I have used three web sites for the first time at school over the last couple of weeks.

**Estimation 180, Andrew Stadel**

The premise here is very interesting: Students acquire number sense better by making mental estimations, than from direct instruction. Since I teach an Algebra class to a large group of high-needs students, who have proven to lack number sense, I thought I would give this one a go. While the name of the site implies estimations for 180 days of the school year, we entered at day 75. The students were hooked right away.

The process that Mr Stadel offers is even more useful than the pictures that drive the site. I have my classes participate in the following manner. My students each record their own estimates, then pair up and record on a lapboard, and then as they hold up their boards, I announce the minimum and maximum values that I see. On the Estimation 180 site, I record either the median of these values or the mode if there is preponderance of one value. Depending on the spread, I decide the level of confidence (1-5), and then submit our collective response under “Great Oak” (our high school). This committment raises the level of engagement of the students, who really want to see how close we get to the actual answer.

The site offers a handout for students to record their estimates, and their margins of error for 20 days on each side of the sheet. The students are to average this margin of error at the end each page. This serves two great purposes: 1) Students must add and divide positive and negative numbers as well as practice calculating a mean, and 2) as students progress through the year, they can see if their estimations are getting anymore accurate (average margin of error getting smaller?). In only three weeks, I have already seen my students posing more accurate numbers.

I have other processes that I also use as warm-ups, so I won’t be using all 180 days, but the mathematical gains and enthusiasm that I am seeing in my students will encourage me to use this site as often as possible. (Chris Shore’s 180Blog)

**Graphing Stories, Dan Meyer & Buzz Math**

The premise of this site is that students will develop understanding of graphing through visual contexts, in this case, through 15 second video vignettes. The genius of the site is the consistency of its structure.

Every coordinate plane is a one-quadrant grid with time as the domain, from 0-15 seconds. The range and its scale is left to be defined for each video. Each video is shown with a clock tracking the 15 seconds, then the video and clock are replayed at half speed. The answer is revealed by superimposing the grid over the video. The graph is drawn in real-time as the video plays out. There is a variety of the types of functions offered, as well as various degrees of difficulty.

In my class I used this as remediation for the most commonly missed question on the semester final, graphing from a verbal context. So I used only about 7 of the 24 videos offered, over the course of a few days. On the next quiz, students showed a drastic improvement in their ability to, graph both from verbal context as well as from given equations. (Chris Shore’s 180Blog)

**Math Mistakes, Michael Persan**

*This site is intended for teacher use, rather than student use. Its purpose reflects the hyper-focus of its author: self-improvement. I used this site in my most recent math department meeting. I posed two entries from the site. One sample dealt with fractions, the other with graphing. The discussion ensued around two questions: 1) Why might the students be making these mistakes, and 2) How should we as teachers respond if this were occurring in our classes?*

The conversation was brief, but very rich. I used it to encourage our PLC meetings to focus more on instructional decisions. It was very well received by my teachers.