Quiz on Sequences and Intro to Sigma Notation
Lesson 5 of 13
Objective: (1) SWBAT demonstrate proficiency in writing, generating, and graphing arithmetic and geometric sequences. (2) SWBAT use sigma notation to express the sum of a finite sequence.
Students will spend the first 45 minutes of class taking this Sequence Quiz which assess their ability to work with arithmetic and geometric sequences. I pause at this point for a quiz because students have learned a lot of vocabulary, notation and skills that we will build on in our study of series and partial sums. This quiz asks students to consolidate what they have learned about sequences and draw correspondences between sequences, equations, and verbal descriptions of patterns. [MP1] The quiz helps students solidify their understanding and allows me to see if students are ready for the next topic.
It is always the case that there is about a 20 minute spread between the students who finish first and those that finish last (when I insist that they turn the papers in). I sometimes provide early finishers with enrichment activities, puzzles, or standardized test practice.
Because most of my Algebra 2 students are juniors, they are generally grateful for some SAT practice questions. I have some print-outs of SAT practice questions available in my classroom, a link to practice at the College Board, and some questions I can send students on their TI NSpire calculators through the Navigator.
Introducing Sigma Notation
Students have just completed their first quiz in Algebra 2 and are not ready for anything too heavy, but they can learn to use sigma notation. Because sigma notation is not a topic that students can really figure out on their own, I do not launch this topic with an exploration. Instead, I do a short lecture on sigma notation or show them a short video like the one below:
Presenting this topic by video has the added benefit of introducing students to a free online resource, Khan Academy, that might be useful to them if they are ever stuck on an Algebra 2 topic.
See this video for background on why I cover sigma notation in Algebra 2.
Practice and Reinforce
Students practice using sigma notation by working in their table groups to complete the worksheet Practice with Sigma Notation. In this work, students are asked to translate among sigma notation and expanded form of a sum. In doing so, they make use of the structure of the original expression. [MP7]
Closure and Assignment
As an exit ticket, I send students two quick polls designed to assess their understanding of sigma notation. One question asks students to evaluate a sum and the other asks a student to write an expression using sigma notation. In the next lesson we will use sigma notation to express partial sums of arithmetic sequences.