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The Splits fluency game from Dr. J Bay-Williams's book Figuring Out Fluency K-8

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Counting Collections Overview is a resource that provides a set of activities designed for teacher educators to begin to engage participants in the activity of Counting Collections. They have been developed to provide support for connecting the content of counting, children's thinking in counting, and pedagogy in classroom practice.

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When do students practice multiplication that's not written as AxB? (for the purpose of automaticity)

When/how is multiplicative reasoning fostered?

When do multiplication strategies become automatized?

When do number strategies become number knowledge?

My answer to all 4 questions....I use multiplication subitizing cards with my daughter whose in 2nd grade so I figured I'd videotape and share.

Download the Resource

My takeaways:

It's easy to identify which facts she's comfortable with and has automatized.

At 1:15- she demonstrates how she used multiplicative thinking for 6×6.

At 2:00- she could use her understanding of the commutative property for multiplication to build fluency. She was quickly is able to recognize that 7×5=35 at , but it took some time to figure out 5×7. She owns this strategy for addition so I'm waiting for it to click with multiplication....no rush:-)

At 2:20- I missed a fact when she was wrong (doh!)

Five minutes spent purposefully building fluency and I gained so much information about my daughter. The great thing is that it works for every 8 year old...even the ones in your school.

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Multiplication Subitizing Cards I've asked myself the following questions: When do students practice multiplication that's not written as AxB? (for the purpose of automaticity) When/...

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Counting Routines, Number talks, etc.

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flynneducation.com – Helping educators and school districts enhance the teaching and learning of mathematics for all students.

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Teach the Math Practices to all students, students with learning disabilities and English language learners. Instructional Routines are the key to mathematical reasoning for all students.

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Credit: Pam Harris

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These problems are different than typical multiple-choice problems, because the exact answer is NOT one of the choices. The goal is for students to choose an answer that is as close to the exact answer as possible. Because the exact answer is not listed, using a series of memorized series of steps is not particularly productive.

The power of using these problems comes in the discussion of students' reasoning as they justify their responses. This routine is powerful for helping students estimate and justify the reasonableness of a solution. You can use one or two of these problems when you have short bits of time.

Click any image below to read teachers' reactions on Twitter.

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Find a collection of problems you can use in your classroom to promote reasoning and thinking!

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

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Math education can lay the groundwork for problem-solving skills, analytical thinking, and even a rewarding career. But not all classroom experiences are created equal. New research shows that teachers have incredible influence in leveling the playing field-and in helping students achieve their potential.

Candace Jackson teaches math. But to say she is simply a math teacher would be reductive.

Jackson is a vital resource to her middle school in Humble, Texas. She mentors students and teachers to ensure that everyone is equipped with the right lessons and skills to help every child succeed.

She's an occasional athletics coach and even an occasional mother figure to her students: "They consider it a term of endearment, to call me 'mama,'" she says with a laugh.

And before all that, Jackson was a mechanical engineer. Students sometimes ask why she left the more lucrative engineering field for the classroom. "I do this because I love you," she tells them, "so I can help you be whatever it is you want to be."

Jackson says that, as an African American woman, she also wanted to debunk the myth that math is inaccessible. "I wanted to open opportunities for people who look like me-whether they want to be a lawyer, a doctor, a veterinarian, or an engineer. Anyone can understand the basic principles of mathematics."

Teachers can be a huge part of determining whether a student simply survives their math education or thrives in STEM.

She says that math, at its core, is about critical thinking. "Critical thinking and problem-solving are the skills we need to make this world better," Jackson adds. "Every student should have access to those skills."

Researchers at RAND agree. In 2022, they launched the American Mathematics Educator Study (AMES), a five-year study to investigate students' math opportunities and what schools and teachers can do to make those opportunities more accessible-from elementary school all the way through college and career preparation in high school.

The researchers' findings so far indicate that teachers can be a huge part of determining whether a student simply survives their math education or thrives in STEM.

"The role of a math teacher is more significant than even they may fully realize," says Julia Kaufman, coleader of the study and a senior policy researcher at RAND. "A student's entire trajectory could change as the result of a teacher's recommendation to place that student in a more advanced math course. It can change when a teacher tells a child that they have what it takes to do well in math. That's incredibly powerful."

Acing the Equity Test

Uneven access to high-quality mathematics education has been a persistent challenge for American public schools.

Students of all ages are often grouped based on their academic performance-or their perceived academic performance. This practice, sometimes known as tracking, can start as early as elementary school. It disproportionately affects Black, Hispanic, and low-income students, who are often placed in lower-level groups or tracks.

Just how commonplace is tracking? In a recent RAND survey, more than 40 percent of elementary school principals reported that students were grouped by achievement level for math instruction.

Tracking students into math courses becomes more common in middle school and is most common in high school. In fact, 68 percent of middle school principals reported grouping students by achievement level; 39 percent reported that students are tracked into different classes. By high school, more than half of schools group students this way.

"Students in lower-track courses typically receive less grade-level content, fewer chances to share or explain their thinking in class, and more teacher lecturing," says RAND policy researcher Elizabeth Steiner, who coleads the study.

