In less than a year on the "MathTwitterBlogosphere," I've collected tons of great resources in Diigo lists, which I've now exported to blog posts here. Some ideas and lessons on these lists are ones I've used already in my middle school math classes; others are on my summer research list.

Here's how I've sorted websites (sometimes arbitrarily):

Math Websites: Specific Lessons

Math Websites: Classroom Culture & Mathematical Practices

Math Websites: Professional Development and Teaching Ideas

Math Websites: Meaty Problems

(Not Just) Math Websites: Games & Puzzles

Math Websites: Educational Technology

And here's one more I forgot to add originally! This is a list of sites I made for my students so they could investigate math in different contexts that interested them:

Math You Can See: Art, Nature, Patterns, Society, and More

## Monday, May 25, 2015

### (Not Just) Math Websites: Games & Puzzles

*Some math games & puzzles are also included in my Meaty Problems list.*

- Yahtzee score sheet
- http://www.hasbro.com/common/instruct/yahtzee.pdf

Yahtzee rules. - MathDice Basic Rules

For an easier version, the target number can be the sum of the two 12-sided dice rolls. - Set Game Routine for Class | Michael Fenton

Technically the puzzles come from online, but they're displayed to the class separately from a network connection. - Pose a Puzzle | Solve My Maths

Collection of great math & logic puzzles from around the web, including Set, KenKen, and many, many more. VERY FUN. - Steve Miller's Math Riddles
- Mathigon | Resources for Teachers
- Puzzles Kingdom | Conceptis via oregonlive.com (Oregonian)

Ad-heavy site where lots of fun puzzles are accessible. Most are logic-oriented. - KenKen Puzzles

Number/logic puzzles, like Sudoku with some number operations and properties. Lots of difficulty levels available. Ad-heavy site. - Lure of the Labyrinth | MIT

Computer game designed for pre-algebra middle schoolers. Rescue a lost pet from monsters in a labyrinth by solving complicated math puzzles. A bit of a pain to set up; some fun, though time-consuming, puzzles once you do. - Lewis Carroll Symbolic Logic Puzzles

"Purposefully inane" statements by Lewis Carroll (Alice in Wonderland author) that can be logically analyzed. Fairly complicated notation used on this page.

### Math Websites: Specific Lessons

### GOOD SOURCES FOR MULTIPLE LESSONS

- Illustrative Mathematics

Website that includes shared lessons to illustrate teaching with Common Core math standards. Started by Dr. Bill McCallum, a Common Core author. - Robert Kaplinsky's Math Lessons

Some very cool real-world stuff here. Math lessons are sorted by grade. - OpenCurriculum Mathematics

Lessons, projects, activities, videos, worksheets & tests that are open-source (from Illustrative Mathematics, Engage NY, Khan Academy, and others). Quality varies widely, but ability to search by CC standards is VERY helpful. - Common Core Problem Based Curriculum Maps | Geoff Krall (emergent math)

Sequences of great CC online math lessons. - Math Teacher Resources from I Speak Math

Big list of math teaching resources, with pointers to lesson plans, problems, professional development... - Teacher Resources on Line (UK)

### RATIO AND PROPORTIONAL RELATIONSHIP LESSON

- Proportional Reasoning: Hamburger Nutrition

Graphite "App Flow" describing use of various apps to do free Mathalicious rates/ratios lesson.

### NUMBER SYSTEM LESSONS

- Fraction Division via Rectangles | Fawn Nguyen
- Drill Bit Fractions | Yummy Math

Drill bits are ordered by size, and the denominators of the fractions (up to sixteenths) are given. Find the numerators. - Long Division from Strip Model | Graham Fletcher

Really aimed at 4th/5th grade division, but can help make sense of standard algorithm. - Life on the Number Line - board game for real numbers | Cheesemonkeysf
- sqrt(2) is irrational: Tennenbaum’s proof | Division by Zero

Proof by contradiction; pretty pictures.

