How to Write a Pattern Rule

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SWBAT develop their understanding of how to write a pattern rule. They will also see my expectations for well-crafted work.

Big Idea

Continue to build those abstraction skills!

Opener: Patterns, Again into a Mini-Lesson

20 minutes

Today's opener is just like yesterday's, and I want to see how well students can recreate the process from yesterday's class on their own.  For a detailed description of how I engage students with this problem, please see my narrative for the previous lesson.

Here is what today's problems look like: Opening Pattern Problems.  These four patterns follow the same procession as those from yesterday's.  There is a direct variation, followed by the same pattern starting on zero, then a decreasing pattern and an increasing one.

The two main shifts in my instruction are as follows.  First, I say less, and try to get students to think more about these patterns.  If they're confident, I want them to try to get these answers on their own.  If they lack confidence, I tell them to look at yesterday's notes, and to try to use those notes to complete these patterns.  I encourage students to volunteer to put their work on the board.  At this point, I expect everyone to be prepared to find the 5th, 10th and 100th terms in the first two patterns, and for mixed results with the next two.

I don't spend as much time demonstrating these problems as I did yesterday, but we'll probably spend the same amount of class time on this opener and a mini-lesson.  For the mini-lesson, I reproduce the chart from yesterday (Pattern Rule Algorithm Table) and I show students the same algorithm.  I make a big deal about the word algorithm.  As with the word abstraction, this is a word that, if I can get kids to understand it, will be a powerful tool to which we can refer as we get the work done.

Tomorrow's opener will be another take on pattern problems, as we complete our week of moving in between generalizations for patterns and abstractions of number tricks.

Number Trick Project Check In

5 minutes

I tell students that I'm going to give them some time to check in with their groups about their progress on Part 1 of the Number Trick Project.  "Compare what you have on the first two tasks, and I'll walk around to see how you're doing," I say.  

This is the third day of class since I initially assigned this work.  Last night's homework was to try to finish it, but I assure students that it is not due today.  "There will be two more parts of this project," I say.  "Tomorrow you'll get Part 2, and next week we'll finish up with Part 3.  For now, I want you to think about what you have accomplished so far, how you can help your group, and how your group can help you."

Textbooks and How to Do Homework

18 minutes

Tonight's homework is the first one that students will complete in the textbook.  Each student gets a copy of McDougal Littel's Algebra 1 book.  My teaching career up to now has lead me to have a mixed opinion of textbooks.  I believe that they are great resources, but I'm never sure how much class time I should spend teaching students how to best use their books.  For me, the primary purpose of this textbook is for students to have a resource at home to which they can refer, and a source of homework problems.  On the syllabus, I tell students that approximately half of their homework will come from this textbook.  

Today I distribute textbooks, telling students that they just have to carry this home once, and that they don't have to bring it back to school until the end of the year. 

After distributing textbooks, I use a document camera to show students how to do their homework.  The results look like this: how to do homework.

Here is the summary of the points I make:

  • Step 1: Write a Perfect Heading -- this is something I'll continue to ask for!
  • Step 2: Try ALL problems, and know what it means to show your work.  I demonstrate what it means to "show work," (and that it doesn't mean you have to write a lot) by doing the first two problems.
  • Step 3: Check your answers in the back of the book.
  • Step 4: Be ready for an open notebook quiz on this material.

The content of the assignment, by the way, is substituting values for variables in simple algebraic expressions.  I know that students have been exposed to this in 8th grade or earlier; I use this assignment to figure out what they've maintained.