This creates a ripple effect. For example, imagine an eighth grader, Andrea, who has access to algebra because she's on a higher track. Andrea's friend Clay is on a lower track, so he takes general math instead. As they enter high school, it's highly unlikely that these two will ever share a math classroom. Clay will find it nearly impossible to take the same advanced courses as Andrea.

Access to advanced math classes in eighth grade can also dictate students' achievement in math at the college level and beyond. That's why any factor that nudges a young person toward more-advanced math classes can make a big difference in their life.

And who wields significant influence in how students are tracked? Teachers. Of the principals who reported that students were in some way grouped by achievement level, more than 80 percent reported using teacher recommendations as one consideration when making their decisions.

Researchers say that teachers should recognize the critical role they can play in determining students' futures.

For instance, the way teachers decide to group students within their own classes could easily lead to a decision to group a child into a lower-track class in the future. And teachers' recommendations could make a difference in whether a child is placed into more challenging math classes.

"When math teachers decide how to group students in their classes, they could reflect more often about whether some kids could benefit from more-challenging material," Kaufman says. "Teachers could also consider whether some students who are struggling should receive interventions. For example, steering a child toward one-on-one tutoring could boost their math performance and set them up for a more challenging math class in middle school and beyond."

Jackson has seen this scenario play out before her eyes.

She recalls a time she spent working as an academic interventionist, an educator assigned to help students overcome learning challenges.

"Often, these students lack confidence because they've been unsuccessful for so long," Jackson says. She remembers one student in particular: "We were able to make math a conversation-something to understand, not just to memorize."

Eventually, the student came to learn how to reason and make sense of the mathematics required to solve problems. It was a game-changer. After a year, he was able to move out of the intervention class and back into an elective class of his choosing.

Teacher Efforts Pay Dividends

Jackson's story highlights the value that students can glean when they receive mentorship from experienced, knowledgeable math teachers.

"Often, they have assigned students to my class who seemed to not have the best chances for success," she says. "But that was just how it looked."

She recalls one year when she was assigned six students whose scores were so low that they weren't expected to pass.

"But after working with them-and to the students' surprise-four of them passed," Jackson says. "And that's because we took the time to slow down, process the material, and look at things differently. It became a safe space for them."

Unfortunately, the RAND data show that many students falling behind in math may not have access to experienced and knowledgeable teachers like Jackson. In fact, on average, only about 40 percent of U.S. principals reported assigning the most experienced, knowledgeable, or effective teachers to students who needed help with math. Another 40 percent reported that they don't have flexibility to assign teachers to struggling students or that they simply assign teachers based on who has an opening in their schedule.

Only about 40 percent of U.S. principals reported assigning the most experienced, knowledgeable, or effective teachers to students who needed help with math.

"Many teachers might see that their students are struggling with math, but they're unsure how to help," Steiner says. "Those teachers should demand that their school support them with more professional learning or additional supports for students, like math specialists and tutors. Teachers can also turn to their more knowledgeable peers for help. And, in turn, those who do have more math knowledge and experience can mentor other teachers in their school."

Jackson says she's noticed that, whether she's mentoring less experienced teachers or her students, the underlying lesson is often the same.

"Math is all about relationships and connections," Jackson says. "If students and teachers can understand why math is important, and that it's primarily about reasoning and critical thinking-not memorization-it becomes easier to see the big picture and retain that knowledge."

While Jackson's 18 years of classroom experience reflect what the RAND data reveal, there's still more to be discovered. Researchers will continue to explore the types of resources that are available to teachers, including professional development, teaching materials, and curriculum coherence.

Those upcoming studies will likely yield more insights for math teachers-and some for principals, administrators, and policymakers. But one takeaway is already clear.

"To put it simply, math teachers and their opinions, recommendations, encouragement, and mentorship matter deeply," Kaufman says. "We hope this study will inspire math teachers to really tap into the full potential of their power. The influence they have can be life-changing for students."

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Math Teachers' Efforts Can Really Add Up

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Uneven access to high-quality mathematics education has been a persistent challenge for American public schools. Teachers wield incredible influence in leveling the playing field in math class-and in helping students achieve their full potential.

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2023 Mathematics Framework

At its meeting on July 12, 2023, the State Board of Education (SBE) adopted the Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve ( Mathematics Framework). The framework is important guidance designed to help educators align classroom teaching with California's rigorous math learning standards.

The Mathematics Framework reflects input from California parents, educators, students, and others who commented during the two 60-day field review periods that were held in 2021 and 2022.

California is committed to achieving excellence in math teaching and learning through curriculum and instructional approaches grounded in research and reflective of best practices across the globe. The Mathematics Framework provides guidance for mathematics learning for all students at all levels of math-including calculus-and ensures students have a wide variety of options including pursuing Science, Technology, Engineering, and Mathematics (STEM) in college and career.

Frequently Asked Questions
Information about the draftMathematics Framework.

Schedule of Significant Events for the Revision of the Mathematics Framework
At its meeting on July 13, 2022, SBE revised the Schedule of Significant Events (Timeline) for the Revision ofMathematics Framework. The Timeline was originally approved by the SBE on May 8, 2019, and was previously revised on September 11, 2019, May 7, 2020, July 14, 2021, and November 3, 2021.

