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When asking for answers, an equitable way to include all student thinking and reasoning.  You can also go with good old-fashioned popsicle sticks.

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What To Do Under Quarantine?

You'll have to take our word for it that the wheel landed on Phone an old friend. Your browser cannot display the wheel of choices. Please upgrade to a newer browser that supports HTML5 (most new ones do). Wheel Decide would normally show a wheel right here with choices that you can set (lunch, games, dinner, anything!). You can spin it to get a random decision. Make your own wheel of dinner, wheel of fortune, wheel of lunch, wheel of whatever you want now!

What's Wheel Decide?

Wheel Decide is a free online spinner tool that allows you to create your own digital wheels for decision making, prize giveaways, raffles, games, and more. Browse through our wheels and spin to randomize your life and make the decisions that have no wrong answers.

Decision Making

Let the wheel decide. Save your energy for the big decisions

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Can't decide? Wheel Decide for you! Set your own custom choices and then spin the wheel to make the random decision of lunch, movie, or anything! Make your own wheel of dinner or whatever now!

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Helping students to develop growth mindsets.

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Jo talks about brain pathways during Walk the Graph activity

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Stealing form Language Arts class?

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When math lessons emphasize collaboration and exploration over performance, students become more engaged and confident math thinkers.

Barrie Fanton / agefotostock / Alamy Stock Photo

Writing, discussing, and revising rough drafts is standard practice in language arts classes. But to Amanda Jansen, a junior high math teacher, author, and professor at the University of Delaware's School of Education, "rough draft thinking" is also a powerful tool for making the math classroom an inclusive, engaging place of shared exploration where students feel comfortable thinking aloud as they problem-solve.

Producing rough drafts of math problems, and discussing them in class, is "liberating for students because they can start to see how they're contributing to their colleagues' learning in a lot of different ways," Jansen says in an interview with KQED's MindShift. "After the initial shift, [students] start to get more excited, like, 'Wow, my ideas actually matter.' Everyone feels included in that kind of environment."

When the focus of math class evolves from emphasizing right or wrong answers-and the frequently public judgement that accompanies that high-stakes style of learning-to a collaborative environment where kids feel motivated to explore and take risks, students respond by becoming more engaged and confident about sharing their ideas. "[Students] show up with this sense of just feeling happy to be there," says Jansen. "They are more likely to just put something out there, whether it's in the group work or coming up to the document camera to share their thinking. They tend to feel proud."

Putting rough draft math into practice

When Christine Hubbard, a math teacher in Middletown, Delaware, uses rough draft thinking with her seventh-grade students, she defines the process briefly for her students and then moves directly into a number talk during which she explains the lesson-in this case: visualizing how to chunk sets of dots to make sets easier to count. Then Hubbard briefly shows her students a domino-like figure and asks them how many dots they see.
Courtesy Stenhouse Publishers
"I want you, in your mind, to be thinking about how many dots there are," she says to the class. All her students report seeing eight dots.

Hubbard steers the conversation toward examining students' strategies with questions like "Can anyone be brave enough to share and justify why they think there's eight dots up there?" On a whiteboard-or using Google Slides during synchronous learning-one student draws a set of five dots, like the side of a dice, plus a group of three dots; another student draws two horizontal lines of three dots and an additional two in the middle; and yet another draws a shape that loosely resembles a diamond composed of six dots.
Courtesy of Stenhouse Publishers
Students discuss what to call the diamond-like shape: maybe a "thingy," suggests one student or a "weird rectangle," says another. "Yes, you could describe it that way," Hubbard encourages. Finally, a student suggests that because the shape has two pairs of parallel sides, it could be a parallelogram. Hubbard confirms that yes, it is indeed a parallelogram. Guided by Hubbard, and with multiple students contributing ideas along the way and engaging in the type of verbal exploration that helps learners absorb and connect mathematical concepts, the class arrived at the "correct" answer.

Rough draft thinking can engage more students

Incorporating rough draft thinking into an existing math curriculum can feel like a big lift, but Jansen says the investment pays off: the practice winds up becoming more efficient over time as teachers become more adept at building in revision expectations and experiences.

Getting frustrated students to re-engage with mathematics, after all, is "not as simple as making problems relevant, or connecting them to the real world," writes K-12 math and science coordinator Matthew Beyranevand. "To get students interested in math, we need to provide opportunities for students to authentically inquire. We want kids-not the textbook or the teacher-to ask the questions."

That's where Jansen says framing math as a shared exploration comes into play, giving more students a chance to contribute to collective problem-solving and communal understanding of mathematical concepts. When "everyone's ideas have strengths in them and the teacher points out what's valuable about the drafts, and [students'] peers start to point out what's valuable, then everyone is seeing each other as having some mathematical strengths," Jansen suggests.

It also provides teachers with the opportunity to be more intentional about helping students, who are often riddled with math anxiety and lack confidence in the subject, see themselves as mathematicians. Math is "plagued by stereotypes and many students think math isn't for people who look like them," writes high school math teacher Dylan Kane. "As a math teacher, it's my responsibility to offer counternarratives that help students see themselves as mathematicians and expand what they think it means to 'do mathematics'."

Keeping track of who is being called on in class is critical here so that teachers aren't inadvertently creating new equity dilemmas by positioning the same group of students-girls or Black or LatinX students, for example-as only capable of presenting work that's rough, versus others being consistently recognized for work that's more developed. Refined and brilliant thinking, Jansen says, can come from any student. "We need to make sure not only are [diverse students] having a voice, but their strengths are being really looked at," she says.

