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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 and techniques for implementing cooperative learning in your class

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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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Whenever I make a mistake I address it and remind students that mistakes are how we learn.

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In class examples. If a student makes a mistakes and a students learns from it turn it into an example and have a debrief.

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I always give students an opportunity to share the mistakes they made and what they learned from it. 

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I always give students an opportunity to share the mistakes they made and what they learned from it. 

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Asking "what questions do you have" versus "does anyone have any questions"

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Instead of spending class time completing a worksheet, students are given one or two problems tops to complete.  The problem(s) should be complex and have multi-steps.

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Instead of spending class time completing a worksheet, students are given one or two problems tops to complete.  The problem(s) should be complex and have multi-steps.

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Cathy Humphreys Teaching a Number Talk - YouCubed

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Cathy Humphreys teaches a number talk to elementary teachers in Stanford's STEP program.

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https://tangmath.com/

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Tang Math is a game changer. We focus on conceptual understanding, provide powerful, user-friendly, teaching tools, offer unparalleled support to teachers and administrators, and challenge students with creative and engaging materials. Tang Math takes the teaching and learning of math to a whole new level!

We have spent over 15 years creating digital math games, card games, board games and flashcards. Many of our most popular games - Ten Frame Mania, Kakooma, Numtanga, Numskill, How Much How Many, Expresso, Math Limbo, and Minus Mania - are licensed by major textbook programs and used by schools around the world.

Looking for an effective way to help your students develop their reasoning and computation skills? Tangy Tuesday and Wordy Wednesday puzzles are part of daily practice in many high-performing district in the U.S. and Canada. We offer 20, cleverly-designed, standards-based puzzles each week for 40 weeks.

We invite teachers and students to join us 2-3 times each month for Greg's virtual student lessons. Experience firsthand how our teaching tools make sense of key concepts and strategies by using a thoughtful progression of concrete, pictorial, and abstract models. Join us live or during your math block with our digital recordings.

Do your students feel overwhelmed by all the strategies they are supposed to learn? Do you feel overwhelmed by all the strategies you are told to teach? Then join us for a more sensible and systematic approach to instruction. Our theme for this school year is "Streamlined and Strategic." We have more student-tested, teaching methods to share than ever before!

Looking to reduce screen time and encourage more student-to-student interaction? We are, too! Our printed card games, board games, and flashcards target key skills and extend learning in every grade level. Together with our digital resources, they work hand-in-hand with our curriculum and provide the practice kids need.

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Tang Math is a game changer. We focus on conceptual understanding, provide powerful, user-friendly, teaching tools, offer unparalleled support to teachers and administrators, and challenge students with creative and engaging materials. Tang Math takes the teaching and learning of math to a whole new level!

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Students come up with creative ways of making sense of math on their own. Then they own the math and do better remembering it.
https://mathmedic.com/

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Free Lessons. By Math Teachers, For Math Teachers. Designed and tested with real students at East Kentwood High School, the most diverse public high school in Michigan.

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Mastery Learning option to encourage students to complete an activity as many times as they need to, to earn a 100%. Students are given as many attempts as they want to complete a FA. The questions from the FA are then used to create the summative assessment. If students know the FA questions they are ready and can do well on FA. Then we can use the FA to create other activities. They can do the FA at home, anytime!

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Teach students how to question.

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Allow students to have time to work independently to solve problem(s).  Students then share work with small group or classroom.

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Allow students to have time to work independently to solve problem(s).  Students then share work with small group or classroom.

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Differentiating instruction and providing those various resources, materials, and models helps students build connections, comprehension and ultimately helps grow.

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Differentiating Instruction: It’s Not as Hard as You Think

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Have the students describe how a wrong answer was calculated by a student.   Discuss the incorrect method and compare to the possible correct methods.

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Talking about how our learning targets relate to their lives.

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Give students the opportunity to fix and learn from their mistakes on tests. This can be done independently or collaboratively.

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Sentence frames

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Allowing all students to have a set at the table.  Students are able to learn from one another when students are allowed to hear how students solved math problems.

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Allowing all students to have a set at the table.  Students are able to learn from one another when students are allowed to hear how students solved math problems.

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In dual language students are teamed and encouraged to discuss their math thinking. Students are always given time to discuss and share. This helps form the framework to "talk math".

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It's important to recognize that not only students make mistakes but so do adults. Letting students know and creating an atmosphere where students can point out your mistakes is important to help them realize that mistakes are okay and are a growing opportunity.  