A professionally-edited and designed PDF version of the framework will be posted at a later date. The content will not substantively change from the version posted below.

Curriculum Framework and Evaluation Criteria Committee

At their January 08, 2020, meeting the State Board of Education appointed 20 members to the Mathematics Curriculum Framework and Evaluation Criteria Committee (Mathematics CFCC) to assist in the development of the Mathematics Framework.

The Mathematics CFCC Meetings and Notices

Focus Groups

Pursuant to the California Code of Regulations, Title 5, Section 9511(c), the California Department of Education (CDE) convened four focus groups across California.

Listserv

Additional Resources

2013 Mathematics Framework

Assembly Bill 250 (Chapter 608, Statutes of 2011) called for the revision of the Mathematics Framework to align with the California Common Core State Standards for Mathematics.

Video: Overview of the Mathematics Framework (Dated 26-Feb-2015)
This video for teachers, administrators, and other educators provides an overview of the Mathematics Framework and how it supports implementation of the California Common Core State Standards for Mathematics.

Common Core State Standards for Mathematics (PDF; 3MB)
Links to the standards adopted by the California State Board of Education in August 2010 (Modified January 2013 Publication Version).

Common Core State Standards (CCSS) Initiative
The multi-state initiative released the CCSS on June 2, 2010. The initiative site includes information about the development and research behind the standards, appendices, the states that have adopted the CCSS, and frequently asked questions.

Appendix A
Designing High School Mathematics Courses Based on the CCSS.

2005 Mathematics Framework (Available on request)
The Framework was adopted by the State Board of Education on March 9, 2005.
*To order a copy of this framework please contact CDE Press.

Content Standards
Links to downloads of all Content Standards.

All Curriculum Frameworks
Links to downloads of all Curriculum Frameworks.

Questions: Curriculum Frameworks and Instructional Resources Division | CFIRD@cde.ca.gov | 916-319-0881

Last Reviewed: Friday, October 20, 2023

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Curriculum frameworks provide guidance to educators, parents, and publishers, to support implementing California content standards.

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The Universal Design for Learning (UDL) model is a framework to address curricular planning that meets the needs of all learners. The framework and its principles were used to design the SFUSD Math Core Curriculum. C&I Math

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Elementary version of SMPs

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Great resource for playful math

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Maths Play acknowledges the Traditional Owners of the land on which we live, learn and work, and pay our respects to Elders past and present. Maths Play is dedicated to learning and operating in ways that acknowledge, respect, celebrate and learn from the original and beautiful cultures of these lands.

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A community project play-working to reunite maths with play.

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

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100 Subitizing Slides & 10 Challenge Patterns - Steve Wyborney’s Blog: I’m on a Learning Mission.

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I have a new resource for you. 100 Subitizing Slides & 10 Challenge Patterns.

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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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Need fraction strips and fraction die or spinner

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How to Use Subitizing | 5 Different Ways - The Recovering Traditionalist

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Have you ever wondered how to use subitizing in your classroom? Subitizing is the ability to instantly recognize ‘how many’.

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To do this, we collected nearly 30,000 in-the-moment student surveys. Using a technology that prompted students in grades six through 12 to answer a few questions at random times during class, we captured a snapshot of their real-time reactions to school. We also surveyed third through fifth graders during the last five minutes of class, and found that elementary students were just as capable as their older schoolmates of providing rich and telling insight into their lives at school.

Across our five partner school systems, we also observed nearly a thousand full-length lessons at all grade levels from K-12, and reviewed almost 5,000 assignments and more than 20,000 individual student work samples. We visited each participating school daily for a week straight at three points in the year, which gave us the chance to see the same teachers and students at the beginning, middle, and end of their time together (and offered a much more comprehensive lens on the learning environment than a single day's lesson could have). These classrooms were not substantially different than the others in their districts, and they represented a wide range: those with new teachers and veterans; those at all age levels; a diverse range of subjects; mixed-ability classes and tracked ones. Four of these school systems were located in states that use standards aligned to the Common Core State Standards; one was not.

To assess the quality of content students worked on, we looked at four elements of every assignment: (1) whether the content in the assignments was aligned to relevant grade-level academic standards; (2) whether the assignments gave students the chance to engage in important content-specific practices, like citing evidence from rigorous texts in literacy, or discussing mathematical ideas using precise mathematical language; (3) whether the assignments gave students a chance to learn relevant content that built their knowledge of the world or helped them see how what they were learning could be applied in the real world; and (4) student performance on both the assignments themselves and against the bar for their grade-level standards.

To study instruction, we observed full-length class periods and assessed (1) whether students were doing what they were asked; (2) whether they were being asked to work on grade-level content; and (3) whether teachers were using instructional practices that gave students the chance to do most of the thinking in the lesson.

We surveyed teachers to capture their knowledge of grade-level standards, their opinions on those standards, and their beliefs about their classroom practices and their students' abilities. We conducted focus groups with nearly 100 teachers and interviewed 24 school leaders at multiple times throughout the year. And we assessed a large set of extant data provided to us by our partner districts on course access, enrollment policies, and district policies on curriculum adoption, among others.