For shy, quiet kids who might prefer to keep their math thinking to themselves, Jansen gently challenges them to share in class. She also likes to offer opportunities for writing-usually when the class is working on revision-as a low-stakes way for introverted kids to participate. "Every time we're being asked to articulate our thinking, we make new connections or crystallize our ideas just by trying to put them into words or into writing," Jansen says.

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Rough Draft Thinking Can Make Math Class More Inclusive

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When math lessons emphasize collaboration and exploration over performance, students become more engaged and confident math thinkers. Barrie Fanton / agefotostock / Alamy Stock Photo Writing, discussing, and revising rough drafts is standard practice in language arts classes.

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Great problems for discussing different approaches and making connections.

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Explore these patterns with your students and watch their natural tendencies to see patterns morph into powerful algebraic thinking and reasoning. It’s an ideal routine to foster mathematical practice #7 - look for and make use of structure.

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Fantastic strategy for showing that mistakes are an important part of the learning process.

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Super fun and really tap into creative problem solving and thinking.  #unitchat on Twitter

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Topics: Mental math, numerical fluency; argument & critique
Materials: White board or projector
Common Core: Variable, but especially MP3, MP1, and NBT

Counting with respect to different units.

Unit Chats are one of the great openers developed in the last few years. The emphasis is on different units within the image. Students can answer "how many" with respect to the different options of units presented by the picture, and also relate the units to each other to build the framework for a deeper understanding of multiplication, division, and fractions.

Truly a knockout opener.

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Topics: Mental math, numerical fluency; argument & critique Materials: White board or projector Common Core: Variable, but especially MP3, MP1, and NBT Counting with respect to different units. Unit Chats are one of the great openers developed in the last few years. The emphasis is on different units within the image.

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Love to use this when introducing a new topic or module. Start with questions !

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Developed by the Right Question Institute, the Question Formulation Technique, or QFT, is a structured method for generating and improving questions. It distills sophisticated forms of divergent, convergent, and metacognitive thinking into a deceptively simple, accessible, and reproducible technique.

The QFT builds the skill of asking questions, an essential - yet often overlooked - lifelong learning skill that allows people to think critically, feel greater power and self-efficacy, and become more confident and ready to participate in civic life.

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What is the QFT? - Right Question Institute

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The Question Formulation Technique (QFT) is a simple but rigorous step-by-step process designed to help […]

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Tons of strategies for incorporating cooperative learning.

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kagan publishing teaching catalog teacher resources school supplies music games cooperative learning differentiated instruction educational products esl ell foreign language posters multiple intelligences textbooks math books science literature social studies

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Kagan's FREE Articles - Kagan Structures: A Miracle of Active Engagement

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Read Dr. Spencer Kagans provocative and insightful articles on Kagan Structures and how they have the power to transform education. Cooperative learning, multiple intelligences, the brain, character development, Win-Win Discipline.

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Have a wall or area in your classroom for students to post questions and perhaps other students can answer or have the teacher answer on a regular basis .

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Make mistakes when presenting a lesson or solving a problem. The students can correct you. You can make this into a game or competition where the students who identify your mistakes can earn points.

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Activities for bringing creativity into your lessons!

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Students solve problems that are real life, Making sure to show understanding of the question being asked, steps used to solve the problem, what the solutions is, creating and extension/expansion, and rating their learning.

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Encourage discourse with activities such as Turn & Talk and Decide & Defend.

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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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Students can write questions they still have on the ticket out the door

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Data Talks and setting goals

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Recognizing all students' efforts and attempts to make sense of mathematics regardless if they're right or wrong.

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Students process information at different times. Make sure to give wait time for everyone and that all students are aware that there is wait time so that they don't shout out answers.

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Students learn to ask the questions that they may not do with a whole group.

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Students learn more when they make a mistake compared to the times when they get everything right.

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Take pictures of students' work that have incorrect steps--making sure it's anonymous--and have the class analyze how to make it right

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Mistakes are more valuable when students are freely able to make them without feeling of judgement and without penalty.

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Mistakes are more valuable when students are freely able to make them without feeling of judgement and without penalty.

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Giving our students time and opportunities to struggle and do their best. Not automatically assuming students aren't capable of doing something.

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United we solve gets the students working together to solve problems!

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Asking questions helps students access material that they need to learn.

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It is difficult to maintain this norm in the classroom when math course teams are required to maintain a specific pace set by the district and also classes need to stay at the team's pace to keep the different classes somewhat equivalent in rigor.  

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It is difficult to maintain this norm in the classroom when math course teams are required to maintain a specific pace set by the district and also classes need to stay at the team's pace to keep the different classes somewhat equivalent in rigor.  

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Establishing norms that promote collaboration and discourse and instruct students to agree on one answer as a group. This encourages them to share ideas and hold each other accountable in contributing to the group.

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https://www.wouldyourathermath.com/

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Would You Rather Math – ASKING STUDENTS TO CHOOSE A PATH AND JUSTIFY IT WITH MATH

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Teachers, sign up for my mini-workshop to learn about how to implement Would You Rather Math into your classroom routines. We will explore some sentence frames, what happens when things don’t go as planned, how to use the prompts in a remote learning setting, and much more. See you there!

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Books and teachers almost always give "nice" answers. When students create their own problems, they find that the procedures still work, answers are not always nice, and they can solve any problem.

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Building connections with students and getting to know them as a whole student and not just a product producer. 

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Building connections with students and getting to know them as a whole student and not just a product producer. 

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Learning happens in productive struggle situations. 

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Learning happens in productive struggle situations. 

