LESSON 1

Interpreting Box and Whisker Plots

Use the box plot that shows the ages of U.S. vice presidentswhen they took office.

1. Describe the distribution of the data.What can you say about the ages ofU.S. vice presidents? / 2. What percent of U.S. vice presidentswere at least 60 years old when theytook office? Explain how you foundyour answer.
3. What percent of U.S. vice presidentswere between the ages of 49 and 60when they took office? Explain howyou found your answer. / 4. Can you determine from the box plotwhether there are any U.S. vicepresidents who took office at exactlyage 55 years of age? Explain.

Use the box plot that shows the number of goals made by membersof the field hockey team during the season.

5. Describe the distribution of the data.What can you say about the number ofgoals made by the members of thefield hockey team? / 6. What percent of team members scoredbetween 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.

Reflect H over the y-axis. Label and identify this point as H’(_ ___,___ _) on the map.

What ocean are you in?

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. What state are you in?

2)Start in Georgia on the black dot. Label and identify this point as G(__ __,__ __) on the map.

Reflect G over the x-axis. Label and identify this point as G’(___ __,__ ___) on the map. What state are you in?

Go back to Georgia. Now, reflect G over the y-axis. Label and identify this point as

G”(__ __,__ __).

What state are you in?

3)Analyze problems 1 and 2, then complete the mapping (algebraic representation)for reflecting over the x-axis, (x,y)→(__ __,__ _) and the mapping for reflecting over the y-axis, (x,y)→(_____,______). Will this always be true? Justify in complete sentences.

4)Start in Ohio on the black point. O(___,___) Describe a translation that would get you to black point in Montana.

Express the mapping for this movement: (x,y)→(______,______)

5)Start in Louisiana on the black dot using the nearest integral coordinates, L(_ ___,___ _). Use the origin as the center of rotation. Rotate 90⁰ clockwise. Name the state you land in. Label this point as L’(____,____). Name the capital of this state.

6)Start in New York on the black dot,N(___,___). Translate point N using.

Label and identify this point as N’(_ _,_ _) on the map. Then reflect this point over the y-axis. Label and Identify this point as N”(_ ___,___ _) on the map. What state are you in?

7)Start is South Dakota on the black dot, S(___,___) on the map. Reflect over the y-axis, label and identify this point as S’(__ _,___ ) on the map. Then reflect that point over the x-axis. Label and identify this point as S”(___ _,__ _). What state(s) and/or body of water did you reflect into?

8)Start in Kansas on the integral coordinates closest on the black dot. K(____,____), label K on the map. Reflect over the y-axis and then translate . Label and identify this point as K’(____,____) on the map. What state are you in?

9)Start in New Hampshire on the black dot. A(_____,_____), label A on the map. Describe a way you could relocate A to any grid point in the state of Texas. You may need more than one transformation.

9a. Give your paper to a partner to have them verify the validity of your transformation.

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 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.

13)Start in Mississippi on the black dot M(___,___) Rotate 270⁰ clockwise. Which state are you in now, and which states’ borders are nearest to this location?

14)Start in North Carolina on the black dot. Reflect over the y-axis. Translate Reflect over the y-axis.TranslateRotate 180⁰ counterclockwise. In which state are you located?

15)Label the vertices N(-9,4.5), E(-7, 4), V(-8, 1), and A(-9.5, 3) on the state of Nevada. Then reflect the state’s vertices across the x axis, list and label the coordinates of N’E’V’A’. Compare and analyze the characteristics of the pre image and the image. Describe the characteristics that are preserved in the image and describe the characteristics that are not preserved in the image.

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.

* Name and describe the characteristics in a dilation that are preserved and not preserved. Sketch an example to support your answer.