### EXPRESSIONS AND EQUATIONS (ALGEBRA) LESSONS

- Central Park: Making Sense of Variables

A Dan Meyer & Christopher Danielson lesson for early algebra. Students solve one problem, then variations, then move to variables for power and sense-making. - Charge! | Michael Fenton

Model the time it takes a cell phone to charge with a linear function... then find out there's a catch! - Scattergories Style Describing Graphs Game | Sarah Hagan (Math = Love)

Good practice at identifying features of graphs and describing them with correct terminology. Competitive group game in which teams win for having the highest number of correct and unique descriptions. - Linear Equation Card Sort | Nora Oswald

Match cards for y=mx+b, std form, slope-int, graph, table. Editable too!! At this time, card 2 is a bit confusing (needs fractional coefficient filled in, but it reads as "-x"). - Substitution with stars | cheesemonkeysf

"Training wheels" to help with substitution: write x (or y) on one side of a star and whatever it equals on the other.

### GEOMETRY LESSONS

- Stained Glass Circle/A/P/Modeling Problem | Illustrative Mathematics

Very cool and realistic scenario in which students need to choose a reasonable model and use knowledge of area (especially of circles), perimeter, and numerical calculations. In PPS, can be used in Math 6. - Rigid Transformations (Grade 8) | Fawn Nguyen

Ideas for student-created procedures for transformations (create, then do someone else's). - Box of Clay (Volume and Units) | Joe Schwartz, Exit 10A

Fantastic post about learning issues and teaching choices involved in a fifth grade lesson about volume and units. - 3 Act Volume | Tap Into Teen Minds + Lisa Bejarano

3-act task around predicting relationships between volumes of various 3-D prisms, pyramids, cones, etc. - Arguing about Shapes (Kate Nowak)

Great intro geometry lesson (could be used in 7th or 8th grade math also). Stresses finding patterns, sense-making, communication and critique of reasoning, math vocabulary... awesome. - Proofs of the Pythagorean Theorem | Mathematics Assessment Project (map.mathshell.org)
- Constructions Castles | Cheesemonkey

Creativity with high-school-level Geometry constructions. - The Secret of Flowchart Proofs #officesupplies | cheesemonkeysf

Flow-chart proofs with post-it notes.

### STATISTICS AND PROBABILITY LESSONS

- Census at School (US) | American Statistical Association

Census questions for classes to take, with answer statistics to be compared against other national & international groups. Requires part of a class period for online activities. - Scatterplots Idea: "Are We Movie Compatible?" | Cathy Yenca

Fantastic idea for introducing scatterplots and correlation: students rank 10 things in order (here, movies), then compare rankings via scatterplot. - Are you reflected in the new Congress? | The Guardian

Enter demographic info (sex, age, etc.) and find out how many members of Congress share it.

### LOGIC/PROOF LESSON

- "Words" Logic/Proof Handout | Justin Lanier (ichoosemath)

Use "rules" to change letter strings, then move to inventing your own rules. Not specifically geometry.

### Math Websites: Meaty Problems

*See also my Games and Puzzles list.*

### GENERAL PROBLEMS AND PUZZLES (ordered very roughly by likely age of interest, youngest to oldest)

- Numeracy Tasks (All Grade Bands) | Peter Liljedahl
- NRICH enriching mathematics

British site with lots of cool problems. - 1001 Math Problems | Sian Zelbo

Fun, fairly complicated visual and logic math problems that don't require more than elementary school math. Same author has very fun site 1001visualpuzzles.blogspot.com, but that's now removed from public view. - Play With Your Math

Most of these puzzles require only elementary-level math content knowledge, but they are not easy to solve! Fun challenges! Many are classics. Recommended by NCTM's Teaching Children Mathematics. - Math Tasks | youcubed
- Brain Teasers | NCTM Illuminations

Various cool problems aimed at different age levels. Good to browse! - 30 Math Starters (Quick Puzzles)

Recommended on a UK site. Quick but interesting puzzle problems. Look mainly geared for upper elementary. - Inside Mathematics

Includes Common Core resources, problems of the month, performance tasks and other assessments, etc. - Open Middle: Challenging math problems worth solving

Problems with a defined beginning and end, but an "open middle": different solution paths and problem solving techniques could be used. - Would You Rather?