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We need to make students believe that they can do best in math

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These 2 gentlemen create some really interesting ways to approach activities and engage students to make moments in the math classroom that matter.
https://makemathmoments.com/

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The Make Math Moments Academy

YOUR ROADMAP TO AN INSPIRING MATH CLASS
Create memorable math moments daily with access to curiosity rich tasks, in-depth PD video trainings, and a system for making these moments a reality. Join the Making Math Moments Academy now. Your first 30 days are for free.

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Make Math Moments | Empowering Teachers with Math Activities

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The Make Math Moments Academy YOUR ROADMAP TO AN INSPIRING MATH CLASS Create memorable math moments daily with access to curiosity rich tasks, in-depth PD video trainings, and a system for making these moments a reality. Join the Making Math Moments Academy now. Your first 30 days are for free.

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https://mathgeekmama.com/8-reasons-making-mistakes-in-math-is-a-good-thing/

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Far too often, math is seen as a subject that is either right or wrong, and so you better get the answers right or you'll fail the test. And while it is technically true that we want students to understand math concepts deeply and be able to correctly solve math problems, creating this kind of mindset can cause students to feel frustration and a sense of failure anytime a mistake is made. The reality, however, is that mistakes are a part of the learning process, and we should be teaching and encouraging kids (and ourselves!) to see mistakes as an opportunity for growth and deeper understanding.
*Please Note: This post contains affiliate links which help support the work of this site. Read our full disclosure policy here.*
And while making mistakes is necessary, and deepens and challenges our thinking (this is true of any new skill or subject, not just math), students often would rather leave a math problem blank than to try, only to get it wrong.

But in contrast, brain research shows that deeper learning and greater neural connections form from making mistakes on difficult tasks, rather than simply having constant success on easy tasks.

So in math class, encourage this kind of view of mistakes, and help your kids learn that mistakes are opportunities for growth!

My kids and I have been reading Mistakes that Worked , by Charlotte Jones to inspire them to embrace their mistakes and encourage perseverance and hard work. It's really a fantastic book for kids (and adults!) of all ages!

8 Reasons Why Making Mistakes in Math is a Good Thing:

Making a mistake shows that you tried:

As a classroom teacher, nothing frustrated me more than students coming to class with empty homework assignments and the excuse, "But I didn't know how to do it." You will never learn until you try. Many of the world's greatest leaders and inventors saw an unbelievable amount of failure before finding success. But their successes would never have happened if they simply sat back and said, "But I don't know how!"

The brain is like a muscle that needs to be used and exercised in order to be strengthened. Wrestling with challenging problems is good and important work for your brain!

Although many see the classroom teacher's role as that of lecturer, the truth is students will learn and remember more if they take ownership of their learning and discover solutions for themselves. When students can recognize mistakes and then take time to understand why it's wrong and how to fix it, they own the understanding and have not simply relied on the teacher to give them the answer.

Understanding what doesn't work is just as valuable in the learning process as knowing the correct method and solution. As Thomas Edison said,

Negative results are just what I want. They're just as valuable to me as positive results. I can never find the thing that does the job best until I find the ones that don't."

You might notice a concept or pattern that you wouldn't have seen otherwise:

Sometimes trying an ineffective method to solve a problem leads to other important mathematical ideas and discussions that might never have been had otherwise. Just because you don't find the correct answer to the current problem does not mean you can't learn some other important math fact or concept.

You understand and can talk about the problem a little bit better:

When you have spent time working out a challenging problem but have not yet found the solution, you can still explain what the question is asking and why what you've tried hasn't worked. Maybe your solution is wrong because you didn't rightly understand the question in the first place, but now you do. This is valuable math learning.

Understanding WHY a method didn't work can lead you to the correct solution:

This goes back to #1: You'll never solve it if you never try. Maybe you get it wrong on the first (or tenth) try, but seeing why that's wrong may point you in the right direction so that you are able to solve it eventually.

Mistakes make the moment you finally solve it that much sweeter:

If all you ever do is solve math problems that are easy for you and you never get any wrong, it will not mean much or feel like much of an accomplishment. But what victory and pride you'll feel when you've gotten ten wrong answers and then finally find the solution!

While mistakes are a good and healthy part of math learning, this is really true of mistakes in all facets of life. I have read a little of the book, Better By Mistake: The Unexpected Benefits of Being Wrong , by Alina Tugend, and have thoroughly enjoyed it so far. I look forward to learning more about brain research and how I can learn to stop being such a perfectionist and instead embrace my mistakes as a catalyst for learning!

Want to help kids see the value of mistakes and learn to analyze math errors? Grab my new Error Analysis Pack!

This includes blank templates to analyze mistakes plus teaching tips and classroom posters to help teach kids about types of mistakes and how we can learn from them.
Buy Error Analysis Here!
What do you think? Do you tend to see mistakes as a sign of failure or as an opportunity to learn something? What kind of message do you want to send to your students?

Want to learn more about making mistakes in math? Check out this post which outlines the types of math mistakes and how to help kids learn from them and prevent them.

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8 Reasons Making Mistakes in Math is a GOOD Thing!

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Don't let your students be afraid to make mistakes in math class! Encourage and empower them with these 8 reasons why making mistakes can be a great thing!

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Personalized Learning Programs such as ALEKS need to be hard-wired into our schools to prioritize depth than speed.

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You can improve by making mistakes rather than not working.

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Great article about how to support public speaking, a.k.a presenting. Building confidence one month at a time will be a focus for next year.

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Small steps can help high school students feel less anxious about speaking in front of an audience.

