Math Twitter Blog-o-Sphere Products and Search Engines

The internet is a great place, and the MTBoS is the best place on the internet! Search through a number of math education blogs and sites for the resources you need.

  • The MTBoS Search Engine: Looking for an activity for class next week, or maybe information on a new educational idea? This search engine is limited to blogs and sites associated with the MTBoS, this blog included.
  • The Problem Based Learning Search Engine: Similar to the MTBoS search engine, but restricted to sites that focus on PrBL.
  • Things We Do Together: A collection of websites and other great resources that have cropped up organically from the MTBoS. Although I've lurked for awhile, I'm a new contributor, so I don't know how I feel about the word "we" in the title.
  • Global Math Department: Every week, math teachers will meet online and spend an hour or so discussing a given topic. Come join the fun!
  • Virtual Filing Cabinets: Many bloggers have virtual filing cabnets where they link their favorite resources by grade level, subject, or topic. Check out the "Blogs" page to see some of the VFC's that I follow.

"All Topic" Lesson Resources

The links below are for general repositories of lesson materials. Some are organized by grade level; others are sorted by standard or topic. In any case, you should be able to find a wide variety of resources on any of these websites.

  • MTBoS Activity Bank: Created during TMC15 by Denis Sheeran and company, this site contains starting problems and activities that provide a tangible hook at the start of a unit or topic.
  • Student Achievement Partners: A great collection of aligned lessons, tasks, and assessments that can be sorted by grade. Although their are are not as many resources on this site as other sites, they can serve as exemplars that model the focus, coherence, and rigor of the Common Core State Standards.
  • Illustrative Mathematics: Contains tasks and problems that illustrate the Common Core State Standards, as well as curriculum blueprints and progressions to outline how the standards may be implemented both within a school year and between years.
  • The Mathematics Assessment Project: A collection of tasks and formative assessment tools to deepen student knowledge.
  • The Math Forum: The home of a number of math education resources including PCMI, Ask Dr. Math, and various Professional Development Modules.
  • NCTM Illuminations: A collection of virtual lesson plans and resources hosted by NCTM. Includes both plans and interactive applets sorted by grade level and standard.
  • Mathalicious: Real-world lessons from Mathalicious help middle and high school teachers address the Common Core Standards while challenging their students to think critically about the world.
  • Yummy Math: A set of "real world" activities, lessons, and resources. The site is updated with multiple activities each week. Often, activities relate to pop culture or current events. 
  • Inside Mathematics: A website that houses a number of model lessons, problems of the month, videos of teachers, performance assessment tasks, and classroom resources that grew out of the Noyce Foundation’s Silicon Valley Mathematics Initiative. Cathy Humphries (from “convince yourself, convince a friend, convince a skeptic” fame) is one of their teacher mentors.
  • Learn Zillion: a community with thousands of standards-aligned resources and lessons. Includes videos that demonstrate the Common Core standards by discussing prerequisite knowledge and common mistakes. 
  • NRICH: Problems and lessons from the University of Cambridge. Since they use "key stages" as well as grades, you should know that stage 3 is equivalent to US grades 6, 7, and 8, while stage 4 is similar to US grades 9 and 10. Sixth form, college, or years 12 and 13 refer to grades 11 and 12 in the United States.

"Specific Topic" Lesson Resources

The websites below don't correspond to any grade level or topic, but they're not general sets of lessons. Rather, they're good for specific types of activities: problem based learning, mistake analysis, graphing, comparing and contrasting, and so on. Many are created by individual teachers and bloggers, so be sure to give thanks if you use them!