Asks students to choose their own path and justify it. - Problems for Developing Mathematical Habits of Mind | NRICH

Problems designed to encourage certain mathematical habits of mind: being curious, collaborative, thoughtful, or determined. - Math Explorers' Club | Cornell Dept. of Mathematics

Advanced math "modules" for middle school & high school students. Wow!! - Five Triangles

Terrific, complicated, fun problems, especially for geometry and for math-lovers. - Brilliant (Math & Science Problems)

Free. Graphite's recommendation says Brilliant has excellent problems and adapts to students' performance, but is probably best for high-end students. Some problems have a test-prep orientation. - Math Teacher Resources from I Speak Math

Big list of math teaching resources, with pointers to lesson plans, problems, professional development... - Sunday Puzzle | io9

Aimed at adults, but likely to have good kid puzzles sometimes too.

### PROBLEMS AND PUZZLES FOR PARTICULAR TOPICS AND SKILLS (ordered roughly by age, youngest to oldest)

- Proof (Elem. & up): Numbers of Squares Making a Square | artofmathstudio
- Factor Craze | NCTM Problems to Ponder

Currently available only to NCTM members. "Which numbers have exactly three factors? Exactly four factors? Exactly five factors? Exactly six factors? Given a positive integer n, how can we tell exactly how many factors it has?" - Car Talk Gone Fishing Puzzler | A Recursive Process
- Stained Glass Circle/Area/Perim/Modeling Problem | Illustrative Mathematics

Very cool and realistic scenario in which students need to choose a reasonable model and use knowledge of area (especially of circles), perimeter, and numerical calculations. Requires knowledge of circle area (7th grade standard). - Conway’s Rational Tangles (of Rope) | Fawn Nguyen

Group activity with rope in which students need to analyze rotating & twisting mathematically. See https://hilbertshotel.wordpress.com/2015/05/06/conways-ropes/ for more on doing this. - Great Circle/Square Problem with Multiple Solutions | Chris Harrow, NCTM

Multiple solution methods for a @Five_Triangles geometry problem. - World's Hardest Easy Geometry Problem | Keith Enevoldsen

Requires only elementary geometry (triangle angle sum theorem, etc.) but is very challenging. I have not solved this yet. The hints are not spoilers at all, at least for me!

### Math Websites: Educational Technology

### ONLINE MATH TOOLS STUDENTS CAN USE

- CUEthink Math Problems App Recommendation | Carpe Ed Tech

Word problems (many from The Math Forum) and prompts for students to break them into 4 clear phases (based on Polya's Problem Solving Techniques): Understand, Plan, Solve and Review. Students' work can be shared within a class. - Learn Desmos | Michael Fenton

Includes a series of challenges. - GeoGebra at TMC14 | John Golden

On Twitter, #ggbchat can help. - Google Sheets: Create Pixel Art | Alice Keeler, Teacher Tech

Using Google Sheets to make pixel art. Teaches lots about spreadsheets; could be used to make visual patterns or do something with proportions or... - Box Plot Generator

Plotly and Geogebra may also be good for this, say Twitter users. - MathDice Online Archive

Online version of MathDice game: make a target number from 3 other numbers ("rolled" on "dice") and any operations. Requires latest version of Flash. Instructions can be found at http://www.mathdice.com/kids/fullinstructions.html (note: I can't find the online tutorial game they mention). - Common Core Standards Explorer | Graphite

Reviews of free and paid software and apps related to different Common Core standards.

