Episode 58  

Math, Math, Math #2  smiller@naperville203.org

dsladkey@naperville203.orgrporter@naperville203.org

Teaching with

SMARTBoard

http://www.ncusd203.org/central/html/what/math/smartboard/

itunes

http://www.ncusd203.org/central/html/what/math/smartboard/http://phobos.apple.com/webobjects/mzstore.woa/wa/viewpodcast?id=272381274

http://www.artic.edu/aic/

http://www.artic.edu/aic/

dsladkey@naperville203.org give me a tweet at dsladkey

smiller@naperville203.org

rporter@naperville203.org

A Lesson by Rob Porter 

Lesson Activity Toolkit 2.0 Goodies

 # 58 Math Math Math

Bees Unit:

Essential Understanding:  Area and Volume have special relationhips.

Essential Question:  What threedimensional shape will hold the most volume?

Bees often must answer this important question.  Bees produce both wax and honey, but wish to produce the least amount of wax to hold the most amount of honey.  So our question become, what shape should a honeycomb be so that the least amount of wax will hold the most amount of honey?

In the bees unit, we will be learning the answers to the following targets to answer our bees question:

1. What is area?2. What are the area formulas for a square, rectangle, parallelogram, triangle, trapezoid, rhombus and kite?3. What is the area formula for a regular polygon of more than 4 sides?4. How can trigonometry help us to solve for the sides and angles of a triangle?5. How do you simplify a radical?6. What special triangles can be used to shortcut solving for sides and angles of a triangle?7. What are Pythagoran Triples?8. What is a prism and what are its parts?9. What is lateral and total surface area and what is the LSA and TSA formulas for a prism?10. What is voume and whare is the volume formulas for a prism?11. What is a cylinder and how can we find the LSA, TSA, and volume of a cylinder?12. What is a net?13. What is a tesselation?14. What is the relationship between surface area and volume?15. Are bees "efficient" with their wax?

Do Bees Build it Best?A Homemade Trig Table

DLT: Students will create their own table of trig values and find patterns associated with the results.

Review Homework  P. 222  224 #9 and #10Review Quiz

CLASSWORK• Homemade Trig Table, P. 221• Sin, Cos, Tan of 0, 10, 20, 30, 40, 50, 60, 70, 80, and 90 degrees• View the drawn triangles.• A preview of Inverse Trigonometry

Homework: Day 6 Worksheet  USE PAGE 21 IN PACKET

Homework #9: P. 222223 14Homework #10: P. 224 12

1. h = 47 inches2. h = 2.52 m3. h = 208.47 cm4. h = 11.87 ft

1a. height of tree is 35.01 ft1b. height of tree is 34.64 ft1c. height of tree is S * tan   ft.2a. x = 1.32 miles, They can make it to shore2b. d = r * sin

where r = distance from stationwhere    = angle between line to boat and shore

Triangle Trigonometry

1. AC = 9.2BC = 7.7

2. MT = 5.4HM = 2.1

3. GR = 8.7GV = 2.5

4. KZ = 87.5KN = 89.1

5. 671.3 ft6. 11.6 ft7. 177.9 m8. 57.7 ft

Adjacent side

Opposite Side

Hypotenuse is always 10cm

Trigonometry Table

Degree Sin Cos Tan

0

10

20

30

40

50

60

70

80

90

Trigonometry Table

Degree Sin Cos Tan

0

10

20

30

40

50

60

70

80

90

0

0

.174

.174

.342

.342

.5

.5

.643

.643.766

.766

.866

.866

.940

.940

.985

.985

1

1 0

.176

.364

.577

.893

1.191

1.732

2.747

5.671

error

What Patterns do you notice?

Why?(note: you must know SOH CAH TOA and draw some triangles to answer this question)

Inverse Trigonometry

Sin (?) = 1/2Sin (?) = 1Cos (?) = 1/2Cos (?) = 1Tan (?) = .839

To answer these questions we could use the chart, but that would only give us approximent degree measures.  So, we use INVERSE TRIG!

Sin  (1/2) = ______Sin   (1) = ______Cos  (1/2) = ______Cos   (1) = ______Tan  (.839) = ______

1

11

1

1

To Find Degree Measures given a ratio of sides!

105

Example, to find angle    ,which inverse function do you use?  What is the answer?

h

What did the compass say when he was attracted to the protractor?

Here's looking at Euclid(YOU KID)

Lesson Activity Toolkit 2.0

NextNext

BackBack

What does a poor man and Barack Obama have in common?

