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Printable Manipulatives | Mathematical Practices

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MathArticles.com provides relevant articles from renowned math journals. The articles are coordinated to the topics of Larson Calculus. Visit MathArticles.com to access articles from:

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edtech teaching technology google "google apps" "google drive" gafe "google apps for education" education tutorials "instructional technology" "free resource...

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Educational Technology and Learning Resources for Teachers and Educators.

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Get access to files anywhere through secure cloud storage and file backup for your photos, videos, files and more with Google Drive.

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Problems of the Week - National Council of Teachers of Mathematics

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Principles to Actions Professional Learning Toolkit

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Principles to Actions Professional Learning Toolkit

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Principles to Actions Professional Learning Toolkit - National Council of Teachers of Mathematics

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These grade band specific professional learning modules are focused on the Effective Teaching Practices and Guiding Principles from Principles to Actions Ensuring Mathematical Success for All. Presentation, presenter notes, and required materials are provided in each module to support professional learning with

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

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Problems of the Week - National Council of Teachers of Mathematics

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Want to learn more? Take the free workshop. All 3rd 4th 5th 6th 7th 8th Alg 1 Geom Alg 2 Stat Calc Water Leak Will service arrive in time?Car Ramp How far did the ca…

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Open MiddleChallenging math problems worth solving

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Open MiddleChallenging math problems worth solving

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Open Middle - Challenging math problems worth solving

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

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

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

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

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Use these five strategies to encourage meaningful classroom discussions.

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Five Practices For Conducting Productive Math Talks

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Five Practices For Conducting Productive Math Talks

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Math.3.NBT.A.2

Common core State Standards

Math: Math

3: Grade 3

NBT: Numbers & Operations in Base Ten

A: Use place value understanding and properties of operations to perform multi-digit arithmetic

2:
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Download Common Core State Standards (PDF 1.2 MB)

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Discussion and Supporting Materials

Thought starters

1. How does Ms. Saul create an environment in which students are comfortable sharing their thinking?

2. What are the advantages of having students share different strategies for solving problems?

3. Why does Ms. Saul ask students about the importance of mental math?

Teachers

English Language Arts Math Science Social Studies Arts / 3 / Teacher

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Math.3.NBT.A.2 Common core State Standards Math: Math 3: Grade 3 NBT: Numbers & Operations in Base Ten A: Use place value understanding and properties of operations to perform multi-digit arithmetic 2: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

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Talking Circles Promote Equitable Discourse

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Talking Circles Promote Equitable Discourse

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Talking Circles Promote Equitable Discourse

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A structured discussion format disrupts patterns of stratified talk and facilitates broader student participation.

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Talk about math. Talk about anything you like about math. Talk about it anywhere, with anyone. Tell them why it's great. Tell them how you think. Tell them how it surprises you, how it charms you, and how it all fits together.

Kids Love to talk! We talk about our reading, our writing, our science, our personal lives. Admit it, people LOVE to talk! We should be talking in our math classes as well! The key however, is to ensure that the talk is productive and leads to deeper mathematical understanding. In the math classroom we can promote higher order thinking by engaging our students in productive and guided math talks.

I am a K-5 collaborative special education teacher and a Masters student focused on Elementary Mathematics Specialist. In my studies two ideas and philosophies have emerged that have changed my life, and thus my student's lives. Those two ideals are constructivist learning and productive math discussions. Of course I have gained unmeasurable knowledge through collaboration and discussions with my fellow learners and together we have grown through our readings and research.

Following are a few of the readings we have utilized and then three presentations I have developed, and one developed by one of my favorite math nerds of all time, Moriah Widener. I would love it if you would use these resources for your personal growth, and please, feel free to share them with your colleagues or in staff development sessions. It is through support and collaboration that we all grow as teachers!

Happy Mathing!
EDITOR'S NOTE: Although we no longer use the Common Core Standards, there is valuable information in these presentations! Click here to see our current Oklahoma Academic Standards.

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Talk about math. Talk about anything you like about math. Talk about it anywhere, with anyone. Tell them why it's great. Tell them how you think. Tell them how it surprises you, how it charms you, and how it all fits together. Kids Love to talk!

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Engaging in Productive Struggle: Number Talks

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Engaging in Productive Struggle: Number Talks

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Math.Practice.MP1

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.Practice.MP3

Common core State Standards

Math: Math

Practice: Mathematical Practice Standards

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

|

Math.2.NBT.B.5

Common core State Standards

Math: Math

2: Grade 2

NBT: Number & Operations in Base Ten

B: Use place value understanding and properties of operations to add and subtract

5:
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Download Common Core State Standards (PDF 1.2 MB)

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Discussion and Supporting Materials

Thought starters

1. What tools does Ms. LaCour use to support her ELL students?

2. What are the benefits of having students lead the number talk?

3. How do number talks encourage students to try new math strategies?

School Details

Acorn Woodland Elementary School
1025 81st Avenue
Oakland CA 94621

Data Provided By:

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Engaging in Productive Struggle: Number Talks

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Students in Monique LaCour's second grade class explore subtraction strategies through student-led number talks. Class begins with a review of number talk roles and sentence frames. Then, students break off into small groups for the number talk, where they share and try new strategies to solve a subtraction problem.

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Open-ended Questions to Encourage Conversation

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Open-ended Questions to Encourage Conversation

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PLEASE CREATE A NEW ACCOUNT OR LOG IN TO ACCESS THIS CONTENT

Enjoy your first three pieces of content for free. Subscribe for unlimited access.

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Discussion and Supporting Materials

Thought starters

1. How do open-ended questions empower students, especially English Language Learners?

2. What advice does Ms. Gelormino have for using open-ended questions?

3. How do you use questions in your own classroom?

School Details

Think College Now School
2825 International Boulevard
Oakland CA 94601

Data Provided By:

Teachers

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Open-ended Questions to Encourage Conversation

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Julia Gelormino shares how she uses open-ended questions to empower her students. She explains how using open-ended questions builds trust and leaves room for students to share their academic thinking. She gives tips for how you can remember to use them.

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Classroom DiscussionsUsing Math Talk in ElementaryClassrooms

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Classroom DiscussionsUsing Math Talk in ElementaryClassrooms

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Teaching Tools | Resources for Teachers from Scholastic

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Book Study Mondays: Math Sense, Chapter 5, The Sound of the Lesson

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Book Study Mondays: Math Sense, Chapter 5, The Sound of the Lesson

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Book Study Mondays is currently taking an in-depth look at Math Sense: The Look, Sound, and Feel of Effective Math Instruction, by Christine Moynihan. You can view summaries of previous chapters by clicking on the links below.