### ONLINE MATH TOOLS & RESOURCES FOR TEACHER PREP

- How to Create Math Expressions in Google Forms | Guillermo Batista
- Google Forms FINALLY Loves Math | fishing4tech.com
- Math Videos for Error Analysis | Andrew Stadel

The particular emphasis here is on videos for error analysis (students identify mistakes), but there are great tips for making any math video. - Dynamic Paper | NCTM Illuminations

Make graph paper, number lines, nets, shapes, ... - MyScript MathPad: Handwriting->LaTeX Generator

Saves as image or LaTeX or MathML. Plays well with Wolfram Alpha for an extra $5.

### ONLINE RESOURCES TO HELP STUDENTS UNDERSTAND MATH CONCEPTS

- SolveMe Mobiles

For algebra - build or play puzzles to figure out value of various shapes balanced on a mobile. Rec'd by Tina Cardone. - Factorization - Visual illustration of divisor pairs | GeoGebraTube
- British Long Division Helper | mathshelper.net

Works much like our long division, but they include all of the dividend and subtract full multiples of the divisor from it. (Longer to write but makes more sense) - Rates and proportional relationships | Graphing and analyzing proportional relationships | Khan Academy

Dan Meyer says: "Proportional relationships is one of KA's better sets. Many different representations. Analysis, not calculation." KA praise from DM is rare enough to be worth checking out.

### OTHER INTERESTING MATH STUFF ONLY AVAILABLE ONLINE

- 10 TED "Math talks to blow your mind" | TED.com

Have not actually watched these yet. All men (sigh)

### Math Websites: Professional Development and Teaching Ideas

Here's a list (exported from Diigo) of some posts and resources I wanted to be able to come back to (often for the links within those posts as well!). The division between this list and some others I've made, especially Classroom Culture and Mathematical Practices, is rather arbitrary.

### FEEDBACK AND ASSESSMENT

- Feedback Research: Butler's Effects on Intrinsic Motivation & Performance (1986) and Task-Involving and Ego-Involving Properties of Evaluation (1987) | mathed.net
- Mathematics Assessment Project | U. of Nottingham + Shell
- Questioning Wiggins' Definition of Feedback | Michael Pershan, Rational Expressions

Things to ponder about feedback... - Giving Student Feedback: 20 Tips To Do It Right | InformED :

Very useful checklist.

### LEARNING ABOUT TECHNOLOGY

- Learn Desmos | Michael Fenton

Includes a series of challenges.

### SPECIFIC MATH TOPICS

- Fraction Division (partitive, quotative, etc.) | Christopher Danielson
- Fraction Divison: Three-eighths of a Pile | Justin Lanier
- Exploding Dots | G'Day Math (James Tanton)

"Exploding Dots" are about thinking of each digit in a number as the same thing as 10 of the digit to right of it, basically. The way James Tanton goes on to use this concept is VERY powerful: see, for instance, Lesson 2.2 on decimal division. Definitely considering using this in class!! - Math Teaching & Ending Racism | Max Ray, Math Forum

Not crazy about their title, so I retitled it! Interesting talk motivating teaching proportional reasoning and statistics to help our students grow into people who can fight "fog" of racism by analyzing and rethinking perceptions. - Quadratics: Mighty Square! | 17GoldenFish

Interesting description of success with quadratics by teaching completing the square first, then quadratic formula, then factoring.

### LESSON DESIGN

- A Designer Speaks | Malcolm Swan of MARS/Shell Centre

Short paper, but LOTS to unpack here: purposes for learning math, lesson design, constructivism, group work, transmission vs. discovery/collaboration, math task types that encourage concept development, misconceptions, questioning, reasoning... Wow! - Thinking Through a (Math) Lesson Protocol

Linked by @mpershan on Twitter. Have not read through extensively yet, but looks sound.