We hypothesized that students' experiences of school were influenced by a confluence of factors-among them, the quality of the work they were doing, the instruction they received, and the expectations of their teachers-and that those factors would interact to have an impact on their academic growth. Taken together with students' in-the-moment survey responses, we were able to triangulate students' perspectives with the classes they were in, the work they were doing and instruction they were receiving, and their academic outcomes.

In addition to amassing this rich data set, we also sat down with a smaller subset of students (more than 50 over two school years), and got to know them. We observed them in class and spoke to them about their experiences, their likes and dislikes, their families, their goals. Just a few of those students are profiled here. While their names and identifying characteristics have been changed throughout this report, their stories help us understand what the data means in the real lives of individual young people.

They also help us understand what real, tangible changes school systems can make-starting tomorrow and over the long haul-to provide more students with school experiences that are meaningful, that honor their aspirations for themselves and their families, and that give them a fighting chance to meet those goals.
For our complete methodology, including further explanation of our analytical approaches and full analysis results, see the Technical Appendix.

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What can 4,000 students teach us about school? Read The Opportunity Myth.

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Download Math Milestones™ Grids

The grade-level grids have been carefully constructed to reflect the concepts, fluencies, applications, and practices of mathematics at each grade level as defined by the Standards. Across the grades, the tasks follow the progressions in each domain, surfacing key themes like the number line, properties of operations, and functional thinking. The reverse side of each grid includes Standards information for each task.

For each task, there is a student-facing handout ( available here). Math Milestones™ tasks are not designed for summative assessment. Used formatively, the tasks can reveal and promote student thinking. Student work on tasks could be collected in student portfolios.

The grade-level grids are © 2021-2022 Math Milestones LLC and licensed under the Creative Commons Attribution 4.0 International License ( CC BY 4.0).

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The grade-level grids have been carefully constructed to reflect the concepts, fluencies, applications, and practices of mathematics at each grade level as defined by the Standards. Across the grades, the tasks follow the progressions in each domain, surfacing key themes like the number line, properties of operations, and functional thinking.

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videos for teachers to see various strategies as well as choices for number talks

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SJCOE Coordinator's Padlet of resources

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

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Fraction Splats! have arrived! The original Splat! post rocketed up to over 35,000 hits in less than a month, which included over 19,000 lesson downloads! All 50 lessons in the Splat! post involved whole numbers. In this post, I've turned my attention to fractions, and have created 20 new lessons for you to download! This is The Fraction Splat! Series. Watch the video, download the lessons, and try them in your classroom!
Note: I've created the lessons in PowerPoint, so I recommend using PowerPoint to view them.
After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.
Note: These lessons use a single splat along with a mixture of unit fractions and whole numbers. In Level 11, you control the Splat! SPLAT 11.1 - Fraction Splats SPLAT 11.2 - Fraction Splats SPLAT 11.3 - Fraction Splats SPLAT 11.4 - Fraction Splats SPLAT 11.5 - Fraction Splats
Instant Fraction Splat!
Note: These lessons use a single Splat! which appears at the same moment as the whole numbers and fractions. Each question instantly presents missing information. SPLAT 12.1 - Instant Fraction Splats SPLAT 12.2 - Instant Fraction Splats SPLAT 12.3 - Instant Fraction Splats SPLAT 12.4 - Instant Fraction Splats SPLAT 12.5 - Instant Fraction Splats
Multiple Splats! with Fractions
Note: These lessons include multiple Splats! and you control the timing of those Splats! The entire screen can be seen, the total can be determined, and then Splat! Remember: Each Splat! that is the same color must be covering the same number. SPLAT 13.1 - Multiple Fraction Splats SPLAT 13.2 - Multiple Fraction Splats SPLAT 13.3 - Multiple Fraction Splats SPLAT 13.4 - Multiple Fraction Splats SPLAT 13.5 - Multiple Fraction Splats
Multiple Splats! with Fractions
Note: These lessons use multiple Splats! which appear at the same moment as the whole numbers and fractions. Each question instantly presents missing information. Remember: Each Splat! that is the same color must be covering the same number. SPLAT 14.1 - Instant Multiple Fraction Splats SPLAT 14.2 - Instant Multiple Fraction Splats SPLAT 14.3 - Instant Multiple Fraction Splats SPLAT 14.4 - Instant Multiple Fraction Splats SPLAT 14.5 - Instant Multiple Fraction Splats
Other Posts and Resources Which May Be of Interest

Splat! The original 50 downloadable Splat! lessons include 10 levels and variations.

Tiled Area Questions is a colorful, powerful, highly visual strategy for decomposing numbers - and offers many downloadable pages.

The Animated Multiplication Table remains one of the most popular downloaded resources from this blog, and this post includes several ideas about how to use it.

The Maze Hundreds Chart is another downloadable resource that can lead to some highly intriguing questions and rich discourse.

You may also be interested in Provide Massive Space to Notice.

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 The Fraction Splat! Series to promote number sense in your classroom!

All my best,
Steve

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

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Fraction Splats! have arrived! The original Splat! post rocketed up to over 35,000 hits in less than a month, which included over 19,000 lesson downloads!

