LESSON 1
Interpreting Box and Whisker Plots
Use the box plot that shows the ages of U.S. vice presidents when they took office.
1. Describe the distribution of the data. What can you say
about the ages of U.S. vice presidents?
2. What percent of U.S. vice presidents were at least 60
years old when they took office? Explain how you
found your answer.
3. What percent of U.S. vice presidents were between the
ages of 49 and 60 when they took office? Explain how
you found your answer.
4. Can you determine from the box plot whether there are
any U.S. vice presidents who took office at exactly age
55 years of age? Explain.
Use the box plot that shows the number of goals made by members of the field hockey team during the season.
5. Describe the distribution of the data. What can you say
about the number of goals made by the members of the
field hockey team?
6. What percent of team members scored between 1 and
3 goals this season? Explain.
LESSON 2
Transformations on a Map
Directions: Use the map of the United States and the coordinate plane that it is drawn on to do the
following transformations. Read each scenario carefully and pay attention to details.
1) Start in Hawaii on the integral (integer)
coordinates closest to the black dot. Label and
identify this as H( ___
_,_
___) on the
map.
4) Start in Ohio on the black point. O(___,___)
Describe a translation that would get you to
black point in Montana.
Reflect H over the y-axis. Label and identify
this point as H’(_
___,___
_) on the map.
Express the mapping for this movement:
What ocean are you in?
(x,y)→(___
___,_____
_)
Go back to the black dot in Hawaii. Now,
reflect H over the x-axis. Label and identify this
point as H”(__
__,__
__) on the map.
5) Start in Louisiana on the black dot using the
nearest integral coordinates, L(_ ___,___ _).
Use the origin as the center of rotation. Rotate
What state are you in?
90⁰ clockwise. Name the state you land in.
2) Start in Georgia on the black dot. Label and
identify this point as G(__
__,__
__) on
Label this point as L’(____,____). Name the
capital of this state.
the map.
Reflect G over the x-axis. Label and identify
this point as G’(___
__,__
___) on the map.
What state are you in?
6) Start in New York on the black dot,N(__ _,___).
Translate point N using ( x, y )  ( x  4, y  2) .
Label and identify this point as N’(_ _,_
_)
on the map. Then reflect this point over the
Go back to Georgia. Now, reflect G over the
y-axis. Label and identify this point as
y-axis. Label and Identify this point as
G”(__ __,__
you in?
__).
What state are you in?
N”(_ ___,___
_) on the map. What state are
7) Start is South Dakota on the black dot,
3) Analyze problems 1 and 2, then complete the
S(_ __,__ _) on the map. Reflect over the
mapping (algebraic representation) for reflecting
y-axis, label and identify this point as
over the x-axis, (x,y)→(__
S’(__ _,___ ) on the map. Then reflect that
__,__
_) and
the mapping for reflecting over the y-axis,
point over the x-axis. Label and identify this
(x,y)→(_____,______). Will this always be
point as S”(___ _,__
true? Justify in complete sentences.
body of water did you reflect into?
_). What state(s) and/or
8) Start in Kansas on the integral coordinates
14) Start in North Carolina on the black dot. Reflect
closest on the black dot. K(____,____), label K
over the y-axis. Translate
on the map. Reflect over the y-axis and then
( x, y )  ( x  4, y  5) Reflect over the y-
1
translate ( x, y )  ( x  4, y  ) . Label and
2
axis.Translate ( x, y)  ( x, y  4) Rotate 180⁰
identify this point as K’(___ _,____) on the
counterclockwise. In which state are you
located?
map. What state are you in?
15) Label the vertices N(-9,4.5), E(-7, 4), V(-8, 1),
9) Start in New Hampshire on the black dot.
and A(-9.5, 3) on the state of Nevada. Then
A(_____,_____), label A on the map. Describe
reflect the state’s vertices across the x axis, list
a way you could relocate A to any grid point in
and label the coordinates of N’E’V’A’.
the state of Texas. You may need more than
Compare and analyze the characteristics of the
one transformation.
pre image and the image. Describe the
characteristics that are preserved in the image
9a. Give your paper to a partner to have them
verify the validity of your transformation.
and describe the characteristics that are not
preserved in the image.
10) Create a mapping (algebraic representation) to
describe the transformations in problem 9.
11) Start in Idaho on the black dot. I(____,____).
Label I on the map. Translate ( x, y )  ( x  6, y  3)
and then reflect over the y-axis. Label and
identify this point as I’(____,____). Label I’ on
the map. What state are you in?
12) From Point I’, describe the translation
algebraically that would get you to the black dot
in Ohio.
Extension Questions:
* Name and describe the characteristics in a
rotation that are preserved and not preserved.
Sketch an example to support your answer.
* Name and describe the characteristics in a
translation that are preserved and not preserved.
Sketch an example to support your answer.
13) Start in Mississippi on the black dot M(___,___)
* Name and describe the characteristics in a
Rotate 270⁰ clockwise. Which state are you in
dilation that are preserved and not preserved.
now, and which states’ borders are nearest to
Sketch an example to support your answer.
this location?