I had a good time this past year playing around with new resources and teaching methods as I worked with my Intensive Algebra students. The Formative Assessment Lessons (FALs) were a great help to me, and I used a number of them both as-is, and as inspiration for developing my own materials.

This year, I will again be teaching two sections of Intensive Algebra 1, along with three sections of IB precalculus. Because the IB curriculum and assessments are pretty clear and established, this will really give me the time and flexibility to focus on the needs of my lower-skilled freshmen, which I am happy about.

My district has been partnering with the Silicon Valley Math Initiative (SVMI), and they provide numerous resources, such as the MARS tasks and Problems of the Month. They have also created a format, based on the work of Phil Daro, for generating units of study to be used as we transition from California State Standards to CCSS, before high-quality curricula are commercially available (if ever!) and districts adopt new materials.

The basic unit structure is as follows:

**Introductory**lesson for engagement, to spark curiosity and interest.- Several
**conceptual development**lessons, after which you can expect student understanding to*still be fragile*. These lessons are what we typically think of as inquiry-based or constructivist lessons. (I think this is a good eye-opener for me, because it has always felt frustrating how my students would still not "get it" after we engaged in, what I considered to be, really powerful learning opportunities. Setting my expectation that students' understanding is going to still be fragile at this point will be key.) - One or two
**getting precise**lessons, in which the teacher attends to precision, definitions, conventions, symbols, etc. This is often going to be a more traditional "I-We-You" direct instruction approach. - One or two
**getting general**lessons. The goal of these lessons is not 100% clear to me, but some ideas for generalization are to use concepts across different contexts, generalize with variables and parameters, use different types of numbers, operations, functions, or structures in the same context, and so on. - A
**formative assessment lesson**(which often takes multiple days). These are intended to be done about 2/3 of the way through the unit. They all start with a pre-assessment, and a well-defined set of tasks to help students further develop their understanding of the concepts. - Additional
**concept development**lessons, as needed. - One or two
**robustness and differentiation**lessons. This is an opportunity to do re-engagement lessons with students who are struggling, as well as enrichment for students who are showing solid understanding. The goal is to move all students from a fragile to a more robust understanding via a variety of rich problem solving opportunities. - An
**expert task**assessment, in which students engage with tasks that have them operate at levels 3 and 4 on Webb's DOK. - A
**closure lesson**to revisit and organize the unit goals and outcomes. - A
**summative assessment**to see if students really have mastered the unit goals.

**structure**of the pattern. They would go right to making an in-out table, and from there, generate the function rule. When we got to the quadratic patterns at the end of the year, they had absolutely no access to them. They kept trying to make in-out tables, would see that the growth was not linear, and then hit a wall. I had to un-teach them the concept of making a table and, instead, try to understand the structure of the pattern.

**subset**of patterns in general. Each time, I will ask students not to just give me the rule, but to also explain the connection between the rule and the visual pattern. For the third unit, we will work on linear equations, which will be motivated by giving them a linear pattern, telling them how many items are in a particular step number, and then having them try to work backwards to figure out what that step number is.