Here's the reading schedule (use the links to visit any of the posts):

I'm going to kick off tonight's book study with a question: When you think of your classroom during math instruction, does it buzz "with engaged talk and conversation"? (pg. 76)

This is, hands down, my favorite chapter in the book! There is so much great material here, I don't know where to start. How about a chapter blueprint? The author lists eight components related to how math instruction should sound, divided into three categories:

1. The sound of teachers

2. The sound of students

3. The sound of students and teachers

Let's look at the role of the teacher as outlined in this chapter: (1) Teachers supporting discourse, (2) Teachers providing lesson summation/reflection/closure, and (3) Teachers engaging all students. I don't know about you, but that's the teacher I want to be. This chapter more than any of the previous chapters references the Common Core Mathematical Practice standards. I highlighted a quote from page 77 about Mathematical Practice 3: Construct viable arguments and critique the reasoning of others (CCSSI 2010):
"When students communicate clearly and articulate their ideas to others, their thinking becomes visible and their understanding deepens."
Moynihan references a book called Classroom Discussions: Using Math Talk to Help Students Learn. I just received that book a couple days ago, and I didn't even get past the Introduction of the book before finding this fabulous quote: "Getting students to talk about mathematical content is one of the best ways to engage in formative assessment. An additional benefit is that students may themselves realize what they don't understand and what they do understand. This allows them to adjust their own reasoning, and over time it may improve their metacognitive abilities."

I love the charts for Rephrase, Rewind, Review, and Recharge on pages 79 and 80. The Amplification column gives teachers the words to use to step out of their comfort zone and become a facilitator of learning, instead of a giver of knowledge. They would be a great couple of pages to copy, keep close by, and glance at right before your math lesson. Change is always easier with baby steps, so maybe choose two or three of the stems to try out at a time, and gradually build your repertoire.

Likewise, the chart on page 85 provides seven excellent strategies for ensuring "that all students are physically, cognitively, and affectively engaged" (pg. 83) in the lesson. I guess that, being from Texas, it's natural that I'd like the True/False Two-Step! Having students step forward or back to indicate if they agree or disagree with a statement is a a nice change of pace from thumbs up/thumbs down. It's no secret that kiddos respond to movement.

I had to laugh when I read the following passage on page 88: "If you have ever taught at a primary grade, see whether this sounds familiar: A student has just finished explaining his answer, and you ask, "Who solved it a different way than Daniel did?" Hands fly up and you choose someone who proceeds to describe the identical solution strategy as Daniel's!" I've been modeling a LOT of number talks in classrooms, and this happens all...the...time! I will definitely be trying out the strategy of asking students to tell me one thing they did the same and one thing that was different.

So I'll end with a slightly different version of the question I started with: What steps will you take this week to increase the buzz of engaged talk and conversation in your math classroom?

Here are links to the recommended resources listed throughout the chapter:

Classroom Discussions: Using Math Talk to Help Students Learn
* I JUST received this book in the mail two days ago! Wonderful resource. A
perfect compliment to Number Talks.
Math Exchanges: Guiding Young Mathematicians in Small-Group Meetings
Total Participation Techniques: Making Every Student an Active Learner Creating the Opportunity to Learn

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Book Study Mondays: Math Sense, Chapter 5, The Sound of the Lesson - Math Coach's Corner

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Book Study Mondays is currently taking an in-depth look at Math Sense: The Look, Sound, and Feel of Effective Math Instruction, by Christine Moynihan. You can view summaries of previous chapters by clicking on the links below. Here's the reading schedule (use the links to visit any of the posts): Aug 19, Chapters 1 & 2 [...]

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So, I'm starting out today with a pop quiz. Ha ha. What do the following number sentences have in common? NO calculators!

They all equal 120, don't they? Do you see why? Each of the expressions is really just another way to write 15 x 8. The numbers 15 and 8 have been broken down into smaller factors in each of the expressions. Rich problem sets such as this one are the basis for number talks in the classroom.

Our district purchased Number Talks: Helping Children Build Mental Math and Computation Strategies as a professional development resource for the campus instructional coaches. What a gem! Now, it doesn't appear to be a friendly book at first glance. In fact, several coaches said they found it intimidating. That's why I would suggest starting with the DVD-look at some of the video clips and you'll be hooked! I have been modeling number talks in our 3-5 classrooms, and it's a blast. Click on the picture below to view a video clip of a number talk.

Number talks, as described in this particular book, are short-10-15 minute- warm-up activities focusing on mental math strategies. The book includes a great section describing what number talks are and how to use them in the classroom, and then the rest of the book is organized by grade levels-explaining what number talks look like at each grade level and providing pages with problem sets that can be used to promote certain strategies.

Now, I want you to think carefully about the title of the book-Number TALKS. Who is doing the talking? If you said the teacher, you'd be wrong! The kiddos are the star of this show. Basically, this is another one of those situations where you don't teach-the kiddos discover! Your job is to plan problem sets that will lead them toward a particular strategy (and they're included in the book), scribe their thinking, and facilitate new learning.

Here's my testimonial. You might think your students won't have the strategies that the kids in the video use. Let me tell you, they will surprise you! I have never seen students more engaged and excited about math than I have when I'm doing number talks. And the speed of the results shocked me! In just a couple weeks time, students became much more confident in their strategies and grew in their ability to explain their mathematical thinking. A teacher in one of the video clips states that she has walked through a door, and she will never go back. I can guarantee that you will feel that way, too!

Can you tell I like number talks? 🙂

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Who's Doing the Talking? Number Talks - Math Coach's Corner

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So, I'm starting out today with a pop quiz. Ha ha. What do the following number sentences have in common? NO calculators! They all equal 120, don't they? Do you see why? Each of the expressions is really just another way to write 15 x 8.

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8 Ways to Pose Better Questions in Math Class

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8 Ways to Pose Better Questions in Math Class

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Have you ever taught a math lesson that seemed to be going well-with students active, engaged and producing the right answers-but when you ask kids to explain the reasoning behind their work, they clam up or veer off on a tangent?It happens to the best of us, which is why it's so important to be intentional with our questioning and to think about not only the types of questions we are asking but also the pattern in which we're asking them.

Below we've rounded up eight tips to help you focus your questioning and, by doing so, deepen students' mathematical reasoning.

Don't let "information gathering" questions dominate your lesson.

These are answer-seeking questions such as "What is the formula for finding the area of a rectangle?" "When you write an equation, what does the equal sign tell you?" While these questions have their time and place (they help to establish what students know), they don't reveal higher-order thinking or reasoning.

Ask probing questions that require students to explain, elaborate or clarify their thinking.

This includes articulating the steps they took to solve a problem or complete a task. For example, "As you drew the number line, what decisions did you make so that you could represent seven-fourths on it?" "Can you show and explain more about how you used a table to find the answer?"

(Source: Minds in Bloom)

Give students adequate time to respond.

Research has shown that we often give students less than five seconds to answer a question in math class! When we move so quickly, we lose the chance to see how students are making sense of mathematics.

Ask students to make the mathematics visible.

By this we mean discussing the connections between mathematical ideas and relationships. For example, "How does that array relate to multiplication and division?" "In what ways might the normal distribution apply to this situation?"

Encourage reflection and justification.

These questions reveal deeper understanding of students' reasoning and actions, including making an argument for the validity of their work. For example, "How might you prove that 51 is the solution?" "How do you know that the sum of two odd numbers will always be even?"

(Source:@TEACHHEATH)
Avoid "funneling" the conversation.

This means landing on a desired conclusion in advance and giving little attention to student responses that veer from the desired path. You may be focused on students arriving at a particular answer, for example, or using a certain strategy to the exclusion of others. In a funneling question pattern, the focus is often on information gathering with one or two higher-order questions at the end.