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In depth explanations of each SMP

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Inside Mathematics illuminates the mathematical practice standards with video excerpts of mathematics lessons. Click the individual standards below to see instances of the practice standards in classroom lessons. Although the practices are presented here individually, it's important to keep in mind that the practices can, and should, be evident together in a lesson. See the Mentors of Mathematical Practice for a holistic view of the practices together.

See also our new resources incorporating social and emotional learning competencies in the mathematics classroom and how they support the mathematical practices.

Practice Standards

1. Make sense of problems & persevere in solving them

2. Reason abstractly & quantitatively

3. Construct viable arguments & critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for & make use of structure

8. Look for & express regularity in repeated reasoning

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Mathematical Practice Standards | Inside Mathematics

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Inside Mathematics illuminates the mathematical practice standards with video excerpts of mathematics lessons. Click the individual standards below to see instances of the practice standards in classroom lessons. Although the practices are presented here individually, it’s important to keep in mind…

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youcubed was created by Stanford University professor

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Cignition’s FogStone Isle lets kids explore, create and engage with math through real-world scenarios. Unlike most game-based learning programs, FogStone […]

Polyup is a free and open computational thinking playground where students can experiment with numbers and functions. Students will “mod”, […]

Refraction focuses on teaching fractions and discovering optimal learning pathways for math education. Refraction lets you bend, split, and redirect […]

This lets you play with math while exploring a 3-D virtual world, filled with number creatures and mathematical machines. It […]

Dragon Box teaches you algebra through visuals. You solve for x and have fun doing it. It really encourages algebraic […]

SET is a board game where any table becomes the board. It is a highly addictive, original game of visual […]

In this app you have to release the creature from jail by turning the gears. It helps you develop number […]

Mancala is a family of board games played around the world, sometimes called “sowing” games, or “count-and-capture” games, which describes […]

Muggins math board games and manipulatives are not only educational but make learning FUN! Built the old fashioned way with […]

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Mancala is a family of board games played around the world, sometimes called "sowing" games, or "count-and-capture" games, which describes [...]

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Week of Inspirational Math for Back to School!

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At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.

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Easily adapted for older grades using decimals

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The author/researcher of BTC

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Peter Liljedahl, PhD Professor Faculty of Education Simon Fraser University 8888 University Drive Burnaby, BC, V5A 1S6, Canada Voice: +778-782-5643 Email: liljedahl@sfu.ca

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Wipebook Flipcharts come in sets of 10 detachable sheets (20 pages). Each sheet (2 x 3 feet) includes a blank side and a graph side for 20X the surface area of a conventional whiteboard of the same size. Are you an educator? Check out our special discounted pricing!

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Welcome to Math Talks for Slides!
This site was created to fill a need for finding ready-to-use slides that can easily be copied and pasted into my daily meeting slide decks for distance learning. I wanted to have a hub of these engaging resources that I could access for distance learning as well

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When does 2+7+8=1 Grace Kelemanik SMP video

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When does 2+7+8=1 Grace Kelemanik SMP video

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national council of teachers of mathematics (organization)

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Grace Kelemanik gives a talk on April 16, 2015, called "When does 2+7+8=1?" at the Math Forum and NCTM Ignite event at the 2015 NCTM Annual Conference in Boston. @GraceKelemanik

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Read about my math classes and things I've learned in the classroom.

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Language is the essential classroom tool, especially in mathematical applications. It's how students process and remember information. But the kind of language defined as mathematical discourse is more nuanced than other classroom discussions. Teaching students how to think, read, write, and speak like mathematicians is how they truly learn math-it becomes something more than the rote memorization of facts and formulas.

When mathematicians engage with math or problem solving, they do more than simply look at a problem and solve it. They view problems through a mathematical lens and engage in purposeful and collaborative expression of internalized processes-mathematical discourse is a way to make invisible thinking visible. If we are to create and activate mathematicians of the future, we need to stop teaching math the way it's been done for the past 150 years. Instead, we need to empower students to think and communicate mathematically-to become conversant in mathematical discourse.

The key to mathematical discourse is a shift that takes place in the role of the teacher from giver of knowledge to facilitator of thinking, enabling students to take ownership of their learning. This, in turn, allows students to make conjectures, connect prior knowledge to current understanding, reason mathematically, and refine and amend problem-solving approaches.

1. Establish mathematics goals to focus learning

2. Implement tasks that promote reasoning and problem solving

3. Use and connect mathematical representations

4. Facilitate meaningful mathematical discourse

5. Build procedural fluency from conceptual understanding

6. Support productive struggle in learning mathematics

7. Elicit and use evidence of student thinking

The list may look abstract and daunting, but we can achieve these goals by creating a discourse-rich classroom. And doing so doesn't add to teachers' tasks-it accelerates and enhances the work that they are already doing.

Building a Discourse-Rich Classroom

A discourse-rich classroom is only possible when we build and nurture relational capacity, the level of trust and safety between student and teacher. By building a culture that celebrates mistakes and takes academic risks, teachers can create what we think of as an ideal learning space. Classrooms where students are both safe and brave, where inquiry, curiosity, and learning to fail forward are integral to learning.