Stígur Már Karlsson /Heimsmyndir / iStock

"According to most studies, people's number one fear is public speaking. Number two is death. Death is number two. Does that sound right? This means to the average person, if you go to a funeral, you're better off in the casket than doing the eulogy." - Jerry Seinfeld

Public speaking is a legitimate fear for many people. I'm not afraid of public speaking, but I am afraid of snakes. If someone forced me into a room with snakes to pass a course, I would be terrified, and I would fail. This is how some students feel about public speaking.

Also, consider that students don't want to feel judged. They don't want to appear dumb, weak, or afraid in front of their classmates. Requiring students to speak in front of each other is asking a lot.

As an English and theater teacher for more than 13 years, I've helped many students become more confident with public speaking. I've also seen other teachers struggle with helping students grow in their confidence. Often, the issue is that they're either not scaffolding the public speaking experience for the student (they're just throwing the student alone in front of the classroom) or they're scaffolding the experience, but they're making the steps too big or rushing the process. Here I'll explain the techniques I use in my high school English and theater classrooms that I've had success with over the years.

First, before we can even begin to expect students to speak publicly, we must first build a strong classroom community. The feeling of safety and community is vital because students need to feel safe and supported before they'll take risks. You need to build the foundation for a strong community in your classroom before beginning the next steps.

Scaffolding

How you scaffold the public speaking experience will make all the difference. Students may need to do these exercises more than once, and it isn't a linear process. This is where the artistry of teaching comes in, as well as the community-building you've worked on.

Start with group presentations from the students' desks. These can be fairly large groups to start (four to six students). The projects don't have to be big, formal assignments. In fact, this works great with a quick check-in of a discussion.

In the beginning, don't require everyone to speak. That's right-the first step doesn't even include speaking. Having everyone looking at them (even in a group) is a first baby step for some students.

For the next step, do the same as above but now in front of the room. Being in front of the room is intimidating, and students will feel safer if they're in a group and don't have to speak yet.

You may want to have the group present a poster, with the person who doesn't yet feel comfortable speaking holding it up. This provides a sense of security. Also, having a podium between the students and the audience makes a big difference in comfort level.

Repeat the above steps, but slowly make the groups smaller and/or have them speak a little bit more each time. Students can also do these steps from their desks first and then move up to standing in front of the class. You'll have to figure out with your students which areas to change and how quickly-again, the artistry of teaching.

Factors in Students' Success

Over the course of the year, make sure you plan out these experiences and think about where each individual student is in their journey to public speaking confidence. This will change as the year goes on, and not always in a straight line. Students will have other experiences outside of your classroom that will either build or damage their progress. They might have a great experience in another classroom or an after-school activity that propels them forward, or you may have to take a step backward with a student because they've had a negative experience somewhere else. It's vital to regularly check in with your students. This can be a quick conversation, a secret hand signal that says how they are doing that day, or a poll.

Think about learning how to drive a car. People most likely don't start out driving on the highways. New drivers work on smaller side streets or in parking lots until they feel comfortable enough and ready to move on to something more challenging and intimidating. Even then, the next step may not be the highway.

Keep these tips in mind when thinking about how to create important, purposeful, and thoughtful experiences with public speaking. Taking these smaller steps will be an investment that will set your students up for success in the long term.

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Guiding Students to Be Comfortable With Public Speaking

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Small steps can help high school students feel less anxious about speaking in front of an audience. Stígur Már Karlsson /Heimsmyndir / iStock "According to most studies, people's number one fear is public speaking. Number two is death. Death is number two. Does that sound right?

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Everyone Can Learn Math to the Highest Level

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Everyone Can Learn Math to the Highest Level

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Give students the encouragement that they can be successful in math.

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On an assessment, I allow the students to bring me their work once before turning it in to have me check their work. I will circle or highlight the questions that have some level of mistake, without telling them what the mistake is. The students are then allowed to go back and review their work to try to fix their mistake. This really helped the students understand that making mistakes are normal and it can help them learn to find their own mistakes. The students were happy that I pointed out their mistakes so they had a chance to fix and find their own mistakes.

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Teaching content vertically is more important than going horizontally.

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Students full potential can be achieved at the highest level if we (teachers) provide tasks that are achievable.

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If using Google Slides when presenting, there is an option to turn on a Q&A feature for your participants to use while you present.
Go to the arrow next to the “Slideshow” button and choose “Presenter View”. Then, choose “Audience Tools” and “Start New”. You can share the link with the audience for their questions to appear on your screen and can even toggle the question feature off when you want to keep the students’ focus on what you’re speaking about.

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Reframing even the term, "mistake" into something more positive like, "an opportunity to clarify" or a time to double check a confusion. These are the places where learning is found

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Have students question each other along with teacher questions.

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Have students question each other along with teacher questions.

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https://www.ascd.org/el/articles/questioning-strategies-that-invite-math-participation

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This situation is a math teacher's worst nightmare. Teachers spend hours planning standards-based lessons and problems designed to engage students (i.e., those raised hands). However, historically, math teaching and learning has focused narrowly on avoiding wrong answers and celebrating right answers. This type of math culture makes students reluctant to participate unless they can guarantee their correctness, and it discourages growth for all students in mathematics. As teachers, we have the power to include all students in a collaborative environment that fosters mathematics growth. We can do this by shifting thinking and questioning to focus more on the process of solving math problems, opening up a world of formative data that lets teachers see what students are thinking.

This list identifies some ways to shift teacher questioning in math from limited answers to open-ended questions that reveal formative data on math thinking skills and processes. These "formative open questions" encourage all students to participate, even if they are not confident in their final answer.

Instead of asking for the answer, ask students "formative open questions" like

What does this problem make you think of?