  • Dan Meyer's List of Three Act Tasks: A spreadsheet containing a number of Dan's Three Act Tasks, organised by grade level, standard and essential question. If you're unfamiliar with the three act structure, find it by reading his blog here.
  • Andrew Stadel's List of Three Act Tasks: Similar to Dan's spreadsheet, but Andrew's tasks take on a little bit more of a middle school focus.
  • 101 Questions: Post an image on this site or respond to other teacher's images by answering: what's the first question that comes to your mind? This site attempts to find those problems that are so perplexing they are truly worth solving. This is another one of Dan Meyer's projects.
  • Open Middle Problems: Nanette Johnson, Robert Kaplinsky and Bryan Anderson have amassed a collection of "open middle" problems. An open middle problem is one with a fixed start point, a fixed solution, but many paths to connect the two. I personally use these to transform procedural problems into thought provoking questions. Michael Fenton also has resources on open middle problems here.
  • Which One Doesn't Belong: Inspired by Christopher Danielson and created by Mary Bourassa, this site features sets of four figures and simply asks, "which one doesn't belong?" A seemingly simple question can spark rich discussion from kindergarten through calculus.
  • Would You Rather: This blog by John Stevens asks students to choose between two options and justify their choice mathematically. It is a new spin on the old game "would you rather".
  • Math Mistakes: This site is about compiling, analyzing and discussing the mathematical errors that students make. The site is edited by Michael Pershan, a middle school and high school math teacher from NYC.
  • Visual Patterns: A site started by Fawn Nguyen in 2013 that contains a number of - you guessed it - visual patterns. Great as a warm up for students to practice pattern hunting and finding explicit equations.
  • Graphing Stories: Dan Meyer and BuzzMath have put together a collection of 15 second videos that demonstrate some sort of motion. The student's job is to create an approximate graph of that motion. This is a great activity for building graph sense, as it uncovers many misconceptions.
  • Estimation 180: Andrew Stadel and Michael Fenton have collaborated to create an estimation challenge for every day of the year. A good warm-up.
  • Number Talks: A set of prompts and conversations with students about math by Fawn Nguyen. Probably best for K-8 teachers.
  • James Tanton's Curriculum Resources: Tanton's ideas about a number of topics spanning the whole high school curriculum. He also has a very intuitive look at number systems that traces through arithmetic, polynomials, decimals, sequences & series, irrational numbers, negative bases, and more. Check out James Tanton's Exploding Dots.
  • Critical Math: A site dedicated to lessons with real context. Although there are no formal lesson plans here, each post can serve as a great starting point for a lesson with a social justice focus. 

Challenges and Extensions

These websites contain sets of single problems or challenges. Some would fit well into a whole class problem based lesson. Others would be best used as an extension.

  • Five Triangles: Concisely stated, unambiguous, and calibrated problems amenable to a variety of approaches, with the essential condition that, throughout the solution process, cognitive stress be maintained. Intended for middle school, but usable throughout high school.
  • Median: Don Steward posts single problems or whole lessons, often with a visual component. Often, sets of problems are a variations on one theme.
  • Math Bits: Fun, yet challenging, lessons and activities in secondary (and college level) mathematics and computer programming for students and teachers.
  • A+ Click: A collection of problem-solving questions sorted by grade and content. As you get more correct, you have the option of progressing to more difficult problems, and eventually to compete and get a score. By Igor Kokcharov.
  • Collaborative Mathematics: Jason Ermer posts a mathematical challenge video each week, and then you explore the challenge, ideally with a team of friends. Once you have finished, or not finished, you make a response video with your thoughts on the challenge and watch other people's videos.
  • mathMINDhabits: The art  and craft of posing problems, making conjectures, and expanding teachers' and students' mathematical habits of mind. This evolving collection of challenges and essays is primarily intended to help teachers think more deeply about aspects of mathematics that they know and are expected to teach. 
  • The Art of Problem Solving: A text designed to prepare students for mathematical competitions, but highly applicable to the general high school setting.
  • The PCMI Problem Sets: These problems were orginally created for use at the Park City Mathematics Institute, but could serve as a great extension in a high school classroom. They are not intended to stand alone. Each problem set flows into the next one, and yet they do not need to be completed in their entirety to be understood.

Curriculum Ideas

These websites are not just for curriculum writers. They contain examples of how the Common Core could be interpreted as well as progressions to see how topics link together from grade to grade.

  • Illustrative Mathematics: Contains tasks and problems that illustrate the Common Core State Standards, as well as curriculum blueprints and progressions to outline how the standards may be implemented both within a school year and between years.
  • Student Achievement Partners: While SAP does not have it's own curriculum, it has some of the best documents for examining the connections between standards and determining which curricular resources serve them best.
    • Coherence Map: A very sleek online tool for seeing the connections between the Common Core Standards K-12. By selecting a specific standard you can determine if it is a priority standard, what other standards are connected to it, where it falls in the progression of topics, and some exemplar tasks. 
    • Focus by Grade Level: a document that outlines the major, supporting, and additional work of each grade.
    • Alignment Rubrics:  A suite of tools for evaluating the alignment of instructional and assessment materials to the Common Core State Standards.
  • University of Arizona, Common Core Projects: A collection of documents, including progressions, to aid in implementing the Common Core.
  • Hung-Hsi Wu's Geometry Progression: Why isn't there a geometry progression document on the University of Arizona website? Bill McCallum says it's quite long, and although it is well written, it could be overwhelming for teachers.
  • Engage NY: A set of complete curricula for middle and high school math and English, complete with lessons and resources. Be warned, there is a high amount of content in this curricula.
  • Georgia Standards of Excellence: Another set of complete curriculum resources. Some say that the Georgia Mathematics Standards are better than Engage NY. I'll let you decide.
  • North Carolina Unpacking Standards:  This Instructional Toolkit is designed to help teachers pattern their instruction and classroom student assessments to the Common Core Standards. 
  • Emergent Math: Geoff Krall has put together problem based learning (PrBL) curriculum maps aligned to Common Core. The problems are a compilation of problem based activities from thoughtful math bloggers.
  • The Marshall Memo: A weekly round up of important ideas and research in education. 