### OTHER CLASSROOM TEACHING PRACTICES

- Implementing the Mathematical Practice Standards

Illustrations, student dialogues, & text describing the Common Core Standards for Mathematical Practice in action. - 7 'great' teaching methods not backed up by evidence | Durham U.

Authors argue evidence does not support certain teaching practices widely regarded as helpful. I probably don't agree with all this, but it's a good self-check. - The Math Resource Primer | Team Mississippi Math

Good resources for lesson and unit planning, arranged by need (example: "my lessons are too boring"). - Problem-Solving Strategies & CC Math. Practices | Max Ray (Math Forum)

### OTHER/NOT YET SORTED:

- Curriculum Inspirations | Mathematical Association of America

Haven't looked through this yet but at a glance, it looks very promising for problem solving/mathematical practices. - EnCoMPASS Analysis of Student Work

Math Forum PLC (more or less) to analyze student work. - Math Teacher Resources from I Speak Math

Big list of math teaching resources, with pointers to lesson plans, problems, professional development... - Basic Skills vs. Conceptual Understanding: Bogus Dichotomy (H. Wu)

Interesting-looking paper arguing that basic skills can be taught in a way that ties in with conceptual understanding; in particular, dividing fractions can be taught as an inverse of multiplication, not just with pictures. - Inside Mathematics

Includes Common Core resources, problems of the month, performance tasks and other assessments, etc.

### Math Websites: Classroom Culture & Mathematical Practices

Here's a list (exported from Diigo) of some posts and resources I wanted to be able to come back to (often for the links within those posts as well!). The division between this list and some others I've made, especially Professional Development and Teaching Ideas, is rather arbitrary.

### BUILDING CONFIDENCE, A GROWTH MINDSET, AND A SAFE CLASSROOM CULTURE

- First, Do No Harm | Ilana Horn, teaching/math/culture

A nice, though partial, summary of math teachers' responsibilities to avoid harming students' sense of competence. - Encouraging Student Sharing: Norms & Status | Ilana Horn, teaching/math/culture

Great list of ideas developed by reflective teachers on how to encourage democratic sharing of ideas in the math classroom. - Positive Math Classroom Norms | Jo Boaler

Jo Boaler's positive classroom norms for math class, with ideas for supporting them. Norms: Everyone Can Learn Math to the Highest Levels; Mistakes are Valuable; Questions are Really Important; Math is about Creativity and Making Sense; Math is about Connections and Communicating; Depth is much more important than speed; Math Class is about Learning not Performing. - The Mathematics of Hope | Jo Boaler

Moving from Performance to Learning - Talking Points & Math Mindset | Math Minds

This post and the ones linked to from it (some cheesemonkeysf's), as well as https://docs.google.com/file/d/0B6W4HKOGaWhdMTM2SUViMVhBMGc/edit , have ideas on how to solicit kid ideas about what is important in doing math. - Talking Up Talking Points | Brian Stockus
- Notice-and-Wonder: When It Works, When It Doesn't

Highlighted description of notice-and-wonder. Article includes details on when it works well and when it doesn't. - Box of Clay (Volume and Units) | Joe Schwartz, Exit 10A

Fantastic post about learning issues and teaching choices involved in a fifth grade lesson about volume and units, including "Notice-and-Wonder" strategy in practice. - Increasing Participation in Classroom Discussions (educating grace)

Steps novice teachers were instructed to try to increase meaningful classroom participation in math class. - Vertical Non-Permanent Surfaces & Visible Random Groupings

Food for thought that SlamDunkMath presented at Twitter Math Camp 2014. Strongly recommends having students work in random groups (different for each task) and at vertical non-permanent surfaces placed around the room. - Positive Reinforcement Award Cards | Mathy McMatherson

"Award" cards for students for mathematical communication, perseverance, and team work. Positive feedback for behaviors, because students will care about the things that the teacher cares about. - Math Animals | Bryan Anderson, MathLab