Try "focusing" your questions instead.

While funneling question patterns are rigid and preset, focusing questions attend to students' needs and are open to being investigated in multiple ways. A focusing question pattern blends information gathering, probing, reflection and justification. It involves asking students what they notice and encouraging them to communicate their thoughts clearly.

This video case study shows the difference between funneling and focusing questions in action.

Encourage students to ask questions of one another.

It is much easier to facilitate a focusing question pattern when you are not the only one in the room directing conversation. Encourage students to support, challenge and question one another. For example, "Why do you think that?" "Could you have solved the problem in a different way?"

You may find that students' own questions take the conversation to a level you never imagined reaching!

(Source: Making Shift Happen)

This article is adapted from the NCTM publication Principles to Actions: Ensuring Mathematical Success for All.

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8 Ways to Pose Better Questions in Math Class - We Are Teachers

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It's so important to be intentional and to think about not only the types of math questions we are asking but also the pattern in which we're asking them.

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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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3 Act Math Tasks By Kyle Pearce, Dan Meyer and Others

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3 Act Math Tasks by Kyle Pearce, Dan Meyer and many others to spark curiosity and fuel sense making.

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Problem Based Learning (PrBL) curriculum maps

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Problem Based Learning (PrBL) curriculum maps

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The following Problem Based Learning (PrBL) curriculum maps are based on the Math Common Core State Standards and the associated scope and sequences. The problems and tasks have been scoured from thoughtful math bloggers who have advanced our practice by posting their materials online.

The Scope and Sequences for Algebra 1, Geometry, Algebra 2, Math 9 (Integrated), Math 10 (Integrated), and Math 11 (Integrated) are from Pearson. Other Scope and Sequences were developed by me, modeling a similar visual style.
Grade 3 CCSS PrBL Curriculum Map Grade 4 CCSS PrBL Curriculum Map Grade 5 CCSS PrBL Curriculum Map Grade 6 CCSS PrBL Curriculum Map Grade 7 CCSS PrBL Curriculum Map Grade 8 CCSS PrBL Curriculum Map Math 9 (Integrated) CCSS PrBL Curriculum Map Math 10 (Integrated) CCSS PrBL Curriculum Map Math 11 (Integrated) CCSS PrBL Curriculum Map Algebra 1 CCSS PrBL Curriculum Map Geometry CCSS PrBL Curriculum Map Algebra 2 CCSS PrBL Curriculum Map
Be sure to check back often as these curriculum maps are bound to change when new cool activities are added on math blogs worldwide. I'll be adding more and more curriculum maps in due time. Also, if you have a favorite particular task that isn't here (or just comments in general), let me know in the comments!

For more on Problem Based learning, you can check out my previous posts on the topic.

- Geoff

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Common Core Problem Based Curriculum Maps

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The following Problem Based Learning (PrBL) curriculum maps are based on the Math Common Core State Standards and the associated scope and sequences. The problems and tasks have been scoured from thoughtful math bloggers who have advanced our practice by posting their materials online. The Scope and Sequences for Algebra 1, Geometry, Algebra 2, Math...

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a ppt is here

an effort to collect together proofs that involve some form of geometrical insight

thanks to Dietmar Kuchemann

there are several good sources for geometrical problems
those by Ed Southall and Vincent Pantolini
and Catriona Shearer
are fairly well known

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a ppt is here an effort to collect together proofs that involve some form of geometrical insight thanks to Dietmar Kuchemann there are several good sources for geometrical problems those by Ed Southall and Vincent Pantolini and Catriona Shearer are fairly well known

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What is the first question that comes to your mind?

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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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K-5 Math Teaching Resources is a leading New York City based math consultancy firm. Our mission is to transform the teaching and learning of mathematics, improving outcomes for all students in elementary and middle school. Click on a tab below for information on our research-based professional development and customizable consulting services. Our results-driven elementary and middle school consultants are committed to working side-by-side with administrators, coaches and teachers to build exceptional quality math instruction and curriculum for schools and school districts, transforming students' math education and achievement.

On this website you will find mathematics to support standards-aligned math instruction. Use the grade level tabs at the top of this page to download sample resources for each grade level from Kindergarten through 5th Grade or visit our EBook Store to purchase a complete set.

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Research based resources and professional learning opportunities to transform math teaching and learning communities.

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This page contains links to other pages focused on project-based learning from my teaching.

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Professional Learning Communities via Social Media

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Professional Learning Communities via Social Media

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"The term professional learning community has become quite commonplace in education circles. The term describes a collegial group who are united in their commitment to an outcome. In the case of education, the commitment would be to student learning"

Technology has provided educators with unlimited tools that make it possible to connect and teach in new and exciting ways!

"These same forces offer the opportunity for new models for the professional growth of teachers. Learning communities share a way of knowing, a set of practices, and shared value of the knowledge that comes from these procedures. These learning communities, with expanded human and technological resources, bring together students, teachers, and community members in directing the course of education in new ways."
Value of Tech-Enabled PLCs
Engage: When teachers engage in quality professional learning communities they are committing to developing excellence within themselves.

The benefits of professional learning community to educators and students include:

reduced isolation of teachers

better informed and committed teachers

academic gains for students

powerful staff-development approach and a potent strategy for school change and improvement

Choosing the Community that is Right For You

Determine your content goals and expectations for participating in an online PLC.

Choose a structure that will support you as you work toward your goals.

Select tools that will help you create the structure you need.

Then There is
To keep your "feed" organized consider using tweetdeck (https:// tweetdeck.twitter.com/) or hootsuite (https:// hootsuite.com/)

Twitter for Your PLN YouTube video: https://youtu.be/8KtC0VrQ0ig

Using Tweetdeck YouTube video: https://youtu.be/jAsN3cA9Qxs

There are many awesome educators utilizing Twitter! Here are a few hashtags and people to follow:#elemmathchat, #mtbos, #okmath, #msmath

·Max Ray-Riek @maxmathforum

·Annie Fetter @MFAnnie

·Marilyn Burns @mburnsmath

·Donna Boucher@MathCoachCorner

·Mark Chubb @MarkChubb3

·Matt Coaty @Mcoaty

·Steve Wyborney @SteveWyborney

·Jeremiah Ruesch @mathkaveli

·Tina Cardone @crstn85

·Justin @JustinAion

·Dan Meyer @ddmeyer

·Steve Leinwand @steve_leinwand

·Brian Stockus @bstockus

·Levi Patrick @_levi_

·Jen Lamb @educatorjen

Robbyn Glinsmann @glinsmannMath

Melynee Naegele @buffalogal03

Twitter Chat Schedules: Sunday

#oklaed: Oklahoma Ed Chat 8 pm

#probchat: Problem Centered Learning 8pm

#TMchat: Thinking Maps Chat 9pm
Monday
#tlap Teaching Like a Pirate 8:00 PM

#msmathchat: Middle School Math Chat 8pm
Wednesday
#educoach Educational Coaching 9pm

Thursday #ElemMathChat 8pm

Facebook is a Great Resource too: Search and Find a myriad of resources and connections!