Desmos, Geogebra, and Ed Tech

These websites allow for deep explorations and rich learning when used appropriately.

  • EdSurge: An index of popular educational technology sorted by purpose.
  • Desmos: Graph functions, plot tables of data, evaluate equations, explore transformations, and much more.
    • Desmos Bank: A searchable data base of user created activities
    • Desmos Classroom Activities: Deep, interactive, online classroom activities that gives the teacher the ability to monitor and foster student learning. Some activities have students work with each other, but other activities are more individualistic. Powered by Desmos.
  • Geogebra: A dynamic mathematics software, similar to Geometer's Sketch Pad, but free. Allows users to graph lines, construct geometric figures, run mathematical animations and traces, and now graph in three dimensions.
    • GeogebraTube: A collection of free searchable Geogebra files posted by teachers.
    • Euclid, The Game: A geometry game that uses a Geogebra applet to explore constructions using primitive tools. Each time you complete a construction, you are given additional tools to build with. A great introduction to both Euclidean constructions and Geogebra.
  • Solve Me Puzzles: A set of intuitive puzzles intended to build skills with solving equations and number sense. Created by the Education Development Center (EDC).
  • The NVLM: The National Library of Virtual Manipulatives hosts a number of interactive applets sorted by grade level and topic.
  • G(Math): An add-on for Google Docs that allows you to write equations using an equation editor or LaTEX. It also allows you to create graphs from a specified function, plot points, and has a “speech to equation” function. 
  • TI-Nspire Activities: A number of interactive applets that provide great for discovery lessons throughout the middle and high school math curricula. 
  • Sheppard Software: A collection of elementary level math games, that are especially interesting for high school students to play on a smart board. More fun than actual content.
  • Plickers: A low-cost quick response system that is similar to clickers. Each student gets a paper with a QR-like code on it and holds it in the air a certain way to submit their answer. The teacher then uses their phone or ipad to scan the room and collect the data.
  • Kahoot: A game based learning platform where users answer timed, multiple choice questions against classmates (teacher-made Kahoots) or students from around the world (public Kahoots). At the end of each round, students are shown a leaderboard with the top four players. Students do not need to sign in to play, and any computer or device with internet can be used.

Math Pedagogy

These websites are less about content and more about practices. They help to answer the question, "How can we best teach mathematics to give students the skills to excel in any field, not just mathematics?"

  • Principals to Actions: Ensuring Mathematical Success for All: The Common Core introduced the eight mathematical practice standards for students, but this book introduces eight research-based essential mathematics teaching practices. It also discusses how to support these eight practices, how to implement the Common Core Standards, unproductive mathematical beliefs, and strategies for engaging students.
  • Principals to Actions Online Professional Learning Toolkit: The online companion to the recent NCTM book.
  • 5-Practices for Orchestrating Productive Mathematics Discussions: A structure for taking any mathematical task and turning it into rich mathematical discourse. The practices include: anticipate, monitor, select, order, and connect.
  • Student Achievement Partners: SAP contains two great rubrics for improving math pedagogy, along with exemplar videos.
    • Coaching Tool: Unlike other 'evaluative' rubrics, this rubric cuts straight to the actions that we know are best practices for teaching and learning mathematics.
    • Lesson Planning Tool: This online tool guides teachers through a series of prompts about the lesson content, structure, and activities to ensure the Shifts required by the CCSS are central to the lesson.
    • Instructional Practice Toolkit: A collection of PD modules and videos to support instruction aligned to the CCSS.
  • Strength in Numbers: Collaborative Learning in Secondary Mathematics: A text by Ilana Horn that outlines how to effectively use group work to create a learning environment in the secondary mathematics classroom.
  • You Cubed: Jo Boaler's website at Stanford University dedicated to promoting growth mindset. The website includes a week long student introduction to growth mindset, and seven classroom norms for promoting growth mindset.
  • Dylan William's Thoughts on Formative Assessment: Dylan Williams spoke at PCMI, and I have compiled a list of his main points.
  • Nix the Tricks: An online book filled with alternatives to the shortcuts so prevalent in mathematics education that tend to damage learning. The book also explains exactly why the tricks are so bad for understanding math.
  • First Like Third: a google spreadsheet called First Like Third where teachers can note common student misunderstandings as well as what to say and how to correct them. The objective is to make the first year of teaching more like the third year of teaching. Thanks to Matt Baker.

Camps, Fellowships, Workshops, and Wiki's

Below are links to some of the workshops and camps I have attended, or associations I belong to:

Below are links to general lesson sites for all subjects, not just math:

  • Better Lesson: A bank of teacher resources including lesson plans with all worksheets and additional resources. Often, resources include videos about the lesson. 

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