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Number Talks

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Number Talks: Fractions, Decimals and Percentages Book

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Number Talks: Fractions, Decimals and Percentages Book

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Number Talks

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Number Talks

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This is a poster that can be used to help teach and remind students of the number talk hand signals. ...

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Number Talks

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FRIENDS! I am offering my number talk posters for FREE! So come and get it now!:) Please leave your feedback and let me know what you think!

'Let's Talk About Math Posters!' can be used as a bulletin board idea or chart to help your students engage in conversations or share math ideas and strategies.

You may cut eat speech bubble out and display them on your math wall, or near your math area to have your students use them as they have their math talk.

There are 12 posters and 2 responses:

-I agree because...

-I disagree because...

-I can prove it by...

-I know this because...

-I used this strategy...

-I noticed that...

-Another way to solve it is...

-This makes sense...

-I can show you that...

-I am thinking this...

-The fastest way to solve it is...

-I can explain it by...

I have also included 2 response sheets for your children to fill out after a number or math talk.

Happy Math Talk!

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FRIENDS! I am offering my number talk posters for FREE! So come and get it now!:) Please leave your feedback and let me know what you think!'Let's Talk About Math Posters!' can be used as a bulletin board idea or chart to help your students engage in conversations or share math ideas and strategies.

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Implementation Resource

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Welcome friends! Today's guest post was contributed by Shametria L. Routt, The Routty Math Teacher, and it is about implementing effective math talk in the classroom. This post includes tips and strategies to get you started, as well as a variety of resources to use on your journey. Happy reading!

Using mathematical discussions in the classroom is a powerful way to increase our students' critical thinking and communication skills. However, what does effective math talk in the classroom look and sound like? This article explores ways to get your students thinking and communicating mathematically from the very first days of school.

The National Council of Teachers of Mathematics (NCTM) defines math talk as "the ways of representing, thinking, talking, and agreeing and disagreeing that teachers and students use to engage in [mathematical] tasks" (NCTM, 1991). Effective communication about mathematics is essential to help students develop the thinking, self-questioning, and explanation skills needed to master required skills and concepts.

A successful mathematics program emphasizes communicating mathematically frequently in the classroom. In addition to NCTM's standards, most state standards include competencies related to communicating effectively through mathematical language, justifying solutions, and evaluating the mathematical thinking of others.

The picture below illustrates the interaction between the teacher and the students during effective math talk and demonstrates how knowledge is constructed through these interactions and exchanged with others. For a free download of my Looks Like/Sounds Like Poster, click here.

In order for math talk to be successful, students must understand how to collaborate fairly and hold a respectful exchange of ideas. Before implementing math talk in the classroom, brainstorm a list of classroom norms for how community members will participate and behave during the discussion. (See the picture below for an example of some of the norms you may want to include.)

As with any lesson, it is essential to create a plan for using math talk in the classroom. During open strategy sharing, students discuss how they solved a particular problem. The students listen and share their ideas. The teacher probes the students with questions related to how they determined the solution and why they chose a particular solution path. In addition, the teacher highlights a variety of strategies and emphasizes the similarities and differences among them.

Use the following steps to help implement math talk in the classroom:

Before the Discussion

Define your goal: What do you hope to accomplish? Goals for math talk include wanting students to: listen and compare methods used to solve a problem, look for the most efficient way to solve a problem, generate explanations for why a particular solution works, or examine why one solution is correct and why another is not.

Choose a Problem: This depends on your goal. If you want to highlight a variety of strategies that can be used to solve a problem, then choose a problem with multiple solution strategies. If you are examining why one solution is correct over another, then choose a problem where students frequently make missteps in their solution strategy. Use my Back to School Math Problem Solving Pack to get you started! You can find it in my TpT store.

Anticipate Student Responses: In order to create the best discussion opportunities, think about how students may respond to a particular problem, and create a plan to address any misconceptions that may develop. In addition, if there is an obscure solution that you think may be missed, then plant the seed with a student group or be prepared to introduce the strategy yourself. For example, you can say, "When I looked at this problem, I thought that I could solve the problem like this (show the strategy). How does this strategy compare to the others we used today?"

During the Discussion

Monitor Student Responses: During this time observe the interactions of the groups and make notes about their solution strategies. Also, note any observed areas of concern to address at a later time.

Select Students to Present: Based on your observations, determine which solution strategies to highlight that will best help you accomplish your goal. For example, if you want to emphasize a variety of strategies to solve a particular problem, select solutions that vary from one another.