NCTM: https://www.facebook.com/TeachersofMathematics?fref=ts

NCSM: https://www.facebook.com/mathedleadership?fref=ts

OCTM: https://www.facebook.com/pages/Oklahoma-Council-of-Teachers-of-Mathematics/205940092775526?fref=ts

Math Coach's Corner: https://www.facebook.com/MathCoachsCorner?fref=ts

ElemMathChat: https://www.facebook.com/profile.php?id=100005368367347&fref=ts

Resources:
Public Schools of North Carolina: http://www.ncpublicschools.org/profdev/resources/proflearn/

Learn NC http://www.learnnc.org/lp/pages/7012

Education Chats on Twitter: https://sites.google.com/site/twittereducationchats/education-chat-calendar

Math Blogs: https://docs.google.com/spreadsheets/d/1sceqJc8PVm6e2xC1GekgP63RHxxgfLkaRSBtE-7c8nw/pub?single=true&gid=0&output=html

Exploring the Math Twitter Blogosphere: https://exploremtbos.wordpress.com/

Math Teacher's Circles: http://www.mathteacherscircle.org/

Twitter for Teachers: http://rossieronline.usc.edu/twitter-for-teachers/

Collaborative Online Continuing Education: Professional Development Through Learning Communities: http://www.edutopia.org/professional-development-through-learning-communities

Mathematics educators on Twitter: http://mathed.net/wiki/Mathematics_educators_on_Twitter#Chats_Focused_on_Mathematics_Education

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Professional Learning Communities via Social Media

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"The term professional learning community has become quite commonplace in education circles. The term describes a collegial group who are united in their commitment to an outcome. In the case of education, the commitment would be to student learning" Technology has provided educators with unlimited tools that make it possible to connect and teach in new and exciting ways!

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below are some things that have cropped up organically through people who blogged and tweeted. click around and see some great stuff!

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The Importance of Debriefing in Learning and What That Might Look Like in the Classroom

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The Importance of Debriefing in Learning and What That Might Look Like in the Classroom

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The act of debriefing means to carefully examine and analyze upon completion, providing succinctness and summary of a situation.

Debriefing is a daily exercise in most professions: business, politics, law enforcement, psychology, healthcare, law, etc. It is often seen as integral to the profession as members reflect on their learning experiences, track their progress, and name their understandings. In truth, debriefing is accepted as an everyday necessity in order for the professional to advance in his/her practice.

Unfortunately, we as teachers, overwhelmed with exhaustive standards, often feel too rushed to tap into the power of debriefing with students. However, the truth is that when students get the opportunity to dwell on and synthesize the work from a lesson, they discover what they have learned and how they learned it, and then consider what they should do next to stretch and grow that learning. When we afford time for a Debrief, our students get the chance to personalize the lesson and determine where their understanding is and where it isn't.

What Debriefing Might Look Like in the Classroom:
Exit Tickets
Exit tickets are a simple but very effective technique for promoting application, analysis, and synthesis of the learning. Students complete their exit tickets before leaving the class. You then use the collected exit tickets as a quick formative assessment to gauge the needs of the class. They thus serve as closure for a day's class and as information that can be used for planning (Allen, 2004, p. 201). They can also be used by students at the beginning of the next class to generate common class questions or to form study groups (p. 24). What do exit tickets look like in math? They can be summaries, problems to solve, questions that remain, visual representations, journals, analogies, examples and counterexamples, reflections on the prog- ress of the lesson, sketches, and so on. Basically, an exit ticket can be any way you want the students to demonstrate what they learned from class that day.
Essential Question Revisited
Determine the Purpose of the lesson. From that statement, create an essential question or two that will help students reach an understanding of the lesson's Purpose. Present it to the students at the Bridge. Ask them to think, write, and discuss their responses. Then put up the same essential question at the Debrief and have the students use their new knowledge to add to or otherwise revise their original responses. Allow time for silence. Make the questions conceptually grounded, with a real-life flavor to them, rather than simply address the behavioral objective of the lesson. You will get more buy-in this way because the students will find relevance in the learning.
Evaluation of Today's Learning Objective
Have the students fill out sheets that summarize their understanding and signal their efforts to reach the goals for the day's lesson (see the sample forms that follow).
Human Continuum
Place cards at the front of your classroom labeled along a continuum as follows (Hollas, 2005, p. 78):

I could teach what we learned today!

If I took a test on what we learned today, I would do pretty well!

I still don't get what we learned today and would like to revisit it with help!

On the floor in front of the cards, make a line with masking tape. Ask students to stand on the masking tape, positioning themselves so that they are near the card that best describes their understanding of the content. Ask each student to turn to a neighbor and discuss what he or she knows about the topic and/or why he or she chose to stand at that location.
GIST: "Generating Interactions Between Schemata and Text"
GIST has been proven to effectively improve students' reading com- prehension and summary writing (Cunningham, 1982, p. 42-47; Forget,

2004, pp. 156-162). At the Debrief component of the lesson, have students generate a summary of 20 or fewer words. Then ask students to share their GIST statements with a partner. Now challenge the students to come to a consensus for a class GIST summary. By restricting the length of students' GIST summaries, the teacher compels the students to use the three major strategies necessary for comprehension and retention of key ideas in any text: They must delete trivial information, select key ideas, and generalize in their own words.
Before and After the Learning
Return to your "anticipation guide" or "preconcept and postconcept check" to review for accuracies and inaccuracies.
Making Connections
What connections link this learning to the big ideas in mathematics (Hyde, 2006, p. 125)? Encourage the students to make math-to-self, math- to-math, and math-to-world connections.
Whip Around
Have your students make a large circle. You state the Focus, and each student quickly states a connection to that Focus. The connection can be a related concept, an important idea, an example, a strategy for problem solving, a personal connection, a math-to-math connection, or a math-to- real-world connection.
Three Facts and a Fib
This activity is a summative assessment. Ask students to write on an index card four statements about any content the class has just studied (Forsten et al., 2002b, p. 88). Three of the statements (examples, equations, etc.) should be true, and one should be false. Tell students to move about the room, sharing their list of statements with each other. Explain that each student should ask his fellow students to try to pick the false statement. An alternative to this activity is to collect the cards and use them as an Ignition the next day.

Summarizing one's understanding or thinking in writing facilitates deep processing. In short, writing is hard, and the act of writing requires not only deep thinking but also processing your knowledge. Writing sum- maries is even harder. A written summary is synthesis in action.
3-2-1 Journal Entry
The 3-2-1 strategy requires students to summarize key ideas from the lesson and encourages them to think independently. First, students write about 3 things they discovered. Next, they write about 2 things they found interesting. Last, they write 1 question they still have. This strategy can be used as a journal entry during the Debrief or as an exit ticket. The 3-2-1 journal has endless options. You can be flexible with what you want the students to write about: 3 examples of the learning, 2 nonexamples, and 1 way you can tell the difference, and so on.
Math Journals
Journaling affords time for students to reflect, reconsider, revise, and reapply the learning. A math journal is the ideal place for students to pro- cess their mathematical thinking. The math journal can also hold reflec- tions, connections, and syntheses, all of which require skills necessary for success on your state's open-ended math questions. Reflective writing allows students to experience the quietness of their own minds at work, which is a gift.
T eaching an Adult at Home!
After you introduce a new math concept, the students' homework could include "teaching" an adult at home what was learned in class that day. During the Debrief, we practice in class by role playing what they will do at home that evening. Only assign a few problems, with the bottom half of the math page a space for the adult's signature as well as any comments.

