19 September, 2014
Volume 19 No. 38
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In This Issue

Annie's Experiment

GeoGebra 5 Goes 3D

Math Girls Talk About Integers


Online PD

Orientation Sessions

Problem Based Learning Courses

Graduate Credit:
Mathematics Teaching and Learning Certificate

Master's Degree


Annie's Experiment


The corner deli sells roses in bunches of 6. If Dylan buys 3 bunches of roses, how many roses does he have?

An answer of 9 came back from almost half of the third graders in some Philadelphia schools supported by the Math Forum many years ago. Ever since, Annie, the Administrator of our Problems of the Week (PoWs), has thought a lot about sense-making in problem-solving — and a few days ago, she invited anyone with students in grades 2-5 to run an informal experiment.

Annie's sense-making experiment consists of three math questions from some Grade 3 benchmark tests; and three drawing questions, which start with content similar to that in the math questions, but instead ask students to "draw a picture of the story."

Teachers have already shared some great comments on her blog; scroll down her post of Tuesday to join the conversation and freely download the questions, which link to an online survey:


"Drawing a picture" of a math task is one way to change its representation. That strategy falls right in the middle of twelve others we've enumerated to move students beyond "I don't get it." See our Problem Solving and Communication Activities for all thirteen strategies, as well as more student handouts that get kids "unstuck" and on to developing, formalizing, and reflecting on their problem-solving strategies:


PoW taking place: math problem-solving moment of the week

"Some mentioned finding the 'least common multiple,' but didn't clearly explain how that would help answer the question. You could extend Kylee's method of writing all the multiples until you got a number to show up in all three lists. You would know that it is the 'least' common multiple because it is the smallest number to show up in all three lists. Kylee didn't actually use that method, but instead found a quicker variation...."
- Annie, commenting on the FunPoW's Latest Solution

GeoGebra 5 Goes 3D


Last Monday, GeoGebra rolled out a major new release. Among many other new features added to the free dynamic mathematics software, version 5 supports three-dimensional geometry.

Try it in action on Dandelin spheres by moving points A, B, or P:


GeoGebra 5 also adds features for

  • translation and rotation of scenes
  • curve-fitting implicit curves
  • CAS commands such as Laplace, InverseLaplace, GroebnerLex, and GroebnerDegRevLex
  • automatic proofs of Boolean expressions

First featured in these pages eight years ago, GeoGebra encompasses geometry, algebra, tables, graphing, statistics, and calculus. The GeoGebra 5 installers for tablets hit the Apple, Android, and Windows app stores this week. To freely download the new app for those devices, or for a variety of desktops, visit


Now taking place: math education conversation of the day

"With the start of a new school year, you get to see what your students are coming into class with in terms of calculators. If you have students with the new TI-84 Plus C Silver Edition and have questions or are curious what is new, see my attached document on the TI-84 Plus Tips. If students purchased a TI-Nspire CX and you are not yet an Nspire guru, see the Getting Started Guide that I have made. Print-share-post. These are mine that I give to you!"
- Dana, posted to the secondary (grades 9-12) discussion group of the Association of Math Teachers of New York State

Math Girls Talk About Integers


Bento Books has published the second volume in its Math Girls spinoff series, Math Girls Talk About...

Math Girls Talk About Integers introduces students to a variety of discrete math topics across five chapters:

  • Checking for Multiples
  • Prime Numbers
  • Number Guessing and Mysterious 31
  • Math on Clocks
  • Mathematical Induction

Each includes review problems and answers. The last chapter tackles a proof from a Japanese college entrance examination, and the appendix gives more challenging, open-ended problems. Read the first chapter and check out the full table of contents and index in this sample download:


As with the first volume from this series, featured here four months ago, the math topics in Math Girls Talk About Integers arise out of conversations among the characters from the young adult novel Mathematical Girls — also by author Hiroshi Yuki — the Japanese language version of which has already gone through some twenty printings. For more of Bento Books' publications, check out



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