Sequence Student Responses: Order the presentation of the solution strategies in a manner that will allow you to maximize the students' learning experience. For example, beginning with the most widely used strategy and then moving to the more abstract strategies may draw students' attention to new methods. Similarly, beginning with the more concrete strategies will give students the opportunity to move from a more concrete to an abstract understanding.

Connect Student Responses: The most important aspect of using math talk in the classroom is the connections between solutions that you and the students make. In the beginning students will need your support to make these connections. For example, if you sequence the presentations from less sophisticated to more sophisticated, you can have students discuss the similarities and differences between the solutions. You can also discuss efficiency. Which process is more efficient?
The "Open-Ended Questions" chart above has a great list of questions both you and the students can use during math talk to make connections and analyze solution strategies. Find the download for my Open-Ended Questions for Accountable Math Talk in my TpT store.

Use the "Math Talk Moves" poster above to teach students how to make connections and respond to others during math talk. The poster describes moves made by the student. The teacher should teach these moves and encourage their use during discussion. You may even want to have a "Move of the Day/Week" to highlight ways to connect student ideas. Additionally, you may want to include these in the students' math notebooks or tape a copy to their desks to refer to during the discussion. Please note: Several resources describe "Turn and Talk" as a math talk move. Because I chose to focus my poster on student moves, I did not include it; however, it is a useful move to use during math talk so that students have another participant to share ideas with during large class discussions. From that point, they can choose a student move to keep the conversation going or choose one move for a class-wide share-out. To get your own copy of my Math Talk Moves poster, please visit my TpT store.

Participation is key! Sometimes it's hard to get all students to participate because they're afraid to take risks. One of the ways you can get your more reluctant students to take part in the conversation is through the use of hand signals, such as teaching students to use the American Sign Language symbol for Y (see picture below) to indicate that they agree with someone else's thinking. Once reluctant students see that they're not alone, they may be willing to participate more.

After the Discussion

After reviewing the students' solutions and listening to their presentations, use the information that you gathered to determine the next steps. The following activities will help extend and deepen the students' understanding of the intended content and skills.

Look for Areas of Concern: Reviewing the solutions for common errors or misconceptions may provide material for a mini-lesson or content for an additional problem solving task at a later date.

Check for Reasonableness: It is essential that students develop the ability to verify their solutions and check them for reasonableness. After the discussion you can ask each group to develop a method to check their strategy for reasonableness or choose a specific solution and ask students to determine a method to check for reasonableness. Be sure to have students share and compare their strategies.

Justify the Solution: In addition to being able to make sense of a solution, students should be able to explain why a specific solution strategy leads to the correct answer. For this activity have students use pictures, numbers, and words to make sense of the solution and explain why it works.

Look for What Went Wrong: One of the most powerful activities for students is to examine their mistakes. Use one of the solution strategies that did not lead to the correct answer (if available) and explore where the solution went wrong. After determining the misstep, allow students an opportunity to complete the remainder of the solution strategy. If you don't have an incorrect solution strategy to use, create one yourself and say, "What if someone had done (show the strategy)?" Then, allow the students to discuss the error(s).

Implementing and planning regular math talk sessions will support the development of strong communication skills and deepen the students' ability to reason and think critically about the intended math content and skills.

Resources

Books: There are several resources that can provide additional structures and methods for implementing effective math talk in the classroom. Check out the following resources for more insight:

Pinterest Board: There are many great resources for all grade levels on Pinterest. Click here to check out my Math Talk Pinterest board.

* Minds in Bloom, Inc. is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon properties including, but not limited to, amazon.com, endless.com, myhabit.com, smallparts.com, or amazonwireless.com.

Shametria is a newlywed and has been a Texas educator for 13 years. She's currently a Teacher Mentor for first- and second-year teachers and is working toward a Doctoral degree in Mathematics Education. She is also a blogger (emerging, anyway) and teacher-author for all things math! Check out her Routty Math Teacher blog and Teachers Pay Teachers store for some additional teaching tidbits and freebies!

Credits

Books and Web Resources

Kazemi, E. & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Stenhouse Publishers: Portland, Maine.

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. Retrieved from http://www.nctm.org/standards/content.aspx?id=26628

Smith, M. S. & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. Corwin: Reston, Virginia.

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Getting Started with Effective Math Talk in the Classroom

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Welcome friends! Today's guest post was contributed by Shametria L. Routt, The Routty Math Teacher, and it is about implementing effective math talk in the classroom. This post includes tips and strategies to get you started, as well as a variety of resources to use on your journey. Happy reading!