This activity allows students to synthesize the learning and provides a worthwhile formative assessment. If the student doesn't truly understand the concept, there is no way he or she will be able to explain it clearly to someone else.
Representation of the Lesson
Have "leftover" containers available for each small group. Their assignment is to place "leftovers" in the container for someone to "mull over" tomorrow. The leftovers should provide the "main dish" from the learning and some of the "side dishes" that supported it that day. The "dessert" should be their favorite part of the lesson. They can do this with pictures, manipulatives, explanations, and so on. Make sure groups can defend their choice of leftovers. Now use the containers the next day as the Bridge to the Learning.
Stump the Teacher
Students represent the learning in some visual way: 2-D models, tables, graphs, sketches, graphic organizers, cartoons, Venn diagrams, examples/nonexamples, and so on. This visualization will promote critical thinking. Challenge the students to explain their visual representations.
Journaling
Students, working in partnerships or small groups, prepare questions or problems to try to "stump their teacher" (Forget, 2004, pp. 221-225). This activity is a high-level way to review just before a test because stu- dents need to have a deep understanding of the content to craft difficult and stump-worthy questions.

Journaling is a great way to Debrief the lesson. The journal prompts below are perfect for debriefing in the math class. Thanks to Donna Boucher, from Math Coach's Corner for collaborating with me on this list.
Download "Put it in Writing"
The following prompts are intended to cultivate deeper mathematical conversations and reflections.

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The Importance of Debriefing in Learning and What That Might Look Like in the Classroom | Corwin Connect

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The act of debriefing means to carefully examine and analyze upon completion, providing succinctness and summary of a situation. Debriefing is a daily exercise in most professions: business, politics, law enforcement, psychology, healthcare, law, etc. It is often seen as integral to the profession as members reflect on their learning experiences, track their progress, and name their understandings.

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The Importance of Debriefing in teaching and learning.

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Wikispaces was founded in 2005 and has since been used by educators, companies and individuals across the globe.

Unfortunately, the time has come where we have had to make the difficult business decision to end the Wikispaces service.

We first announced the site closure in January 2018, through a site-wide banner that appeared to all logged-in users and needed to be clicked on to dismiss

During the closure period a range of banners were shown to users, including a countdown banner in the final month. Additionally, the home page of Wikispaces.com became a blog, detailing the reasons for the closure. Private Label Site Administrators were contacted separately regarding the closure

Wikispaces Tier

Closedown Date

Classroom and Free Wikis end of service

31st July 2018

Plus and Super Wikis end of service

30th September 2018

Private Label Wikis end of service

31st January 2019

Why has Wikispaces closed?
Approximately 18 months ago, we completed a technical review of the infrastructure and software we used to serve Wikispaces users. As part of the review, it became apparent that the required investment to bring the infrastructure and code in line with modern standards was very substantial. We explored all possible options for keeping Wikispaces running but had to conclude that it was no longer viable to continue to run the service in the long term. So, sadly, we had to close the site - but we have been touched by the messages from users all over the world who began creating wikis with it and now running them on new platforms.

The Wikispaces team

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Wikispaces was founded in 2005 and has since been used by educators, companies and individuals across the globe. Unfortunately, the time has come where we have had to make the difficult business decision to end the Wikispaces service.

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Are you ready to move from theory into practice with PBL? Then our courses and workshops are for you.

We offer a variety of workshops and support services for teachers, school and district leaders, and instructional coaches to get started with Project Based Learning.

We're here for you! See our health statement

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Are you ready to move from theory into practice with PBL? Then our courses and workshops are for you. We offer a variety of workshops and support services for teachers, school and district leaders, and instructional coaches to get started with Project Based Learning. We're here for you!

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NC Department of Public Instructioncreature 5.jpg

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NC Department of Public Instructioncreature 5.jpg

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Mr. Bowen's Fifth Grade - Site has moved to http://www.bowenpeters.com

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Number Talks Math Talk Bookmarks Talk Stems for Students Asking Effective Questions Number Talks Collection Number Talks Number Suggestions Number Sense Tricks Math Talks Overview Number Talks...

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Big Ideas and Understandings as the Foundation forElementary and Middle School Mathematics 

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Big Ideas and Understandings as the Foundation forElementary and Middle School Mathematics 

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Mathematically Minded:  The Recovering Traditionalist

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Mathematically Minded:  The Recovering Traditionalist

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IT'S THE NUMBER THAT A STUDENT WORKS WITH UNTIL HE KNOWS IT "UPSIDE DOWN AND BACKWARDS" WITHOUT HESITATION. THAT IS WHY WE CALL IT A "JUST RIGHT NUMBER."

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Represent and solve problems involving addition and subtraction

1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with a symbol for the unknown number to represent the problem

1.OA.A.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g. by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

1.OA.B.3 Apply properties of operations as strategies to add and subtract. Examples: If 8+3=11 is known, then 3+8=11 is also known (Commutative property of addition). To add 2+6+4, the second two numbers can be added to make a ten, so 2+6+4=2+10=12 (Associative property of addition).

1.OA.B.4 Understand subtraction as an unknown-addend problem. For example, subtract 10-8 by finding the number that makes 10 when added to 8.

1.OA.C.5 Relate counting to addition and subtraction (e.g. by counting on 2 to add 2).

1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g. 8+6=8+2+4=10+4=14); decomposing a number leading to a ten (e.g., 13-4=13-3-1=10-1=9); using the relationship between addition and subtraction (e.g. knowing that 8+4=12, one knows 12-8=4); and creating equivalent but easier or known sums (e.g., adding 6+7 by creating the known equivalent 6+6+1 =12+1=13).

1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6=6, 7=8-1, 5+2=2+5 , 4+1=5+2

1.OA.D.8 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8+ ? =11, 5 = □ - 3, 6+6 = □

NUMBER AND OPERATIONS IN BASE TEN

1.NBT.A.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
a. 10 can be thought of as a bundle of ten ones - called a "ten."
b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

1.NBT.B.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten.

1.NBT.C.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

1.NBT.C.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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Represent and solve problems involving addition and subtraction 1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g.

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Represent and solve problems involving addition and subtraction

2.OA.A.1 Use addition and subtraction within 100 to solve one and two step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with a symbol for the unknown number to represent the problem.

2.OA.B.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Work with equal groups of objects to gain foundations for multiplication

2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g. by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

2.OA.C.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

NUMBER AND OPERATIONS IN BASE TEN

2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Understand the following as special cases:
a. 100 can be thought of as a bundle of ten tens - called a "hundred."
b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, nine hundreds (and 0 tens and 0 ones).

2.NBT.A.2 Count within 1000; skip count by 5s,10s, and 100s.

