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The numeracy continuum chart

The continuum outlines a progression of learning that can be used when observing students working on problems in mathematics.
Details
The National Numeracy Learning Progressions have replaced the Numeracy continuum. This website will be decommissioned at the end of the 2020 school year. For more information on the Learning Progressions, .

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The continuum outlines a progression of learning that can be used when observing students working on problems in mathematics. Details The National Numeracy Learning Progressions have replaced the Numeracy continuum. This website will be decommissioned at the end of the 2020 school year. For more information on the Learning Progressions, .

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Math Trajectories

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Educational Technology and Mobile Learning

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A Collection of Good YouTube Channels for Math Teachers

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2D, 3D Shapes

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The Common Core mathematical practice standards are the foundation for mathematical thinking and practice for students as well as guidance that helps teachers modify their classrooms to approach teaching in a way that develops a more advanced mathematical understanding. Think of these standards as a guide to creating a more complex and absorbing learning experience that can be applied to everyday life, instead of being left in the classroom.

1. Make sense of problems and persevere in solving them

The first Common Core mathematical practice standard is found in almost every math problem across the board. It means that students must understand the problem, figure out how to solve it, and then work until it is finished. Common Core standards encourage students to work with their current knowledge bank and apply the skills they already have while evaluating themselves in problem-solving. This standard is easily tested using problems with a tougher skill level than already mastered. While students work through more difficult problems, they focus on the process of solving the problem instead of just getting to the correct answer.

2. Reason abstractly and quantitatively

When trying to problem solve, it is important that students understand there are multiple ways to break apart the problem in order to find the solution. Using symbols, pictures or other representations to describe the different sections of the problem will allow students to use context skills rather than standard algorithms.

3. Construct viable arguments and critique the reasoning of others

This standard is aimed at creating a common mathematical language that can be used to discuss and explain math as well as support or object others' work. Math vocabulary is easily integrated into daily lesson plans in order for students to be able to communicate effectively. "Talk moves" are important in developing and building communication skills and can include such simple tasks as restating a fellow classmate's reasoning or even supporting their own reason for agreeing or disagreeing. Prompting students to participate further in class mathematical discussion will help build student communication skills.

4. Model with mathematics

Math doesn't end at the classroom door. Learning to model with mathematics means that students will use math skills to problem-solve real world situations. This can range from organizing different types of data to using math to help understand life connections. Using real world situations to show how math can be used in many different aspects of life helps math to be relevant outside of math class.

5. Use appropriate tools strategically

One of the Common Core's biggest components is to provide students with the assets they need to navigate the real world. In order for students to learn what tools should be used in problem solving it is important to remember that no one will be guiding students through the real world - telling them which mathematics tool to use. By leaving the problem open ended, students can select which math tools to use and discuss what worked and what didn't.

6. Attend to precision

Math, like other subjects, involves precision and exact answers. When speaking and problem-solving in math, exactness and attention to detail is important because a misstep or inaccurate answer in math can be translated to affect greater problem-solving in the real world. The importance in this step comes in the speaking demeanor of students to explain what is understood and what isn't. This is confusing to me.

7. Look for and make use of structure

When students can identify different strategies for problem solving, they can use many different skills to determine the answer. Identifying similar patterns in mathematics can be used to solve problems that are out of their learning comfort zone. Repeated reasoning helps bring structure to more complex problems that might be able to be solved using multiple tools when the problem is broken apart into separate parts.

8. Look for and express regularity in repeated reasoning

In mathematics, it is easy to forget the big picture while working on the details of the problem. In order for students to understand how a problem can be applied to other problems, they should work on applying their mathematical reasoning to various situations and problems. If a student can solve one problem the way it was taught, it is important that they also can relay that problem-solving technique to other problems.

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Breaking down the Common Core's 8 mathematical practice standards - TeacherStep

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The Common Core mathematical practice standards are the foundation for mathematical thinking and practice for students as well as guidance that helps teachers modify their classrooms to approach teaching in a way that develops a more advanced mathematical understanding. Think of these standards as a guide to creating a more complex and absorbing learning experience [...]

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Good for Interventions

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This collection of free math resources from Strategic Intervention Solutions includes math with writing and problem solving, teacher-led math activities, math games, organization of math workshop, math with technology integration, and math professional development.