Student answers to prompts "When I walk into math class I feel like a(n) _______" (which animal?) and "What animal do you think would be best for math class?" On Day 6, SPEED is seen as the main desirable quality... - The Wall of Champions | Mathy McMatherson

Students get Post-Its (colored by class) to write their names on when they do exceptionally well on an assessment. Encourages excitement about excellence. - You're Correct Horse - YouTube

Ridiculous animation of a sax-playing horse saying "You're correct!" and "You are smart!" So over-the-top it should not undermine a culture of positivity about mistakes. - Group Work Norms: Engage in Math

Group work norms/ground rules from four sources. - Why 2 > 4 | Max Ray at NCTM Ignite

Great, brief talk on the effect of students (and teacher) listening to students. - Bad at Math Is a Lie | Math Horizon's Aftermath

Matt Waite, a professor and software pioneer, had to take remedial algebra to get an MBA degree at 37, and found he was not actually Bad at Math: "the truth is anyone can get math." - Math Anxiety | American Educator
- Mathematics, the Common Core, and Language | Understanding Language

Paper on developing math instruction for ELL students, referenced by @MathEdnet (Raymond Johnson). - Classroom Management Strategies To Take Control Of Noisy Students | Rob Plevin

This video gives a nice explanation of advantages of establishing positive behavior at the start of class through interactions with students outside the classroom. Considering for next year. - When I Was an 8th Grader Again… | What is 5?

Lots of thoughtful discussion of what the student POV is like in 8th grade.

### REASONING, SENSE-MAKING, AND PROBLEM SOLVING

- Making Sense | Tracy J. Zager
- How Old Is the Shepherd? An Essay About Mathematics Education | Katherine Merseth

A very well-written article from 1993 on math education in the US. Some things have changed since then, some haven't. References "How old is the shepherd?" problem. - Warm-Ups Transformed My Classroom | powersfulmath

Transforming warmups into engaging opportunities for mathematical reasoning and real-world problem solving. - Filing Cabinet of (Warm Up) Activities | Crazy Math Teacher Lady

Nice list of lots of activities from the MathTwitterBlogosphere. - Two-Column Proofs that Two-Column Proofs are Terrible | Ben Orlin, Math with Bad Drawings

### HOMEWORK AND TEST REVIEW

- Homework Strategies | cheesemonkeysf

@cheesemonkeysf's homework thoughts. See #4 in particular: 2-week homework packets (students review together daily). - Red, Yellow, Green | Ryan Adams, Math Edumacation

Fantastic idea for self-assessment & setting positive & efficient classroom routines for pre-test review.

### FUN AND GAMES IN MATH CLASS

- Games in Math: List of Resources | Math Hombre

This is AMAZING. A list of big and small games, for review and not, from many sources. - Math Free Choice (Part 1) | Amanda Northrup

Food for thought! How a (5th grade?) teacher set up 30-45 minute sessions of Math Free Choice, with activities and goals chosen by students (from logic puzzles, tangrams, games, etc.). - Math Free Time (Part 2): Refinements | Amanda Northrup

Refinements to Math Free Time system described in Part 1. Resource links at bottom of page. - Games for Math & Social Skills (Math Forum)

Cooperative games.

### POSTERS

- Kid Friendly Math Practices Posters (Everybody Is a Genius)

These are attractive and editable! Most are nice kid-friendly versions, but consider changing #4; to me, modeling with math is not about showing work in different ways. - Problem Solving Strategies Posters

pdf with Polya-esque problem solving strategies. - Math Munch Classroom Poster

Gorgeous poster that needs to be printed out. I did it at Office Depot for $15 (actually $12 with a coupon) and it looks great! Comes with puzzle.

### OTHER/NOT SORTED YET:

- Math Teacher Resources from I Speak Math

Big list of math teaching resources, with pointers to lesson plans, problems, professional development... - Half Century (Comments on Teaching) | Math Teacher Mambo

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