2.NBT.A.3 Read and write numbers to 1000 using base-ten notation, number names, and expanded form.

2.NBT.A.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols.

Use place value understanding and properties of operations to add and subtract

2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

2.NBT.B.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

2.NBT.B.8 Mentally add 10 or 100 to a given number 100-900 and mentally subtract 10 or 100 from a given number 100-900.

2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

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Represent and solve problems involving addition and subtraction 2.OA.A.1 Use addition and subtraction within 100 to solve one and two step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using drawings and equations with a symbol for the unknown number to represent the problem.

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Base ten blocks or ten frames flash on the screen for a set time limit. The student is then asked to identify what number was shown.

Directions:

Watch carefully! After the timer runs out, enter the correct number to proceed to the next flash. The timer decreases with each correct answer and increases with each incorrect answer. At the end of the interactive, data is displayed showing the incorrect and correct answers and what time limit the slide was in view.

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Base ten blocks or ten frames flash on the screen for a set time limit. The student is then asked to identify what number was shown. Watch carefully! After the timer runs out, enter the correct number to proceed to the next flash. The timer decreases with each correct answer and increases with each incorrect answer.

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Adblock Detected

If you are enjoying Symbaloo, please support us by disabling your ad-blocker or whitelisting our site.

We depend on ad revenue to keep Symbaloo free and fund future developments. Thank you.

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Symbaloo - Save bookmarks and favorite websites online

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Save your bookmarks and favorite websites online with Symbaloo! The best way to store, manage, and organize your bookmarks on the web. Create a free account to share your favorites with friends, colleagues or students. With over 10 million users, Symbaloo is a trusted edtech tool of teachers and educators worldwide!

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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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Discover math on geogebra.org, the home of our free online graphing calculator, geometry calculator, 3D calculator, spreadsheet, CAS, probability calculator and classroom activities

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Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

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The NCES Kids' Zone provides information to help you learn about schools; decide on a college; find a public library; engage in several games, quizzes and skill building about math, probability, graphing, and mathematicians; and to learn many interesting facts about education.

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Stretch virtual bands around pegs to form line segments and polygons.

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CutOutFoldUp --Interesting things to make out of paper.

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CutOutFoldUp --Interesting things to make out of paper from mathematical models to toys.

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Graphic Organizers & Choice Boards

This collection of ready-to-use graphic organizers will help children classify ideas and communicate more effectively. All of our printable graphic organizers are designed to facilitate understanding of key concepts by allowing students to visually identify key points and ideas. By using graphic organizers across all subject areas, you will be empowering your students to master subject-matter faster and more efficiently. We have graphic organizers for reading, science, writing, math, and for general classroom use. You'll also find blank printable templates like graph paper, dot arrays, and other useful tools.

Popular Graphic Organizer Collections

Self-assessment Graphic Organizers

Growth Mindset Graphic Organizers

Graphic Organizers (PreK-2)

Help students, grades pre-K-2, with their reading comprehension, main idea organization, and more using our graphic organizers.

Graphic Organizers (Grades 3-5)

Help your grade 3-5 students with their organization by using our graphic organizers and reading webs.

Graphic Organizers (Grades 9-12)

These graphic organizers for grades 9-12 will aid students in reading comprehension, writing abilities, and sequencing.

Writing Graphic Organizers

Help students organize their writing with these sequence charts, reading organizers, outlines, webs, and more!

Research Graphic Organizers

Support students to practice and develop essential research skills.

Science Graphic Organizers

Use our venn diagrams, graphic organizer worksheets, and instructions to help your students organize their scientific thought.

Timelines and Sequence Charts

Sequence stories and picture orders with these timeline and sequence charts.

Reading Comprehension

Enhance your student's reading comprehension with these webs, main idea charts, plot summaries and more with our reading comprehension graphic organizers!

Concept Maps and Idea Webs

These concept maps and idea webs will help students organize their thoughts, whether they are history, science, or language arts related.

Math Graphic Organizers

Help your students enhance their math skills and stay on track with these homework checklists, KWL charts, column charts and more.

Galleries

These galleries provide you the best graphic organizers for every occasion. Whether it be writing, science, literature, or animal related, we have a slideshow for it all!

Customizable Graphic Organizers

Use our customizable graphic organizers to tailor each one to the specific lesson of the day.

KWL Charts

Help students organize what they know, what they want to know, and what they have learned with these KWL charts relating to all subjects.

Venn Diagrams

Venn Diagrams are a great way for students to compare and contrast two (or three) concepts. Use our venn diagrams to accompany your lesson for any subject.

Cause and Effect

Each effect has a cause. Help students identify the two in their readings, writing, and more with our cause and effect printable worksheets.

Main Idea and Supporting Details

It is important for students to distinguish main ideas and supporting details in order to comprehend their readings. We have provided printable graphic organizers, such as a stair step organizer, to help students organize the main idea from the supporting details.

Choice Boards

Choice Boards are similar to graphic organizers because they can be downloaded, printed, and given to students. What sets Choice Boards apart is that they provide students with the opportunity for choice. Rather than a graphic organizer that has one assignment, a choice board provides multiple ways that students can explore a topic or skill and demonstrate their learning. Choice boards also help you differentiate your instruction, as you can support students to make a choice that best aligns with their learning needs and learning preferences. Access our library of choice boards below.

Holiday Choice Boards

Math Choice Boards

English Language Arts Choice Boards

Social Studies Choice Boards

Science Choice Boards

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Graphic organizers for teachers grades K-12.

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This activity will help students make the transition from one-variable representations (e.g., number lines) to the TWO-variable representation of the coordinate plane. Students will watch 15-second videos and translate them into graphs with your help. Special thanks to Adam Poetzel (@adampoetzel) for his videos. (Used under CC-BY license.)

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Finding the Mean of a Data Set as a "Balance Point"

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The Mean as a Fair Share and a Balancing Point

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When we are asked what the mean average is, we typically think about the process of finding the mean which we do by adding all the data values and then dividing the sum by the number of data values. In this video, we will look at what we physically mean by the mean.

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Hosted by Chris Shore of The Math Projects Journal

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San Antonio, CA , April 2017
I have summarized each session with some simple (*) bulleted notes,red underline quotes to encapsulate my major take-aways, and occasionally a brief italicized commentary.

The Big Take Away = Differentiation should not mean different tasks for different students, but instead should offer different depths with same task.

Technology can be used effectively to address Inequality, Disabilities and Differentiation.

Marbleslides is an example of a high cognitive demand task that naturally differentiates.

Our (math ed community) work of offering High Quality, Meaningful, and Relevant mathematics for ALL has never been more important. Non-routine Cognitive jobs are becoming a growing percentage of employment opportunities.

Inequality:
1) 51% of American students are on free and reduced lunch, which equates to 25 million kids!
2) The two great equalizers: Mass Adoption of Technology and Public Education.

Disabilities: For students with disabilities, technology opens doors that have always been closed. Desmos is currently working with a blind person to develop an audio feature that converts graphs to music and sound.