What skills have we learned in class that you can apply to this problem?

What would be the first step in solving this problem? Or, tell your shoulder partner where you started.

How did you solve this problem? Or, let's look at your work.

Is there another way to solve this problem?

Whether or not they have the correct answer, this type of questioning invites every student to participate in classroom discussion because everyone knows something about the problem. What's more, the answers to formative open questions provide teachers with immediate feedback on what students are thinking. It is much easier to clear up misconceptions and get a broader picture of what student know using these questions. When the focus is not on the final answer, students are less likely to feel defeated by errors in the learning process. Errors become learning points that assist students in adjusting their thinking and reforming their solution pathway.

Formative open questions also lend themselves to collaborative work. The teachers I work with use a strategy that promotes both individual thinking as well as collaboration. Working in groups of four, students share a large piece paper with room for each student's work as well as a collaborative space for a final answer. The teacher poses a question to each group and allows time for students to problem solve in their individual sections of the shared work space. Students have the benefit of seeing how their team members are approaching the problem, which provides a starting place for any students who are truly stuck.

Then, during time allotted for collaboration, students share their individual thinking and process for solving the problem. Based on this discussion, each group comes up with a collaborative answer to share with the class. During this activity, the teacher circulates the room, monitoring individual work and collaborative conversations. This unobtrusive and low stakes approach to assessment provides rich data on student thinking that can be used for small group differentiation.

We will learn more about our students, and they about mathematics, when we design questions that invite everyone to participate in the process of learning.

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Questioning Strategies That Invite Math Participation - ASCD

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This situation is a math teacher's worst nightmare. Teachers spend hours planning standards-based lessons and problems designed to engage students (i.e., those raised hands). However, historically, math teaching and learning has focused narrowly on avoiding wrong answers and celebrating right answers.

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https://mathequalslove.net/twos-to-nines-challenges/

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Day one and two are in the books! I'll share a bit more about what I did with my classes on the first two days in a later post, but I want to go ahead and share the mathematical challenge I used with my students on the first day since I have got several questions about it on twitter.

This summer, my husband and I ran across a treasure trove of puzzle books at Goodwill. We *had* to buy them. As Shaun was driving us home, I flipped through the books and would occasionally pose puzzles for us to solve together in the car. We had a lot of fun with this, and in the process I found some puzzles that would be PERFECT for use in the classroom.

One of my favorite new puzzle books from this Goodwill trip is 100 Numerical Games by Pierre Berloquin. If you don't believe me that this book is awesome, just take a look at who wrote the foreword. THE Martin Gardner!

You can a free peek at some of the puzzles in the 100 Numerical Games book by using the "Look Inside" feature from Amazon.

One particular set of puzzles which is sprinkled throughout the book really caught my eye. This version was based on the number two, but the book also featured puzzles for the numbers three through nine.

The task is to use exactly four twos (or threes, fours, etc) to make each target number. Add arithmetical symbols between the numbers to make every equation true. You may use plus, minus, times, and divide symbols, as well as parentheses and brackets for grouping.

Originally, I thought about turning this into a puzzle for my puzzle table, but I never got around to it. Fast forward to this past week. I needed an activity to do on day one, and I decided I wanted to do something a bit different than what I've done in the past. For reference on past activities, check out my post on 30+ Ideas for the First Week of School!

One of the messages I communicate to my students on the first day of school is that we do math everyday. I can't just say this. I also have to give them math to do on day one.

Yes, there were some groans. We carried on anyway.

My students are arranged in six groups of five, so I decided to set up six challenges around the room. The book featured challenges using the numbers between 2 and 9, so this meant that I had not used the challenges based on the numbers 8 and 9.

To introduce the task, I threw the Eights Challenge up on the TV. (It's going to take me a while to get used to saying TV and not SMARTBoard!)

After a quick overview of the rules, I gave them a few target numbers to work towards.

Students quickly got to work. Some grabbed paper and a writing utensil. Others got out their graphing calculator or phone calculator. Still others just sat and thought about the task.

Within a couple of minutes, a student in each period would announce that they had found the answer to 10. I asked them to read me their solution so I could write it on the board.

Almost every single time, I ended up hearing 8 + 8 / 8 + 8 = 10. So, I would tell them that we needed to check their work. This was when I asked them what the order of operations says that we need to do first. Unanimously, the class would say divide. Then, a bit of panic would set in. 8/8 is 1. So, 8 + 1 + 8 is 17, not 10.

Without me saying a word, the class would start to suggest either a different way to solve the problem OR a way to salvage this attempt. It usually wasn't long before someone would suggest that we could use PARENTHESES! So, from this, I learned that we do know our order of operations. We're just a bit rusty, but I can deal with that.

After the class found a few of the solutions for the Eights Challenges, I decided to change things up a bit. I told them that now that they understood how the puzzle's structure worked, it was time to try a

Around the room, I had marked off six four-foot sections of white board space so that each group of students could have their own space for working problems throughout the year.

At each station, I had posted a challenge based on a different number.

I typed up the instructions for each challenge. My students didn't really need this since we had done part of the eights challenge as an example, but I did see a few groups reference it. One group used their dry erase marker to actually write symbols between the numbers. Good thing I laminated them!

Then, I typed up the target numbers that students had to find. I thought about making them into magnets so the students could move the target numbers around, but I wasn't sure where all magnets were. Let's just say that moving classrooms sucks. I can't find anything right now!

I ended up just taping them to the dry erase board. This worked just fine. Most groups left the numbers stationary and just wrote their solutions next to the appropriate number. A few groups did move the numbers around.