In these classrooms, students work together to problem solve. They are taught to ​​welcome mistakes and to use them as learning points to articulate what they understand and what points of confusion they still have. Right or wrong, they express their thought processes to gain a stronger understanding of the concept.

Strategies for Scaffolding Discourse

As starting points, consider three strategies-developed by the nonprofit (Advancement Via Individual Determination), for which we both work-to begin integrating mathematical discourse in your classroom. Easy to implement and actionable, these strategies provide a launch pad for weaving mathematical discourse into your classroom practice. They can serve to create a culture of belonging, where students understand that the classroom is a safe space to make mistakes.

1. Use academic language scripts to provide students with the formal language needed to engage in academic discourse. Intentionally embed opportunities for students to use the language of math to describe their thinking about math. Examples include:

2. Create communal word banks of high-leverage, content-specific academic vocabulary to assist students in expressing their mathematical thinking. Word banks should be visible, accessible to students, and collaborative. They anchor and support the mathematical content students are currently learning. A communal word bank in a 4th grade classroom could include:

It is important that students and educators both add to the word bank throughout instruction. The word bank could be housed on a wall, in notebooks, in a collaborative digital document, or anywhere that students can readily access. This passes ownership to the students, creating a new awareness of the language of math, and accessible scaffolds supporting using the language of math.

3. Celebrate the use of mathematical language. Design opportunities within lessons and daily interactions for students to begin to use scaffolds-like language scripts, sentence frames, and word banks. Acknowledge and celebrate their bravery in trying new words and describing their thinking using the language of math.

For example, have the class snap their fingers in a finger snap celebration when a student uses academic vocabulary.

Or have the class celebrate with two stomps and a clap when a student expresses themselves using an academic language script.

Coach students to celebrate each other when they hear peers using mathematical language: "Great job your brain is growing!", motioning a hammer hitting a nail and saying, "Nailed it!"

When students are able to express their thinking and problem-solving strategies, they make deeper, more meaningful connections to content. When they feel empowered to ask questions, to make mistakes and to celebrate new ways of thinking, they become more confident in how they approach mathematics.

And when discourse is intentionally built in the math classroom, they learn how to talk and think like mathematicians.

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3 Strategies for Scaffolding Mathematical Discourse in Your Classroom

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A discourse-led classroom is only possible when we intentionally build trust with our students.

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Visual Patterns perfect for teaching Math Practice 7- look for and make use of structure

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Welcome! 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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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 Solutions Number Talks  K 1 Ten Frames and Dot Cards

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Read about how Math Talks can strengthen accuracy, efficiency, and flexibility in this article by Sherry Parrish from Teaching Children Mathematics.

More sources for Math Talks:

Other Tools
This folder includes a variety of helpful tools for deepening math talks, planning, and assessing. Including:

Another source of information and resources for Math Talks from Math Perspectives is here.

30 ways to make number strings more inclusive...

Anchor number strings in context.

Never underestimate the importance of models.

Explicitly represent language that helps students be precise mathematically.

Explicitly ask students to try new strategies

​More on NumberStrings.com

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Download the Math Talks Descriptions from our Math Teaching Toolkit here > > >

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My growing list of free real world problem-based lessons for grades 2 through high school. Includes links to download multimedia and teacher guide.

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KristenAcosta.com | Where Math is an Active Subject

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Great to use with BTC

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Make a copy before using

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DO NOT DELETE ONLY ADD RESOURCES

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Check out 10 Frame Mania for K-2!

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Click grade level, then routines. Huge bank of routines to support number sense.

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

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For my educator friends who have access to Google Slides, but do not have access to PowerPoint, this post is for you. Since Google Slides does not have the animation that makes the Splats become transparent, the Splat! reveal does not work in Slides. Now - with these materials - it will. I've rewritten the first 20 Splat! lessons and the first 20 Fraction Splat! lessons with a different method so they will now include the reveal when using Google Slides.

The content of the lessons is the same as the original lessons.

Visit these links to see the original videos about how to use the and the Fraction Splat! slides.

Quick Note: The file sharing power of Google Drive is impressive and highly useful. However, for the purposes of sharing these resources, I need to use a method that I can personally maintain, update and support - and I've learned that the best way to provide resources from my blog is through the download links and the sign-up forms.

I hope you enjoy these Splats! formatted to work in Google Slides!