1. OK, OK already ... I'll finally start using Marbleslides!

2. I will also place more "extensions/challenge" problems on tasks to offer deeper differentiation.

Gut Instincts: Developing ALL Students' Mathematical Intuition - Tracy Zager (Stenhouse Publishers)

"Intuitive experiences must be acquired by the student through his/her own activities - they cannot be learned through verbal instruction." - Erich Wittmann

Following mathematical intuition needs to precede the logic. Logic then further encourages the intuition:

Tracy had us practice this explicit development of intuition with a simple challenge and manipulative. "Can you try and discover the size of some of these other angles?" We were given the fact that the squares had 4 right angles, but no protractor. Go!"

Intuition can also be developed through estimates before the algorithmic practice occurs.

The Big Take Away = "The Brain Has 3 Learning Networks: The WHAT, the HOW and the WHY."

The WHAT Network = Different parts of the brain ...

Approximate Number System
All animals can picture quantity especially when comparing a lot vs a few. It gets harder as the ratio approaches 1:1

Language Retrieval
Association between number and name (assigning "eight" to a collection of eight items). Math facts are retrieved in the language that they were learned.

Symbol Procedure
Association between number and symbol (assigning "8" to a collection of eight items).

Feeding the WHAT Networka) Connect the Visual, Symbolic & Linguistic parts of the brain through multiple representations
b) Make Sense through Coherence: What is learned today should be related to what was learned yesterday.

2. The HOW network = Executive Function

Cognitive Flexibility

Working Memory

Concentration

Emotional Control

Feeding the HOW Networka) Incentives for inputs not output
b) Develop the Math Practices, focus on process, not results.
c) Notice: Define the desired learning behaviors and call them out during lesson. Thisvideo of the "Monkey Business Illusion" demonstrate how the human mind focuses intensely on what you want it to notice. What behaviors do you want students to focus on?
d) Nudge: Use Norms to encourage target behaviors. Compare past, less productive behaviors to current successful behaviors.

3. The WHY Network = The Affective State

The 3 Mindsets of Why
-Purpose & Relevance
- Growth
- Belonging

Feeding the WHY Network
a) Purpose & Relevance: It is more powerful connecting a cause (Self-Transcendance) than to a career, knowing math will help you make a difference in the world.
b) Growth: Give feedback like you are giving advice (vs judgement). Carole Dweck, "The brain is like a muscle. The harder it works, the stronger it gets." This should be the norm. We have to believe in our students abilities before they will believe in themselves.
c) Belonging: Establish a culture where it is safe to learn (vs perform). We cheer each other's growth.

Feeding the Entire Network Intentionally

Manage teacher cognitive load - don't look for everything all the time.

Match the tasks to illuminating the beliefs, behaviors or knowledge and skills that you want to notice.

Behaviors aren't one-and-done; they need constant nurturing of the mindsets that drive them.

Have the right food ready - anticipate, notice and respond.

YOU and the adults have to believe.

In regards to praising inputs, not outputs. Dr. Dockterman shared a study on financial incentives. Monetary rewards for better grades showed no improvement; monetary rewards for the behaviors that leads to better grades (notes, homework, questions) showed significant improvement.

What Every Math Leader Needs to Know and Be Able to Model to Support the Classroom Development of Numerical Fluency - Patsy Kanter & Steve Leinwand (AIR)

5 Steps to Implementing Numerical Fluency

1. Commitment: Fluency is more than speed. It takes ongoing, protected time and assessments to develop.

2. 10 Pivotal Understandings of Numerical Fluency:
1. All quantities are comprised of parts and wholes that can be put together and taken apart.
2. Numbers can be decomposed.
3. Storytelling is key, because vocabulary of the four operations is critcial.
4. Properties of Operations reduces memory load (like 29 x 25).
5. Requires discussion of alternate strategies.
6. 5 & 10 are cornerstones.
7. Understanding that 9 and (10-1) are the same quantity.
8. Groups or 2, 3, 5, & 10 are cornerstones of Multiplying.
9. Ideas of equality and equivalency are key.
10. Place value dominates fluency of large numbers.

3. Cement Number Fluency:
a) Concrete Representations
b) Verbal Representations
c) Pictorial Representations
d) Discussion & Justification

4. Calendarize:10-15 minutes daily
For example ...
Monday: Make it Number Sense Activity
Tuesday: Operational Practice
Wednesday: Word problems
Thursday: Making math connections
Friday: Counting patterns, Games, Puzzles (week 1) and Assessment (week 2)

5. Assess: Include Numerical Fluency (not speed) on assessments. For example, "Write everything you know about two."
1+1=2
2 is even
2 is the only even prime number
2 is the square root of 4 ! 5-3=2
Multiplying by two doubles any number

Though the examples here were mostly elementary the 5 steps still apply to secondary, particularly to the planning of daily activities.

Happiness boosts our productivity and heightens our influence over peers.

Engagement. From Gallup Poll:
31% are Engaged Teachers (seek ways to be better)
57% are Not-Engaged. (unlikely to devote discretionary effort)
12% are Actively Disengaged (intentionally sabotage)

Alliances: Collaborate with other teachers.*

Risk. Take chances towards the Clear Vision and using Clear Results (data) to guide journey for OUR students (vs my students).

Thought. Are you a person of deep knowledge capacity and wisdom?

I have been sporadic with my use of reflections and exit tickets at the conclusion of the lessons. Steve & Patsy have challenged me to be more intentional and diligent in these practices.
This was an inside peek at Tim's recently published and highly acclaimed book, Heartprint. It was one of the most emotional, inspirational presentation I have ever witnessed. Tim really called us to focus on the core purpose of why we are teachers.
* I refer to Dr. Kanold as the 'Prince of the PLC movement." The 'King' was Rick Dufour, his friend and mentor. Tim dedicated this book to Rick who passed away this year.

This speaks to the power of observations and particularly the use of video to model best practices. The question is how to find the time to record and edit lessons, without outside finding.

The Big Take Away = A Math Instruction Improvement Program needs a long term plan.

The case study that was shared is a project in which the non-profit group provided funding and support of the University of Chicago STEM .

Video recordings of exemplary teachers teaching a lesson that was requested by teachers through PD survey.

Conceptual Understanding and Exploration in Mathematics Via Desmos. - Eric Milou (Rowan University)

Desmos allows you to:
- Engage with dynamic motion
- Create with animation and art
- Monitor with instantaneous feedback

Ross Taylor Past Presidents Session.

Hank Hepner: Have a shared vision and question the assumptions that lead to unproductive beliefs.

Steve Leinwand: How can we help our colleagues envision more effective pedagogy? Get teachers to observe each other and debrief every other week:
- What was impressive, what would you different, a call action?
- Video recording of exemplar.
- Focus on only two things, you pick one and I pick one.

More talk of vision and modeling of exemplars.

Directions: Brainstorm how a leader would address the challenges connected to the sample scenario. There are a group of parents in your school who are very unhappy about the math curriculum. They think the program holds back their students. They want their sons and daughters to be challenged, to be successful (generally based on grades or tests scores), and to be able to move ahead in grade level or math courses. The parents indicate that mathematics is a discipline that is learned in steps. The steps need to be clearly defined and when the students succeed in accomplishing the steps, they are moved to the next level or the next course.

