A pirate’s life for me

The mathtwitterblogosphere has easily revealed the booty of Fawn, Andrew, Michael, John and others. Here are two more we can loot: Eric Bright and Emily Hecht. They don’t blog or tweet. If they do then they’ve done a good job of covering their tracks. That’s why they’re a hidden treasure. They are classroom teachers from Charleston Middle School in central/southern Illinois.


What’s their swag? Instead of complaining about the cost of purchasing new common core pre-algebra textbooks the two sat down to create their own, and in the spirit that permeates the teaching profession they have made it available here…for free.

Eric and Emily set out to design a “bare bones” textbook to keep printing costs down and provide students a resource. The e-textbook is a series of nine units with 5-8 lessons per unit. It also includes pre-tests and unit reviews. According to their teacher website, “No, there are no bells and whistles in this book, but it’s meant to be a resource only. The bulk of the bells and whistles should come from the teacher. No amount of cool pictures in a textbook showing kids having fun riding a roller coaster will actually help them learn more.”  Eric calculates the cost of printing the pdf files is $5.70 per student.

If you know of other teachers or school districts that are doing something similar please reveal the hidden treasure. I discovered this one while digging through conference resources from the 2013 Illinois Council of Teachers of Mathematics annual meeting.


Those doing the most thinking are doing the most learning

I am taking baby steps towards converting to a math workshop model with the help from reading Minds on Mathematics. There is much more to the model than breaking the class time into chunks:  1) roughly 10% of class time on an opening task, 2) 20% devoted to the mini lesson, 3) 50% work time in which the teacher confers with the students, and 4) 20% sharing and reflection. It’s about creating a culture of learning, where students…

engage with worthy, minds-on tasks and important mathematical ideas; enjoy time to think, work, and communicate; construct mathematical understanding for themselves; and notice their own development as mathematicians.

A lot of planning and preparation goes into this approach, but once class begins those doing the most thinking are doing the most learning. Over break I’ve been doing a lot of thinking about my “practice” and I have learned that I am not pleased with myself. In terms of planning and preparation to create this culture of learning, I’d rate myself as mediocre–which is a scoch to the right of basic on the Danielson model.

I’d be fool to say I’m going to fully implement a workshop model as a New Year’s resolution but there are some measures I can take along the way.  Originally I thought the “right” thing to do would be to commit to one change then slowly implement another. For example if I don’t like the way I begin class (which I don’t) I’ll work on the opening task. But since the opening task leads into the mini-lesson, which leads into work time, etc. I need to rethink the entire class period for that day.

Wendy Ward Hoffer, the author of Minds on Mathematics, suggests an opening task be: a new problem, a problem from previous homework, recent class work, or a concept central to the unit of study. The task should also be a springboard into that day’s lesson and it should have multiple entry points so all students have access to the problem.

When we return from break the seventh graders will be multiplying and dividing fractions. Based on their pre-assessment they don’t have a deep understanding of the concepts. So I’m working on a series of brief, scaffolded tasks that will lead into two mini-lessons.

multiplying fractions1

The recipe problem is heavily scaffolded, suggesting repeated addition as a visual representation, and using multiplication to represent the problem. At this point I’ll conduct a skinny, mini lesson on multiplying fractions by whole numbers.

The next problem is less scaffolded.

multiplying fractions2

At this point the lasagna problem will launch a mini-lesson on multiplying fractions by fractions. I created a video for students who will be absent.

Plus the students will have this handout  to take notes during the mini-lesson. I’ll do some white board work to check for understanding the visual model. Now here’s where I’ve  run out of gas for the time being. I need to find or create some differentiated resources to use following the mini lesson. Some students will catch on immediately and I may want them to explore simplifying fractions by examining their common factors:

factors and simplifying

For students who struggle, I’ll need to have at the ready some additional visual model problems for in class practice.

Additionally, I may have the students work on this MARS yogurt problem while I’m conferring.

Sharing and reflection will be students presenting a variety of problems they’ve been working on during their work time.

I’ve spent hours thinking about this ONE lesson and I’m still not fully prepared. The sheer fact of thinking about it however will make it a thousand times better.

Next up will be dividing fractions by a whole number then dividing fractions by fractions. I haven’t sketched out the whole number mini lesson yet, but here’s the direction I’m headed with dividing fractions by fractions.

Dividing fractions by fractions

I know I’m getting ahead of myself but the dividing fractions by fractions lesson will look similarly. I haven’t yet created a video or handout but it will be based on these problems.

dividing fractions1

I’m troubled by section 4. It’s too scaffolded and not enough discovery. I need to work on that. Suggestions???

dividing fractions2

Again, I’m troubled by section 4.

The visual models you see in this post are based on a handout I found while scouring the internet. I liked the overall idea, but tweaked it to be a bit less paint by numbers. This is still a work in progress.

Playing with eduCanon

I played with eduCanon for the first time today. The webtool allows you to take a screencast that has been uploaded to YouTube or Vimeo and insert multiple choice questions to create a flipped or blended learning lesson.

Update: This is the remix of Karl Fisch‘s one step equations video. He does a terrific job explaining the concept. Originally I had thought to keep the remix private, but I think crowd sourcing for feedback on how this tool can improve learning is important.

Here’s a screenshot when in the editor mode.

The ? above the timeline indicates where questions have been inserted. I spent more than an hour thinking up about 15 questions and multiple choice distractors. And that doesn’t include the time creating the video. Look. I’m “complaining” and I didn’t even make the screencast!

And here’s a screenshot of the students’ view when watching the lesson.


The product is incredibly worthwhile. On the other hand it can be incredibly time consuming. It’s easy to use, a downside is the question editor doesn’t automatically position the question next to the video. You have to scroll down to line them up. Before you know it, you’ve spent several hours polishing a short video.

I’ll be interested in learning how long the product will remain free to content creators.

Pre-assessment yields two random, but important, lessons learned

Lesson 1: be flexible when grouping students.

Earlier in the week I posted on my 180 math post-its blog that students were pre-assessed on fractions. I was disappointed to see that only two pre-tested out of many of the concepts. Given the caliber of this class there should have been at least five more ready for enrichment on the skill of adding and subtracting fractions.

I probably should have started the class immediately by differentiating for the two students, but I didn’t. I had enrichment ready for them,  yet I launched into a whole class whiteboard/quick check activity of adding and subtracting fractions. I admit I short changed those two girls, but I’m glad I did the whiteboard work because within 10 minutes five more students revealed to me that their pre-assessment was a signal that they simply forgot.

It troubles me that students do not retain their learning, but that’s for another post. In this instance I truly believe those five kids had, as they say, a brain fart.

For the rest of the block they worked at two tables on challenge problems. Which leads to…

Lesson 2: Students can be completely engaged with non-real world problems.



The kids loved the challenge. I know there is little context with these problems, yet they were engaged for the entire block. You can’t describe them as puzzles, but for 7th graders the problems were puzzling and they wanted to solve them.

By the way this same class is enjoying the NCTM palette of problems I’ve been using for determining importance.

determining importance2

Recently I’ve been presenting them at the start of class. Students work independently then we share solutions, discuss their “arguments” etc. Some students want me to do this everyday.