The tape stayed sticky, so they were able to change the number positions without any issues. Since this activity went SO well, I think I will definitely add magnets at some point.

Each table group chose a different number based challenge to work on. They instantly got to work, and the room was soon abuzz with awesome conversations. Students were excited and joyful as they found various solutions.

Students were checking other students' ideas and pointing out any issues. Lots of parentheses were being used. Were all their answers perfect? Nope. But, it's day one, and it gave me a great snapshot of where my students are starting from.

It was the first day of school and every kid was engaged. In fact, I would say this was the most engaged my students have ever been on the first day of school. This was my favorite first day of teaching EVER.

Check out this awesome group work!

Each group was given one dry erase marker and one graphing calculator to encourage collaboration. Every few minutes, I would announce "SWITCH!" This meant that the person holding the marker needed to pass it to another person in the group. The calculator person did the same thing.

Every once in a while, I would introduce a new twist. About five minutes into the activity, I had the groups pause and look at me. I instructed them to nominate one volunteer from each group. This person was to hold their hand up so I could ensure that I had one volunteer from EVERY group. They asked what they were volunteering for. I just said "You'll find out soon."

Once one hand was up from every group, I informed the class that these students would be rotating one group clock-wise. So, each group would lose one member and gain a different member. There were a few groans with this announcement, but students complied.

I was excited to try this strategy since each group was working on the same type of challenge, but no two groups had the same problems to solve. This meant that the new group member could bring STRATEGIES from their previous group, but they could not just bring ANSWERS.

After a few times of rotating a single group member, I changed things up yet again with having the entire group rotate to the next station. I did run into a few issues that I hadn't figured out how to handle beforehand.

The groups assigned to the challenges based on lower numbers (2s, 3s, and 4s especially) were sometimes able to completely finish their challenge. When this happened, I did one of two things. In my smaller classes, there was often a challenge that had not yet been started. In these classes, I sent the finished group to this untackled challenge. In my larger classes, I had the finished group split apart and join other groups.

The Sevens Challenge ended up being the most difficult for my students to tackle. Often, there would only be two or three target numbers solved by the end of the class period.

Digital Adaptations of the Twos to Nines Challenge

Google Slides

The Twos to Nines Challenge has been turned into a Google Slides activity by Meghan Smeenk. Check it out here.

KellyLove shares a slightly different Google Slides version.

Desmos Activity Builder

Scott McEwen has created Desmos versions of this activity as well. Each challenge is a separate Activity Builder.

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Day one and two are in the books! I'll share a bit more about what I did with my classes on the first two days in a later post, but I want to go ahead and share the mathematical challenge I used with my students on the first day since I have got several questions about it on twitter.

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Students in my class have to utilize the 3 before me strategy. To promote the discourse and growth mindset strategies, students have to ask questions of at least three of their classmates before they can ask me any questions. The students embrace this very well after they have practice doing it and aren't afraid to ask each other questions to better understand.

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Students should be made to see connections with real world and other content areas.

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https://www.saravanderwerf.com/week-1-day-1-name-tents-with-feedback/

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Sara VanDerWerf - Inspiration and resources for mathematics teachers

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UPDATE May 2020: In the era of Remote/Distance/eLearning, teachers have stepped up to adapt this activity for use when we are not in our classrooms with our students. If you are interested in their ideas, scroll down to the bottom of this post to see more and get links to what they have created.

Last year I taught Advanced Algebra (your might call this course Alg 2 or Alg/Trig) at a school new to me. I was smart-I entered the year relying on the expertise of those that had taught Adv Alg recently (for me it had been 11 years ago). Every day last year I co-planned my Advanced Algebra lessons with Morgan - the same Morgan I blogged about who made our Backwards Bike. I have had a lot of first days of schools in my career but

I know I can learn more. I asked Morgan what she did day 1. She said she uses name tents and for the first week of school she writes a quick note to students responding to whatever they put inside the name tent. I had not done this before, but I thought - 'I'm game'.

Why Morgan choose to use name tents in her high school classroom for the first week of school matches the best practices about teaching urban students, students in poverty or students of color (and frankly it is good for all students). We must build relationships with students. We must work hard to know our students. Students grow more through feedback vs. a number/letter grade. We must create a community of learners in our classroom. We must make our classrooms safe spaces for everyone.

Morgan, and several other of my new peers, did not start our first official district math unit for Adv Alg until day 6 or 8 or 10 of school. Morgan's goals for week 1 is simply to build relationships with her students and create community with the entire class. (and she also does some math). Here is one way how Morgan did this and how it played out in my own classroom.

Here was my very first slide of class day 1 of school last year in our High School Math Classrooms..

At the table were 4-5 sheets of white card-stock with printing on one side (to be folded inside) and markers. I asked students to record their first name on both sides.

Here is the original of this document from last year. (note, I've changed it a bit for this year and attached it further down in the post): NameTentFeedback This document is the exact Word Doc Morgan gave me. I asked Morgan if she created this or received it from someone else. Morgan received this from one of the AVID leaders in our school, Tonya Hodge (a ELA teacher).

After having students make a name tent, I posted our very first learning target for Day 1. I asked them to introduce themselves to the people they were sitting with. (I start the year with an alphabetical seating chart and change it after week 1).

I told my class that their first class assignment for week one in Advanced Algebra was to learn the first names of every student in our class. Day one their task was to learn at least 5 new names. My class had 9th/10th/11th and 12th grade students in it. Most did not know the names of more than 1/4 of the class. Morgan's goal and my goal was to build a community of math learners week 1.

