Last year's Algebra 1 implementation was a mess. Not even a hot mess, just a mess. The materials from our district were inadequate and even with my enrichments, I found that the whole was not coherent enough or challenging enough for my students. It also started waaaaaaayyyy too slow out of the gate. And it didn't provide nearly as much work on modeling and sense-making as I wanted.
Other than that, it was fine.
So this year, to start with, here's my game plan for reordering units for the fall semester.
Sequence of Units
- Mathematical Modeling and Problem-Solving (EQ: How can we use mathematics and logic to make sense of real-world situations?)
- Equations, Proportions, and Number Lines (EQ: How can we use our existing algebra toolkit to solve equations involving proportions, variables, and absolute value?)
- Lines and Linear Functions (EQ: How do lines and linear functions enable us to analyze and predict real-world phenomena?)
- Functions and Functional Thinking (EQ: How can functions and functional thinking help us in our modeling work?)
- Systems of Linear Equations (EQ: How can we use multiple equations to model real-world situations?)
- Working With Exponents (EQ: What makes exponents such powerful tools?)
Begin At The Beginning: Unit 1
This is going to work because M1:1 – 8 cover all of the things I want to deal with as review topics anyway, but in a novel and challenging way: rates and units; "micro-" modeling (going from words to mathematics) and functional thinking; using the number line; modeling with non-standard rates, fractions, ratios, and proportions; distributive property and order of operations; "like" terms; and modeling with area and volume.
Meanwhile, the most important thing about the first two weeks is to really drive home my routines and norms and structures. That creates space to get to know students and do some formative assessment so I can make intentional groupings and establish the tone for the course.
This year, the material for the first 9 days will be the first eight pages of lightly adapted Exeter problems, i.e., replacing "Exeter" with my school's name and replacing all the kid names with character names of my own choosing (I tend to favor Batman and the character names from Sesame Street and Harry Potter).
Day 1 is a complete loss because (a) it's a ridiculously short period and (b) we are required to go over our syllabus (don't ask). But I think I will put M1:1#5, which I refer to as J-1000 (the "journey of a thousand miles" problem) on the opening slide as the intro task for students to do once they've found their seats. It's a little bit of math, but it sets the tone I want, which is that we get down to mathematical business in my classroom.
Day 2 is my true Day 1, so that will be my M1:1 day.
Background: Organizing Principles
For any day that I am using a page of Exeter problems, I want to organize the problems according to Bowen and Darryl's PCMI-based framework of Important Stuff / Interesting Stuff / Tough Stuff.
That way, I can also use their twin strategies of (a) intentional groupings (keep the speed demons away from the katamari) and (b) deliberately featuring katamari solutions and insights during whole-class discussion segments. For background on all of this, including PCMI, Bowen, and Darryl's group work strategies, first read Ben Blum-Smith's Lessons from Bowen and Darryl and then my post on Lessons from Lessons from Bowen and Darryl.
Any remaining problems left over from the day's classwork can be done as homework problems that night, and those can then be discussed during the next day's Home Enjoyment/Burning Questions segment. A beautiful thing.
Day 1: M1:1#2
Problem 1:#2 is a perfect rich task for starting off an Algebra 1 course. You can demand that students let go of their habits of learned helplessness and use whatever they know. You can encourage them with problem-solving process hints and without robbing them of the opportunity to do the thinking for themselves.
Everything else on page 1 is just review and activation of prior knowledge.
OK, that's all I've got for page 1.