Data Sampling

Unit Objective: Students will use simple data sampling techniques. Although the activities were written for a Trigonometry course, they could easily be adapted for other courses.

Activity 1: How Many Characters?

Objective: Students will use sampling techniques to approximate the number of characters on a newspaper page.

Wyoming Standards:  Math 1.3-Students explain their choice of estimation and problem solving
strategies and justify results of solutions in problem-solving situations
involving real numbers.
Math 2.5-Students connect geometry with other mathematical topics.
Math 3.1-Students apply estimation and measurement using he appropriate
methods and units to solve problems involving length.
Math 3.3-Students identify and apply scale, ratios., and proportions in solving
measurement problems.
Math 5.4-Students determine, collect, organize, and analyze relevant data needed
to make conclusions
Sci 2.2-Students use inquiry to conduct scientific investigations.

Materials Needed: Copy of one page of classified ads from a newspaper, meter stick, piece of cardboard (~ 4cm X 6cm), scissors, calculator, (note: one set of materials for each group), handouts from AstroCappella web site for each student

Time:  35 minutes

Directions: (Note: We will closely follow the “How Many Stars in the Milky Way?” activity from the AstroCappella web site. All handouts and images are available there. We will be doing Procedure 1 and Procedure 2. There would be no point in rewriting the directions when they were so well done by AstroCappella originally. For my classes I will not be using the introduction and go right to Procedure Part 1. I will tie in finding number of stars on the next activity).

To begin the activity split the class into small groups and give them a copy of the classified ads. It is best if all groups have a copy of the same classifieds from the same issue. When preparing the handouts I would copy and paste Procedure 1 and Procedure 2 from the AstroCappella web site, giving credit and the URL at the end of the text.

It would look like the following page. Notice the clip art and the table did not copy. I removed the graphic and left space for the table. The students can copy the table from the board. I also had to manually add the reference at the bottom of the second page.

Procedure (Part 1)- Collection of Data

Your task is to examine a page from the classified section of a newspaper, and to approximate the number of characters on the page by using `sampling'. Each character (a letter, symbol, or punctuation mark) counts as one. Begin by making an estimate.

1. I estimate that there are _____________ characters on the page.

2. The average estimate in our group is ___________ characters.

3. Determine the area of the printed portion of your page.

_________cm X __________ cm = __________ sq. cm.

4. Cut out six squares of cardboard that measure 2 cm by 2 cm and have an area of 4 square centimeters.

5. Lay the classified ad page flat on the floor. While standing about half a meter from the edge of the page, toss each of the six squares onto the printed portion. All must land within the printed portion of the page to be considered. If a square falls outside the printed portion, toss it again. Carefully trace an outline around each square. This enables us to take a `sampling' of characters on a newspaper page.

6. Count the number of characters in each square. Where characters are split by the boundary, they are counted only if half or more of the character lies within the square.

7. Find the number of characters in each square, and complete the chart below.

Number of Characters in an Area of 4 Square Centimeters

Procedure (Part 2)- Analysis of Data

1. The mean number of characters per 4 square centimeters is ________.

2. The median number of characters per square centimeter is ________.

3. The calculated number of characters on the page is ________.

4. Using your data, how many such pages would be required to hold 100,000,000,000 characters, the estimated number of visible suns or stars in the Milky Way Galaxy, our home? __________

5. If an average issue of the newspaper has 20 such pages, how many issues would be required to show 100 billion characters? _________

6. If 365 issues are published annually, how many years of publication would be required to display 100 billion characters? __________

7. If such a newspaper had been published long enough to reach the 100 billion character level today, when would it have had to begin publishing? _________

8. If the longest wall in your class room was papered with such pages, what would be the estimated number of characters on the wall? _________

9.    How many such wall spaces would be required to display 100 billion characters? ___________

Reference: AstroCappella “How Many Stars in the Milky Way?”

Activity 2: How Many Stars?

Objective: The students will use sampling techniques to counting stars from images.

Wyoming Standards:    Math 1.3-Students explain their choice of estimation and problem solving
strategies and justify results of solutions in problem-solving situations
involving real numbers.
Math 2.5-Students connect geometry with other mathematical topics.
Math 3.1-Students apply estimation and measurement using he appropriate
methods and units to solve problems involving length.
Math 3.3-Students identify and apply scale, ratios., and proportions in solving
measurement problems.
Math 5.4-Students determine, collect, organize, and analyze relevant data needed
to make conclusions
Sci 1.9-Students develop an understanding of scientific content through inquiry.
Sci 2.2-Students use inquiry to conduct scientific investigations.

Materials Needed: Computer lab, computer with projector

Time: 15 minutes

Directions:  Have the students go to the web site. It will work best to have the students work individually for this activity. Once they are at the Hubble Academy web site have them select 'Stellar Statistician'. This will launch activity 1. For high school students this activity is very short but it is a good follow up for our classified ad activity.

When the students are finished the teacher should go through the activity quickly on the projector. Emphasize the part about the Hubble field image is the size of the eye on the dime. That will give students a reference point to how many objects are in such a small field.