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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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Capturing Disappearing Data and Strategy Development

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Capturing Disappearing Data and Strategy Development

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Capturing Disappearing Data and Strategy Development Article

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Common Core & Sharma Scope & Sequence Draft 2012 Legal-4

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The Sequence of Strategies for Teaching Addition Facts

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The Sequence of Strategies for Teaching Addition Facts

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The Sequence of Strategies for Teaching Addition_Multiplication Facts

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Improving Mathematics Instruction for all: Vertical Acceleration

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Improving Mathematics Instruction for all: Vertical Acceleration

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Improving Mathematics Instruction for All- Vertical  Acceleration

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How Children Learn Math: Developmental Milestones in Mathematics Learning

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How Children Learn Math: Developmental Milestones in Mathematics Learning

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How Children Learn Math- Developmental Milestones in Mathematics Learning

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Non-negotiable Mathematics Skills by Grade Level

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Non-negotiable Mathematics Skills by Grade Level

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Non-negotiable Mathematics Skilss by Grade Level Summary of CCSS

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PD on the components of Everyday Math, Spring 2019

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Spring 2019

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Spring 2019

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Chapter 12: Presenting Professional Development | SAGE Companion

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Chapter 12 Sample Vignette (Coaching Lessons From the Field) (PDF)Chapter 12 Sample Vignette (Coaching Lessons From the Field) (Word)Tool 12.1 Professional Development Overview Planning (PDF)

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High-Yield Routines Book

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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.

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Erica Millet

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The true story of eighteenth-century mathematician Sophie Germain, who solved the unsolvable to achieve her dream.

When her parents took away her candles to keep their young daughter from studying math...nothing stopped Sophie. When a professor discovered that the homework sent to him under a male pen name came from a woman...nothing stopped Sophie. And when she tackled a math problem that male scholars said would be impossible to solve...still, nothing stopped Sophie. For six years Sophie Germain used her love of math and her undeniable determination to test equations that would predict patterns of vibrations. She eventually became the first woman to win a grand prize from France's prestigious Academy of Sciences for her formula, which laid the groundwork for much of modern architecture (and can be seen in the book's illustrations).

Most people think of mathematicians as solitary, working away in isolation. And, it's true, many of them do. But Paul Erdos never followed the usual path. At the age of four, he could ask you when you were born and then calculate the number of seconds you had been alive in his head. But he didn't learn to butter his own bread until he turned twenty. Instead, he traveled around the world, from one mathematician to the next, collaborating on an astonishing number of publications. With a simple, lyrical text and richly layered illustrations, this is a beautiful introduction to the world of math and a fascinating look at the unique character traits that made "Uncle Paul" a great man.

Every colorful page of Christopher Danielson's children's picture book, Which One Doesn't Belong?, contains a thoughtfully designed set of four shapes. Each of the shapes can be a correct answer to the question "Which one doesn't belong?" Because all their answers are right answers, students naturally shift their focus to justifications and arguments based on the shapes' geometric properties.

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The true story of eighteenth-century mathematician Sophie Germain, who solved the unsolvable to achieve her dream. When her parents took away her candles to keep their young daughter from studying math...nothing stopped Sophie. When a professor discovered that the homework sent to him under a male pen name came from a woman...nothing stopped Sophie.

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Meagan White - Pedagogy Teacher Resources

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NCSM book templates

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Free Resources for Mathematics | Solution Tree

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Access free worksheets, study guides, and templates focusing on effective math instruction, math best practices, math interventions, and more.

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Math Games, Math Worksheets and Practice Quizzes

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Math games online that practice math skills using fun interactive content. Over 1000 free skill testing apps and games - tablet and chromebook friendly.

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EDU 532, Mathematics Teacher Leaders Research Paper

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EDU 532, Mathematics Teacher Leaders Research Paper

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Math Coach/Interventionist

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EDU 532-Mathematics Teacher Leadership Research Paper without scoring rubric

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Reports and Research

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Both the House and Senate are continuing their fitful efforts to complete action on their versions of the 12 fiscal year 2024 Appropriations bills. The Labor,

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Esti-Mysteries: Estimation Meets Math Mysteries - Steve Wyborney's Blog: I'm on a Learning Mission.