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It's important to recognize that not only students make mistakes but so do adults. Letting students know and creating an atmosphere where students can point out your mistakes is important to help them realize that mistakes are okay and are a growing opportunity.  

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Idea: have students work on high-level problems that are "beyond" their capabilities regularly and reward their efforts TOWARDS the solution

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Idea: have students work on high-level problems that are "beyond" their capabilities regularly and reward their efforts TOWARDS the solution

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Have students reinforce their learning/knowledge of a math concept by having them be the teacher and explaining the steps to solve.

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I love how the questions/answers she collected were anonymous. Also pointing out the positive.

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Every week students in groups explore different hands on activities to make meaning of math and create math.

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I have my students "Conference" in their groups to compare their homework.  I want them to find their mistakes without me showing them.  They seem to learn better from each other.

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This is a task that combines art, mathematics and design. Students are asked to see and design optical illusions, think about the mathematics inside them and pose mathematical questions for […]

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The importance of understanding how to reteach a specific problem is by modeling using a students example

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The importance of understanding how to reteach a specific problem is by modeling using a students example

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We did this last year for several units. Students complete a task, then use exemplars to place on a rubric. They compare their own work to the learning progression and rubric and see what they can do to move to the next level.

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My team and I have chunked/ moved parts of modules. I think it will be beneficial to the students as the lessons will fit better and give us more time to on a standard rather than jumping around.

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https://www.khanacademy.org/map-accelerator

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If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Sometimes students are scared to ask questions during class. Allow students to ask questions on a sticky note or create a google form that they can complete on their own. 

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Sometimes students are scared to ask questions during class. Allow students to ask questions on a sticky note or create a google form that they can complete on their own. 

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speaking and listening is for all students, using sentence stems for students to retain the strategy but also to develop their language in math is essential, talk math is an amazing way  

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speaking and listening is for all students, using sentence stems for students to retain the strategy but also to develop their language in math is essential, talk math is an amazing way  

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Great resource from Jo Boaler.

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Choose your own maths adventure with our interactive tools that allow you to build a custom playlist of inspirational activities!

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https://www.youtube.com/watch?v=EgjCLhoI9Mk

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Multiplication Mash Up - A Fun Way to Learn Your Multiplication Facts!

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I do a lot of "I do, we do, you do."
I teach and model, then students work together to complete work, then students work independently.

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Mistakes are proof that you are learning! 

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Mistakes are proof that you are learning! 

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Anchor tasks.  Exploration, hands on, share out

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Anchor tasks.  Exploration, hands on, share out

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When a mistake is made or seen students use the frame "I disagree because___" and explain that is the error in the math.

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Students have a 5 minute class number talk at the beginning or end of class. There doesn't necessarily need to be a definite, correct answer. However, students must prove their answer. Open discussions encouraged. Create norms for how students should agree or disagree.

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Create a PowerPoint with all source of Math questions, from simple ones like addition or multiplication, to more complicate ones like story problems, picture problems, etc.  Students have to solve them individually and show their answer in their little board.  They earn points, some answers are worth more than one point. Later, they can cash with treats.
It was suggested it can be done also with small groups of students. In that case, I think it should be a little more elaborated problems.

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Students write in a journal explaining concept as if writing to an absent student

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We need to make sure that we teach students that learning happens through making mistakes

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Khan Academy
Moby Max
Xtra Math

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Rich tasks like Star Battle help students to not have small successes but allow for mistakes to learn from and that they can do it.

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Develop questions that are engaging and relevant to your students. Get something they are excited about and turn it into a math problem.

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Relating math to real world situations. Examples: Fractions with pizza

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cross content units.
discuss with other teachers ways to do the same content at the same time.

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allows students to give any answer and then ask any question about the picture.

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Practice makes progress. Mistakes make progress as well!

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Don't grade math assignments on correctness, grade on attempt to do. Save grading correctness for summative assessment.

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Don't grade math assignments on correctness, grade on attempt to do. Save grading correctness for summative assessment.

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Give students a chance to make mistakes first before grading anything! 

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Give students a chance to make mistakes first before grading anything! 

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Mistakes should be celebrated and a natural part of the classroom.

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Mistakes should be celebrated and a natural part of the classroom.

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Opportunities show improvement (retake test etc...).

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Opportunities show improvement (retake test etc...).

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Inquiry based learning and Low floor-high ceiling tasks

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Inquiry based learning and Low floor-high ceiling tasks