Splat Through 10
How many dots are under the Splat?
SPLAT 1.1 - numbers through 10 (Google Slides compatible version)
SPLAT 2.1 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.2 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.3 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.4 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.5 - with numbers 12-20 (Google Slides compatible version) SPLAT 1.2 - numbers through 10 (Google Slides compatible version)SPLAT 3.1 - multiple splats (Google Slides compatible version) SPLAT 3.2 - multiple splats (Google Slides compatible version) SPLAT 3.3 - multiple splats (Google Slides compatible version) SPLAT 3.4 - multiple splats (Google Slides compatible version) SPLAT 3.5 - multiple splats (Google Slides compatible version)
SPLAT 4.1 - instant multiple splats (Google Slides compatible version) SPLAT 4.2 - instant multiple splats (Google Slides compatible version) SPLAT 4.3 - instant multiple splats (Google Slides compatible version) SPLAT 4.4 - instant multiple splats (Google Slides compatible version) SPLAT 4.5 - instant multiple splats (Google Slides compatible version) Note: These lessons use a single splat along with a mixture of unit fractions and whole numbers. In Level 11, you control the Splat! SPLAT 11.1 - fraction splats (Google Slides compatible version) SPLAT 11.2 - fraction splats (Google Slides compatible version) SPLAT 11.3 - fraction splats (Google Slides compatible version) SPLAT 11.4 - fraction splats (Google Slides compatible version) SPLAT 11.5 - fraction splats (Google Slides compatible version) SPLAT 1.3 - numbers through 10 (Google Slides compatible version)Note: These lessons use a single Splat! which appears at the same moment as the whole numbers and fractions. Each question instantly presents missing information. SPLAT 12.1 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.2 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.3 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.4 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.5 - Instant Fraction Splats (Google Slides compatible version) Multiple Splats! with Fractions Note: These lessons include multiple Splats! and you control the timing of the Splats! The entire screen can be seen, the total can be determined, and then Splat! Remember: Each Splat! that is the same color must be covering the same number. SPLAT 13.1 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.2 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.3 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.4 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.5 - Multiple Fraction Splats (Google Slides compatible version)
Note: These lessons use multiple Splats! which appear at the same moment as the whole numbers and fractions. Each question instantly presents missing information. Remember: Each Splat! that is the same color must be covering the same number. SPLAT 14.1 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.2 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.3 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.4 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.5 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 1.4 - numbers through 10 (Google Slides compatible version)
SPLAT 1.5 - numbers through 10 (Google Slides compatible version)

Splat Through 20
How many dots are under the Splat?

Multiple Splats
Note: Splats that are the same color must cover the same number.

Instant Multiple Splat
Note: An additional feature of this level is the opportunity to ask, "What could the total be?"

Instant Fraction Splat!

Multiple Instant Splats! with Fractions

After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

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Splat! for Google Slides - 40 Lessons - Steve Wyborney's Blog: I'm on a Learning Mission.

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For my educator friends who have access to Google Slides, but do not have access to PowerPoint, this post is for you. Since Google Slides does not have the

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Ask students to reflect on the idea discussed in the video that math in NOT about speed. What is important in math is to think carefully, deeply, and the make connections.

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Ask students to reflect on the idea discussed in the video that math in NOT about speed. What is important in math is to think carefully, deeply, and the make connections.

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Over the past couple of decades, teachers have seen a new generation of students: those who have never known a world without the Internet. Many of them grew up immersed in a digital world. They are the digital natives.

The earliest digital natives are now sending their own children to school. Today's teachers, many of whom are digital immigrants-people who transitioned from an analog world to a digital one-must find ways to reach digital native students and their caregivers.

The great news is that digital natives want to learn. It's just up to educators to help them succeed in finding answers while staying safe in a digital environment.

What Does it Mean for a Student to be a Digital Native?

What is a digital native? The term was coined by author Marc Prensky to describe a person who grew up surrounded by technology and is familiar with the Internet from an early age on. Today's students are digital natives, and increasingly, so are their parents (and many of their teachers). This can be tremendously beneficial-for instance, when scheduling online learning or virtual parent-teacher conferences when in-person learning isn't possible.

Non-natives could be considered "digital immigrants." These are people who were born in the pre-digital world, but have since adapted to the Internet and everything that comes along with it.

The educational system structure was designed for that analog world. It was created and cemented before the Internet revolution. That's why it's important for teachers, whether they're digital immigrants or digital natives themselves, to change the traditional approach to learning.

How Digital Natives Process Information in the Classroom

Prensky wrote that digital natives are used to receiving information quickly, and they are used to multitasking. They like graphics before text instead of after, and they function best when networked. They respond to instant gratification and frequent rewards. The "accent" of a digital immigrant (preferring a printed report rather than one online, for instance) strikes digital natives as odd.[4]

Others caution against taking the "digital native" concept too far. Hillary Scharton writes that children aren't born knowing technology, and that the belief that digital natives excel at multitasking can be detrimental to their learning.

"Children face increasingly packed schedules, so they're more likely to multitask-by frequently task-switching and/or using different kinds of media at the same time. Studies show that's hard on our cognitive load, so people who multitask consistently end up taking longer to shift their attention and having a harder time filtering out irrelevant information," she writes.[5]

Even taking that into account, today's students are different because their reality is different. And that means schools will have to adapt to the way these new students think and learn. To the typical digital native, learning comes from doing, not from a lecture.[2] More than half of students surveyed say they learn best by doing, not by listening.[3] Getting the students involved is the key to helping them learn.

Using Technology in the Classroom to Teach Digital Natives

Integrating technology into the classroom is a necessity.[1] Many educators, especially digital immigrants, struggle to find the best way to do this. There are some handy guidelines for the proper role of technology in education. Six key points are:

Try the technology yourself: Go through the program on your own before using it with your students. That way you can troubleshoot any problems in advance.[8]

Listen to your students: Listen to what your students know about technology. They can likely teach you something.[9]

Communicate with parents through tech: Use digital resources (like apps, texts, or social media groups) to keep parents informed about class activities and upcoming assignments.[10]

Be active: Prioritize active digital activities, like online learning games or interactive lessons, over passive activities, like watching a video.