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Introducing Esti-Mysteries! Each image invites students to wonder what number is represented by the image. As you click through the each Esti-Mystery, clues

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Learn about simple fractions. Equal, unequal, Halves, Thirds, Fourths with this fun math arcade game

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Fractions, Decimals, and Percent Clothesline

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Fractions, Decimals, and Percent Clothesline

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Fraction, Decimals, Percent Clothesline Activity

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This is a fun way to practice placing fractions, decimals, and percentages on a number line! Students will practice this skill by hanging up some laundry to dry. Practice with just one of the skills at a time, or add rigor by mixing the laundry up! Perfect for a guided or an independent math center for your math workshop!

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 Grade 4 Mid to End of Year Math Assessment – Number Sense 

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 Grade 4 Mid to End of Year Math Assessment – Number Sense 

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27 Formative Assessment Tools for Your Classroom

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In this post, you will find 27 Formative Assessment Tools for Your Classroom! Formative assessment is such an essential part of the learning process and student success, and many digital tools can help support this process.This list has a wide variety of features and options to help you solidify your formative assessment strategies! Many of the tools below are great for both formative and summative assessments.

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Revised Unit Plan-10-27-18, Julie Nugent

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4th grade Ordering Lesson Plans using benchmark numbers and number lines

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EDU 584 Project on Teaching Students Number Sense

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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3 Acts Learning

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Home | Spark Curiosity to Fuel Sense Making

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Home. Spark Curiosity With Tasks That Are Contextual, Visual and Concrete

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username:  EDU 529, password portaportal

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Welcome to portaportal, the original online bookmarking utility!

Store your bookmarks on the web for easy access anywhere

Share your links with guests through a read-only url

Add links for use through a school year, but only show students the links currently being studied

Create personal pages, class pages, school pages, topic based pages... The uses are limitless!
It's free! So signup today!

Your basic membership permits up to 5 portals, allowing each one to be viewed unlimited times.

You can start by importing your current bookmarks, or by collecting links as you browse the internet.

Upgrade to a pro account. Starting at $15/year!

No ads on your portals

Create up to 20 portals

Storage space for you to upload flyers and handouts, whatever you want!

Gain access to extra portal tools

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Welcome to portaportal, the original online bookmarking utility! Store your bookmarks on the web for easy access anywhere Share your links with guests through a read-only url Add links for use through a school year, but only show students the links currently being studied Create personal pages, class pages, school pages, topic based pages...

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Curriculum integration has been on my mind a lot lately in the work I've been doing with multiple schools and educators who are looking to take an experiential approach to learning. James Beane's ideas were very timely for me as I quickly approach a summer institute where teachers will be working on such transformation of teaching and learning.

In reflecting on this article, three thoughts have stuck with me:

1. A purpose for integration beyond the assessment results and research data

2. How can we pilot curriculum integration while still working inside the confines of politics?

3. My personal experience as a student of a subject-area curriculum and how I know there are better ways out there.

A Purpose for Curriculum Integration

First of all, I should probably share my understanding of "Curriculum Integration." In a curriculum that is fully integrated, learning is centered around a problem or theme that exists in the learner's world and often driven by their own interests. Beane's examples include "conflict; living in the future; cultures and identities; jobs, money and careers; or the environment." From there, disciplines of knowledge support students in learning about, analyzing and/or solving that problem. School schedules are no longer built around distinct subject areas like math, history and music, but instead they are driven by time in the field or communicating and collaborating with others around the problem or theme. Teachers focus on teaching content as the need arises, rather than teaching it just in case a student might need it down the road.

When I first started this experiential learning project, the purpose of it seemed to be to better engage students in making meaning of content. It was also driven by the research and assessment data that is out there on how students learn best, but Beane's article was a good reminder to me for thinking about the deeper purpose of why we started this project in the first place. Without an integrated approach, subject matter is in isolated silos and often taught the way someone decided it should be taught. There are distinct boundaries between each area, which doesn't leave room for questions and ideas outside or in the overlap. I appreciated Beane's example of such ideas:

"For example, in exploring the influences of media, young people might investigate the use of the word "average" in the context of the presumed consumer interests of the "average person." What does "average" mean here? How is "average" arrived at when used in this way? How can mathematics be used to manipulate meanings?"

If we have students doing the "doing" they will come across the basic content they need, but they will also gain skills far beyond those. Sure they may not master every standard, but there is space for them to get what they need to be successful.

Do I have questions about how this could possibly work within the confines of our current system where states dictate standards, students move between schools, and teachers who cling to specific identity? YES. But do I think it is possible, and do I support this approach to teaching and learning? YES. I'll address more of these concerns in my next post.

