Day 1: Variables, Solving Equations and DMS

This year I’ll be teaching AP Statistics, Algebra II Honors and Precalculus.  I want transparency and an open dialogue about how to transform my curriculum in these classes.  Two of the classes, I’ve taught for a few years.  One of the classes is brand new to me.  I won’t tip you off to which is which, but feel free to comment freely.

My hope is to post something about each class every day…so here we go…

AP Statistics:

Today’s focus was on types of variables.  Mainly the difference between quantitative and categorical variables.

We started with this warm up:

Chapter 1 Introduction_1

The hope was that they would talk to each other about the questions, and I was curious who would ask me about question #1 (I have three cats…just so you know).

Without answering any of the questions, I showed this slide:

Chapter 1 Introduction_2

I loved that most of the students grouped the questions in two important ways. 1) They grouped the questions based on whether there was one distinct answer versus the answers having possible variability (which showed that they knew there was a difference with a statistical question versus a non-statistical question).  2) They grouped the questions based on whether the possible answers were numerical or non-numerical.

At this point they’ve stated that they know of quantitative versus categorical variables.  So, I wanted to dive into the grey areas and get a really good definition of quantitative and categorical.  I asked them to classify the following situations:

Chapter 1 Introduction_5

Through working on classifying these variables, my students came to some interesting conclusions.  First, they were able to better state that quantitative variables require measurement, not just a numerical response.  Second, and most interestingly, there was an in depth conversation (student started) that quantitative variables could be treated categorically; they concluded that someone has to be clear in stating their expectations for measurement.

Algebra II Honors:

To ease into the new year, I wanted to make sure my algebra II students were able to solve one variable linear equations.  Sounds easy enough (and they thought it was too), but I wanted to give a different spin on it.

Unit 1 Intro (Solving Equations)_1

This question required that they keep everything in balance.  I wanted to encourage my students to work together and be self-sufficient in checking whether their solution is correct.  After having a consensus on a solution, they were asked to find the value of the missing shape in each of the following mobiles:

Unit 1 Intro (Solving Equations)_2 Unit 1 Intro (Solving Equations)_3

The first one was to build confidence; no problems…the triangle is worth 10.  In the second one, there were a bunch of methods used.  Some guessed and checked.  Others set up an equation.  A few noticed that a triangle and square cancelled each other out on the two sides and they were really solving 2 squares equals 1 triangle…which someone quickly noticed that they did the exact same thing if they set up an equation.  Amazing conversations.  Then we solved some equations.

Precalculus:

We started the period with practice using dimensional analysis to convert value.

1.1 Measuring in Degrees_1

The purpose of this was to put a seed in their mind for figuring out how to convert angle measurements from degrees into degree-minutes-seconds form.  After defining how many minutes are in a degree (60) and how many seconds are in a minute (60) (then explaining how the Sumerians worked in a base 60 number system…which is why we measure time the way we do), I had them complete the following conversion:

1.1 Measuring in Degrees_5

I question whether I made this too leading, but everyone came up with a method that worked for them.  I challenged them for homework to come up with a method to convert an angle measured in DMS back to degrees.  We’ll see how they did tomorrow.

 

Summer Lesson Building (Algebra II Honors: Solving One Variable Equations)

The first day of Algebra II is a chance to get my students up and running with something they know how to do, but may not remember the meaning behind it. They’ll walk in the door to the following warm-up:

Solving Equations Lesson_1

For the first ten minutes or so of class, we’ll focus on the idea of the solution is the value that balances each mobile:

Solving Equations Lesson_2

Solving Equations Lesson_3

I expect my students to bring equations into this with some sort of notation (whether it’s using squares and triangles, or variables). We’ll discuss the connection between the solution to an equation and it being the value that balances the two sides.

Next, we’ll practice solving one variable equations:

Solving Equations Lesson_4

Solving Equations Lesson_5

My students will solve them and explain the process. We’ll start the process of talking about inverses during the discussion about “the reverse order of operations.”

This lesson is meant to be a review of something they’re already comfortable with and a nice way to begin the year. The second half or so of class will focus on procedures and expectations.

Thoughts?