Math Ed Page Updates

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.


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 participants’ 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.)