Reflection: Unit Planning From Patterns to Arithmetic Sequences - Section 1: Opener: Fill in the Blanks

 

On the second day of school, I assigned the first homework assignment of the year.  Given the first four terms of some sequences, students were tasked with determining the 5th, 10th, and 100th terms in each.  At the time, all students found it easy enough find the 5th and 10th terms, and the recognized that finding the 100th terms was more challenging.

Since then, "patterns openers" have been a regularly-occurring structure of this course.  On the fifth day of school, we started generalizing algebraic rules from patterns, and I've made a continued effort to use patterns problems to build some foundations of algebraic thinking throughout the fall.  I also used patterns quizzes early in the year to assess the kinds of algebraic thinking that my new students were capable of.

Throughout this course - looking both backward and forward - you can see that the common structure of patterns openers is used to review previously-covered concepts, and like today, to build toward new ones.  In a few weeks, students will learn to distinguish between arithmetic and geometric sequences, and therefore between linear and exponential functions.  A few weeks after that, they'll see that quadratic functions are different from either of these.

The style of problem that is featured in today's opener also helps students revisit some of the thinking they did about number lines.  Check out the opener of the first lesson from that unit.  It's really the same idea - if I'm trying to move from one value to another, and the space in between is split into some number of equal partitions, how would I figure out what to count by?  I'll look for students to make that connection today.  Often, some will, but if it doesn't happen, I'm sure to talk about it.

  How Did We Get Here?
  Unit Planning: How Did We Get Here?
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From Patterns to Arithmetic Sequences

Unit 7: Lines
Lesson 1 of 10

Objective: SWBAT identify arithmetic sequences, determine the common difference, and use the common difference to write an explicit expression to represent the sequence.

Big Idea: Students have been with working pattern problems all year. Now, it's finally time to name some key concepts.

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