Polar battleship

Learning target: student can convert between polar and rectangular coordinates.

Introduction: do they collide?

https://vimeo.com/67260095

Practice:



Activity:

5/28/13 London Eye

Learning target: students can model periodic functions.

Act 1: Video:

https://vimeo.com/67157216

Act 2: acquire relevant information.

Act 3: model the scenario.


In your groups:

1.) Create a sine or cosine equation that models the London Eye over time

Create a parametric equation that models the London Eye over time


2.) make a poster
-sine equation
-sine graph
-parametric equation
-parametric graph
-location after 12 minutes (x,y)
-location after 12 minutes (r, θ)
-how long does it take for one revolution?





Materials available for download:

5/10/13 Moon Safari

Learning target: students can model scenarios using trig functions.

I would like to thank Kate Novak for posting the moon safari lesson on her blog, and would like to redirect you if you would like more info.  Additionally, this lesson is best delivered on the date of a new or full moon.


Act 1: introduction.
I show this video, give then a minute and ask what they notice.


common responses include:
-something about the wave pattern.
-something about the new and full moon.

Students write a sentence about what they notice about the table, and what they are wondering using this piece of paper that I hand them at the door.


 Act 2: Work time
I give them the task and their groups and have them create an equation that models this.

Common difficulties include:
-How to I know what the period is? Many students want to say the period is 27 days because the first full moon happens on the 27th of Jan.
-How do I know which to use: sine or cosine?
-How far do I have to translate it?
-For some students they got what would be considered reasonably close to the right answer but it wasn't close enough for them until I told them that it was close enough.
-What to x and y stand for?

Act 3: solutions
At the end of class we came back together and talked about what equations students used and why different equations will work equally well to predict what the moon will look like tonight.  It helped to get some equations on the board and show where students were getting stuck.  Also, this activity was very frustrating for some students and acknowledging the frustration and commending the efforts put forth to overcome those frustrations helped everyone leave feeling like they gained something from the lesson.


Homework: look at the moon tonight.  How close were your predictions.

5/1/13 Trig transformations

learning target: students can graph trigonometric transformations.

Activity: watch this first:

Then, using what you know about function transformations create a function of the Minneapolis sun height throughout the year:

Homework: due Friday:

Solutions to the last HW set

Friday 4/26/13 trigonometry function transformations

Learning target: students can identify characteristics of trig function transformation from graphs and equations.

Wed/Thurs 4/17/13-4/18/13 arcfunctions

Learning target: students can find angles using arc-functions.
Supporting learning target: students can explain the difference between inverse-trig functions and arc-trig functions

Activity: We will put a new entry in our periodic functions table of contents: trig identities.   Then I will have students create a new page, titles trig inverse and arc-functions.  Here are the directions:


1.)Pick a partner next to you.

2.) trade notebooks.

3.) Your partner will neatly draw 4 right triangles on your page, and you will draw 4 on theirs.

4.) When you are done hand the notebook back to the owner.

5.) Correctly identify the angles of the triangles drawn by only measuring the side lengths, finding a trig ratio, and referencing the trig values chart.

(use any of the three trig functions per triangle, but do at least one of each overall)

Handout:


Test for understanding, half page, students do the front 4 triangles and high challenge students can practice #5 & #6 on the back.


Classwork solutions:


 Homework (due Friday) worksheet


Homework (due Tuesday)  classroom for success

Friday 4/11/13 - find trig values using the unit circle

Learning target: students can evaluate trig functions using the unit circle.

Activity: trig values war.  Students who can do this and determine values using only their unit circle are considered "pro" and those that want to crunch them with their calculators are "novice"

Homework (due Weds.)

Thursday 4/11/13 Calculating arc length and area

Learning target: students can calculate arc length and the area under an arc.

Demo on radians, degrees, arc length and area of a sector


Homework: 

Thursday 3/28/13 - Train jousting and the unit circle

Relationship of Sine and Cosine to the Unit Circle from the Wolfram Demonstrations Project by Noel Patson

Relationship of Sine and Cosine to the Unit Circle from the Wolfram Demonstrations Project by Noel Patson

Wednesday 3/27 Train Jousting

learning target: students can understand situations using periodic functions.

The following are videos of the lesson available through Vimeo.

Act 1 https://vimeo.com/63675037

Act 2 (monorail) https://vimeo.com/63675077

Act 2 (train) https://vimeo.com/63675078

Act 3 https://vimeo.com/63675079