In addition to my blog on WordPress (this site) I maintain a huge **math education site**, featuring articles about teaching math and tons of curricular materials. You should definitely check it out. I keep track of updates to the site on this page.

I added Parisa Safa’s Python program to the **Infinity** page, for the iteration of “dome” functions.

I added 11 **videos about the Lab Gear** for teachers, a free at-home professional development program. I reorganized the **Lab Gear** page.

I tweaked the **Complex Numbers** page.

I added **Boxer: A Teacher’s Experience**, an overview of my long involvement with this computer language.

I added **Leonardo’s Areas** and made a PDF of my **Polyarcs** activity. Both worksheets involve perimeter and area of circles.

I added links between **A New Path to the Quadratic Formula**, **Constant Sums, Constant Product**, and **Parabolas and Quadratics**.

I added a video presentation of **A New Path to the Quadratic Formula**. This is an approach that does not involve parabolas or completing the square. (It is based on **Constant Sums, Constant Products**.)

I added **Slumber Theory**, an exploration involving prime numbers and divisibility tests. I included **The Vampire Riddle,** a TED-Ed animation I scripted on this topic.

I embedded **A Riddle of Fire and Ice** —a TED-Ed animation I scripted— in my **Map Coloring** page.

I annotated the links in **Constant Sums, Constant Products**. This is a mega-unit with content spanning from middle school to teachers’ mathematics — an untraditional approach to traditional topics. In the **Annotated Site Map**, I moved the link to **Algebra / All Levels**.

I updated **my résumé.**

I tweaked and updated: the **Site Map**, the * Algebra: Themes, Tools Concepts* home page,

**Completing the Square**, the

**Constant Sums and Constant Products**applet, and

**Parabolas and Quadratics**.

I updated the **Lab Gear** home page, and the **Site Map**.

I tweaked and updated the **Algebra 2** home page.

I added the outline of a unit on **Completing the Square**.

I added a complete **lesson plan** for the classic McNuggets problem, including an extension / generalization. This was adapted (with Amanda Cangelosi’s help) from my 1994 book ** Algebra: Themes, Tools, Concepts** (co-authored with Anita Wah, free download

**here**). See also a condensed proof of a generalization in a

**letter to the editor**of

*Mathematics Teacher: Learning and Teaching*.

I added a slide show about **A Graphical Path to the Quadratic Formula**. I also tweaked and updated the **Parabolas and Quadratics** home page.

I tweaked and updated the **Electronic Graphing** home page.

I added **an applet **about the graph of *y = ax ^{2}+bx+c* : what is the locus of the vertex when we change one of the parameters

*a, b,*or

*c*?

With permission, I posted materials from the legendary **Project SEED**: *Guidelines for Discovery Teaching*, and *Discovery Mathematics Modules*.

I made a PDF for the two toughest superTangram puzzles: the **14-piece convex hexagons**, which are mentioned in **SuperTangram Labs**, and do not appear in any of the **SuperTangram books**.

I added a compass and straightedge construction by Dan Bennett to the **Soccer Angles** generalization.

I added a couple of pattern block creations (by Kathy Paur and Hana Murray) to the **six-fold rotation** page of my **Wallpaper Catalog**.

I updated **Infinity**‘s **Chaos** handout to include instructions on editing the accompanying GeoGebra files.

I added a **Number Puzzles** directory.

I tweaked and reformatted **SuperTangram Labs** and **Pentomino Labs**.

I added **The Three Meanings of Minus**, a short discussion-provoking lesson from * Algebra: Themes, Tools, Concepts*.

I don’t have many games on my site, but I added a **Games** (and game-like activities) launch page.

I added a page on **Big-Picture Planning**: my thoughts on how to map out a program, a course, a unit.

I tweaked the site’s **Annotated ****Map**.

I added yet more evidence that all parabolas are similar on my **Geometry of the Parabola** page. This time a GeoGebra figure showing that given two parabolas with parallel axes of symmetry, one is a dilation of the other.

I fixed a bug and made a few tweaks in the **complex number arithmetic** games.

I added four GeoGebra applets: games to help students’ understanding of **signed number arithmetic.** (Note that the Snap! version of the games is currently unavailable.)

On my **Geometry of the Parabola** page, I added a video guide to a construction of the parabola, and a new GeoGebra applet to show the parabola as the envelope of a family of lines.

On my **Doctor Dimension** page, I added *Window Shades*, a bunch of Precalculus lessons by Rachel Chou, inspired by the flat Doctor, and somewhat more “real world”.

