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Hilights from Weeks 4 & 5 & 6 in Algebra (Really getting behind on my blogging)

So every year around this time, my school shuts down and takes all the kids on retreat. I typically accompany upwards of 200 9th graders on a canoe trip down the Colorado River. It is an awesome trip and a great way for the class to bond. I have this year off though and while I will miss being part such a formative experience for my students, I am so excited to sleep in my own bed and get caught up with work and blogging.

Week 7 = catch up on grading, planning, blogging and interleaving project.

The last few weeks in algebra have been challenging for my students as we have been exploring complicated word problems. We worked on showing our thinking by writing and labeling all helpful expressions for a problem. The most challenging were the coin problems, interest problems and mixture problems. For each type, I lead my class through a discussion on how to translate the verbal expressions to algebraic ones. While it wasn't lecture, it also wasn't inquiry.

A few days after working through our first coin and mixture problems, students were given Dan's Coin task one day and Yummy Math's Chocolate Milk task the next. Both experiences were evidence of lack of smooth transfer. I thought they had mastered each of these sort of problems as they had been dutifully completing them on their daily problem sets. I thought these tasks would be easy. I was surprised how long it took each group to use algebra to solve each task. Next year I will think about doing the tasks first, before modeling the algebraic approach. Perhaps then the concepts will stick and transfer to slightly different tasks.

Luckily, Julie posted her lesson on literal equations just in time to improve my class. I loved how the number magic lead nicely to inverse operations. I wish that I had longer class periods though as we only had enough time for two rounds of group speed dating. I loved using the white boards though and changing it so that pairs travelled together.

Students have been graphing via tables and calculating slope using a graph all year because of their interleaved problem sets. We started the year with key concepts from pre-algebra and have been slowly mixing in new content. Hence, when it was time for our graphing unit to begin, the transition was smooth and there was absolutely no need for a lecture on graphing vocabulary. Instead, students played Polygraph (Lines). I left the teacher view on the projector so that students could see what type of questions others were asking. Then we discussed which questions were the most helpful. Lastly, they listed all the vocabulary associated with graphing that they could think of with a partner.

The rest of week 6 was spent learning the intercepts method for graphing, working on the T-shirt task from MAP (the 2nd part is great with desmos, btw) and developing a formula for slope. Since students were using the slope triangle method proficiently, getting to the formula was a short math talk away. Using white boards and a partner, they were able to express the slope of the line in terms of (x1,y1) and (x2,y2). The lesson closed not with 5 more for practice, but rather with one problem to extend using the formula to a rate of change problem, which they did with their groups.

Teaching this way makes students think more. They aren't passively listening and copying from the board. The interleaved problem sets also feel harder as they have to think both about the type of problem and how to do it. Everyday they are actively building on prior knowledge and remembering what they have already learned. Combined with frequent, formative assessments, standards based feedback and corrections makes for a busy math class (and a tired teacher too). When we feel overwhelmed, I remind them (and me) of the goal: retention, transfer and confidence.