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How to Engage Students in Mathematical Discourse

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How to Engage Students in Mathematical Discourse

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The importance of engaging students in meaningful mathematical discussion has long been identified as an essential component of students' mathematics learning.

When students share and exchange their ideas, both they and their teachers benefit.
Dr. Gladis Kersaint
Understanding the Importance of Mathematical Discourse

Talking about mathematical concepts allows students to reflect on their own understanding while making sense of and critiquing the ideas of others. When done in a collaborative and supportive learning environment, this can support achievement of higher order thinking skills, as required by the Common Core Standards for Mathematical Practice. Students can make conjectures, link prior knowledge to current understanding, reason about mathematics, refine and amend their approaches, and take ownership of their mathematical knowledge.

Students benefit greatly from learning to use the tools of mathematical discourse-including words, symbols, diagrams, physical models, and technology-to present and defend their ideas. Imparting these new skills on students allows teachers to access, monitor, and evaluate students' mathematical understanding and development.

Mathematical Discourse in Action

One approach to giving students the information needed for a mathematics lesson involves the teacher simply telling the students what they need to know. Far more productive, however, is more a thoughtful approach to student engagement that encourage a productive dialogue, as seen in the example below. As educators, we need to structure lessons to encourage student interaction, address gaps in student understanding, and help students express mathematical concepts more precisely. Providing opportunity for conversation does just that.

Does this look like a classroom dialogue you've seen before? To further your understanding of the importance of facilitating mathematical discourse, ask yourself:

How did these students benefit by sharing what they knew as part of the mathematics discussion?

Why did the teacher allow students to evaluate the correctness of Julie's answer?

Why did the teacher ask another student to restate what James said?

Establishing a Discourse-Rich Mathematics Learning Community

To engage students in productive mathematics discussions, it is important to establish a learning environment that welcomes student involvement. The first step is setting the expectation that every student will contribute to the discourse community.

Students must be encouraged to use their problem-solving, reasoning,and communication skills to make conjectures, explore their own ideas and approaches, and find solutions to routine and non-routine mathematics problems.

In particular, the five process standards-problem solving, reasoning and proof, communication, connections, and representation-can be seen in action in a discourse-rich mathematics community as students interact, question one another and convey their understanding. During this dialogue, teachers can recognize errors in context and reinforce that they are natural occurrences that enhance learning.

What does a classroom rich with mathematical discourse look like? Walk into one and you'll likely see:

Students and teachers acknowledging and discussing errors and the reasons behind them to help students build greater understanding.

Students questioning each other using mathematics arguments to establish the correctness of solutions.

Students reaching and justifying conclusions based on their own mathematics knowledge without relying on the authority of teachers.

Students engaging in "productive struggle" with appropriate scaffolds for support.

Students encouraged to use a variety of approaches to convey their knowledge and solution strategies, including oral presentations; written explanations; and physical, graphical, pictorial, or symbolic representations.

Understanding Student and Teacher Roles in Mathematical Discourse

Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction. The tasks they use, the ways in which they organize the classroom, and the behaviors they model communicate expectations for classroom norms, including the ways students are expected to engage in classroom discussions.

Depending on prior experiences, students might find these new expectations for engagement uncomfortable and may not be ready to plunge into mathematical dialogue feet first. Teachers must ease the transition to a dialogue-rich mathematics classroom and prepare students to engage in such discussions. It is also important to carefully consider the best ways to coordinate student interaction in pairs, small groups, or whole-class interactions to ease transitions and maximize learning.

To support students, teachers must help students create avision for expected behaviors and actions, prepare them for their roles by modeling or role-playing, and reinforce these behaviors consistently. Teachers need to monitor progress as students engage in mathematics discussions, supporting them as their mathematical knowledge grows and they become more skilled at expressing ideas coherently and using vocabulary, syntax, and semantics precisely.

Teachers should observe, listen to and monitor students to support instructional decision-making. Determining what questions to ask, which students to call on, when to intervene and when to extend student thinking provides opportunities to understand student thinking, monitor growth and assess knowledge. A discourse-rich classroom enables teachers to gain insights not only about what students know, but also about the approaches they use, how-and how well-they understand the ideas, and the ways they present their knowledge.

In addition to content knowledge, mathematical discourse allows teachers to monitor students' dispositions and gauge their developing confidence, interest, and perseverance. Teachers can use this information to determine areas of confusion or frustration in order to decide when an intervention might be needed. They also examine understandings and misconceptions revealed during classroom discussions and adjust lesson plans accordingly.