In the meantime, I'll share a progression chart accessed from Kathy Lake's Integrated Curriculum, sourced from Jacobs & Shoemaker (1989). It distinguishes ways of thinking about structuring learning all the way from a "fragmented approach" to "networked" integration approach and the advantages and disadvantages of each. I wonder what a fifth column might look like with driving questions or processes for moving from one to the next. Should we read this as steps in a progression, or is the ideal to scrap everything and strive for integration? I think Beane would say the latter.

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Curriculum integration has been on my mind a lot lately in the work I've been doing with multiple schools and educators who are looking to take an experiential approach to learning. James Beane's ideas were very timely for me as I quickly approach a summer institute where teachers will be working on such transformation of teaching and learning.

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Terry Burr designed that beautiful educational infographic for Osiris Educational and Visible Learning Plus. The infographic is based on data from John Hattie's research and the work of the Visible Learning Plus team.

(c) www.osiriseducational.co.uk / www.visiblelearningplus.co.uk

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Visible Learning visualized in a beautiful infographic - VISIBLE LEARNING

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Terry Burr designed that beautiful educational infographic for Osiris Educational and Visible Learning Plus. The infographic is based on data from John Hattie's research and the work of the Visible Learning Plus team. (c) www.osiriseducational.co.uk / www.visiblelearningplus.co.uk Visible Learning Infografik Visible...Read more ›

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5th Grade Assessments - Common Core Mathematics Assessments

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Resources for Math Teachers

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A collection of sites for maths teachers made by a maths teacher.

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This binder is a toolkit of resources for math standards, best instructional practices, assessment and leadership.

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Welcome! I've designed a math site to help navigate the world of elementary mathematics. Enjoy the collected resources

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EDU Math Classes

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EDU 530, 4-1-18

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Illustrating the Standards for Mathematical Practice

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Illustrating the Standards for Mathematical Practice

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Templates

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Templates for Mathematics Formative Assessment- Volume 2: 50 more Strategies for Linking Assessment, INstruction, and Learning | Uncovering Student Ideas

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Click on a link below to download a template for selected FACTs from the book. Most of these templates are provided in Microsoft Word so that you can customize them for your instructional or assessment purpose. The font used for the templates is Arial or Verdana.

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Grade 3-5 Formative Assessment Resources

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Grade 3-5 Formative Assessment Resources

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ATOMIM

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EDU 530 Assignment

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What IS Teacher Clarity?

Simply put, teacher clarity means an educator has absolute clarity about what students are to learn, know, and be able to do for an upcoming instructional focus before they plan any instruction and assessments.

The Clarity Problem

Today there's a lot of fuzziness around learning outcomes. Teachers aren't crystal clear about what they're supposed to be teaching. Students often confuse what they're learning with what they're doing. They can tell you about the activities they're engaged in, but not the intended learning those activities are designed to achieve.

The Clarity Solution

When teachers are certain about their learning intentions-what they want students to know and be able to do in a unit of study and in specific daily lessons-they can intentionally design assessments, plan instruction, and select appropriate curriculum materials directly aligned to those learning intentions. Teachers write the learning intentions in student-friendly language so students will be clear about what they are expected to learn.

Success criteria-specific descriptors of how students will achieve the learning intentions-provide teachers and students with a detailed "roadmap to the destination" that focuses instruction and motivates students to engage in the learning.

Learning progressions are the "building blocks" or instructional scaffolds that teachers pre-plan in order to help students achieve the learning intention. They are the pre-requisite skills and concepts that lay out the sequenced pathway of learning. The learning progressions provide clarity for the "Where to next?" element of teaching and learning.
Powerful and Empowering
Learning intentions, success criteria, and learning progressions are both powerful and empowering; powerful for the clarity and sharp focus they provide, and empowering for teachers and students to know:
Keep It Simple!
Corwin and I planned the one-day workshop to be a step-by-step, straightforward process that any teacher in any grade and content area could immediately apply in their own classroom. To keep the process simple, I designed six steps to apply to only one standard at first. Once teachers feel comfortable with the process, they can then apply it more easily to multiple standards for a unit of study. In each step, you will see how clarity is created for both teachers and students!

The Six Steps-Plus One

Step 1: Identify one standard for an instructional focus within a unit of study.

