Episode 58
Math, Math, Math #2
[email protected]
[email protected]
[email protected]
Teaching
with
SMARTBoard
http://www.ncusd203.org/central/html/what/math/smartboard/
itunes
http://www.artic.edu/aic/
[email protected]
[email protected]
give me a tweet at dsladkey
[email protected]
# 58 Math Math Math
A Lesson by Rob Porter Lesson Activity Toolkit 2.0 Goodies
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 #10
Review 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 1­4
Homework #10: P. 224 1­2
Triangle Trigonometry
1.
1. h = 47 inches
2. h = 2.52 m
3. h = 208.47 cm
4. h = 11.87 ft
1a. height of tree is 35.01 ft
1b. height of tree is 34.64 ft
1c. height of tree is S * tan ft.
2a. x = 1.32 miles, They can make it to shore
2b. d = r * sin
where r = distance from station
where = angle between line to boat and shore
AC = 9.2
BC = 7.7
2. MT = 5.4
HM = 2.1
3. GR = 8.7
GV = 2.5
4. KZ = 87.5
KN = 89.1
5. 671.3 ft
6. 11.6 ft
7. 177.9 m
8. 57.7 ft
Hypotenuse is always 10cm
Opposite Side
Adjacent side
Trigonometry Table
Degree
0
10
20
30
40
50
60
70
80
90
Sin
Cos
Tan
Trigonometry Table
Degree
Sin
Cos
1
Tan
0
0
0
10
.174
20
.342
.940
.364
30
.5
.866
.577
40
.643
.766
.893
50
.766
.643
1.191
60
.866
.5
1.732
70
.940
.342
2.747
80
.985
.174
5.671
90
1
0
What Patterns do you notice?
.985
.176
error
Why?
(note: you must know SOH CAH TOA and draw some triangles to answer this question)
Inverse Trigonometry
Sin (?) = 1/2
Sin (?) = 1
Cos (?) = 1/2
Cos (?) = 1
Tan (?) = .839
To answer these questions we could use the chart, but that would only give us approximent degree measures. So, we use INVERSE TRIG!
­1
Sin (1/2) = ______
­1
Sin (1) = ______
­1
Cos (1/2) = ______
­1
Cos (1) = ______
­1
Tan (.839) = ______
To Find Degree Measures given a ratio of sides!
10
5
h
Example, to find angle ,
which inverse function do you use? What is the answer?
What did the compass say when he was attracted to the protractor?
Here's looking at Euclid
(YOU KID)
Lesson Activity
Toolkit 2.0
Next
Back
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