Asking the right questions can help support instructional decision making and direct student focus. Some examples are below:

Engaging Every Student in Mathematical Discourse

All students are mathematics language learners, regardless of their level of English language proficiency, and discourse allows ALL students to develop mathematical language.

While it is important to build scaffolds to support students who are learning English and mathematics at the same time, it is essential to recognize that mathematics is a technical language that all students must learn. Students who are English speakers also require support as they learn the language of mathematics.

As outlined in the Standards for Mathematical Practice, students should become fluent in mathematical language, including vocabulary, symbolic representations, syntax, semantics, and linguistic features. In addition, they must have ample opportunities to use the language of mathematics as they engage in various forms of communication. Discourse allows students to practice precision in multiple areas, including:

1.Vocabulary

English words with a different meaning in mathematics, such as "negative," "table," or "rational."

Specialized terms, such as "hypotenuse" or "trapezoid."

Terms with multiple meanings in mathematics, such as "median" or "base."

2. Symbols

Ways to read and interpret symbolic representations. For example, "a × b" can be expressed as "a times b," "the product of a and b," or "multiply a and b."

3. Syntax

Understanding the rules that govern the structure of sentences. For example, "A number y is 4 more than a number x" is translated symbolically to "y=x+4."

4. Semantics

The process of making meaning from language.

The same mathematics word may be interpreted differently depending on the context. For example, the median of a set of numbers versus the median of a triangle.

Teachers support mathematical language development by asking key questions and encouraging students to ask for clarity. By doing this, teachers motivate and encourage students and facilitate productive discussion, fostering a supportive classroom culture that maximizes learning.
This blog is part of a three post series on the importance of mathematical discourse from Curriculum Associates Dr. Gladis Kersaint is the Dean of the Neag School of Education at the University of Connecticut and an author of the Ready® Mathematics and Ready® Classroom Mathematics programs from Curriculum Associates. Stay in-the-know with all things EdTech and innovations in learning by signing up to receive the weekly Smart Update. , a Getting Smart Advocacy Partner, and Dr. Gladis Kersaint, the author of the recently published whitepaper Orchestrating Mathematical Discourse to Enhance Student Learning. Download your free copy here.
For more on Curriculum Associates, check out:

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Talking Math: How to Engage Students in Mathematical Discourse

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By Gladis Kersaint - Engaging students in meaningful mathematical discourse is an essential component of students' mathematics learning.

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Implementation Resource

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Update 2022: For a recent article on how to talk about math, click here.
Think about the questions that you ask in your math classroom. Can they be answered with a simple "yes" or "no," or do they open a door for students to really share their knowledge in a way that highlights their true understanding and uncovers their misunderstandings? Asking better questions can open new doors for students, helping to promote mathematical thinking and encouraging classroom discourse. Such questions help students:

Work together to make sense of mathematics.

Rely more on themselves to determine whether something is mathematically correct.

Learn to reason mathematically.

Evaluate their own processes and engage in productive peer interaction.

Discover and seek help with problems in their comprehension.

Learn to conjecture, invent and solve problems.

Learn to connect mathematics, its ideas and its applications.

Focus on the mathematical skills embedded within activities.

Below are 100 questions from mathematics expert Dr. Gladis Kersaint to help you address these core areas and promote mathematical thinking and discourse in the classroom. Want these questions visible in your classroom? Curriculum Associates has released an infographic that you can print and have at your desk or in your class for quick access! Here's a preview:

For more, please download Dr. Kersaint's new whitepaper:Orchestrating Mathematical Discourse to Enhance Student Learning.
Dr. Gladis Kersaint
Help students work together to make sense of mathematics

1. What strategy did you use?

2. Do you agree?

3. Do you disagree?

4. Would you ask the rest of the class that question?

5. Could you share your method with the class?

6. What part of what he said do you understand?

7. Would someone like to share ___?

8. Can you convince the rest of us that that makes sense?

9. What do others think about what [student] said?

10. Can someone retell or restate [student]'s explanation?

11. Did you work together? In what way?

12. Would anyone like to add to this?

13. Have you discussed this with your group? With others?

14. Did anyone get a different answer?

15. Where would you go for help?

16. Did everybody get a fair chance to talk, to use the manipulatives, or to be recorded?

17. How could you help another student without telling the answer?

18. How would you explain ___ to someone who missed class today?

Refer questions raised by students back to the class.