Train: If you're an administrator, schedule a faculty training session on how to use your school's technology and answer any questions.[11]

Focus on citizenship: Focus your technology-based lessons on teaching your students digital citizenship, or skills that will help them thoughtfully and effectively navigate digital media.[12]

The good news is this doesn't mean teachers need to be intimately familiar with every new form of tech or social media platform. Remember, tech is only the means to an end, not the end itself.[6] Focusing solely on the technology ignores one thing: the students. Instead, embrace and encourage your students' desire to find things out through methods they're familiar with. And keep in mind that even students who are inclined to non-tech careers will need to be literate with technology.

Teaching Strong Digital and Media Literacy Skills

Instead of debating over allowing students' technology in the class, schools should support their students and let them explore their digital world. Using the Internet for research will increase student enthusiasm about finding things out on their own.[7]

Be sure to introduce your students to Internet safety and elements of digital citizenship as a key focus. These elements include balance, safety and privacy, respect, connecting, learning, and critical thinking.

Here's a guide to media literacy skills that will help your students navigate the virtual world. Media-literate students should be aware how to combat misinformation, think critically, and evaluate their sources.

Communicating with Digital Native Parents

Many students are now the children of digital natives themselves. Those parents are most likely to respond to reminders and notifications over digital channels, like emails, SMS messages, Facebook groups, or app notifications.[10] They are less likely to believe face-to-face meetings (when possible) are the best way to discuss their students, and are more accepting of digital methods.

That notion is backed by research. Several studies have found that weekly text messages about children's performance in school, or with tips for at-home practice, led to increased communication with teachers, better performance in school, and fewer absences.[13]

Commonsense.org has a list of some popular apps, such as ClassDojo and Bloomz, that teachers can use to communicate with parents. Teachers should remember that not every family may be able to afford Internet access, so old-fashioned printed notes and bulletins still have a place in the student's backpack.
Sources:

1. "Teaching Digital Natives." ASCD InService. June 2017. https://inservice.ascd.org/teaching-digital-natives/

2. "We Need to Rethink Education for Digital Natives." Adobe Blog. September 2018. https://blog.adobe.com/en/publish/2018/09/05/we-need-to-rethink-education-for-digital-natives.html

3. "Getting to Know Gen Z." Barnes & Noble College. https://www.bncollege.com/wp-content/uploads/2015/10/Gen-Z-Research-Report-Final.pdf

4. Prensky, Marc. "Digital Natives Digital Immigrants." MarcPrensky.com. October 2001. https://www.marcprensky.com/writing/Prensky%20-%20Digital%20Natives,%20Digital%20Immigrants%20-%20Part1.pdf

5. Scharton, Hilary. "Busting the Myths of the Digital Native." OurChildren.org. May 2019. https://ptaourchildren.org/busting-the-myths-of-the-digital-native/

6. Bowman, Sam. "Educating the Digital Native: Teaching Students in a Binge-Watching World." Faculty Focus. March 2020. https://www.facultyfocus.com/articles/teaching-with-technology-articles/educating-the-digital-native-teaching-students-in-a-binge-watching-world/

7. Lynch, Matthew. "How to Teach a Room of Digital Natives." EdWeek.org. June 2016. https://www.edweek.org/education/opinion-how-to-teach-a-room-of-digital-natives/2016/06

8. "How to Integrate Technology." Edutopia.org. November 2007. https://www.edutopia.org/technology-integration-guide-implementation.

9. Reissman, H. "7 smart ways to use technology in classrooms." Ted.com. September 2017. https://ideas.ted.com/7-smart-ways-to-use-technology-in-classrooms/

10. Venezky, R.L. "Technology in the classroom: steps toward a new vision." Education, Communication & Information, 2004, 4(1), pp. 3-21.

11. Couse, L.J., and Chen, D.W. "A Tablet Computer for Young Children? Exploring its Viability for Early Childhood Education." Journal of Research on Technology in Education, 2010, 43(1), pp. 75-96.

12. Keswani, B., Patni, P., and Banerjee, D. "Role Of Technology In Education: A 21st Century Approach."Journal of Commerce and Instructional Technology, 2008, 8, pp.54-59.

13. Minero, Emelina. "Parent Engagement in the Digital Age." Edutopia. November 2017. https://www.edutopia.org/article/parent-engagement-digital-age

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Understanding, Teaching, and Reaching Digital Native Students-and Digital Native Caregivers - Waterford.org

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Over the past couple of decades, teachers have seen a new generation of students: those who have never known a world without the Internet. Many of them grew up immersed in a digital world. They are the digital natives. The earliest digital natives are now sending their own children to school.

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Michelle Brosseau, Mrs. Brosseau's Binder

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Use to focus on quantities and strategies instead of rushing to be "done."

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Take out the numbers to make word problems make sense Learn More Try one tomorrow Primary (K-2) Older Students Explore ready-made problems Problem Banks More Problems This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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Look at the week of inspirational math resources.

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At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.