On my **Sequences and Series** page, I added a short video on the use and misuse of formulas for arithmetic and geometric sequences and series.

I added two linked function diagram applets that can be used to make images for copy-pasting into a word processor or presentation software. **Composition of functions**, and **Iterating Linear Functions**.

I added **Tri, Tri Again**, an interesting application of **iterating linear functions** to geometry. (Inspired by Rachel Chou.)

I added **Pent**, a two-person strategy game played on a stretched out soccer ball — an invention of George Mills.

I improved my **Spirograph Simulation**: it is faster, and it is now possible to hide the moving parts so as to better see the final image.

I added pattern block creations by Hana Murray and Simon Gregg to the **Dodecagons** and **Wallpapers Catalog** pages.

I added three free-download **Pentomino Puzzle Books** to the site.

I made a couple of applets (**Fraction Rectangles**) to support **Fraction Arithmetic on Grid Paper**.

I updated my **Summer Workshops** page with descriptions of my two online workshops: Symmetry (grades 6-8) and No Limits! (Algebra 2, Trigonometry, Precalculus).

I added Hana Murray’s mind-boggling side-10 creation to the pattern block **dodecagon** exhibit.

I added links, fixed formatting, and made assorted tweaks in **Tiling Rectangles with Polyominoes**, * Geometry Labs*,

**,**

*Manipulatives***Tiling**,

**About Teaching**,

**For a Tool-Rich Pedagogy**, and

**Teachers’ Mathematics**.

I added two online presentations to my **Talks** page: “Transformational Geometry for Teachers”, and “Geometric Puzzles, Virtually”.

**Résumé**: updated

I added a new site map: an alphabetical **Directory of Directories**.

**The Ten-Centimeter Circle**: I made a few tweaks, mostly to suggest a slightly different sequencing of the labs in this intro to trig (from * Geometry Labs*.)

**Four Basic Isometries**: I made a few tweaks.

**Home page**: I added three “Selected Start Pages”: **Pythagorean Theorem**, **Symmetry**, and **Manipulatives**. I also added links in **Pattern Blocks**, **Symmetry with Pattern Blocks**, and **Tiling**.

I added two online presentations to my **Talks** page: “Virtual Manipulatives”, and “Symmetry”.

In my **Comprehensive Site Map**, I highlighted all the links to pages which lend themselves to distance learning.

I added a new unit for remote instruction: **Symmetry Labs**, a dozen activities for virtual middle school and high school. Because much of it can be used in the classroom, and in elementary school, I linked to many relevant items that were designed with that in mind.

I much improved my **Virtual Tangrams** and **Virtual Circle Geoboard** by using “fixed to grid” point capture.

**Algebra Lab: High School**: I made the PDF of the book searchable.

I added some links under “Manipulatives” on the **Annotated Site Map**. Also links to each other and to relevant activities in the **virtual manipulatives**‘ pages.

**Virtual Grid Paper**: I added “Pen” to the tool bar, set default colors, turned on “fixed to grid” point capture, and made it so that the grid did not change under your figures when you zoom in or out. I added links to relevant activities.

**Virtual Geoboard**: I added “Point” to the tool bar, and set default colors for each tool. I also turned on “Fixed on Grid”, which means that all points, segment endpoints, and polygon vertices will have whole-number coordinates. I added links to relevant activities.

**Isometries **(rigid motions) applets: I made some cosmetic changes, and added some links. Likewise, **Dilation**.

**Pattern Block Dodecagons: **I added designs by Hana Murray.

**Virtual Pentominoes**: A new GeoGebra applet — suitable for remote learning.

**Virtual Manipulatives**: I added links to all my virtual manipulatives on the **Manipulatives** home page. I tweaked the **Symmetry with Pattern Blocks** applet so that the target polygons cannot move.

**Virtual Circle Geoboard**: More along the same lines. I added the ability to hand-write to this, the Virtual Geoboard, and the Virtual Grid Paper.

**Virtual Geoboard**: No rubber bands, but that will not interfere with the math! You should be able to use it for any * Geometry Labs* geoboard activities, or any of the activities I link to on the

**Geoboard home page**.

**Symmetry Home Page**: I added a link to my** Spirograph Simulation**.

**Symmetry with Pattern Blocks**: I added an applet to make it possible to explore *Geometry Labs* 5.6 online.

**Virtual Lab Gear**: I made these more user-friendly, both in the design and in the instructions.

**Symmetry in Spain**: I posted photos from a 2013 vacation, mostly because they include the amazing Islamic tile work at the Alhambra.