Help students rely more on themselves to determine whether something is mathematically correct

1. Is this a reasonable answer?

2. Does that make sense?

3. Why do you think that? Why is that true?

4. Can you draw a picture or make a model to show that?

5. How did you reach that conclusion?

6. Does anyone want to revise his or her answer?

7. How were you sure your answer was right?

Help students learn to reason mathematically

1. How did you begin to think about this problem?

2. What is another way you could solve this problem?

3. How could you prove that?

4. Can you explain how your answer is different from or the same as [student]'s?

5. Let's see if we can break it down. What would the parts be?

6. Can you explain this part more specifically?

7. Does that always work?

8. Is that true for all cases?

9. How did you organize your information? Your thinking?

Help students evaluate their own processes and engage in productive peer interaction

1. What do you need to do next?

2. What have you accomplished?

3. What are your strengths and weaknesses?

4. Was your group participation appropriate and helpful?

Help students with problem comprehension

1. What is this problem about? What can you tell me about it?

2. Do you need to define or set limits for the problem?

3. How would you interpret that?

4. Would you please reword that in simpler terms?

5. Is there something that can be eliminated or that is missing?

6. Would you please explain that in your own words?

7. What assumptions do you have to make?

8. What do you know about this part?

9. Which words were most important? Why?

Help students learn to conjecture, invent and solve problems

1. What would happen if ___? What if not?

2. Do you see a pattern?

3. What are some possibilities here?

4. Where could you find the information you need?

5. How would you check your steps or your answer?

6. What did not work?

7. How is your solution method the same as or different from [student]'s?

8. Other than retracing your steps, how can you determine if your answers are appropriate?

9. What decision do you think he or she should make?

10. How did you organize the information? Do you have a record?

11. How could you solve this using (tables, trees, lists, diagrams, etc.)?

12. What have you tried? What steps did you take?

13. How would it look if you used these materials?

14. How would you draw a diagram or make a sketch to solve the problem?

15. Is there another possible answer? If so, explain.

16. How would you research that?

17. Is there anything you've overlooked?

18. How did you think about the problem?

19. What was your estimate or prediction?

20. How confident are you in your answer?

21. What else would you like to know?

22. What do you think comes next?

23. Is the solution reasonable, considering the context?

24. Did you have a system? Explain it.

25. Did you have a strategy? Explain it.

26. Did you have a design? Explain it.

Help students learn to connect mathematics, its ideas and its application

1. What is the relationship of this to that?

2. Have we ever solved a problem like this before?

3. What uses of mathematics did you find in the newspaper last night?

4. What is the same?

5. What is different?

6. Did you use skills or build on concepts that were not necessarily mathematical?

7. Which skills or concepts did you use?

8. What ideas have we explored before that were useful in solving this problem?

9. Is there a pattern?

10. Where else would this strategy be useful?

11. How does this relate to ___?

12. Is there a general rule?

13. Is there a real-life situation where this could be used?

14. How would your method work with other problems?

15. What other problem does this seem to lead to?

Help students persevere

1. Have you tried making a guess?

2. What else have you tried?

3. Would another recording method work as well or better?

4. Is there another way to (draw, explain, say) that?

5. Give me another related problem. Is there an easier problem?

6. How would you explain what you know right now?

Help students focus on the mathematics from activities

1. What was one thing you learned (or two, or more)?

2. Where would this problem fit on our mathematics chart?

3. How many kinds of mathematics were used in this investigation?

4. What were the mathematical ideas in this problem?

5. What is the mathematically different about these two situations?

6. What are the variables in this problem? What stays constant?

Facilitating student engagement in mathematical discourse begins with the decisions teachers make when they plan classroom instruction. In the next and final blog in this series, we will dive into the specific strategies that teachers can use to foster meaningful conversations about what students are thinking, doing and learning.

This blog is part of a three-post series on the importance of mathematical discourse from Curriculum Associates and Dr. Gladis Kersaint, the author of the recently published whitepaper Orchestrating Mathematical Discourse to Enhance Student Learning. Download your free copy .
For more on mathematical discourse and Curriculum Associates, check out:
Dr. Gladis Kersaint is a Professor of Mathematics Education at the University of Connecticut. Stay in-the-know with all things EdTech and innovations in learning by signing up to receive the weekly Smart Update. This post includes mentions of a Getting Smart partner. For a full list of partners, affiliate organizations and all other disclosures please see our Partner page

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Talking Math: 100 Questions That Help Promote Mathematical Discourse

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Update 2022: For a recent article on how to talk about math, click here. Think about the questions that you ask in your math classroom. Can they be answered with a simple "yes" or "no," or do they open a door for students to really share their knowledge in a way that highlights their true understanding and uncovers their misunderstandings?

