Basically, the beginning of the year goes something like this –
- Week 1: Team Building / Communication (the beach towel, handcuffs) & Four 4s to review Order of Operations Some Sol Lewitt to intro Notice/Wonder and Creating their own questions.
- Week 2: Barfing Monsters Stations Day 1, Barfing Monsters Days 2/3 and an intro to Visual Patterns
- Week 3: We began each day with some WODB, then Speed Dating – Problem Solving with Patterns/Sequences to intro/focus on Standards of Mathematical Patterns, Mathematical Models (NAGS) and finally someone asks – is there a quicker way to do these sequences?
We ended the week with Arithmetic Sequences…and tomorrow will be Geometric Sequences.
At the end of class on Friday, I asked them to reflect on which of the 3 options they preferred. In 5 different classes, not one method was favored any more than another…almost an equal split. I could tell a difference in students who prefferred the algebraic to numerical – no big surprises there. When asked why they preferred continuing the pattern, several said it just made sense to them and they understood it. Though while sharing preferences, several said they preferred numerical – however, they realized it was not the most efficient one to choose sometimes and could see the value in the algebraic models. Option A: an=a1+(n-1)d and Option B: y = the terms BEFORE the starting value +(common difference)x
After a first run with AP Statistics last year and listening to students describe their patterns the first week, I like beginning with the starting value in my equation model.
Looking back over my examples, I often chose a term number that allowed us to continue the sequence to confirm the rules worked. I need to give them outlandish term numbers to give them a real reason to turn to the equation models, I suppose.
Even as 9th graders, some are simply not confident enough or are not quite at the level they need to intuitively see the algebraic, YET.
When asked why I felt so strongly about beginning with patterns/sequences. After taking Jo Boaler’s course a few summers ago and working with repeat Algebra I students last year, I saw it made Algebra accessible. Students intuitively like patterns. It allows them to get their footing and share their thinking which allows me to play off their ideas to intro some of the concepts I am responsible for.
The next unit will be an Intro to Functions then Linear Functions (modeling). I feel like Systems provides a reason/context for Solving Equations and Inequalities. I hope that I play off of inverse operations enough to build a good conceptual understanding for solving equations, at multiple types / function connections.
At that point, I would like to take a slight break and do Probability prior to Polynomials which I will use to “build” quadratic functions, then some work with Exponential Functions and end with solving quadratics with connections back to our graphical models. I am interested in what others think of this sequence of topics. This is sort of the the order we had planned when I was transferred to Geometry / Algebra 2 back in 2012 just as we were getting our footing with CCSS.
I am very happy to be back in 9th grade and Algebra I. I always felt like I had a more positive impact on students at this age/level. My first 3 weeks have been enjoyable in the classroom – its going to be a great year.
A snapshot of a few students after paint wars prior to football game Friday night…