**Virtual Grid Paper**: Another GeoGebra applet, useful for grid paper activities if you don’t have the physical kind, or if you need greater accuracy and absolutely straight lines.

**Tangrams**: I added virtual tangrams (in a GeoGebra applet).

**Geometry Labs**: I corrected the wording in Lab 3.9 (Triangulating Polygons). The original version allowed for situations where the answer given in the back was incorrect. Thanks to Austin Shapiro (and his students) for making me aware of this issue. His analysis is still on the site, to help people who used the old version.

**Virtual Lab Gear**: I created Google Drawings that teachers and students can use to make Lab Gear graphics. Useful for remote learning and collaboration, for presentations, to include in other documents — and who knows what else.

**Lab Gear home page**: I made some small changes, and added a link to my** Sum and Difference of Cubes **blog post.

**Symmetry**: I created a home page for this topic, including links to existing materials, to photos of student-created designs, and to a brand new 10-lesson unit for elementary school.

**Simon Gregg** is creating his own pattern block wallpapers, which I’ll add to the **Wallpapers Catalog.**

**Kathy Paur** contributed quite a few pattern block designs to the **Wallpapers Catalog.** Also check out her excellent paper-scissors puzzles: **Cutting Out Hearts**

**Pattern Block Dodecagons**: I added several figures to that page, all suggested by math educators on Twitter. I also expanded the discussion questions.

**Wallpapers Catalog:** I used pattern blocks to create examples of all 17 mathematically different wallpaper designs. I’m hoping this will provide a friendly environment to explore symmetry, and that it will inspire others to create their own version of the patterns.

**Résumé**: updated

**Geogebra files**: Many GeoGebra files on my site would not open. Some of them are associated with applets — I fixed those some time ago. I have now fixed the remaining ones. From now on, all the **.ggb** files you download from **MathEducation.page** should open normally.

**Infinity** and **Iterating Functions**: I made some tweaks and fixed some links. The biggest change was to the Infinity Teacher’s Guide.

**Applets:** I restored many GeoGebra files which could not be opened by recent versions of the software. I think I got all of them, but let me know if I missed some!

**Summer Workshop**: This is the page about Hands-On Geometry, my 2020 summer workshop for middle school teachers. It will be hosted by Atrium School near Boston, July 21-23 and Synapse School in Silicon Valley, Aug 4-7.

**Résumé**: updated

**Make your own Pentominoes**: I added a laser cutter file (made by Eben LaPier) to my site. You can download it from my **Geometric Puzzles** page, where I explain why laser-cut pentominoes are preferable to the commercially available ones. The same page, of course, links to lots of puzzles for the classroom.

**Fraction Arithmetic on Grid Paper**: I drastically expanded this page, adding details, graphics, and five homemade videos. One big idea, with many uses across that domain.

**Left or Right?**: I tweaked and linked to this activity which can serve as review or assessment of understanding of *y = mx + b*. Answer without actually graphing: given these two linear functions, do the lines meet to the left or to the right of the y-axis?

**Off and On / Add Till It’s Plaid**: Two lessons that illustrate *ax + by = c* through possibly unfamiliar activities: what does *ax + by* add up to for a generic point (*x,y*) somewhere in the plane? what happens visually when we add or subtract a pair of equations in this form? I used video to present the core of the lessons. I also added an **Off and On applet** so you and your students can conduct that experiment using an equation of your choice.

**Stairs**: This is a beginner’s “rise over run” activity which I designed ages ago for TI calculators. Later, I attempted a Desmos version, which (perhaps due to my lack of expertise) had various issues. I replaced it with a GeoGebra applet, something I knew how to make.

**Number Pyramids**: I added a puzzle-solving and puzzle-creating activity for upper elementary and middle school, mostly based on the addition of whole numbers.

**Doctor Dimension**: I added **Window Shades**, two precalculus lessons by Rachel Chou, inspired by Doctor D.

**Completing the Square**: I fixed the link to a** blog post **outlining how this applet fits in the algebra curriculum.

**Geometry of the Parabola, 2D**: I added a paragraph (by Rachel Chou). Yet another argument to convince the reader that all parabolas have exactly the same shape. They cannot be “pointier” or “wider”.

**Talks**: I added information on the free professional development session **Lessons from Lew**, as well as links to an expanded version of the handouts.

**Iterating Functions**: This page includes interesting materials on this topic, ranging from pre-algebra to precalculus. I added a new lesson by Rachel Chou, about an unexpected application of these ideas to geometry: **Triangles and Iterations**.