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Math Warm-Up

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Math Warm-Up

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Teaching Tools | Resources for Teachers from Scholastic

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Developing a Classroom Where Students Feel Safe to Talk

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Developing a Classroom Where Students Feel Safe to Talk

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Developing a Classroom Community Where Students Feel Safe to Talk

Tessa Kaplan and Rozlynn Dance

Mathematical discourse is essential for deep mathematical learning. We often spend a lot of time teaching our students how to talk to one another with sentence stems, practiced conversations, and teacher talk moves. However, before we can even teach students how to talk, we must make sure that our classroom is a place where students feel comfortable talking.

When students justify their thinking aloud or explain a strategy they have used, they are putting their ideas on display for their classmates. This can be intimidating for many of our students. Their ideas may be different from their classmates, they may have made a mistake, or they may have tried a unique strategy that no one has used before.

As teachers, we must set up a classroom environment where students feel safe enough and brave enough to share their ideas. They should be able to trust that their classmates and their teacher will treat their ideas with respect and curiosity.

There are a few things that can be done at the beginning of the school year and throughout the year to make a classroom a safe community where students feel comfortable sharing their thinking, having mathematical arguments, and questioning ideas.

1. Teach students to respect others' ideas, especially when they are different from their own. Respecting others' ideas is something that we encourage in our classrooms from day one and work hard to maintain throughout the year. We teach our students to treat everyone's ideas with respect, even if they may disagree. We reinforce the idea that respectful disagreements are not something negative, but are rather an opportunity to help us think deeper about a problem and learn more about the math. We use respectful sentence and question stems, such as "Can you explain why you ___________?" or "I respectfully disagree because ____________" to promote this discourse. We also teach respectful signals that show that they are thinking something different-for example, tapping a pointer finger on the forehead to indicate, "I'm thinking something different"-rather than a negative reply like, "You're wrong!"

Most important, our students know that we have multiple teachers in our classroom. Every student at some point becomes a teacher when they share their thinking or question their classmates. Students learn to ask questions when they disagree with something or when something doesn't make sense. They know that we (the teachers) are not the only ones that have valuable knowledge to share, and that we all learn from each other.

2. Celebrate mistakes and encourage risk taking. Many students come to us afraid of making mistakes or getting the answer wrong. We must help our students believe that their deepest learning can stem from their mistakes. We do this by celebrating "great mistakes" daily. We ask students who have made mistakes to share their thinking with the class and then celebrate them for doing so. We talk through the great thinking behind the mistakes and then thank the students for letting us learn from their mistakes.

When students are feeling unsure about a strategy or way of thinking, we encourage them to be brave mathematicians. If they feel comfortable making mistakes, then they become more confident in their ability to try new strategies because they know that they won't be looked at negatively for trying something new or difficult and struggling with it. We tell our students that if we've given them a math problem that is easy, then we haven't done our job as teachers! We apologize for that easy problem and promise our students that we will challenge them with something more difficult so that their brains can grow stronger.

3. Value multiple strategies and focus less on the answer. Mathematics is a subject that is creative and unique. Yet the way we traditionally teach math-through rote practice and memorization-keeps students from seeing the beauty of the subject. We teach math through problem solving, where students must find their own way to an answer using different strategies and learning to justify their reasoning. In our classroom communities, we focus more on how students got their answers and less on what the answer is. In one given lesson, we may have three or four different students share completely different ways of getting the same answer. We focus on helping students develop the skills they need to justify their answers and explain their thinking. We encourage students to compare strategies, make connections between representations, and celebrate the different ways our brains see mathematical problems.

4. Question everything. At the beginning of the year, we often see students erasing their papers the minute we ask them a question about their work. Teachers know that we must question our students' thinking to deepen their understanding; however, many teachers spend a lot of time questioning students who get the wrong answer and simply pass over or give a "Good job!" to the students who get the answer right. When we do this, we are training our students to believe that a question means they got the wrong answer.

In a discourse-rich community, students regularly justify their thinking and explain their ideas to others, regardless of whether they got the right answers. In our classrooms, we strive to question all thinking. When students get the right answer, we push them to "prove it." We want our students to be confident in their reasoning, and by pushing them with questions, they learn to justify their thinking and grow their confidence as mathematicians. When students become more used to our questions, they begin to answer them before they are asked.

Classrooms where students feel safe to make mistakes, share their thinking, and ask questions set the stage for productive mathematical discourse. Although it can be easy to want to dive into teaching students how to talk to one another, it is important to remember that there is work that must be done to build a trusting community before deep mathematical conversations can happen.