Side note: Building community during the first week of school is a very normal thing to do in Middle School - it has not been my experience that it is as common in HS math classrooms. Morgan does not know it, but she has some natural MS skills.

We went on wi

th our day 1 activities. If you are wondering about the rest of my day 1 activities, here is a PDF of how it played out in my room. AA Day 1 of school slides. (If you look at it you will notice I told them about myself - stealing ideas from old Dan Meyer Posts with a bit of Jo Boaler and a little notice/wonder). I also blogged about another part of my day 1 lesson yesterday HERE.

With 10 minutes left of class, I had the class look around and learn the names of students not at their table. I then asked for one volunteer to stand up and say the first names of at least 5 people in class as we covered our name tents.

During the last 5 minutes of class, I finally had the class open their name tent and write me a note in the yellow highlighted box about anything they wanted to on day one. What is below is a copy of what was inside their name tents.

That afternoon I wrote a response back to every single student in my classroom. Here is a few random things students wrote on day 1. I love the variety of responses from my students.

By the end of day 4, here is what the inside of each student's name tents looked like with y comments:

As you can see, I did not write a ton to each student, what was important is that I wrote something. What was important is every day I spent 1-2 minutes intentionally reading what every student was thinking and responding to it. Not only did it help me learn names even a bit quicker, I also learned things about my students and their relationship to my class.

Here are a couple of things I learned after using name tents in my HS math classroom week 1 of school.

1. I have homework assignments I use during week 1 that have students write a lot more about themselves. This does not replace those, this was a great addition. It had the added bonus of having me give immediate feedback to students.

2. After 3 days of a prompt of 'comments' - some student's were writing very little or things like "It was OK". On day 4 at the last minute I asked students to 'Ask me a question' instead of writing a comment and I would answer anything they asked me either about this class or about me personally. This worked GREAT. I received a lot of great questions. I responded to everyone as honestly as I could. In addition I put up several questions for the entire class to see so everyone could get feedback on what their peers asked of me. I have made a new & improved Name Tent for this year's first week of school (bottom of post) that includes having students ask me a question. Here are a few questions that students asked me. Love them.

3. Despite reading and responding to students everyday with what they wrote in their name tents - I still missed clues that they sent me I re-looked at the name tents to write this post and I noticed some information my students sent me that I ignored. For example, look at the inside of this student's tent: Here was the outside back of his tent - it was beautiful:
What I know now about this student now that I missed week 1 is that he worked best in math class when we were doing something more creative. This student did the least amount of homework & classwork of any student I had this year until 2/3 of the year when I did my Desmos Art Project and he created this in 24 hours:
Looking back I wish I would have noticed his amazing doodles in week 1 and used this as a clue to build lessons to engage him sooner. I will change this - this year. (I have also changed this year's name tent to encourage drawing as an option to responding to me).

4. I know many people reading this may think, "Sara, name tents are totally cool, but I just don't have the time to do them.". Let me encourage you that this was totally worth the time I spent on the them. During the first week of school last year I was not only teaching all day, I would leave school each day and go to the Minnesota State Fair to work at our Math On-a-Stick booth in the evenings. I was BUSY. I still did this and I was so glad I did. I HIGHLY encourage you to consider using these name tents OR do something else week 1 to hear daily from every student AND for you to give them feedback.

5. I did read my name tents again at the end of September once I knew my students a bit better and I learned a lot more. I plan to do this again this year. I also may find a way to do something similar to get more student comments like this in October or November this year.

6. Every day during week 1 I spent time (5 minutes) having students learn EVERY first name of every student in the class. In fact I tested them on it week 2. Each day I had 1-2 groups stand up and introduce their group to the class. I would say 60% of my students knew every name by day 6 and another 35% knew at least 80% or more of the names. It was great for community in the classroom. Students responded later in quarter 1 that they appreciated that other students knew their name.

I would love to hear what you do to build relationships with your math students week 1. What do you do to give students feedback? How do you build community in your classroom? These are some of the important goals I have week 1. I am always looking for more ideas. Have a great start to your school year.

The NEW & IMPROVED Name Tent for 2016-17: 2016 Name Tent for 1st week

The Name Tent is now translated into French thanks to Update 8.20.18: Jocelyn Dagenais You can download it here: Tentes des noms 1re semaine (name tents in french)

UPDATE #1 August 2019: I often get asked about prompts for Name Tents. I generally don't give them other than saying something like this day 1 and 2 - " Everyone, please fill up the whole box with words or pictures about something you want me to know. (note: My goal is to get students to say more than 3 words, so 'filling up the boxes' and 'everyone' is intentional) For example, you can tell me that you hate math or that your pet turtle is named t-rex or that you are at soccer practice every night and will not be able to do homework or that your favorite math word is perimeter or that you know how to juggle 9 flaming torches at once or.....tell me about a passion, something you care about, something you fear, something about this class or anything else you think it is important for me to know." I leave it relatively open to students because I want to hear what they want me to hear, My goal is to study my students.

For those of you wanting prompts, there are lots of people on twitter who have shared examples. Here are a few. First a google Slide of 100 prompts for name tents from Kristen Fouss. Amazing. Here is a tweet from Jennifer White:

"if math were an animal it would be.... because..."

"whats something you do to take care of yourself when you're feeling like you need a pick-me-up?"

"What would you do with a free $3 mill?"

"what questions do you have for me?"

Those were the ones I did this year.

- Jennifer White (@JennSWhite) September 5, 2019

UPDATE #2 August 2019: I often get asked, " My students want to continue with name tents but I can't do this everyday. What is your advice?" After Chris Nho (he's amazing) asked this online, I decided to ask the #mtbos community. Click on the twitter thread below to see what they said!

