Period Puzzle

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Objective

Students will be able to identify the amplitude of a sine graph given the parent graph.

Big Idea

Master the concept of period with this puzzle

Warm-up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Period Puzzle which asks students to use a trigonometric model to answer questions about a respiratory scenario.

I also use this time to correct and record the previous day's Homework.  

Quiz on Trigonometry

10 minutes

The lesson includes a quiz that covers the previous material in my Trigonometry Unit.  I have included two versions of the quiz as I alternate quizzes like a checkerboard.  Please see this short document for more information on my Quiz Procedures.

Period Puzzle

5 minutes

Once the students are finished with their quiz, they are to work on this puzzle*.  I really like this puzzle for a couple of reasons.  First of all, it gives students practice with Math Practice 7.  Given the graph of the parent function for sine, students must figure out the period of other sine functions.  The key is that there are no unit marks and the x axis.  Students have to use that they know about periodic functions and period itself to figure each one out. 

The second reason I really like this puzzle is that it is highly differentiable.  The author of the puzzle suggests that one uses the purple graph as the parent graph.  This will make for the easiest conversions to other periods and will be an acceptable challenge for most students.  The green function has a period that is half the length of the purple and would be a bit bigger of a challenge but still doable for many students.  For those high level students, the gray function would provide a serious challenge.  It has two thirds the period of the purple function. 

I do not have access to a color printer at school so I highlight the parent function.  I choose beforehand which student gets which parent function.  I inform the students that they will be getting different parent graphs in advance.  They will work on this alone and then possibly in pairs once everyone is finished with the quiz.  For those students who finish faster than I expect, I will extend the lesson by assigning them a new parent function and have them re-evaluate the period of each function (Math Practice 7). 

*This puzzle comes from nrich.math.org.

Exit Ticket

2 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

This Exit Ticket checks ask the students to answer, "What strategies or tricks did you use to solve the puzzle?" This will provide a look into their thought process as they attempted to make sense of the puzzle.