Tessa Kaplan is a K-6 instructional coach in Shoreline, Wash. Rozlynn Dance is a 1st grade teacher in Federal Way, Wash. Their recent book is Thinking Together: 9 Beliefs for Building a Mathematical Community (Heinemann, 2018).

ASCD Express, Vol. 13, No. 22. Copyright 2018 by ASCD. All rights reserved. Visit www.ascd.org/ascdexpress.

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Developing a Classroom Community Where Students Feel Safe to Talk

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Developing a Classroom Community Where Students Feel Safe to Talk Tessa Kaplan and Rozlynn Dance Mathematical discourse is essential for deep mathematical learning. We often spend a lot of time teaching our students how to talk to one another with sentence stems, practiced conversations, and teacher talk moves.

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Problem Solving

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

This post includes 50 (fifty!) free, downloadable PowerPoint math lessons!

Watch the video, download some (or all) of the lessons, and experience what happens when you unleash this resource in your classroom!

I've been excited to click the Publish button on this post for several weeks! It's time!
UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

Splat Through 10
How many dots are under the Splat?

Splat Through 20
How many dots are under the Splat?

Multiple Splats
(Note: Splats that are the same color must cover the same number.)
Splat 3.1 - multiple splats Splat 3.2 - multiple splats Splat 3.3 - multiple splats Splat 3.4 - multiple splats Splat 3.5 - multiple splats
Instant Multiple Splat
(Note: An additional feature of this level is the opportunity to ask, "What could the total be?")

Splat 4.1 - Instant Multiple Splats Splat 4.2 - Instant Multiple Splats Splat 4.3 - Instant Multiple Splats Splat 4.4 - Instant Multiple Splats Splat 4.5 - Instant Multiple Splats
2-Color Splat
(Splats of different colors must have different values.)

Splat 5.1 2-color Splat Splat 5.2 2-color Splat Splat 5.3 2-color Splat Splat 5.4 2-color Splat Splat 5.5 2-color Splat Splat 6.2 Instant 2-color Splat Splat 6.3 Instant 2-color Splat Splat 6.4 Instant 2-color Splat Splat 6.5 Instant 2-color Splat
Instant 2-Variable Splat
(Splats of different colors must have different values. Splats of the same color must have the same value.)
Splat 7.1 Instant 2-variable Splat Splat 7.2 Instant 2-variable Splat Splat 7.3 Instant 2-variable Splat Splat 7.4 Instant 2-variable Splat Splat 7.5 Instant 2-variable Splat
Number Splat
(Note: Only the numbers circled on the screen may be used.)
Splat 8.1 - Number Splat Splat 8.2 - Number Splat Splat 8.3 - Number Splat Splat 8.4 - Number Splat Splat 8.5 - Number Splat Splat 9.1 - Instant Number Splat Splat 9.2 - Instant Number Splat Splat 9.3 - Instant Number Splat Splat 9.4 - Instant Number Splat Splat 9.5 - Instant Number Splat
Instant Number Splat with 2 Variables
(Note: Only the numbers circled on the screen may be used, and Splats of different colors must have different values.)
Splat 10.1 - Instant 2-Variable Number Splat Splat 10.2 - Instant 2-Variable Number Splat Splat 10.3 - Instant 2-Variable Number Splat Splat 10.4 - Instant 2-Variable Number Splat Splat 10.5 - Instant 2-Variable Number Splat
NOTE: I wrote each of these lessons using PowerPoint, so I recommend playing them in PowerPoint. If you do not have PowerPoint, you may want to download the PowerPoint viewer so that you can play the lessons.

UPDATE: The Fraction Splat! Series (with 20 more downloadable lessons) is now available!
Other Posts and Resources Which May Be of Interest Tiled Area Questions The Maze Hundreds Chart
Introducing Cube Connectors
Provide Massive Space to Notice
Primary Tile Questions
3 Powerful Tile Strategies (and 40 new downloadable pages)
Please take a moment to subscribe to the blog so you'll be notified each time new resources are posted!

I would treasure hearing about your experiences using Splat! to promote number sense in your classroom!

All my best,
Steve

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Splat! - Steve Wyborney's Blog: I'm on a Learning Mission.

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Welcome to Splat! You are only moments away from a VERY POWERFUL, highly interactive number sense strategy that can be used at any grade level!

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Math Warm-Up

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A garden snail's average speed is about ​0.029 mi/h. The North American X-15's top speed is about 4,520 mi/h. How much time would it take for each to travel across the United States, a...