**Doctor Dimension**: This is a small unit with big ideas mostly about rate of change, including several GeoGebra applets and a selection of worksheets. It can be used in different ways, in grades 8-12. I added a link to another lesson about piecewise functions.

**Stairs:** This is a Desmos-powered applet that can be used to explore “rise and run”. Unfortunately, it doesn’t work in Chrome on Windows. I added a note to that effect.

**Puzzles in Math Curriculum:**
I combined a couple of blog posts into an article where I break down
what makes a good puzzle, and more specifically, what makes a good
puzzle in math class.

**Function Diagram for y=1/x**: I added a cool-looking static diagram. (If you’re baffled, here’s the **function diagrams home page**.)

**Applets Directory**: I added links to my off-site arithmetic games (**signed numbers**, and **complex numbers**). Programmed in Snap! by Parisa Safa.

**Letters and Postcards: **This is an introduction to linear inequalities and “linear programming.” I added a link to Liz Caffrey’s Desmos Activity Builder version of the lesson.

**Stairs**: I added **a worksheet** to support this Desmos-powered applet about slope and linear functions. (Unfortunately, the applet doesn’t seem to work on Chrome on a PC. I’ll try to fix it, but until I do, try a different browser.)

**Staircases**: I made minor tweaks to this worksheet, which is a great activity about adding up strings of consecutive numbers. It works at all levels from 4th grade, to high school, to math teacher!

**Name That Function!** This is a popular GeoGebra applet where you’re supposed to guess the function by watching an animated **function diagram**. I added links to worksheet versions of it, which can be used instead or in addition to the applet.

**How to Get Some of My Publications:** I removed some out-of-print items. I updated the links to the* Geometry Labs *template and the CircleTrig Geoboard.

**Summer Workshops**: This is the page about my 2019 summer workshop: *Visual Algebra (grades 6-9)*, in two locations: June in Silicon Valley, August near Boston. I added a link to** the part****icipants’ website**. I also added mentions of continuing education / graduate school units, the 75% scholarship for public school teachers, and the free and discounted manipulatives from Didax and Nasco.

I added links to Liz Caffrey’s Desmos versions of **Letters and Postcards** and **Geometry Labs** 9.3 and 9,4. I added a note about Geometry Labs 6.1.

**Symmetric Polygons**: I corrected a mathematical error and expanded the teachers’ notes in this activity for grades 8-10. Co-authored with Lew Douglas.

**Seems Isosceles!**: I added some interactive GeoGebra images to this “teachers’ mathematics” exploration.

** Geometry Labs**: minor tweaks.

**Résumé**: updated.

**SuperTangram Labs**: I replaced an html worksheet which was not really usable with a **downloadable PDF**. (For more information about supertangrams, go to **Geometric Puzzles in the Classroom**.)

**For a Tool-Rich Pedagogy**: This page consists of an argument for the use of manipulative, technological, and paper-pencil tools in math education, followed by a long (but probably incomplete) list of **links** to related pages on my site. I added a link to my popular page about **pattern block** **dodecagons**.

**Pythagorean Theorem home page**: I added an image.

**Geoboard home page**:
I added “Connect the Dots” — lattice puzzles and problems for teachers,
which can also be used in math clubs and in the classroom. (We worked
on those at Math Teachers’ Circles.)

**Summer Workshops**: I set up that page to announce my 2019 summer workshop: *Visual Algebra (grades 6-9)*, in two locations: June in Silicon Valley, August near Boston.

**Soccer Angles**: I added interactive GeoGebra applets to this page, which is an extension of the low-tech Lab with the same name in *Geometry Labs*.

**Spirograph Simulation**:
For some reason, while the online applet worked, the GeoGebra file I
included did not open when downloaded. I got some help on Twitter, and
posted a corrected version.

**Résumé**: updated.

**Math Ed Consulting**: minor tweaks.

**Electronic Graphing**: minor tweaks.

**Errata**: I added a bunch of downloadable corrected pages to the **Lab Gear** books Errata page.

**Front Page**: I added a short intro at the top, and a link to my Twitter page at the bottom. I made similar tweaks to the **About** page.

**Pattern Blocks**: I added a link to Jen Silverman’s GeoGebra pattern blocks applet.

**Site index:** I added links to the games Parisa Safa coded for me in Snap! (Signed Numbers | Complex Numbers)

I created **a conic sections home page****.** (Links to the geometry of the parabola and ellipse, 2D and 3D, and more.)