They both want change

Attachments

x and y intercept game denise.notebook

great lakes game denise.notebook

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page0.svg

Apr 14-6:05 AM X- and y-intercepts game D Langley 4/09

page1.svg

Apr 14-6:19 AM 2410undefined292truefalse 2x + 3y = -6 154185x-intercept270259y-intercept

page2.svg

Apr 14-6:43 AM 2410undefined281truefalse-5x +2 y = -10 331179x-intercept260362y-intercept

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Apr 14-6:43 AM 2410undefined0truefalse3x - 4y = -12108.2175.35x-intercept256.763.45y-intercept

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Apr 14-6:43 AM 2410undefined0truefalse6x + 4y= -12188.2180.9x-intercept262.5293.4y-intercept

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Apr 14-6:44 AM 2410undefined0truefalsex - y = -3141.05190.9x-intercept255.7577.7y-intercept

flash/flash/hot spots.swf

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flash/flash1/hot spots.swf

flash/flash1/hotSpot.txt

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flash/flash2/hot spots.swf

flash/flash2/hotSpot.txt

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flash/flash3/hot spots.swf

flash/flash3/hotSpot.txt

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&password=Password&&questionLabel=Question&&timerLabel=Timer&&password2=Password incorrect&

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flash/flash4/hot spots.swf

flash/flash4/hotSpot.txt

&m_vInfo=Create your own hotspot activity. Press "Edit" to get started.Set the image. If you want your own image, choose custom, drag an image into a Notebook file and send it to the back.Set the score option. "Score by distance" calculates how far away your try is from the target as a percentage out of 100. For example, if you hit the target exactly, you score 100."Score by region" allows you to set a perimeter around the target. If your try is within the perimeter, you score 100 points.Set the timer to show or not show.Change the question text to suit your needs.Add a password to protect the edit menu.Press "OK" to finish setting up the activity.Press "Start" to begin.Press "Reset" to start again.&

&password=Password&&questionLabel=Question&&timerLabel=Timer&&password2=Password incorrect&

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SMART Notebook

images/glkoutline.gif

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preview.png

page7.svg

Apr 12-7:31 AM Game: Great Lakes and the surrounding states D Langley 4/09 Teacher notes: Game: When you hit start, it will ask for a location. Click on the location

page6.svg

Apr 12-7:06 AM 16421undefined2155truefalse125211Wisconsin152294Illinois254311Ohio342310Pennsylvania412252New York198314Indiana49158Minnesota224245Michigan22589Ontario351123Quebec187250Lake Michigan191140Lake Superior259216Lake Huron349241Lake Ontario285275Lake Erie81265Iowa

flash/flash2/hot spots.swf

flash/flash2/hotSpot.txt

&m_vInfo=Create your own hotspot activity. Press "Edit" to get started.Set the image. If you want your own image, choose custom, drag an image into a Notebook file and send it to the back.Set the score option. "Score by distance" calculates how far away your try is from the target as a percentage out of 100. For example, if you hit the target exactly, you score 100."Score by region" allows you to set a perimeter around the target. If your try is within the perimeter, you score 100 points.Set the timer to show or not show.Change the question text to suit your needs.Add a password to protect the edit menu.Press "OK" to finish setting up the activity.Press "Start" to begin.Press "Reset" to start again.&

&password=Password&&questionLabel=Question&&timerLabel=Timer&&password2=Password incorrect&

&label1=Congratulations&label2=You scored:&&label3=Top score:&

&cityLabel=Enter text here&&soundText=Sound&&scoreLabel1=Time bonus&&scoreLabel2=Score&&scoreLabel3=Top score&

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SMART Notebook

Page 1: Jan 4-11:04 PMPage 2: Feb 12-2:51 PMPage 3: May 22-5:06 AMPage 4: Apr 9-1:20 PMPage 5: Jan 4-11:08 PMPage 6: Mar 10-10:25 AMPage 7: Mar 6 - 6:50 PMPage 8: Mar 6 - 9:41 PMPage 9: Mar 15 - 8:11 AMPage 10: Mar 15 - 7:28 AMPage 11: Mar 15 - 7:28 AMPage 12: Mar 15 - 9:09 AMPage 13: Mar 20 - 9:21 AMPage 14: May 22-5:18 AMPage 15: Apr 16-9:13 AMPage 16: May 22-5:43 AMPage 17: Random image pickerPage 18: Vortex sort - imagePage 19: Apr 16-9:13 AMAttachments Page 1