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Problem Solving

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search

Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Math Warm-Up

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Same But Different is a powerful routine for use in math classrooms. The images can be used for teaching a way of thinking: grayscale thinking, categorical thinking; helping students to build a network of ideas and an approach for learning and thinking about mathematics.

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Problem Solving

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"I always learn something new, and leaves me wanting to learn more." - Sarah Hempel, HCISD "I really enjoyed the day, I usually spend PDs grading papers - and I didn't grade a single one!" - Molly O'Brien, NYC DOE

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Math Warm-Up

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Number Talks

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Math Warm-Up

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Mashup Math activities make your math lessons fun and engaging for students

K-8 math activities designed to be highly engaging for students.

We inspire kids to learn math in a way that isentertaining and fun.

Our unique approach boosts academic achievement and participation.

Over 100,000 math teachers rely on Mashup Math resources to supplement their lessons.

Standards-aligned math resources for grades K-8+

Gain On-Demand Access to All of our K-8 Math Puzzles, Worksheets and Activities

Inspire Your Students to Learn Math in a Fun and Engaging Way

Join our mailing list to get free resources in your inbox every week

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Math Education Teacher Resources Common Core Cool Video Lesson Free Worksheets Elementary Middle High School Homeschool Algebra Geometry Lessons Help Tutor Homework

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Math Warm-Up

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Math Warm-Up

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Math Warm-Up

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Problem Solving

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Problem Solving

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Design - Graphics, University of Waterloo

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CEMC - Web Resources - Problem of the Week - University of Waterloo

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The CEMC has become Canada’s largest and most recognized outreach organization for promoting and creating activities and materials in mathematics and computer science.

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Math Warm-Up

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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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Math Warm-Ups

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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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Problem Solving

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Math Warm-Up

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Problem Solving

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Open Middle - Challenging Math Problems Worth Solving

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Open Middle - Challenging Math Problems Worth Solving

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Problem Solving

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Open Middle - Challenging math problems worth solving

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Open Middle offers interactive math problems designed to foster critical thinking. Explore unique challenges that boost problem-solving skills and creativity.

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Number Talks

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Problem Solving

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search

Enriching mathematics for all learners

A free-to-use collection of mathematics activities, lessons and problems designed to nurture curious, resourceful and confident learners of mathematics. Produced by The University of Cambridge.

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The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

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Problem Solving

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Problem Solving

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Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 For a free poster of MathPickle's ideas on elementary math education go

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Problem Solving

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Problem Solving

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Inquiry Maths is a model of learning that encourages students to regulate their own activity while exploring a prompt (an equation, statement or diagram). Inquiries involve the class in questioning, conjecturing, generalising and proving and, when required, in listening to an explanation. In

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Problem Solving

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Puzzles - EMMAths: Learning and Teaching

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Problem Solving

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Problem Solving

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achievethecore.org's digital tools and resources for teachers have been made possible by contributions from teachers across the country as well as through generous support from the Leona M. and Harry B. Helmsley Charitable Trust and the GE Foundation.

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Math Warm-Up

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ESTIMATION 180 is a place for both students and teachers to enjoy making sense of math and develop their number sense together.

Pick from over 200 visual estimation tasks that invite all your students to be part of rich math conversations and learning.

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How do I get started? 1 USE THE FREE MATH LESSONS Estimation 180 Tasks 3-Act Tasks 2 SUBSCRIBE Email Newsletter Podcast

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Number Talks

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Math Warm-Up

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Provide your students with a powerful teaching tool. Quick Draw is an excellent lesson opener to get student's attention and encourage spatial reasoning. Quick Draw improves mathematical learning and helps establish a classroom atmosphere conducive to real learning. Quick Draw activities are effe...

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Math Warm-Up

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Same But Different is a powerful routine for use in math classrooms. The images can be used for teaching a way of thinking: grayscale thinking, categorical thinking; helping students to build a network of ideas and an approach for learning and thinking about mathematics.

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Math Warm-Up

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Math Warm-Up

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Math Warm-Up

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Are the following statements always true, sometimes true or never true?
How do you know?

Can you find examples or counter-examples for each one?

For the 'sometimes' cards can you explain when they are true? Or rewrite them so that they are always true or never true?

What about these more complex statements?

You could cut out the cards from this sheet ( word, pdf) and arrange them in this grid.

Alternatively, you may like to try out your ideas using the interactivities below:

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Are the following statements always true, sometimes true or never true? How do you know? Can you find examples or counter-examples for each one? For the 'sometimes' cards can you explain when they are true? Or rewrite them so that they are always true or never true? What about these more complex statements?

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Math Warm-Up

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.