Shift emphasis from Answer Getting to Mathematical UnderstandingHigh Leverage Practice #1:
Once kids know how to do something they don't want to understand why... You can't take it back. Understanding facilitates initial learning and retention.

High Leverage Practice #2: Collective Professional Growth.
Support Collaborative Team Culture. All kids are our kids. The unit of change is the teacher team.

High Leverage Practice #3: Implementing the 8 Effective Teaching Practices (Principles to Action).
Tasks First... Examine the tasks in your instructional materials (Higher/lower cognitive demand tasks)? Do ALL students have the opportunity to grapple with challenging tasks. Examine the tasks in your assessments (Higher/lower cognitive demand tasks)?
... Then focus on Discourse. What do you do after the students do the task? DISCOURSE to advance the math learning of the whole class. It's not about doing the task; it's doing the task for a reason, so planning is key, and planning with someone else is even better. Facilitate theanticipation phase of the planning.

High Leverage Practice #4: Awareness of the Micromessages about math and students.
Comments like, "It is immediately obvious that...," Effort-based vs intelligent-based praise. Observe number of interactions and nature of questions teacher offer based on gender or race.

Shrinking the Equity Gap in Secondary Mathematics Coursework: Implications for College Coursework and Completion. - Dr. Amy Wiseman & Chritine Bailie (E3 Alliance)

8th Grade Algebra is Key.

Auto Enroll and allow parent "opt-outs" rather than "opt-in."

PD for teachers on supporting "Bubble Students" critical.

Thank you San Antonio for an Epic Trip!

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San Antonio, CA , April 2017 I have summarized each session with some simple (*) bulleted notes,red underline quotes to encapsulate my major take-aways, and occasionally a brief italicized commentary. The Big Take Away = Differentiation should not mean different tasks for different students, but instead should offer different depths with same task.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.
Watch the video to learn how sharing works.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

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Not have enough time for grading?

Want useful measurements on student performance?

Want to assess student understanding in real-time?

If so, then Flubaroo can help!

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Get reporting and analysis on student performance.

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Over 10 million installs and millions of assignments graded!

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Teachers, do you... Not have enough time for grading? Want useful measurements on student performance? Want to assess student understanding in real-time? Need a free solution to help? If so, then Flubaroo can help! Grade assignments and assessments in under a minute! Get reporting and analysis on

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This extension launches the Goobric web app, a rubric based assessment tool that works with the Doctopus Add-on for Google Sheets.

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Emily Seesaw Product Manager

Teachers and students can add work created in Google apps like Docs, Slides or Sheets directly into Seesaw portfolios! There are two options:
Here's how to Upload a Google File:

1. Link to Google Files: If you want students to be able to access Google Docs, Google Slides, Google Sheets, Google Drawings, Google form, videos or other files in Google Drive, you can add a link to those files into a post, activity example or template or message. Just choose the "Link" option and paste in a link to the Google file. Students will need to be logged into their Google account to access the Google links or the file permissions need to be set to "anyone with the link can view".

2. Upload Google Files: If you want students to annotate on top of a Google Docs, Google Slides, Google Sheets, Google Drawings, you can upload to those files into a post, activity example or template or message. Just choose the "Upload" option, then choose Google Drive, then select the file. Seesaw will convert your file into a series of annotatable pages. Studnets will also able to access a link back to the original file as a PDF and in Google. Families will be able to view these files in their child's journal even if they don't have access to Google apps or access to Google drive.

1. Tap the Green Add+ to add a new post, you can also add Google files as attachments to messages or activities.

2. Tap 'Select from Google Drive'. You will need to sign in to your Google account before you can browse files in your Google Drive.

3. Select a file. If the file can be added into Seesaw, the 'Select' button will turn blue.

You will be taken to the annotation screen. If you are adding a Photo, PDF, Google Doc, Google Slide or Google Sheet, you will have access to all of the annotation features including drawing, text labels, voice annotation tools, and captions.

Chromebook Tip

Free users can upload 1-20 pages of a Google item or PDF and add a voice or text caption.

Premium users can upload 1-20 pages of a Google item or PDF and use all creative tools on all of the pages.

If you try to upload a file from Google Drive from the 'Select a File' option, you will only be able to add jpg, png or pdf files. But if you choose 'Select from Google Drive' instead, you can add all Docs, Slides, Sheets, Drawings, plus any photos you have stored in Google Drive!

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How do I use Google Apps or Google Drive with Seesaw?

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Emily Seesaw Product Manager Teachers and students can add work created in Google apps like Docs, Slides or Sheets directly into Seesaw portfolios!

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Emily Seesaw Product Manager

Teachers and students can add work created in Google apps like Docs, Slides or Sheets directly into Seesaw portfolios! There are two options:
Here's how to Upload a Google File:

1. Link to Google Files: If you want students to be able to access Google Docs, Google Slides, Google Sheets, Google Drawings, Google form, videos or other files in Google Drive, you can add a link to those files into a post, activity example or template or message. Just choose the "Link" option and paste in a link to the Google file. Students will need to be logged into their Google account to access the Google links or the file permissions need to be set to "anyone with the link can view".

2. Upload Google Files: If you want students to annotate on top of a Google Docs, Google Slides, Google Sheets, Google Drawings, you can upload to those files into a post, activity example or template or message. Just choose the "Upload" option, then choose Google Drive, then select the file. Seesaw will convert your file into a series of annotatable pages. Studnets will also able to access a link back to the original file as a PDF and in Google. Families will be able to view these files in their child's journal even if they don't have access to Google apps or access to Google drive.

1. Tap the Green Add+ to add a new post, you can also add Google files as attachments to messages or activities.

2. Tap 'Select from Google Drive'. You will need to sign in to your Google account before you can browse files in your Google Drive.

3. Select a file. If the file can be added into Seesaw, the 'Select' button will turn blue.

You will be taken to the annotation screen. If you are adding a Photo, PDF, Google Doc, Google Slide or Google Sheet, you will have access to all of the annotation features including drawing, text labels, voice annotation tools, and captions.

Chromebook Tip

Free users can upload 1-20 pages of a Google item or PDF and add a voice or text caption.

Premium users can upload 1-20 pages of a Google item or PDF and use all creative tools on all of the pages.

If you try to upload a file from Google Drive from the 'Select a File' option, you will only be able to add jpg, png or pdf files. But if you choose 'Select from Google Drive' instead, you can add all Docs, Slides, Sheets, Drawings, plus any photos you have stored in Google Drive!

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How do I use Google Apps or Google Drive with Seesaw?

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Emily Seesaw Product Manager Teachers and students can add work created in Google apps like Docs, Slides or Sheets directly into Seesaw portfolios!

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An octopus for docs! Teacher-built tool for scaffolding, managing, organizing, and assessing student projects in Google Drive.

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An octopus for docs! Teacher-built tool for scaffolding, managing, organizing, and assessing student projects in Google Drive.

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Password = mathfam

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Being a part of the Math Fam has it's perks. Enjoy these free resources and downloads only available to the math family. To access the files, simply click on the image and download to your computer.Resources for All GradesKdg. - 2nd Grade Resources3rd - 5th Grade Resources