Select a standard that is important for students to learn in depth. You might think of this as a Priority Standard, an Essential Standard, or any standard that you know will require greater instructional emphasis than other standards for students to "master."

Step 2: Restate the standard in student-friendly wording-without losing the rigor. This is called the learning intention-the "what" that students are to learn.

Translate the targeted standard into "kid-speak," using age-appropriate language students will understand. But be careful not to lose the rigor or intent of the original standard when doing so. "Unwrapping" or deconstructing the standard will help you be clear on what it requires students to know and be able to do.

Step 3: Decide why the learning intention is important-for students and teachers.

Understanding why we want students to learn something is important to determine upfront. Sharing the why with students so they see the point or purpose of learning is critical to their engagement. Often called the Big Ideas, this step identifies the intended "take-aways"-for students and teachers.

Step 4: Write the details of what students will do to achieve the learning intention. These are the success criteria-the "how."

John Hattie describes success criteria as the "way of knowing that the desired learning has been achieved ( Visible Learning, 2009, p. 47). Success criteria, written first for the unit of study, are specific descriptors that spell out exactly what students need to show as evidence they have achieved the learning intention.

Step 5: Break the learning intention into learning progressions-the skills and concepts that lead to the learning intention.

Learning progressions are the smaller "increments" or "building blocks" of instruction that students will need in order to achieve the broader learning intention. Teachers brainstorm several verb phrases (skills followed by concepts) to show the progression of cognitive rigor from simple to complex. They then plan out a suggested order for teaching those progressions during the unit.

Step 6: Select one learning progression and write the related success criteria. Then write the success criteria for another learning progression.

The Step 4 success criteria are for the entire unit; Step 6 success criteria are for specific lessons. Teachers write them to match the learning progressions they will teach in daily lessons. In this way students will know exactly how to show they have achieved lesson goals. Clarity!

Plus One: Formative Assessment

With the clarity of learning intentions, learning progressions, and success criteria created for both the unit and the lessons, all that's needed are short formative assessments- Quick Progress Checks matched to the learning progressions and lesson success criteria-to provide credible evidence of student learning. Teachers and students use the results from those quick progress checks to make immediate adjustments in their teaching and learning tactics, respectively.

Your Own Next Steps

1. Which of the above six-plus-one steps are you currently utilizing to bring greater clarity to your own learning outcomes?

2. How are you sharing these critical elements with your students?

3. Where do you need to focus next?

4. How can these steps help you "fill in the gaps" of where you want to go next to further impact student learning in your own classroom, school, and district?

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The Clarity Problem-and the Teacher Solution - Corwin Connect

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What IS Teacher Clarity? Simply put, teacher clarity means an educator has absolute clarity about what students are to learn, know, and be able to do for an upcoming instructional focus before they plan any instruction and assessments. The Clarity Problem Today there's a lot ...

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What to look for, for Teaching Math Practices

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What to look for, for Teaching Math Practices

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Teacher resources and professional development across the curriculum

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IMPS | Implementing the Mathematical Practice Standards

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Each Illustration of the Standards for Mathematical Practice (SMP) consists of a mathematics task; a student dialogue based on that task; information about grade level, standards, and the context for the dialogue; teacher reflection questions; a mathematical overview; and optional student materials.

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Math Resources

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Written in friendlier language.

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Teaching Tools | Resources for Teachers from Scholastic

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10 Books to Spark a Love of Math in Kids of All Ages

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EDU 529

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The History of the Standards Research Paper

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EDU 531 Mathematics Pedagogical Knowledge Research Paper

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EDU 531 Mathematics Pedagogical Knowledge Research Paper

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Research about what teachers need to do to effectively teach math

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Mathematical Content Knowledge Research Paper

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Mathematical Content Knowledge Research Paper

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EDU 530

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Algebra-Linear Equation Problems

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A group of 15 EL Education staff members wrote long-term learning targets aligned with the Common Core State Standards for English Language Arts (K-12), Disciplinary Reading (6-12), and Math.

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MCK Resources

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Provide relevant texts that consider complexity, academic success, cultural competence, and critical consciousness.

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Good place to find articles

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Great for Teaching Math Intuition

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Photomath - The Ultimate Math Help App | Math Explained

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Solve even complex math problems with Photomath, the top-rated math camera solver app. Download now and understand your math homework step-by-step.