I've received this question from several people this week. #MTBoS what are your ideas? https://t.co/kRBRhfChpF

- Sara VanDerWerf (@saravdwerf) August 31, 2019

UPDATE #3 September 2019: An amazing, amazing math teacher, Sarah Streitz from Richfield HS, in Minnesota shared her Spanish version of the name tents with me. Here it is for you. Enjoy. Spanish Name Tent (word doc)

UPDATE #4 September 2019: Mary Bourassa blogged about keeping the conversation going. A common question I get online about name tents. Check out Mary's solution HERE.

UPDATE #5 May 2020: The world has changed due to COVID-19 and so must how we use Name Tents. Check out these resources....

1. Kristen Fouss has put Name Tents into Desmos so she can give Feedback to her students using this vehicle. Thank you to Desmos and Kristen for improving on the ideas in this post. Check out what Kristen did HERE (you can copy and adapt her work) on Desmos, and read comments when she posted on FACEBOOK. Also, here are 100 prompts others have collected to use.

2. My Friend Erica Heinzman in San Diego shared her google version of the form HERE...

Here's my Google name tent. After we finished the 5 rounds, sometimes Ss will still email me a"Name Tent" entry. https://t.co/Kymgl4RvLI #iteachmath #MTBoS

- Erica Heinzman (@eheinzman1) May 22, 2020

Nanette Johnson asked how to adapt Name Tents and a bunch of you responded with ideas of how to do it with Google resources within google classroom. Check it out here:

Hey @mrsjohnsonCA , @ClaireVerti and I were chatting about how to begin to establish culture and relationships w and among students.

We brought up @saravdwerf 's name tents and I thought you came up w a modification to use digitally...is that right?#MTBoS #iteachmath ideas?? pic.twitter.com/3LtCFaoICR

- Nanette Johnson (@Math_m_Addicts) May 21, 2020

The Idea below came out pre-COVID-19, but I loved how they adapted the form. If you do this in Google Classroom - this form may be one you love.

Hey @saravdwerf our department adapted your Name Tents to look like a text message conversation 🙂

Google doc here, for folks on a late semester turnover like us.#iteachmath #MTBoS https://t.co/PhBMg2WGxW pic.twitter.com/GNWI74LYz6

- Idil A. (@Idil_A_) January 30, 2020

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Week 1 Day 1 - Name Tents with Feedback - Sara VanDerWerf

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UPDATE May 2020: In the era of Remote/Distance/eLearning, teachers have stepped up to adapt this activity for use when we are not in our classrooms with our students. If you are interested in their ideas, scroll down to the bottom of this post to see more and get links to what they have created.

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What is considered the “highest level”?

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I use this as warmups as well as exit tickets.

Exit takes longer but we review student answers on the overhead, and students turn and talk to figure out the mistake in the incorrect exit tickets

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Mistakes are more valuable than having a “correct” answer….mistakes are a foundation for learning

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Mistakes are more valuable than having a “correct” answer….mistakes are a foundation for learning

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Be your students loudest cheerleader by making them feel special 

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Be your students loudest cheerleader by making them feel special 

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Questions can help teacher reevaluate their instruction - exit tickets.

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The Coherence Map shows the connections between Common Core State Standards for Mathematics.

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Use logic to solve visual, interactive mathematical puzzles. Create your own puzzles to share with your friends or the SolveMe Community.

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Having student to become comfortable with explaining and justifying their work is essential.

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Having student to become comfortable with explaining and justifying their work is essential.

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Having students work together and collaborating to share their thought process so that it can help those who don't know, and help those who do know reach a higher level of thinking by sharing and teaching.

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Wheel of Names picks the student to answer the question

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https://wheelofnames.com/

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Enter names, spin wheel to pick a random winner. Customize look and feel, save and share wheels.

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It takes a higher level thinking skill to explain to others how to do a skill than to just do it.

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It takes a higher level thinking skill to explain to others how to do a skill than to just do it.

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Let go of your ego and let the student see that you make mistakes.

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On my whiteboard, I keep a running number of all the mistakes I make during the year. When a student finds a mistake that I make, I increase the number by one. I want students to see that teachers make mistakes and it is okay to make mistakes. 

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On my whiteboard, I keep a running number of all the mistakes I make during the year. When a student finds a mistake that I make, I increase the number by one. I want students to see that teachers make mistakes and it is okay to make mistakes. 

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Teacher has to 1st believe that a student can learn math to the highest level before a student will believe it!

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Inside Mathematics is a professional resource for K-12 teachers, coaches, and administrators.

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Does the SBAC reflect learning or does it reflect performing?

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Does the SBAC reflect learning or does it reflect performing?

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Establish classroom norms with the students

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Practice is required to attain fluency. Fluency is required to be memorable and therefore useful. Fluency requires basic skills be at hand, not that you know a lot of things,

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Students need to believe in themselves personally first before believing that they can learn math to the highest level.

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Students need to believe in themselves personally first before believing that they can learn math to the highest level.

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Mistakes should be made by the teacher as well, where the students can see that we make mistakes too.  Students then correct the teacher's mistakes :)

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Mistakes should be made by the teacher as well, where the students can see that we make mistakes too.  Students then correct the teacher's mistakes :)

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Let the students be creative when figuring out the math.  Instill that there is more than one way to solve problems.  

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Let the students be creative when figuring out the math.  Instill that there is more than one way to solve problems.  

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Understanding the concept, no matter how long it takes, is what's important!

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Understanding the concept, no matter how long it takes, is what's important!

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I want to know how you got your answer not what your answer is.