Currently, my favorite resource is the Mathematics Assessment Project website. They have Formative Assessment Lessons, Summative Assessment Tasks (aka MARS Tasks, which we used to give as a district), and Tests. They are all aligned to the Common Core content and Mathematical Practice Standards.

I started using the formative assessment lessons last year. We used them in Common Core training. I found them frustrating because it always took me more time than the instructions said it would. But, I really liked them. Forming Quadratics

This summer I went to an SVMI (Silicon Valley Mathematics Initiative) week-long training with some of my coworkers. It was great! I got some fabulous training on using those lessons and tasks, and others available on the web.

The Formative Assessment Lessons (FALs) usually start with a pre-assessment task, a short class lesson, group work activity, group comparisons, whole class closure, and a post-assessment. They are meant to be done approximate 2/3 through your unit (I didn’t know that last year!)

This year I have already done two of the FALs. The first was in Algebra, and it was a lower level lesson, but I wanted an easy one to start with. Laws of Arithmetic was perfect. It helps with area models and expressions, some with exponents. We also had just reviewed properties and order of operations, which the students used in their explanations. I wanted to make sure to keep it within a short time frame, so I actually eliminated a couple of the cards in the card sort. I think it went really well. I have the post-assessments to look at tomorrow. (My class posters did not looks that nice!)

I also did one this week in 6th grade Pre-Algebra, after finishing the adding and subtracting integers (which was supposed to review for them). They did the lesson Using Positive and Negative Integers in Context, which discusses temperature. Another teacher did the same lesson in Algebra the week before and warned me it would take a longer time than suggested. And then I read Dan, at the Exponential Curve blog (so glad he is back), did the same lesson and it took him 4 days for his high school intensive class. I couldn’t believe it, but, it took my students about 4 lessons, too. And not only that, I decided, for the group comparison, to actually make a giant class version of the card sort. That went well, but would have been better if they really were able to compare as groups to that more students would talk. I have their post-assessments to still read, too.

I am also still a fan of Dan Meyer, too. His resources are great. Friday, I used the Penny Pyramid 3-Act (or Pyramid of Pennies) problem in all of my classes, for the second year. I’m so glad I did…I forgot how engaging the problem can be for the students. I was lucky to actually experience the problem from Dan Meyer, himself, at a class at Stanford in the summer of 2012. The Act I video is perfect. Everyone was asking questions, before I could even tell them to write down some questions. It works so well. I had hoped to finish it up and take a quick simplifying quiz at the end of the period, but they were so involved, I just couldn’t stop.

I kept asking them if there was an easier way to do the problem. They were figuring out each layer and then adding the layers together. A couple of students (mostly the 6th graders) realized you could multiply figure out all of the stacks in the pyramid, and then multiply by 13. One student told us she could write a C++ program to calculate the answer. I was shocked! There was one teacher in the summer class that could do that, too. I pulled up Excel, and she told me she could do it in Excel, too.

So they will have to wait until Monday to close it all up. So wonderful to hear them talking math.

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I really like the penny pyramid. I am currently studying to be a teacher with a concentration in math, and I am currently learning the importance of number talk. Allowing that time for students to problem solve and discuss math; the penny pyramid sets up an opportunity for that. Thank you for sharing.

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