of the MPs into daily practice.

The Framework:
Go for the goals—What are the major purposes of the practice?
Open your eyes & observe—what should you see students doing as they utilize the practice? What should you see yourself doing?
Listen—What should you hear students saying as they utilize the practice? What should you hear yourself saying?
Decide—What do you need to do as a teacher to mine the gold?

I identified three major goals for each mathematical practice, fully aware that there are many more goals to be found within each. In the link you will find what I have identified as the second goal of Mathematical Practice #3: Construct viable arguments and critique the reasoning of others. What’s not to love about MP3? When you can analyze your thinking enough that you can clarify it, defend it, justify it, and represent it, you have learned something that will be valuable in all areas of life. In terms of mathematics, that ability leads you straight to the path of being mathematically proficient—a goal we all have for our students. I hope that the chart for the second goal I identified for MP3 can help in your work to make this MP come alive for the students in your classrooms.

Accept that viable explanations of mathematical thinking must be organized, reasonable, and justifiable/laden with proof.

8 comments July 6th, 2015

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